Organized by: Tin Phan (Los Alamos National Laboratory), Yun Kang (Arizona State University); Tracy Stepien (University of Florida)

Note: this minisymposia has multiple sessions. The other sessions are: Part-2, Part-3, and Part-4.

1. Yun Kang Arizona State University
   "Recognizing and Honoring Yang Kuang’s Contributions to Mathematical Biology"
This presentation is dedicated to celebrating the extraordinary career of Professor Yang Kuang, whose pioneering contributions have left a lasting impact on the field of mathematical biology. Professor Kuang's research, spanning ecological stoichiometry, delay differential equations, partial differential equations, and data-driven modeling, has shaped critical directions in both theoretical and applied biosciences. Beyond his influential scientific achievements, Dr. Kuang is widely recognized for his collaborative spirit and unwavering dedication to mentoring. Over the course of his career, he has guided 29 Ph.D. students and mentored numerous postdoctoral fellows, master’s students, and undergraduates, many of whom have gone on to make significant contributions to academia, industry, and government. In this talk, we will share personal reflections, quotes, and experiences collected from Dr. Kuang’s former students, postdoctoral scholars, and collaborators. Through their stories, we aim to highlight not only his profound academic influence but also his remarkable legacy as a mentor, role model, and community builder. This celebration honors both the depth of Dr. Kuang’s scholarship and the far-reaching impact he has had in shaping the next generation of mathematical biologists.
2. Jiaxu Li University of Louisville
   "A class of delay differential equation system and its applications"
Time delays are inherent in biological systems, appearing in processes such as physiological feedback loops, drug delivery, therapeutic interventions, and the cyclical harvesting of fish and restocking of fry in aquaculture operations. Numerous delay differential equation (DDE) models have been developed to study these systems. However, many of these models fall short in fully capturing the dynamics and delayed effects of interventions that are administered at discrete time intervals and gradually absorbed by the system. Despite advances in artificial intelligence (AI), modeling complex biological systems—such as glucose-insulin regulation—remains a significant challenge. Personalized algorithms often face limitations due to insufficient training data, while delay-induced uncertainties (DIUs) can lead to chaotic behavior, further complicating the development of effective control strategies. A deep understanding of these dynamic behaviors and their implications is essential for designing accurate and robust interventions. In this talk, we present a novel modeling framework that accounts for both the intrinsic time delays in biological systems and the delayed effects of time-distributed interventions, with the goal of improving system effectiveness and sustainability. Applications include artificial pancreas systems for single-hormone (insulin) and dual-hormone (insulin and glucagon) delivery, tumor treatment strategies, and population dynamics models incorporating optimized intermittent restocking and harvesting to promote ecological balance.
3. Bingtuan Li University of Louisville
   "Forced Traveling Waves in a Reaction-Diffusion Equation with a Strong Allee Effect and Shifting Habitat"
Renewed interest in spatial ecology has emerged, largely due to the threats posed by global change. Shifts in habitat suitability for many species have already occurred and are expected to continue, profoundly affecting invasion dynamics. In this study, we consider a reaction-diffusion equation modeling the growth of a population subject to a strong Allee effect within a bounded habitat that shifts at a constant speed c. We demonstrate that the existence of forced positive traveling waves depends on the habitat size L and on c∗, the wave speed for the corresponding reaction-diffusion equation defined over an unbounded spatial domain with the same growth function. Specifically, we show that when c∗>c>0, there exists a positive threshold L∗(c) such that two positive traveling waves exist if L>L∗(c), while no positive traveling wave exists if Lc∗, then for any L>0, no positive traveling wave exists. These theoretical results are complemented by numerical simulations that explore the equation’s dynamics in greater detail.
4. Clay Prater University of Arkansas
   "I get by with a little help from my friends: Adventures in stoichiometric modeling of a mathematically challenged empirical ecologist"
Organisms interact with their environments through the exchange of elements and energy. However, predicting the effects of insufficient supplies of these resources on organismal growth has been a longstanding challenge. To this end, we developed a conceptual framework, the growth efficiency hypothesis, which posits strong mechanistic relationships among organismal resource contents, use efficiencies, and growth rate. We tested this hypothesis by exposing consumers to multiple forms of resource limitation, which resulted in unique differences in their resource composition. These differences reflected physiological changes serving to optimize resource use efficiencies and were used to generate accurate predictions of consumer growth rate. Our findings demonstrate the growth efficiency hypothesis to be a powerful framework for understanding the multivariate nature of resource limitation.

Organized by: Daniel Cooney (University of Illinois Urbana-Champaign), Olivia Chu (Bryn Mawr College) and Alex McAvoy (University of North Carolina, Chapel Hill)

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

Note: this minisymposia has been accepted, but the abstracts have not yet been finalized.

Organized by: Hermann Eberl (University of Guelph), John Ward

1. Maria Rosaria Mattei University of Naples Federico II
   "A modeling and simulation study of horizontal gene transfer in biofilms"
The global spread of Antibiotic Resistance Genes (ARGs) and Metal Resistance Genes (MRGs) represents an increasing health concern, and has been mainly attributed to antibiotics abuse and misuse. Dissemination of ARGs and MRGs is largely associated to plasmids, extra-chromosomal genetic elements. Plasmid-carried resistance is transferred to new host cells through Horizontal Gene Transfer (HGT) mechanisms, which play a crucial role in the ecological success of plasmids in bacterial communities. HGT occurs through three main mechanisms, namely conjugation, transformation and transduction, the latter referring to the case where foreign DNA is acquired by the recipient bacterium through infection by bacteriophages. In this talk, we present a biofilm model formulated as a Wanner-Gujer type free-boundary problem describing the impact of HGT on plasmid spread in biofilm communities. Nonlinear hyperbolic PDEs govern the advective transport and growth of the solid-phase components constituting the biofilm, while parabolic quasilinear PDEs model the diffusion-reaction of soluble substrates and bacteriophages. Conjugation is modelled as a mass-action kinetics process subsequent to gene expression, modelled as a nonlocal term to account for recipient-sensing mechanisms. Natural transformation is modelled as a frequency-dependent process. The presence of transducing phages is included in the model and their production is considered as a deterministic process resulting from the infection by lytic phages of bacterial cells carrying the plasmid. We investigate through numerical simulations the comparative influence of conjugation and transformation on the spread of antibiotic resistance and biofilm compartmentalisation due to differences in metabolisms and sensitivity to toxic stressors. We also show through numerical studies the impact of phage predation on bacterial communities and plasmid spread. This is joint work with Julien Vincent, Alberto Tenore and Luigi Frunzo.
2. Rachana Mandal University of Guelph
   "Modeling and Simulation of Biofilm Growth in a Counter-Diffusion System, Coupled with Biozone Formation in the Aqueous Phase by Chemotactic Bacteria"
In marine environments, sessile bacteria in biofilms and planktonic bacteria suspended in the aqueous medium, critically influence nutrient fluxes, particularly around plumes of marine snow that serve as moving nutrient hotspots. We develop a mathematical model on bacterial biofilm study that accounts for biomass growth, surface attachment and detachment, and chemotactic-diffusive movement of planktonic bacteria and perform a numerical simulation study. The biomass density controls the spatial expansion of biofilm, whereas biomass growth depends on the concentration of the substrates, such as carbon, an electron donor, and oxygen, an electron acceptor. Carbon, sourced from marine snow, diffuses into the domain from one boundary, while oxygen enters from the opposite boundary, establishing a counter-diffusion system. Under these conditions, chemotactic planktonic bacteria accumulate in regions with favorable growth conditions. The system is described by a one-dimensional set of four highly nonlinear partial differential equations. The flux-conservative finite volume method is used for space discretization of the transport terms corresponding to the biomass in biofilm and suspension. Later the substrate equations are discretized and numerically solved using the time-adaptive method from ‘ReacTran’ library in ‘R’. Simulation results demonstrate biofilm expansion toward the aqueous phase and the dynamic migration of suspended bacteria toward optimal nutrient zones. The interplay between chemotaxis, attachment, detachment, and counter-diffusion is shown to significantly influence biofilm maturation dynamics.
3. Fabiana Russo Naples University
   "Modeling biofilm growth and microbially induced corrosion in wastewater concrete pipes: a double free boundary problem"
Microbially induced corrosion (MIC) is a significant global issue impacting infrastructure, economies, and environment. In wastewater systems, MIC is primarily associated with biofilm formation on concrete sewer pipes, leading to severe degradation due to microbial metabolic activity. The proliferation of sewer biofilms occurs in both submerged and unsubmerged conditions, leading to distinct microbial communities. Commonly, these biofilms host microorganisms such as fermentation bacteria, hydrogen-producing acetogens, denitrifying bacteria, sulfate-reducing bacteria, sulfur-oxidizing bacteria, and methanogens. In particular, sulfur-oxidizing bacteria play a crucial role in corrosion, as they oxidize hydrogen sulfide from wastewater effluents, generating sulfuric acid that accelerates concrete deterioration. A one-dimensional model with double free boundaries has been developed to investigate the proliferation of biofilms and the related corrosion process in wastewater concrete pipes. The domain is composed of two free boundary regions: a biofilm that grows towards the interior cavity of the pipe, sitting on a gypsum layer formed by corrosion, which penetrates the concrete pipe. Diffusion-reaction equations govern the transport and the metabolic production or consumption of dissolved substances, such as hydrogen sulfide, oxygen, and sulfuric acid within the biofilm layer. The biofilm free boundary tracks the growth of the microbial community, regulated by microbial metabolic activity and detachment phenomena. The corrosion process is incorporated into the model through a Stefan-type condition, which drives the advancement of the gypsum free boundary into the concrete pipe, governed by microbial production of sulfuric acid. Numerical simulations have been carried out to investigate the model behavior, encompassing the development and progression of the biofilm as well as the corrosion advancement, with the aim of elucidating the key factors governing both phenomena.
4. Blessing Emerenini Rochester Institute of Technology
   "Modeling Biofilm Induced Corrosion Inhibition - what do we know?"
Corrosion mitigation represents a significant scientific and engineering challenge, with associated costs exceeding half a trillion dollars annually in the United States alone. Advancing corrosion prevention and control strategies is essential for enhancing the resilience and sustainability of civil infrastructure. Emerging evidence highlights the critical role of naturally occurring microbial biofilms, particularly through a phenomenon known as microbially induced corrosion inhibition (MICI), where biofilms on metal surfaces can reduce or slow corrosion processes. Developing an effective and reliable MICI-based biotechnologies requires an integrated approach, and comes with questions on sustainability. In this study, we investigate a range of modeling frameworks to identify and optimize key parameters influencing the long-term sustainability of such technologies.

Organized by: Tin Phan (Los Alamos National Laboratory), Yun Kang (Arizona State University); Tracy Stepien (University of Florida)

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-3, and Part-4.

1. Jianhong Wu York University
   "Population dynamics involving perceived risk-structured behavioural changes"
Behaviour changes and intervention takes place in response to perceived risks in the vector-host and pathogen-host interactions, leading to rich and complex population dynamics including multi-stability and oscillation birth and death. We will review a few models and analyses involving coupled systems of delay-differential equations and algebraic-integral equations.
2. Angela Peace Texas Tech University
   "Nutrient-Driven Adaptive Foraging Behaviors"
This study investigates nutrient-driven adaptability of foraging efforts in producer-grazer dynamics of simple food web models. Using dynamical systems theory, we develop and two systems of ordinary differential equations using adaptive dynamics theory; a two-dimensional base model incorporating a fixed energetic cost of feeding and a three-dimensional adaptive model where feeding costs vary over time in response to environmental conditions. By comparing these models, we examine the effects of adaptive foraging strategies on population dynamics. Our adaptive model suggests a potential mechanism for evolutionary rescue, where the population dynamically adjusts to environmental changes—such as fluctuations in food quality—by modifying its feeding strategies. However, when population densities oscillate in predator-prey limit cycles, fast adaptation can lead to very wide amplitude cycles, where populations are endanger of stochastic extinction. Overall, this increases our understanding of the conditions under which nutrient-driven adaptive foraging strategies can yield benefits to grazers.
3. Rebecca Everett Haverford College
   "Stoichiometric ontogenetic development influences population dynamics: Stage-structured model under nutrient co-limitations"
Ecological processes depend on the flow and balance of essential elements such as carbon (C) and phosphorus (P), and changes in these elements can cause adverse effects to ecosystems. The theory of Ecological Stoichiometry offers a conceptual framework to investigate the impact of elemental imbalances on structured populations while simultaneously considering how ecological structures regulate nutrient cycling and ecosystem processes. While there have been significant advances in the development of stoichiometric food web models, these efforts often consider a homogeneous population and neglect stage-structure. The development of stage-structured population models has significantly contributed to understanding energy flow and population dynamics of ecological systems. However, stage structure models fail to consider food quality in addition to food quantity. We develop a stoichiometric stage-structure producer-grazer model that considers co-limitation of nutrients, and parameterize the model for an algae-Daphnia food chain. Our findings emphasize the impact of stoichiometric constraints on structured population dynamics. By incorporating both food quantity and quality into maturation rates, we demonstrate how stage-structured dynamics can influence outcomes in variable environments.
4. Irakli Loladze Bryan College of Health Sciences
   "From Information Strings to Ocean Stoichiometry: Why Life's Atomic Constraints Drive Convergence to the Redfield Ratio"
The Redfield ratio (N:P ≈ 16), a cornerstone of marine biogeochemistry, represents a striking global pattern whose fundamental origins remain debated. Why this specific ratio? This talk presents a perspective rooted in the very nature of biological information. Unlike human technologies that often rely on elementary particles, biological information processing is fundamentally atom-bound. Specifically, genetic information is stored and processed using linear molecular strings – DNA, RNA, and associated proteins. Synthesizing these 'information-rich' molecules imposes non-negotiable demands for specific atoms, particularly nitrogen (N) for proteins and both N and phosphorus (P) for nucleic acids, in precise elemental ratios. These immutable atomic requirements constrain the core cellular machinery of information expression: the coupled synthesis of N-rich proteins and P-rich ribosomal RNA (rRNA). Mathematical modeling reveals that the interplay between translation and transcription creates a powerful biochemical attractor. Under optimal conditions, this balance naturally stabilizes at a protein:rRNA ratio corresponding to an elemental N:P stoichiometry remarkably close to the canonical Redfield value of 16. This biochemically optimal ratio is more than a cellular characteristic; it acts as a dynamic attractor on much larger scales. Incorporating evolutionary dynamics and biogeochemical feedbacks like nutrient recycling (mimicked by an iterative chemostat framework and analyzed using contraction mapping) demonstrates convergence towards N:P ≈ 16. This ratio emerges as an evolutionary stable strategy and a powerful stoichiometric attractor, pulling the system towards Redfield proportions even under varying nutrient limitations over ecological and evolutionary time. This talk proposes that the canonical Redfield ratio is a planetary-scale echo of the fundamental constraints imposed by the need to faithfully replicate and express genetic information using atoms. It shows how the deep rules governing information in biology can sculpt the chemistry of our planet.

Organized by: Abigail Barlow (The University of Bath), n/a

1. Abby Barlow The University of Bath
   "Integrated tick management strategies in fragmented peridomestic environments"
The spirochetal bacterium Borrelia burgdorferi is a tick-borne zoonosis that circulates in various wildlife populations in temperate rural regions of Europe, North America and Asia. Humans are not usually competent for transmission, but spillover infections can lead to Lyme disease (LD). The infection is passed to human hosts via the bite of an infected tick. Ticks have multiple life stages and complex phenology. Over the last decade, there has been a sustained increase in Borrelia prevalence in wildlife in North America, leading to an increase in spillover events, often via residential areas that back onto woodland. Understanding tick ecology is essential for predicting the spread of LD, informing control strategies, and assessing impacts of environmental change. In this talk, we will discuss the development of a tick population model for a fragmented peridomestic environment. We will consider a metapopulation framework of residential patches, where humans might encounter ticks. Our principal goal is to understand the impact of deer dispersal on the tick ecological dynamics. Deer are the primary host for adult ticks and a necessary component of tick reproduction. They visit the residential patches in very small numbers (1 or 2 per hectare/ patch) and can disperse over large distances, transporting any feeding ticks in the process. Consequently, the location of the deer is inherently stochastic and the tick population dynamics are drawn into this stochasticity. Protective measures against LD often involve treating the deer population with an arcarcide-based treatment. We incorporate these features into our model by employing a hybrid modelling framework. Our results will explore the impact that deer dispersal and treatment on the tick population dynamics, in particular on the density of infected nymphs.
2. Folashade B. Agusto University of Kansas
   "Modeling the effect of lethal and non-lethal predation on the dynamics of ticks and tick-borne ehrlichiosis disease"
Tick-borne illnesses, including ehrlichiosis, from both endemic and emerging pathogens have shown a dramatic rise in recent years, posing an increasing public health threat in the United States. However, fewer studies have explored the cascading effects of lethal and non-lethal predation on the dynamics of tick-borne diseases. The fear induced by predators can alter prey behavior, impacting predation rates and ultimately influencing disease transmission dynamics. This study seeks to clarify the effects of both lethal and non-lethal predation through mathematical modeling of tick-borne disease dynamics. Theoretical analysis and sensitivity tests were conducted to examine how fear-driven changes in host behavior affect tick populations and disease prevalence. Stability conditions for various equilibria of the reduced model were established under constant tick fecundity and mortality rates. The study shows that the combined effects of lethal and non-lethal predation trigger a cascade: as predator attack rates rise, prey and tick populations, along with disease prevalence, decrease. Moreover, an increase in predator-induced fear further reduces prey populations, leading to a subsequent decline in tick populations.
3. Kyle Dahlin Virginia Tech
   "Down with the sickness: modelling the effect of disturbed blood-feeding on mosquito-borne disease transmission"
Mosquito-borne pathogens remain a major global health challenge, and transmission depends critically on mosquito blood feeding. This process involves behavioral interactions between mosquitoes and vertebrate hosts, including host defenses that can disturb feeding and increase mosquito mortality. We develop a mathematical model that treats blood feeding as a predator-prey interaction, incorporating mosquito decisions to persist or quit in response to host defense and the associated risk of mortality. The model links individual-level feeding outcomes to population-level traits, such as the average multiple biting number, the gonotrophic cycle duration, and vectorial capacity. We analyze how these traits are shaped by host defensive behavior and mosquito responses, and quantify the resulting effects on disease transmission. The results highlight how host-mosquito interactions can shape key parameters in transmission models and suggest directions for incorporating behavior into epidemiological predictions.
4. Christina Cobbold The University of Glasgow
   "Incorporating adult age dynamics into mosquito population models: implications for predicting abundances in changing climates"
Mosquito-borne diseases (MBDs) pose increasing threats under future climate change scenarios and an understanding of mosquito population dynamics is pivotal to predicting future risk of MBDs. Most models that describe mosquito population dynamics often assume that adult life-history is independent of adult age and yet mosquito senescence is known to affect mosquito mortality, fecundity and other key biological traits. Despite this, little is known about the effects of adult age at the level of the mosquito population, especially under varying temperature scenarios. We developed a stage-structured delayed differential equation model incorporating the effects of the abiotic environment and adult age to shed light on the complex interactions between age, temperature, and mosquito population dynamics. Taking Culex pipiens, a major vector of West Nile Virus, as our study species our results show that failing to consider mosquito senescence can lead to underestimates of future mosquito abundances predicted under climate change scenarios. Moreover at temperature extremes age-dependent mechanisms combined with the effects of density-dependent mortality on the immature stages at also act to decrease mosquito abundances, highlighting a complex interplay between adult aging dynamics and population abundance.

Organized by: Joshua S. Weitz (University of Maryland, Department of Biology & Physics and U of Maryland Institute for Health Computing), Asher Leeks, University of British Columbia, Department of Zoology

1. Antoni Luque University of Miami
   "Impact and prediction of phage decay in natural microbial communities"
Phage decay is a key factor in the ecology and evolution of phages and their bacterial hosts. However, estimating the phage decay of different viruses in a community remains challenging. In this talk, I will share the approach that my lab is developing to address this problem. It relies on three complementary strategies. First, I will introduce a new transient dynamic method that facilitates identifying when phage decay and other processes are relevant in the community and under what circumstances a tipping point is expected to occur and significantly impact the community’s dynamics. Second, I will share the multiscale methods we are integrating to obtain phage decay rates for different phages from genomic data. This step relies strongly on the ability to identify structural proteins in metagenomes and the combination of several biophysical models. Third, I will show our initial attempts to relate our modeling approaches to phage decay experiments from aquatic environmental communities. I will conclude by emphasizing how the strategies discussed here could be valuable for other viruses and for optimizing phage biotechnological applications.
2. Asher Leeks University of British Columbia
   "Modelling the dynamics of cheating in natural populations of filamentous phages"
Diverse species of filamentous phages are found across natural environments, often encoding bacterial virulence traits, antimicrobial resistance, and novel metabolic capacity. In the laboratory, filamentous phages are vulnerable to cheating: mutants spontaneously emerge which have deleted shared gene products, and as a result can out-replicate full-length cooperative phages in coinfection. If these cheat mutants also emerge and spread in natural filamentous phage populations, this would have profound consequences for our understanding of phage population dynamics, and the dependent ecological and pathogenic consequences. However, it is difficult to detect cheating in natural populations for two key reasons: we lack longitudinal data, and so cannot directly measure the fitness of putative cheats; and most filamentous phage species are known only from sequence data, hence we cannot predict a priori which genes might have been deleted by cheats. Here, we use a quantitative approach to overcome these limitations, in order to measure cheating in natural filamentous phage populations. We construct a birth-death model that incorporates mutation, demographic noise, and a frequency-dependent selective advantage to cheating. We explicitly model the distribution of genome lengths expected under different dynamical regimes possible in the model, showing that the selective advantage to cheating can be quantified without requiring longitudinal data, analogous to signatures of selection commonly used in population genetics. This approach allows us to identify which environments allow cheats to spread, which genes are cheated across uncharacterised filamentous species, and to explore the demographic consequences of cheating for natural filamentous phage populations.
3. Jaye Sudweeks University of British Columbia
   "Environmental feedback can maintain cooperation in phages"
The evolution and maintenance of cooperation is a fundamental problem in evolutionary biology. Because cooperative behaviors impose a cost, cooperators are vulnerable to exploitation by defectors that do not pay the cost to cooperate but still benefit from the cooperation of others. Bacteriophages exhibit cooperative and defective phenotypes in infection: during replication, phages produce essential gene products in the host cell environment. Coinfection between multiple phages is possible, so if a phage cannot guarantee exclusive access to its own gene products, the products act as a public good; cooperators contribute to the common pool while defectors contribute less and instead appropriate goods from cooperators. Defective phage phenotypes experience negative frequency dependence in coinfection. For some phages, negative frequency dependence is strong enough to maintain the cooperative phenotype. For other phages, negative frequency dependence alone is not sufficient to maintain the cooperative phenotype, in which case the fate of cooperation is unclear. Here we propose that if coinfection is not enforced, and host and viral densities can vary, environmental feedback can maintain cooperation in such phage populations by modulating the rate of co-infection and shifting the advantages of cooperation versus defection. We build and analyze an ODE model and find that for a wide range of parameter values, environmental feedback maintains cooperation.
4. Nanami Kubota University of Pittsburgh
   "Cheater phages drive bacterial and phage populations to lower fitness"
How can a less reproductively fit antagonist invade a seemingly fitter population? In this study, we can partially explain such a paradox in the context of Pseudomonas phages and game theory. Most Pseudomonas aeruginosa strains carry filamentous phages called Pf that establish chronic infections and do not require host lysis to spread. However, spontaneous mutations in the Pf repressor gene (pf5r) can facilitate extreme phage production, slowing bacterial growth and increasing cell death, violating an apparent détente between bacterium and phage. Furthermore, high intracellular phage replication enables another evolutionary conflict: “cheater miniphages” lacking capsid genes invade populations of full-length phages within cells. Despite the lower absolute fitness of the pf5r bacteria, bacteria carrying both hyperactive full-length phages and miniphages outcompete the wildtype bacteria in direct competition. Surprisingly, infection by both full-length phages and miniphages can shift games between infected bacteria and naïve, uninfected cells to prisoner’s dilemma, undermining coexistence. Finally, although bacteria containing full-length phages and miniphages are most immune to superinfection by limiting the Pf receptor, this hybrid is extremely unstable, as a classic Tragedy of the Commons scenario results in complete prophage loss. The entire cycle–from phage hyperactivation to miniphage invasion to prophage loss–can occur within 24 hours, showcasing rapid coevolution between bacteria and their filamentous phages. This study demonstrates that P. aeruginosa, and potentially many other bacterial species that carry filamentous prophages, risk being exploited by Pf phages in a runaway process that reduces the fitness of both host and virus.

Organized by: Alex Safsten (University of Maryland), Abba Gumel

1. Thomas Hillen University of Alberta
   "Go-or-Grow Models in Biology: a Monster on a Leash"
Go-or-grow approaches represent a specific class of mathematical models used to describe populations where individuals either migrate or reproduce, but not both simultaneously. These models have a wide range of applications in biology and medicine, chiefly among those the modeling of brain cancer spread. The analysis of go-or-grow models has inspired new mathematics, and it is the purpose of this talk to highlight interesting and challenging mathematical properties. I present new general results related to the critical domain size and traveling wave problems, and I demonstrate the high level of instability inherent in go-or-grow models. We argue that there is currently no accurate numerical solver for these models, and emphasize that special care must be taken when dealing with the 'monster on a leash'' (joint work with R. Thiessen, M. Conte, T. Stepien).
2. Mark Lewis University of Victoria
   "Nonlocal Multispecies Advection-Diffusion Models"
Nonlocal advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modeling non-local advection mathematically. These often take the form of partial differential equations, with integral terms modeling the nonlocality. One common formalism is the aggregation-diffusion equation, a class of advection-diffusion models with nonlocal advection. This was originally used to model a single population but has recently been extended to the multispecies case to model the way organisms may alter their movement in the presence of coexistent species. Here we analyze behaviour in a class of nonlocal multispecies advection-diffusion models with an arbitrary number of coexisting species. We give methods for determining the qualitative structure of local minimum energy states and analyze the pattern formation potential using weakly nonlinear analysis and numerical methods. Joint work with Valeria Giunta (Swansea), Thomas Hillen (Alberta) and Jonathan Potts (Sheffield)
3. Rebecca Tyson University of British Columbia Okanagan Campus
   "The Importance of Exploration: Modelling Site-Constant Foraging"
Foraging site constancy, or repeated return to the same foraging location, is a foraging strategy used by many species to decrease uncertainty and risks. It is often unclear, however, exactly how organisms identify the foraging site. Here we are interested in the context where the actual harvesting of food is first preceded by a separate exploration period. In this context, foraging consists of three distinct steps: (1) exploration of the landscape (site-generation), (2) selection of a foraging site (site- selection), and (3) exploitation (harvesting) through repeated trips between the foraging site and ”home base”. This type of foraging has received scant attention in the modelling literature, leading to two main knowledge gaps. First, there is very little known about how organisms implement steps (1) and (2). Second, it is not known how the choice of implementation method affects the outcomes of step (3). Typical outcomes include the foragers’ rate of energy return, and the distribution of foragers on the landscape. We investigate these two gaps, using an agent-based model with bumble bees as our model organism foraging in a patchy resource landscape of crop, wildflower, and empty cells. We tested two different site-generation methods (random and circular foray exploration behaviour) and four different site-selection methods (random and optimizing based on distance from the nest, local wildflower density, or net rate of energy return) on a variety of outcomes from the site-constant harvesting step. We find that site-selection method has a high impact on crop pollination services as well as the percent of crop resources collected, while site-generation method has a high impact on the percent of time spent harvesting and the total trip time. We also find that some of the patterns we identify can be used to infer how a given real organism is identifying a foraging site. Our results underscore the importance of explicitly considering exploratory behaviour to better understand the ecological consequences of foraging dynamics. Joint work with Sarah A. MacQueen, Clara F. Hardy, and W. John Braun.
4. Chris Cosner University of Miami
   "Mean Field Games and the Ideal Free Distribution"
The ideal free distribution in ecology was introduced by Fretwell and Lucas to model the habitat selection of animal populations. It is based on the idea that individuals can assess their fitness at any location, making allowances for crowding, and will move to optimize it. In the context of the evolution of dispersal, movement strategies that can produce an ideal free distribution have been shown to be evolutionarily stable from the viewpoint of adaptive dynamics in many modeling contexts. In this paper, we revisit the ideal free distribution from the viewpoint of a habitat selection game in ecology. We specifically use the approach of mean field games, as introduced by Lasry and Lions. In that approach, an individual agent using a given strategy competes with the “mean field” of the strategies used by other agents. We find that the population density of agents converges to the ideal free distribution for the underlying habitat selection game, as cost of control tends to zero. Our analysis provides a derivation of ideal free distribution in a dynamical context.

Organized by: Daniel Cooney (University of Illinois Urbana-Champaign), Olivia Chu (Bryn Mawr College) and Alex McAvoy (University of North Carolina, Chapel Hill)

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

Note: this minisymposia has been accepted, but the abstracts have not yet been finalized.

Organized by: Valeria GIunta (Swansea University), Yurij Salmaniw - University of Oxford

1. Raluca Eftimie Université de Franche-Comté, France
   "Mathematical models for non-local cell-cell interactions in health and disease"
Non-local cell-cell interactions via long cellular protrusions seem to be more and more prevalent in cell biology: from airineme-mediated inter-cellular communication between different skin cells in zebrafish, to cytoneme-mediated cell-cell interactions between keratinocytes in epidermal remodelling, and even tunnelling nanotubes-mediated interactions between cancer cells and surrounding non-tumour cells. In this talk, we will present a class of non-local mathematical models developed to investigate normal and abnormal wound healing processes such as keloids (these abnormal processes lead to tissue overgrowth, remodelling and invasion similar to those observed in benign tumours). The models account for non-local cell-cell and cell-matrix interactions via different signalling molecules as well as long-distance cell protrusions. We will discuss various analytical and numerical aspects associated with these non-local models from the perspective of biological applications.
2. Junping Shi College of William & Mary, Williamsburg, USA
   "Biological Aggregations from Spatial Memory and Nonlocal Advection"
We present a nonlocal single-species reaction-diffusion-advection model that integrates the spatial memory of previously visited locations and nonlocal detection in space, resulting in a coupled PDE-ODE system reflective of several existing models found in spatial ecology. We prove the existence and uniqueness of a Hölder continuous weak solution in one spatial dimension under some general conditions, allowing for discontinuous kernels such as the top-hat detection kernel. A robust spectral and bifurcation analysis is also performed, providing the rigorous analytical study not yet found in the existing literature. In particular, the essential spectrum is shown to be entirely negative, and we classify the nature of the bifurcation near the critical values obtained via a linear stability analysis.
3. Sara Bernardi Politecnico di Torino, Italy
   "Variations in nonlocal interaction range lead to emergent chase-and-run in heterogeneous populations"
In a chase-and-run dynamic, the interaction between two individuals is such that one moves towards the other (the chaser), while the other moves away (the runner). This interaction is observed in various biological systems, including cells and animals. In this talk, I will explore the behaviors that can emerge at the population level in a heterogeneous group containing subpopulations of chasers and runners. A wide variety of patterns can form, ranging from stationary patterns to oscillatory and population-level chase-and-run, with the latter describing a synchronized collective movement of the two populations. A key aspect of our study is the role of interaction ranges—the distances over which cells or organisms can sense one another’s presence. I will show that robust population-level chase-and-run emerges when the interaction range of the chaser is sufficiently larger than that of the runner. Our findings are contextualized with examples from cellular dynamics, specifically neural crest and placode cell populations, and offer insights into similar phenomena observed in ecological systems. This talk will aim to provide a deeper understanding of chase-and-run dynamics within nonlocal advection-diffusion models and contribute to the broader understanding of how simple individual interactions can lead to complex, coordinated behaviors at the population level.
4. Jun Jewell University of Oxford, UK
   "Long-ranged interactions shape populations and patterns in biology"
Movement shapes how populations distribute across space and evolve over time. Across biological scales, individuals move in response to interactions that are often long-ranged (nonlocal). Animals use scent cues to establish territorial boundaries, predators pursue prey based on sight or sound, and cells can aggregate by extending pseudopodia toward distant neighbours. We explore these processes using nonlocal advection-diffusion models, analysing their bifurcations to gain insight into emergent spatial and temporal dynamics. A key result is that, unlike in local models (e.g. Fickian diffusion), Turing bifurcations in these nonlocal systems fundamentally depend on spatial dimension. For example, purely repulsive interactions cannot generate spatial patterns in one spatial dimension, but can in two. Additionally, even simple interactions, such as attraction and logistic growth within a single species, can produce spatio-temporal oscillations that exhibit signs of chaos. This provides an example of spatio-temporal complexity of relevance to ongoing debates on how common chaos is in ecosystems. We also explore more complex mechanisms like chiral movement, which is often exhibited by cells and also used by prey to evade predators. We show how it can suppress oscillations, and instead promote stationary patterns. Finally, we highlight cautionary cases where linear stability analysis fails to predict long-term behaviour, including populations with a Turing instability that forms patterns only transiently before collapsing to extinction. These results emphasise the need for analytical tools which go beyond local linear stability analyses in order to understand complex biological systems in the long-term.

Organized by: Tin Phan (Los Alamos National Laboratory), Yun Kang (Arizona State University); Tracy Stepien (University of Florida)

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-2, and Part-4.

1. Kevin Flores North Carolina State University
   "Biologically-informed neural networks for modeling of BKV infection dynamics in renal transplant patients"
BK virus (BKV) nephropathy is a significant cause of kidney transplant failure, with no effective antiviral treatments currently available. Clinicians manage BKV by adjusting immunosuppressive medications, balancing the risks of infection progression and transplant rejection. To support clinical decision-making, we propose a biologically-informed neural network (BINN) model for predicting BKV infection dynamics. Our approach integrates patient data from electronic health records, including BKV levels, creatinine, vital signs, lab results, demographics, and medication dosage. A key challenge in modeling BKV infection is the lack of mechanistic detail in existing equations, particularly for creatinine levels. To address this, we applied BINNs to refine a previously validated differential equation model of BKV infection; in particular, the functional form for the equation used to describe creatinine was learned from time series data. Additionally, we used symbolic regression to extract simpler, interpretable mathematical expressions from the learned neural network-based function. Our study shows how machine learning can enhance the accuracy of mechanistic models, thereby enabling future clinical applicability and a personalized predictive framework for optimizing BKV management in kidney transplant patients.
2. Kyle Nguyen Sandia National Laboratory
   "Mathematical modeling of multicellular tumor spheroids quantifies inter-patient and intra-tumor heterogeneity"
In the study of brain tumors, patient-derived three-dimensional sphere cultures provide an important tool for studying emerging treatments. The growth of such spheroids depends on the combined effects of proliferation and migration of cells, but it is challenging to make accurate distinctions between increase in cell number versus the radial movement of cells. To address this, we formulate a novel model in the form of a system of two partial differential equations (PDEs) incorporating both migration and growth terms, and show that it more accurately fits our data compared to simpler PDE models. We show that traveling-wave speeds are strongly associated with population heterogeneity. Having fitted the model to our dataset we show that a subset of the cell lines are best described by a “Go-or-Grow”-type model, which constitutes a special case of our model. Finally, we investigate whether our fitted model parameters are correlated with patient age and survival.
3. Erica Rutter University of California, Merced
   "Methods for Modeling and Estimating Treatment Heterogeneity in Tumors"
Heterogeneity in biological populations, from cancer to ecological systems, is a fundamental characteristic that can significantly affect outcomes. Despite this, many mathematical models in population biology do not account for inter- or intra-individual heterogeneity. In systems such as cancer, this means assuming cellular homogeneity and deterministic phenotypes, even though heterogeneity is thought to play a crucial role in therapy resistance. In this talk, I will discuss several innovative approaches towards incorporating and estimating cellular heterogeneity in models of tumor growth. I will focus on random differential equations to model treatment heterogeneity and the Prohorov metric framework for estimating parameter distributions from aggregate data (e.g., tumor volume). We validate our method on synthetic and in vitro tumor volume data.
4. Eric Kostelich Arizona State University
   "Mathematical modeling for cancer dynamics and patient counseling"
In this talk, I will describe a mathematical approach to model the clinical evolution of recurrent glioblastoma. Given the poor prognosis, patient counseling and quality of life are key concerns. Because responses to treatment vary considerably, any modeling effort must account for the inevitable uncertainty in a given patient's clinical course. The goal of this project is to develop a system that can provide personalized estimates of the likely range of outcomes with a time horizon of two to three months. Our system can provide results in less than a minute on a laptop computer and so potentially could be packaged as an 'app' that can be used in a clinical setting for patient counseling. This talk will present the results of a preliminary retrospective modeling analysis of 137 magnetic resonance imaging studies of 46 unique patients who were previously treated at the Barrow Neurological Institute. This is joint work with Yang Kuang at ASU and Mark Preul of BNI.

Organized by: Daozhou Gao (Cleveland State University), Xingfu Zou, University of Western Ontario

Note: this minisymposia has multiple sessions. The other session is: and Part-2.

1. Sebastian Schreiber University of California, Davis
   "Impacts of the Tempo and Mode of Environmental Fluctuations on Population Growth"
Populations consist of individuals living in different states and experiencing temporally varying environmental conditions. Individuals may differ in their geographic location, stage of development (e.g. juvenile versus adult), or physiological state (infected or susceptible). Environmental conditions may vary due to abiotic (e.g. temperature) or biotic (e.g. resource availability) factors. As survival, growth, and reproduction of individuals depend on their state and the environmental conditions, environmental fluctuations often impact population growth. Here, we examine to what extent the tempo and mode of these fluctuations matter for population growth. We model population growth for a population with $d$ individual states and experiencing $N$ different environmental states. The models are switching, linear ordinary differential equations $x'(t)=A(sigma(omega t))x(t)$ where $x(t)=(x_1(t),dots,x_d(t))$ corresponds to the population densities in the $d$ individual states, $sigma(t)$ is a piece-wise constant function representing the fluctuations in the environmental states $1,dots,N$, $omega$ is the frequency of the environmental fluctuations, and $A(1),dots,A(n)$ are Metzler matrices representing the population dynamics in the environmental states $1,dots,N$. $sigma(t)$ can either be a periodic function or correspond to a continuous-time Markov chain. Under suitable conditions, there exists a Lyapunov exponent $Lambda(omega)$ such that $lim_{ttoinfty} frac{1}{t}logsum_i x_i(t)=Lambda(omega)$ for all non-negative, non-zero initial conditions $x(0)$ (with probability one in the random case). For both random and periodic switching, we derive analytical first-order and second-order approximations of $Lambda(omega)$ in the limits of slow ($omegato 0$) and fast ($omegatoinfty$) environmental fluctuations. When the order of switching and the average switching times are equal, we show that the first-order approximations of $Lambda(omega)$ are equivalent in the slow-switching limit, but not in the fast-switching limit. Hence, the mode (random versus periodic) of switching matters for population growth. We illustrate our results with applications to a simple stage-structured model and a general spatially structured model. When dispersal rates are symmetric, the first order approximations suggest that population growth rates increase with the frequency of switching -- consistent with earlier work on periodic switching. In the absence of dispersal symmetry, we demonstrate that $Lambda(omega)$ can be non-monotonic in $omega$. In conclusion, our results show that population growth rates often depend both on the tempo ($omega$) and mode (random versus deterministic) of the environmental fluctuations. This work is in collaboration with Pierre Monmarch'{e} (Institut universitaire de France) and '{E}douard Strickler (Universit'{e} de Lorraine).
2. Adrian Lam Ohio State University
   "Can Spatial Heterogeneity Alone Lead to Selection for Dispersal?"
In a seminal paper, A. Hastings showed by pairwise invasbility analysis that in a stationary environment, species modeled by the diffusive logistic equation evolves towards smaller diffusion rate. A particular consequence is that in the competition model of N species differing only by the diffusion rate, an equilibrium is locally stable if and only if it is the one dominated by the slowest moving species, assuming other factors are equal. It is conjectured that such an equilibrium is also globally attractive, namely, the slowest moving species always competitively exclude all other species. In the first part of the talk, we survey some recent progress on the conjecture. In the second part of the talk, we describe a recent competition experiment with nematode worm population performed by B. Zhang, in which fast dispersal can be advantageous even though there is little temporal fluctuation in the environment. Motivated by the experimental observation, we introduce a single population model where the organism switches between two alternative physiological states (high vs low food storage), and demonstrate that for such a population model, fast diffusion can be selected in stationary environments.
3. Yijun Lou The Hong Kong Polytechnic University
   "Dynamics of a Reaction-diffusion System with Time-periodic and Spatially Dependent Delay: A Quotient Space Approach"
Understanding the impact of temporal and spatial heterogeneity on population dynamics has significantly advanced mathematical theories in reaction-diffusion systems. This talk reports the global dynamics of a reaction-diffusion system with time delay, where all model parameters are spatially and temporally dependent. The main focus lie in threefold: (i) formulating a stage-structured model that incorporates diffusion and temporally and spatially inhomogeneous development delay; (ii) proposing a dynamical systems framework that employs a quotient phase space to establish strong monotonicity of the periodic semiflow; (iii) establishing a threshold-type result under minimal assumptions, for both increasing and unimodal birth functions. This synthesized approach is expected to motivate further studies when strong monotonicity of the solution semiflow fails in conventional phase spaces.
4. Chunyi Gai University of Northern British Columbia
   "Resource-mediated Competition between Two Plant Species with Different Rates of Water Intake"
We propose an extension of the well-known Klausmeier model of vegetation to two plant species that consume water at different rates. Rather than competing directly, the plants compete through their intake of water, which is a shared resource between them. In semi-arid regions, the Klausmeier model produces vegetation spot patterns. We are interested in how the competition for water affects the co-existence and stability of patches of different plant species. We consider two plant types: a “thirsty” species and a “frugal” species, that only differ by the amount of water they consume per unit growth, while being identical in other aspects. We find that there is a finite range of precipitation rate for which two species can co-exist. Outside of that range (when the rate is either sufficiently low or high), the frugal species outcompetes the thirsty species. As the precipitation rate is decreased, there is a sequence of stability thresholds such that thirsty plant patches are the first to die off, while the frugal spots remain resilient for longer. The pattern consisting of only frugal spots is the most resilient. The next-most-resilient pattern consists of all-thirsty patches, with the mixed pattern being less resilient than either of the homogeneous patterns. We also examine numerically what happens for very large precipitation rates. We find that for a sufficiently high rate, the frugal plant takes over the entire range, outcompeting the thirsty plant.

Organized by: Frank M. Hilker (Osnabrück University), Rebecca C. Tyson (University of British Columbia Okanagan)

1. Brian Beckage University of Vermont
   "Why We Do What We Do: A Mathematical Framework for Modeling Human Behavior in Coupled Human-Environmental Systems"
Many 'wicked' problems superficially appear to be problems in management of environmental systems but are actually problems in the interactions of human social and behavioral systems (HSBs) with biophysical systems. Prominent examples include climate change, loss of biodiversity, emerging diseases, or any number of the planetary boundaries that the Earth system is being pushed beyond. The models used to address these wicked problems have traditionally paid minimal attention to the social and behavioral system using static scenarios or low dimensional representations of the human system while expending great effort to represent the biophysical system in great detail. The focus on the biophysical system stems in part from the fundamental limitation in how to represent the human behavioral and social system in mathematical and computational models. There are a large number of diverse theories proposed to understand various aspects of human behavior but few of these have been translated into mathematical or algorithmic representations. We present a framework that represents a minimal set of processes for constructing computational models of human behavioral systems. This framework, based on key processes of contagion and cognition within a cultural context, enables more realistic modeling of human-environment interactions and could improve our ability to address critical environmental challenges.
2. Jonas Wahl Osnabrück University, Germany
   "Evolutionary dynamics of constant and proportional harvest strategies in a coupled human-environment system with dynamic resources"
Two of the classical harvesting strategies considered in ecological modelling are constant and proportional harvesting. They show different characteristics in their impact on a harvested resource or population. While these strategies and their consequences are well-documented on their own and fully analyzed in isolation, this talk will put the strategies in a competition within one joint model: each of the two strategies is represented by the fraction of harvesters applying it to an underlying logistically growing resource, and the fractions dynamically change according to the replicator equation from evolutionary game theory, which is set up based on the economic payoff of the strategies. This is done for a model with a fixed number of harvesters and a model with a dynamic number of harvesters. The talk will present an analysis of the models' equilibria and their stability leading to a bifurcation analysis, which is then used to derive the economical and ecological implications of the models as well as to interpret the results of the competition of the harvesting strategies with an additional focus on the management of such a system, especially regarding the regulation of access to the resource.
3. Amrita Punnavajhala University of Waterloo
   "Region-level mitigation in a coupled social-climate model"
Mathematical models of climate change have traditionally described anthropogenic carbon emissions as functions of evolving socio-economic scenarios. A drawback of this approach is that the underlying dynamics of human behaviour that are, ultimately, responsible for the carbon emissions causing contemporary climate change, are ignored. So far, there exist a handful of `social-climate’ models that address this shortcoming, results from which make a compelling case for the inclusion of social and behavioural processes in models of climate change. We have constructed and analyzed a coupled social-climate model with region-level structure, parameterized by data on costs of renewables, vulnerability to climate change and the strength of social norms, combined with socio-economic data. Our results show that social learning rates have an outsized effect on mitigation across all regions, mitigation progresses spreads faster in regions more vulnerable to climate change impacts and that interventions to increase mitigation are more effective when introduced early and universally. While increasing the social learning rate always reduces the magnitude of the peak temperature, the time at which this peak occurs can be move forward or backward, depending on which region the increase is implemented in.
4. Christina A. Cobbold University of Glasgow
   "Mathematics for Rewilding: opportunities and challenges"
Achieving a sustainable coexistence of humans with well-functioning ecological systems providing key essential ecosystem services is now vitally important under global change. Rewilding is an increasingly popular approach which provides a paradigm shift to return degraded ecosystems to a state regulated by natural processes, by using and recovering ecological processes, interactions and conditions. Crucially, rewilding occurs in complex systems over large spatio-temporal scales, under high uncertainty. Predicting such ecological changes also requires integration with socio-economic dimensions and thinking. We evaluate the current state of the quantitative treatment of rewilding, highlighting significant deficiencies and opportunities for harnessing mathematics for rewilding. We present an emerging quantitative framework, encompassing four key areas across the entire cycle of rewilding projects - design and planning, metrics for assessment, ecological modelling, and coupled human-ecological systems, informed by recent progress in multiple areas of mathematics and ecological modelling.

Organized by: Zhisheng Shuai (University of Central Florida), Junping Shi, College of William & Mary; Yixiang Wu, Middle Tennessee State University

Note: this minisymposia has multiple sessions. The other sessions are: Part-2, and Part-3.

1. Tingting Tang San Diego State University
   "Exploring the impact of household size on COVID-19 with coupled SEAIR mode"
During the COVID pandemic, studies have found increasing evidence indicating indoor transmission is very significant and secondary infection rate from household transmission is high. Heterogeneity of transmission among different household has shown higher contact frequency contribute to higher transmission. In this talk, we study the role of household size in the spreading of the virus by developing a coupled SEAIR model. The reproduction number is calculated analytically under simplified condition. Global sensitivity study shows that the contact frequency among family members has high impact on the basic reproduction number, peak infection time and volume. In comparison, quarantined effectiveness from large or small household has little implications.
2. Collin Kilmer University of Tennessee at Chattanooga
   "Modeling Zoonotic Disease Transmission Under the Impact of Land Use Change"
Land conversion is occurring worldwide due to a growing population and expanding economy. This process increases the likelihood of pathogen spillover, posing significant economic and public health risks. The objective of this presentation is to investigate pathogen spillover from three distinct reservoir species to humans under the impact of land use change. Our models introduce a land conversion index to capture the dependence of the carrying capacity and death rate of wildlife on the proportion of converted land. This index is then used to examine how different levels of land conversion influence pathogen spillover. This is a joint work with Prof. Xiunan Wang at the University of Tennessee at Chattanooga.
3. Han Lu University of Alberta
   "Analysis of a diffusive host-pathogen epidemic model with two-stage mechanism in a spatially heterogeneous environment"
Due to the spatial heterogeneity present in many aspects of disease transmission, the rate of transmission of infectious diseases, human birth/mortality rate, and the mobility ability of infected humans should be different in different geographical locations. On the other hand, infected humans may exhibit distinct differences in symptoms during the different stages of the disease transmission. This paper aims to study threshold dynamics of a reaction-diffusion host-pathogen model governed by two-stage mechanism and no flux boundary condition. By carrying out strict analysis, the paper establishes the threshold-type results with the basic reproduction number. Specifically, in a homogeneous case that all parameters are constants, we establish the global attractivity of the endemic equilibrium. Our numerical results validate the theoretical results and indicate the importance of the infected humans in the second stage and pathogens in the environment in disease transmission, which greatly contribute to disease spread in a bounded domain and should not be ignored.
4. Sameras Pal University of Kalyani, India
   "The impact of microbial diseases of corals under macroalgal toxicity, overfishing and rising sea surface temperature (SST)"
Competition between macroalgae and corals for occupying the available space in sea bed is an important ecological process underlying coral-reef dynamic. We investigate coral-macroalgal phase shift in presence of macroalgal allelopathy and microbial infection on corals by means of an eco-epidemiological model under the assumption that the transmission of infection occurs through both contagious and non-contagious pathways. We also investigate coral-macroalgal phase shift in presence of elevated SST and macroalgal toxicity. We found that the system is capable of exhibiting the existence of two stable configurations by saddle-node bifurcations.

Organized by: Daozhou Gao (Cleveland State University), Xingfu Zou, University of Western Ontario

Note: this minisymposia has multiple sessions. The other session is: and Part-1.

1. Wenxian Shen Auburn University
   "Front Propagation Dynamics in Fisher KPP Equations on Unbounded Metric Graphs"
This talk is concerned with front propagation dynamics in Fisher KPP equations on unbounded metric graphs. Such equations can be used to model the evolution of populations living in environments with network structure. There are several studies on front propagation phenomenon in bistable equations on unbounded metric graphs. It is known that, in such equations, the network structure of the underlying environment may block the propagation of the fronts. It will be shown in this talk that the network structure of the environments does not block the propagation of the fronts in Fisher-KPP equations. In particular, it will be shown that the Fisher-KPP equation on an unbounded graph with finite many edges has the same spreading speed $c^*$ as the Fisher KPP equation on the real line $mathbb{R}$ and has a generalized traveling wave connecting the stable positive constant solution and the trivial solution with averaged speed $c$ for any $c > c^∗$.
2. Rachidi Salako University of Nevada, Las Vegas
   "On a Cross-diffusive SIS Epidemic Model with Singular Sensitivity"
We investigate the dynamics of solutions to a repulsive chemotaxis SIS (susceptible-infected-susceptible) epidemic model with logarithmic sensitivity and with mass-action transmission mechanism. Under suitable regular assumptions on the initial data, we firstly assert the global existence and boundedness of smooth solutions to the corresponding no-flux initial boundary value problem in the spatially one-dimensional setting. Second, we investigate the effect of strong chemotaxis sensitivity on the dynamics of solutions through extensive numerical simulations. Our studies on the asymptotic profiles of the endemic equilibrium indicate that the susceptible populations move to low-risk domains whereas infected individuals become spatially homogeneous when the repulsive-taxis coefficient is large. Additionally, our numerical simulations suggest that the susceptible population with larger chemosensitivity, tends to respond better to the infected population, revealing the effect of strong chemotaxis sensitivity coefficient on the dynamics of the disease.
3. Yun Kang Arizona State University
   "Migration Dynamics and Collective Decision-Making in Social Insect Colonies"
Social insects are among the most ecologically and evolutionarily successful organisms on Earth, known for exhibiting robust collective behaviors that emerge from local interactions among individuals. Colony migration is a particularly striking example of collective decision-making in these systems. In this talk, we introduce a piecewise dynamical model of colony migration incorporating recruitment switching to investigate the underlying mechanisms and synergistic effects of colony size and quorum thresholds on decision outcomes. Our theoretical findings suggest that larger colonies are more likely to successfully emigrate to a new site. Notably, the model also reveals several intriguing behaviors: (a) the system may exhibit oscillatory dynamics when the colony size falls below a critical threshold; and (b) it may display bistability, where the colony either migrates to a new site or remains at the original nest, depending on the initial distribution of recruiters. Bifurcation analysis further highlights how variations in colony size and quorum thresholds critically influence the overall system behavior. These results underscore the importance of distinguishing between different recruiter populations in modeling and offer valuable insights into how simple, local interactions can lead to complex and coordinated migratory behavior in social insect colonies.
4. Carolin Grumbach Osnabrück University
   "Allee Pits in Metapopulations: When Increasing Dispersal Can Backfire"
Habitat fragmentation divides populations into smaller subpopulations, while the Allee effect diminishes the viability of small populations. Together, these processes can synergistically amplify negative impacts on spatially structured populations. Conservation strategies often aim to counteract these effects by enhancing connectivity between subpopulations, for example, through corridors or stepping stones. However, increasing connectivity does not always lead to the desired positive outcomes. In this talk, I will demonstrate that due to the Allee effect, low connectivity leads to a decline in the asymptotic total population size, which we call the 'Allee pit'. However, increased connectivity facilitates the rescue effect, wherein a persistent subpopulation in one patch can save an extinction-prone subpopulation in another patch, ultimately increasing the total population size. Using simulations based on a generic discrete-time patch model with positively density-dependent growth, I will explore how enhanced connectivity influences a fragmented population subject to the Allee effect. Our results highlight that conservation strategies must carefully consider dispersal dynamics. Simply increasing connectivity is not enough; ensuring dispersal rates exceed a critical threshold is essential for achieving long-term benefits.

Organized by: Zhisheng Shuai (University of Central Florida), Junping Shi, College of William & Mary; Yixiang Wu, Middle Tennessee State University

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-3.

1. Yuanwei Qi University of Central Florida
   "Mathematical Analysis of a Cancer Invasion Model"
In this talk I shall present some recent results on Global Existence, Stability of various equilibrium points as well as existence of traveling wave to a well established reaction-diffusion system modeling cancer invasion. This is a joint work with Xinfu Chen of University of Pittsburgh, Xueyan Tao and Shulin Zhou of Peking University.
2. Chunhua Shan University of Toledo
   "Transmission dynamics and bifurcations of a diffusive epidemic model with a nonlinear recovery rate"
In this talk we study the disease transmission dynamics of a diffusive epidemic model with a nonlinear recovery rate. The Hopf bifurcation and Bogdanov-Taken bifurcation are first considered for the corresponding ODE model. Then we analyze the Turing instability and the Turing-Hopf bifurcation. Numerical simulations and biological interpretation are also provided.
3. Yixiang Wu Middle Tennessee State University
   "Analysis of a parabolic-hyperbolic hybrid population model: an integrated semigroup approach"
We consider the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison principle, and demonstrate the asymptotic smoothness of the solution semiflow. Through the spectral analysis of the linearized system, we derive and characterize the net reproductive rate $mathcal{R}_{0}$. Furthermore, an explicit relationship between $mathcal{R}_{0}$ and the principal eigenvalue of the linearized system is analyzed. Under appropriate monotonicity assumptions, we show that $mathcal{R}_{0}$ serves as a threshold parameter that completely determines the global stability of the system. This is a joint work with Qihua Huang and Mingling Wang.
4. Poroshat Yazdanbakhsh Rollins College
   "A Novel Approach to Understanding Disease Spread and Population Persistence in Heterogenous Environments"
How do infectious diseases or species populations evolve in heterogeneous environments? This has been one of the most sought-after questions in the field of mathematical biology. In this talk, we aim to address this question by introducing a new measure called the network heterogeneity index, denoted by H. We offer a fresh perspective to better understand how diseases spread and populations persist in heterogeneous environments. Our analysis shows that how H is influenced by several key factors, including the structure of such networks, regional disease or population dynamics, and the movements between regions. To highlight the importance of H, we conclude our talk by exploring its applications in epidemiology and ecology across various heterogeneous settings.

Organized by: Tin Phan (Los Alamos National Laboratory), Yun Kang (Arizona State University); Tracy Stepien (University of Florida)

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, Part-2, and Part-3.

1. Bruce Pell Lawrence Technological University
   "Stability Switching Induced by Cross-Immunity in a Two-Strain Virus Competition Model with Wastewater Data Validation"
We study a two-strain virus competition model incorporating temporary immunity through a discrete delay. After reducing and analyzing the system, we identify stability switching phenomena at the strain-1-only equilibrium, including the occurrence of Hopf bifurcations. A detailed characterization of the stability dynamics at this equilibrium is provided. We further validate the model using wastewater surveillance data and apply it to investigate the viral shedding behavior of recovered individuals.
2. Tianxu Wang University of Alberta
   "Derivations of Animal Movement Models with Explicit Memory"
Highly evolved animals continuously update their knowledge of social factors, refining movement decisions based on both historical and real-time observations. Despite its significance, research on the underlying mechanisms remains limited. In this study, we explore how the use of collective memory shapes different mathematical models across various ecological dispersal scenarios. Specifically, we investigate three memory-based dispersal scenarios: gradient-based movement, where individuals respond to environmental gradients; environment matching, which promotes uniform distribution within a population; and location-based movement, where decisions rely solely on local suitability. These scenarios correspond to diffusion advection, Fickian diffusion, and Fokker-Planck diffusion models, respectively. We focus on the derivation of these memory-based movement models using three approaches: spatial and temporal discretization, patch models in continuous time, and discrete-velocity jump process. These derivations highlight how different ways of using memory lead to distinct mathematical models. Numerical simulations reveal that the three dispersal scenarios exhibit distinct behaviors under memory-induced repulsive and attractive conditions. The diffusion advection and Fokker-Planck models display wiggle patterns and aggregation phenomena, while simulations of the Fickian diffusion model consistently stabilize to uniform constant states.
3. Lifeng Han Tulane University
   "A Simplified Model of Cancer Vaccine with Two Different Tumor-Immune Functional Responses"
This talk is dedicated to celebrating Dr. Yang Kuang’s profound influence on the field of mathematical biology and his pivotal role in shaping my own journey into mathematical oncology. In this work, I explore a simplified model of cancer vaccine incorporating two commonly used functional forms for immune-mediated tumor cell killing: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Through analytical techniques, we uncover how each functional response yields distinct biological insights. Notably, we find that under the LPR formulation, tumor elimination depends on the initial condition—offering mathematical support for the clinical practice of using cancer vaccines as an adjuvant therapy.
4. Tin Phan Los Alamos National Laboratory
   "The development and validation of a modeling framework for HIV treatment"
Most people living with HIV-1 experience rapid viral rebound once antiretroviral therapy is interrupted; however, a small fraction remain in viral remission for extended periods. Understanding the factors that determine whether viral rebound is likely after treatment interruption can inform the development of optimal treatment regimens and therapeutic interventions aimed at achieving a functional cure for HIV-1. Building upon the theoretical framework proposed by Conway and Perelson, we iteratively formulated and examined hundreds of dynamic models of virus–immune interactions to identify those that both recapitulate viral dynamics across all studies and generate predictions consistent with clinical observations. We evaluated these models using extensive longitudinal viral-load and immunological data from multiple clinical trials. The best-performing models accurately capture the heterogeneity of viral dynamics from the acute phase through rebound. Our results robustly demonstrate that the expansion capacity of effector cells is a key determinant of viral control.

Organized by: Zhisheng Shuai (University of Central Florida), Junping Shi, College of William & Mary; Yixiang Wu, Middle Tennessee State University

Note: this minisymposia has multiple sessions. The other sessions are: Part-1, and Part-2.

1. Christopher Heggerud University of California, Davis
   "The many mechanisms behind regime shifts and tools to predict them"
Transient dynamics and regime shifts pose unique challenges when dealing with predictions and management of ecological systems yet little headway has been made on understanding when an ecological system might be in a transient state, or if a regime shift is imminent. In particular, given an ecological timeseries, it is difficult to detect the underlying mechanism causing a regime shift, or if one is occurring at all. Through a series of simplifications, we analyze synthetic data known to exhibit crawl-by type transient dynamics or that undergo some nonlinear excursion through state space that appears as a transient dynamic. Using dynamical systems theory, we create metrics that predict transient dynamics and furthermore to understand useful characteristics of the regime shift. These new metrics are additionally compared to typical early warning signals in ecology and the utility of both are discussed.
2. Tao Feng Yangzhou University
   "Modeling Collective Foraging Dynamics in Social Insect Colonies: Deterministic Structures and Stochastic Transitions"
In this talk, we explore the collective foraging dynamics of social insect colonies through mathematical models. Starting from a classical framework, we incorporate nonlinear recruitment and recruiter interference, and analyze how these factors influence system bistability and bifurcation behavior. To enhance analytical tractability, we introduce a reduced two-dimensional model that preserves key features of the original system. We then examine the impact of environmental stochasticity arising from multiple ecological processes—including recruitment efficiency and mortality rates—on foraging state transitions, critical thresholds, and colony resilience. Our results reveal how both intrinsic mechanisms and extrinsic variability shape the robustness of collective foraging behavior.
3. Amy Veprauskas University of Louisiana at Lafayette
   "Examining the impact of periodicity on population dynamics: with applications to agroecosystems and conservation science"
Population responses to repeated environmental or anthropogenic disturbances are shaped by complex interactions among disturbance patterns, population structure, and stage-specific vulnerability. Here, we introduce a matrix-based modeling framework designed to capture these dynamics and identify critical population thresholds. To demonstrate the versatility of our approach, we apply the framework to two distinct scenarios, one rooted in agroecosystem management and the other in conservation biology. By conducting sensitivity analyses across both cases, we reveal how variations in disturbance intensity and pre-disturbance demographic composition can lead to markedly different outcomes. The contrasting outcomes between these applications underscores the importance of incorporating demographic detail into ecological risk assessments.
4. Zhian Wang Hong Kong Polytechnic University
   "Global dynamics on the persistence and extinction of a periodic diffusive consumer-resource model"
we consider a reaction-diffusion model describing the consumer-resource interactions, where the resource's input rate may be temporally periodic and spatially heterogeneous. By employing the parabolic comparison principle, method of super-lower solutions for the mixed-quasilinear monotone system, theory for asymptotically periodic systems, uniform persistence theory for infinite-dimensional dynamical systems, and principal eigenvalue theory, we classify the persistence and extinction dynamics of the consumer population in terms of dispersal rates and relaxation time classified by the mortality rate of the consumer. Furthermore, we derive the asymptotic profiles of positive periodic solutions as the resource's dispersal rate is sufficiently small or large. Our results elucidate how the consumer's mortality rate, the relaxation time, the spatiotemporal heterogeneity of the resource's input, and the dispersal rates affect the global dynamics of consumer and resource populations. In particular, our analytical results derive the following implications:  (a) the resource's decay is the dominant factor that can prevent the resource abundance from blowing up; (b) the consumer’s mortality rate is a key factor determining the persistence and extinction for the consumer population; (c) the temporally homogeneous resource  input may be more beneficial to the consumer's persistence  than the temporally varying input when the consumer’s mortality is moderate.

Organized by: Diana White (Clarkson University)

Note: this minisymposia has been accepted, but the abstracts have not yet been finalized.

1. Maria Kuruvilla University of Victoria
   "Quantifying the Impact of Forest Harvesting on Chum and Pink Salmon Populations in Coastal BC"
Forest harvesting in coastal British Columbia (BC) has altered watersheds, impacting salmon habitat by increasing sediment, reducing riparian cover, and altering hydrology. These changes can affect the survival and growth of salmon through mechanisms like reduced egg-to-fry survival, increased stream scour, increased thermal stress, and loss of stream complexity which is essential for salmon rearing. Despite numerous localized studies, no comprehensive analysis has examined the population-level effects of forestry on salmon across BC. After assembling forest harvest histories for 1,746 salmon-bearing watersheds (1883-2022) and salmon abundance data (1950-2022), we used stock-recruit models (Ricker and Beverton-Holt) in a hierarchical Bayesian framework to test the effects of forestry metrics (Equivalent Clearcut Area, Cumulative Percent Disturbed) on chum and pink salmon productivity. Our results show a strong negative effect of forestry on chum productivity (e.g. 25% equivalent clearcut area reduces productivity by more than 20%) and a negligible effect on pink salmon. This highlights forestry’s significant role in the decline of chum salmon populations over recent decades.
2. Morgan Lavenstein Bendall University of California, Merced
   "Exploring Climate-Driven Population Changes in Aster Leafhoppers Using Age-Structured Models"
Due to their diversity and abundance, insects play essential ecological roles, including crop pollination, nutrient cycling, and serving as a food source for other species. However, climate change is predicted to heavily impact insect populations, with some expected to decline by up to 18% globally by the end of the 2020s, raising concerns about the future health of the bioeconomy. To investigate these impacts, we conducted a temperature study on Aster leafhoppers (Hemiptera: Cicadellidae: Macrosteles quadrilineatus). Using five temperature conditions, we collected physiological data over a month to assess the impact of temperature on survival, maturation, and egg production. We then developed an age-structured population model to explore how environmental temperature influences insect fitness and mortality rates. Our model is parameterized with experimental data across various climate change scenarios, providing insights into the effects of rising temperatures on insect survival and population dynamics. This work highlights the cascading effects of climate change on ecological networks and emphasizes the importance of understanding insect responses to environmental stressors.
3. Alexander Moffett Northeastern University
   "Detecting selection with a null model of gene order evolution"
Recent progress in genome assembly techniques has led to an explosion in chromosome-length genome sequences. These unfragmented assemblies have enabled biologists to study molecular evolution at unprecedented scales, providing insight into the evolution of genome architecture. Microsynteny, the conservation of gene order, has proven to be a key concept in our understanding of genome evolution. However, it remains unclear when microsynteny occurs due to random chance or selection. Here, we develop a mathematical model to discriminate between these two cases. Our model describes the dynamics of synteny block size distributions in the absence of selection or other biases. By fitting this null model to data from a comparative analysis of mammalian genomes, we identify synteny blocks larger than expected in the absence of selection. This approach allows us to rigorously determine which sets of genes are likely to have selection on their ordering in a lineage-specific manner. Our model presents a powerful tool for uncovering functional relationships between genes based on their ordering and for understanding the evolution of gene co-regulation.
4. Silas Poloni University of Victoria
   "Evolutionary dynamics at the leading edge of biological invasions"
Empirical evidence shows that evolution may take place during species' range expansion. Indeed, dispersal ability tends to be selected for at the leading edge of invasions, ultimately increasing a species' spreading speed. However, for organisms across many different taxa, higher dispersal comes at the cost of fitness, producing evolutionary trade-offs at the leading edge. Using reaction-diffusion equations and adaptive dynamics, we provide new insights on how such evolutionary processes take place. We show how evolution may drive phenotypes at the leading edge to maximize the asymptotic spreading speed, and conditions under which phenotypic plasticity in dispersal is selected for under different dispersal-reproduction trade-off scenarios. We provide some possible future research directions and other systems where the framework can be applied.
5. Jacob Serpico University of Alberta
   "Decoding the spatial spread of cyanobacterial blooms in an epilimnion"
Cyanobacterial blooms (CBs) pose significant global challenges due to their harmful toxins and socio-economic impacts, with nutrient availability playing a key role in their growth, as described by ecological stoichiometry (ES). However, real-world ecosystems exhibit spatial heterogeneity, limiting the applicability of simpler, spatially uniform models. To address this, we develop a spatially explicit partial differential equation model based on ES to study cyanobacteria in the epilimnion of freshwater systems. We establish the well-posedness of the model and perform a stability analysis, showing that it admits two linearly stable steady states, leading to either extinction or saturation. We use the finite elements method to numerically solve our system on a real lake domain derived from Geographic Information System (GIS) data and realistic wind conditions extrapolated from ERA5-Land. Our numerical results highlight the importance of lake shape and size in CB monitoring, while global sensitivity analysis using Sobol Indices identifies light attenuation and intensity as primary drivers of bloom variation, with water movement influencing early bloom stages and nutrient input becoming critical over time. This model supports continuous water-quality monitoring, informing agricultural, recreational, economic, and public health strategies for mitigating CBs.
6. Farshad Shirani Emory University
   "Environmental “Knees” and “Wiggles” as Stabilizers of Species Range Limits Set by Interspecific Competition"
Whether interspecific competition is a major contributing factor in setting species' range limits has been debated for a long time. Theoretical studies using evolutionary models have proposed that the interaction between interspecific competition and disruptive gene flow along an environmental gradient can halt range expansion of ecologically related species where they meet. However, the stability of such range limits has not been well addressed. In this talk, I present our work on investigating the stability of competitively formed range limits using a deterministic model of adaptive range evolution. We show that the range limits are unlikely to be evolutionarily stable if the environmental optima for fitness-related traits vary linearly in space. However, we demonstrate that environmental nonlinearities such as “knees” and “wiggles”, wherein an isolated sharp change or a step-like change occurs in the steepness of a trait optimum, can strongly stabilize the range limits. We show that the stability of the range limits established at such nonlinearities is robust against moderate environmental disturbances. Although strong climatic changes can still destabilize the range limits, such destabilization depends on how the relative dominance of the competing species changes across the environmental nonlinearity. Therefore, our results highlight the importance of measuring the competitive ability of species when predicting their response to climate change.
7. Maximilian Strobl Cleveland Clinic
   "Towards Quantitative and Predictive Models of Tumour Ecology: A Framework for Calibrating Evolutionary Game Theory with Experimental Data"
Tumours are complex ecosystems where diverse cancer cell subpopulations interact with each other and with non-cancer cells around them. Evolutionary game theory (EGT) has established itself as a powerful mathematical framework to study the implications of such ecological interactions, demonstrating an important role in shaping oncogenesis and treatment response. However, much of this work has been theoretical using parameters that are only loosely grounded in biological data. To move towards quantitative and predictive models of tumour ecology it is crucial to develop theoretical and experimental methodology to empirically calibrate and validate EGT models. We present an in silico study to optimize the 'Game Assay' for measuring ecological interactions between cancer cell populations in vitro. This assay, originally developed by Kaznatcheev et al (2017), involves co-culturing populations at different ratios, monitoring growth rates via time-lapse microscopy, and inferring frequency-dependent interactions. We begin by characterizing the accuracy and precision of this assay in a simulation study in which we use the replicator equation as the “ground truth”. Our simulations reveal potential biases in estimating fitness differences and interaction parameters, highlighting the need for careful experimental design. We provide guidelines for optimizing seeding ratios, number of replicates, and frequency of measurements, and present a new analysis techniques to improve the accuracy and precision of interaction measurements. Finally, we apply our optimized protocol to quantify interactions between 4 drug-sensitive and resistant lung cancer cell lines, revealing diverse ecological dynamics. This work demonstrates the power of integrating mathematical modeling with experimental approaches to develop robust empirical protocols and gain a quantitative understanding of tumour ecology.
8. Sureni Wickramasooriya University of California - Davis
   "Mathematical Model for Gene Drive Mosquito Releae On Principe Island"
Genetically engineered mosquitoes (GEMs) offer a promising malaria control strategy, yet their ecological interactions, dispersal, and long-term effects remain uncertain. Accurate modeling is essential to optimize GEM release strategies and assess their effectiveness in natural ecosystems. This study presents a high-performance, exascale agent-based model (ABM) simulating gene drive dynamics in wild mosquito populations. Incorporating mosquito population dynamics, spatial ecology, and genotype inheritance, the model provides insights into optimizing release timing, locations, and dispersal strategies. Our findings indicate that under optimal dispersal conditions, GEMs can achieve a 95% prevalence in wild populations within 112 days. Furthermore, our findings indicate that strategically coordinating GEM releases across multiple sites does not significantly impact gene drive establishment on the island. By capturing mosquito behaviors and movement in heterogeneous environments, this ABM serves as a powerful tool for evaluating GEM interventions, supporting evidence-based malaria control strategies, and enhancing ecological understanding of gene drive propagation..
9. Brian Zambrano University of Alberta
   "Cyanobacteria Hot Spot Detection Integrating Remote Sensing Data with Convolutional and Kolmogorov-Arnold Networks"
Monitoring cyanobacterial blooms promptly and accurately is crucial for public health management and understanding aquatic ecosystem dynamics. Remote sensing, particularly satellite observations, offers a viable approach for continuous monitoring. This study utilizes multispectral images from the Sentinel-2 satellite constellation in conjunction with ERA5-Land data to facilitate broad-scale data collection. We proposed a simple deep convolutional neural network (CNN) architecture to analyze cyanobacteria (CB) concentration dynamics in Pigeon Lake, Canada, over a five-year period. Utilizing the Local Getis-Ord statistic, we identified and analyzed trends in hot and cold spots under the null hypothesis of random distribution. We observed changes in the distribution and median CB concentration in hot spots over time. Additionally, we trained a Kolmogorov-Arnold Network (KAN) to classify segments of the lake shoreline into hot and non-hot spots using the Dynamic World dataset within a 500-meter radius of the lake.
10. Jia Zhao University of Alabama
    "Experimental and theoretical investigations of rotating algae biofilm reactors (RABRs): Areal productivity, nutrient recovery, and energy efficiency"
Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. In this talk, I will introduce a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). Experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential–integral equation‐based mathematical model for microalgae biofilm cultivation guided by laboratory experimental findings. The predictive mathematical model development is coordinated with laboratory experiments of biofilm areal productivity associated with ammonia and inorganic phosphorus uptake by RABRs. The unified experimental and theoretical tool is used to investigate the effects of RABR rotating velocity, duty cycle (DC), and light intensity on algae biofilm growth, areal productivity, nutrient uptake efficiency, and energy efficiency in wastewater treatment.
11. Joseph Baafi Memorial University of Newfoundland
    "Effect of Climate Warming on Mosquito Population Dynamics in Newfoundland"
Mosquitoes are key vectors of several infectious diseases affecting humans and animals. In North America, Culex mosquitoes are primary vectors of West Nile virus, St. Louis encephalitis, and Japanese encephalitis, as well as viral diseases in birds and horses. The Culex mosquito life cycle consists of four stages: eggs, larvae, pupae, and adults, each with unique development and mortality rates. Only active (non-diapausing) adults can reproduce, and environmental factors such as temperature, photoperiod, and rainfall influence population dynamics and stage-specific abundances. We develop a data-driven, stage-structured model that incorporates experimental data to describe how key climate variables regulate life history parameters. Specifically, egg laying rates depend on temperature, while maturation and survival rates are influenced by both temperature and rainfall. Mortality is temperature-dependent, and diapause induction and reactivation rates in adults are driven by temperature and photoperiod. Unlike many previous models that focus on tropical mosquitoes, our study explicitly includes diapause, a dormancy period in adult Culex mosquitoes essential for accurate modelling of temperate mosquito populations. Our results show that mosquito populations peak during summer months when temperatures exceed 10°C. Seasonal fluctuations in abundance highlight the need for adaptive vector control strategies. Since control measures often target specific life stages, such as larvicides for larvae or insecticides for adults, our findings suggest that optimal intervention strategies should vary by season to effectively reduce mosquito populations and disease risk.
12. Alexander Browning University of Melbourne
    "Heterogeneity in temporally fluctuating environments"
Many biological systems regulate phenotypic heterogeneity as a fitness-maximising strategy in uncertain and dynamic environments. Analysis of such strategies is typically confined both to a discrete set of environmental conditions, and to a discrete (often binary) set of phenotypes specialised to each condition. In this talk, we extend on both fronts to encapsulate both a discrete and continuous spectrum of phenotypes arising in response to two broad classes of environmental fluctuations that drive changes in the phenotype-dependent growth rates. We present a series of analytical and semi-analytical results that reveal regimes in which both discrete and continuous phenotypic heterogeneity is evolutionary advantageous.
13. Kyunghan Choi Postdoctoral Research Fellow/ University of Alberta
    "Animal movement models with spatiotemporal memory"
In this study, we examine how explicit spatial memory influences different mathematical models in various ecological dispersal contexts. Specifically, we analyze three memory-based dispersal strategies: (1) gradient-based movement, where individuals respond to environmental gradients; (2) environment matching, which promotes a uniform population distribution; and (3) location-based movement, where decisions are based solely on local suitability. These strategies correspond to diffusion-advection, Fickian diffusion, and Fokker-Planck diffusion models, respectively. Additionally, we explore steady-state problems for each strategy to highlight the differences between models incorporating temporal memory and those incorporating spatiotemporal memory.

1. Juancho Collera University of the Philippines Baguio
   "Bifurcations in a Patch-forming Plankton Model with Toxin Liberation Delay"
Harmful algal blooms (HABs) are characterized by rapid growth of algae, and can be caused by toxin-producing phytoplankton (TPP). When HABs occur, oxygen in the water depletes and thus can kill fish and other marine creatures causing both environmental and economic damages. In this talk, we consider a zooplankton-phytoplankton model under the assumption that the TPP exhibits group defense so that zooplankton predation decreases at high TPP density. Furthermore, we assume that toxin liberation by the TPP is not instantaneous but is rather mediated by a time lag, which is also known as the toxin liberation delay (TLD). Our results show that the model system undergoes a Hopf bifurcation around a coexistence equilibrium when the value of the TLD reaches a certain threshold. For values of the TLD just above the threshold, the stable limit cycle that is created depicts the manageable periodic fluctuation of the populations. However, when the value of the TLD is increased further, recurring blooms of various periodicity were observed which can be attributed to the occurrence of period-doubling bifurcations.
2. Matt Dopson Newcastle University
   "Understanding the cyclic populations of the short-tailed field vole in the UK using long term experimental data"
The short-tailed field vole (microtus agrestis) is the most abundant mammal in the UK, with populations reaching up to 80 million individuals. However, voles experience huge fluctuations in population numbers with up to a tenfold change over the course of regular 3.5 year cycles. Previous research has aimed to understand the mechanics behind these oscillations, but most of this work focuses on tundra regions. The ongoing Glen Finglas grazing experiment spans over 20 years, focusing on how managing grazing pressures affects various groups of species - including voles - in the more temperate upland acid grasslands of Scotland. Here, I will first present new data analysis on the Glen Finglas experiment, in particular the relationship between voles and the vegetation they use as a food source and shelter. I will then show how this data can be used to create and fit a mathematical model, capturing the vole's complex life history and interactions. Understanding these small animals is important as they are a key prey species for many predators and can also cause massive damage to plants and tree saplings. This mathematical model furthers our understanding of vole dynamics in temperate regions.
3. Valeria Giunta Swansea University
   "Understanding self-organisation in nature: Patterns and Bifurcations in Nonlocal Advection-Diffusion Models"
Understanding the mechanisms behind the spatial distribution, self-organisation and aggregation of organisms is a central issue in both ecology and cell biology. Since self-organisation at the population level emerges from individual behaviour, a mathematical approach is essential to elucidate these dynamics. In nature, individuals - whether cells or animals - inspect their environment before moving. This process is typically nonlocal, meaning that individuals gather information from a part of their environment rather than just their immediate location. Empirical research increasingly highlights nonlocality as a key aspect of movement, while mathematical models incorporating nonlocal interactions have gained attention for their ability to describe how interactions shape movement, reproduction and well-being. In this talk, I will present a study of a class of advection-diffusion equations that model population movement driven by nonlocal species interactions. Using a combination of analytical and numerical tools, I will show that these models support a wide range of spatio-temporal patterns, including segregation, aggregation, time-periodic behaviour, and chase-and-run dynamics. I will also discuss the existence of parameter regions with multiple stable solutions and hysteresis phenomena. Overall, I will explore various methods for analysing the bifurcation and pattern formation properties of these models, which provide essential mathematical tools for understanding the many aggregation phenomena observed in nature.
4. Ariel Greiner University of Oxford
   "Can tourism drive effective coral reef management? A modelling study."
Coral reefs are some of the most threatened ecosystems on the planet but also some of the most important, hosting upwards of 25% of marine biodiversity while also providing food and livelihood to almost 1 billion people. Coral reefs are also connected together into reef networks by coral larval dispersal, meaning that management or damage at one reef may have consequences for any reefs it is connected to. For this reason, coral reef management is of interest to many industries (e.g., fisheries, tourism) and governments. The potential impact of tourism in the context of coral reef management is unclear, as tourism is a source of damage for reefs but may also be a source of income that motivates conservation actors to keep reefs healthy for future tourists. Tourism groups also often focus on a subset of coral reefs, meaning that any management initiatives driven by tourism income would also only be focused on a subset of coral reefs in a reef network. We develop a socio-ecological model composed of a system of differential equations. This model represents a network of coral reefs visited by tourists to determine whether tourism income could help sustain a healthy network of coral reefs into the future. We explore this question under a variety of different tourism paradigms, management methods (coral restoration, fisheries management) and network types. Overall, we find that management funded by tourism can help counteract tourism damage, but is unable to save reefs that are unhealthy (low initial coral cover, high fishing). Management also has limited potential to help connected reefs in the network. This study demonstrates the limited effectiveness of tourism to drive coral reef conservation and instead encourages active investment in management methods that focus on the entire reef network.
5. Vincenzo Luongo University of Naples Federico II
   "Modeling photo-fermentative bacteria evolution for H2 production in a bio-reactor"
We propose a mathematical model describing the dynamics of photo fermentative bacteria leading to hydrogen production and polyhydroxybutyrate accumulation in an engineered environment. The model is derived from mass balance principles and consists of a system of differential equations describing the biomass growth, the substrate degradation and conversion into hydrogen and other catabolites, such as intracellular polyhydroxybutyrate, a precursor for bioplastics. The model accounts for crucial inhibiting phenomena and catabolic interactions affecting the evolution of the process. The study of the model has been performed also in terms of calibration with real experimental data related to specific photo-fermentative species, and it is supported by a sensitivity analysis study. The effective application of photo-fermentation for the concomitant hydrogen production and polyhydroxybutyrate accumulation was investigated.
6. Kayode Oshinubi Northern Arizona University
   "Forecasting Mosquito Population in Maricopa County Using Climate Factors and Filtering Techniques"
Mosquito-borne diseases pose a significant public health challenge, and effective prevention requires accurate forecasting of mosquito populations. In this study, we developed a statistical forecasting framework that leverages climate factors, such as temperature and precipitation, to improve mosquito population predictions in Maricopa County, Arizona. Our approach combines adaptive modeling techniques and filtering methods to infer precise model parameters and address previously observed limitations, particularly the inability to capture spring dynamics. By incorporating an Ensemble Kalman Filter (EnKF) method, we estimated time-varying parameters (baseline population growth rate) and static parameters while resolving the spring problem observed in prior models. Using Generalized Additive Models (GAMs), we forecasted the baseline population growth rate on a weekly basis, integrating precipitation and temperature data as covariates. These forecasts were further used to run a mechanistic ordinary differential equation (ODE) model to predict mosquito abundance and estimate associated uncertainties. Our iterative framework was applied weekly over a 52-week period, successfully capturing seasonal variations in mosquito populations from 2014 to 2015. The EnKF demonstrated superior performance compared to traditional Markov Chain Monte Carlo (MCMC) approaches for fitting mosquito abundance data. This enhanced methodology provides actionable insights for public health decision-makers, supporting resource allocation and improving outcomes in mosquito-borne disease prevention. Our findings underscore the value of integrating climate data and adaptive filtering techniques to address forecasting challenges, ultimately enabling more effective responses to emerging or reemerging pathogens of mosquito-borne disease risks, which can be driven by human behavior to become a pandemic.
7. Ryan Palmer University of Bristol, UK
   "Modelling electrostatic sensory interactions between plants and polinators: a guide from AAA to Bee"
Plant-arthropod relationships are crucial to the health of global ecosystems and food production. Through co-evolution, arthropods have acquired a variety of novel senses in response to the emergence of floral cues such as scent, colour and shape. The recent discovery that several terrestrial arthropods can sense electrical fields (e-fields) motivates the investigation of floral e-fields as part of their wider sensory ecology. That is, how does a flower's morphology and material properties produce and propagate detectable, ecologically relevant electrical signals? To investigate this, we modelled the e-field interior and exterior of a flower using a novel modification of the popular AAA-least squares algorithm, extending it to two domain boundary value problems. Physically, flowers typically act as dielectrics that inductively charge in the presence of a background electrical field, e.g. charged pollinators or the Earth's atmospheric potential gradient. We therefore present the development and application of this new method for these cases and discuss the biological relevance of the results for sensory and ecological studies. Our adapted AAA algorithm gives accurate and rapid results dependent on only three parameters: the relative permittivity of the flower, flower shape and the location of the pollinator(s). The results show how flowers display distinct information about their morphology, pollen availability and nearby pollinators, at distance, through the perturbed e-field. As well as how predators, such as the crab spider, can use flowers to mask their own electrical presence and draw in unsuspecting prey. The results of the two-dimensional AAA method also shows good qualitative agreement with equivalent three-dimensional finite element models. Biologically, our results highlight the significant role floral electrics may play in plant-pollinator and predator-prey relationships, unveiling previously unstudied facets.
8. Tamantha Pizarro Arizona State University
   "Impacts of Social Organization and Competition on Social Insect Population Dynamics"
In this study, we utilize the species Pogonomyrmex californicus, a type of queen ant that exhibits two distinct behavioral subtypes, as inspiration for our mathematical model. The first, known as solitary queens, establish colonies independently and represent the ancestral lineage. The second subtype, cooperative queens, form groups that collectively found a single colony—an evolutionary adaptation. Laboratory experiments have revealed that these queen types display distinct behavioral traits, or personalities. To better understand the ecological implications of these differences, we develop an ordinary differential equations (ODE) model that incorporates the effects of resource availability and social organization among adult ants, particularly in relation to brood care and foraging behaviors. Our model allows for Hopf bifurcations, enabling us to analyze the conditions under which colony coexistence is promoted or collapses. With this framework, we seek to address the following key questions: How does dependency on resource availability impact the survival of each queen type? How do social organization and resource dependency together influence queen survival, and what new conditions must be met for their persistence?
9. Femke Reurik Osnabrueck University
   "Connectivity, conservation, and catch: understanding the effects of dispersal between harvested and protected patches"
Overharvesting is a pressing global problem, and spatial management, such as protecting designated areas, is one proposed solution. This talk examines how dispersal between protected and harvested areas affects the asymptotic total population size and the asymptotic yield, which are key questions for conservation management and the design of protected areas. We utilize a two-patch model with heterogeneous habitat qualities, symmetric dispersal and density-dependent growth functions in both discrete and continuous time. One patch is subject to proportional harvesting, while the other one is protected. Our results demonstrate that increased dispersal does not always increase the asymptotic total population size or the asymptotic yield. Depending on the circumstances, dispersal enables the protected patch to rescue the harvested patch from overexploitation, potentially increasing both total population size and yield. However, high levels of dispersal can also lead to a lower total population size or even cause extinction of both patches if harvesting pressure is strong. The population in the protected patch needs to have high reproductive potential and the patch needs to be the effectively larger patch in order to benefit monotonically from increased dispersal. These findings provide a fundamental understanding of how dispersal influences dynamics in fragmented landscapes under harvesting pressure.
10. Shohel Ahmed University of Alberta
    "Stoichiometric theory in optimal foraging strategy"
Understanding how organisms make choices about what to eat is a fascinating puzzle explored in this study, which employs stoichiometric modeling and optimal forag- ing principles. The research delves into the intricate balance of nutrient intake with foraging strategies, investigating quality and quantity-based food selection through mathematical models. The stoichiometric models in this study, encompassing pro- ducers and a grazer, unveils the dynamics of decision-making processes, introducing fixed and variable energetic foraging costs. Analysis reveals cell quota-dependent pre- dation behaviors, elucidating biological phenomena such as “compensatory foraging behaviors” and the “stoichiometric extinction effect”. The Marginal Value Theorem quantifies food selection, highlighting the profitability of prey items and emphasizing its role in optimizing foraging strategies in predator–prey dynamics. The environ- mental factors like light and nutrient availability prove pivotal in shaping optimal foraging strategies, with numerical results from a multi-species model contributing to a comprehensive understanding of the intricate interplay between organisms and their environment.
11. Alberto Tenore Department of Mathematics and Applications, University of Naples Federico II, Italy
    "Phototaxis-Driven Dynamics in Phototrophic Biofilms: Modeling Invasion and Light-Dependent Behavior of Planktonic Cells"
Phototaxis, the ability of microorganisms to move in response to light, plays a crucial role in shaping the dynamics of phototrophic biofilms. While sessile cells remain typically embedded within the extracellular polymeric matrix, planktonic cells can navigate through the biofilm’s porous structure, adjusting their position in response to light cues. This directed movement optimizes exposure to favorable light conditions while avoiding harmful intensities, influencing the spatial organization and development of the biofilm community. In this talk, I will present a mathematical model for planktonic cell invasion in biofilms, where phototaxis acts as a driver of directed motility. The model incorporates a volume-filling term into the transport equation for planktonic cells, enabling the representation of phototactic behavior. A light-dependent sensitivity function captures both positive and negative phototaxis, governing cell movement toward favorable light conditions and away from excessive illumination. The biofilm is modeled as a homogeneous, viscous, incompressible fluid, with velocity described by Darcy’s law. The governing equations are solved numerically to explore the role of phototaxis in shaping biofilm dynamics. Numerical simulations reveal that motile cells accumulate in well-lit regions, enhancing sessile phototrophic growth and promoting biofilm development. The distribution of phototrophic biomass results from the interplay between random diffusion and phototactic movement. Under high-light stress conditions, photoinhibition reduces phototrophic growth and reverses phototaxis, slowing overall biofilm growth. Additionally, biofilm density modulates light penetration, either limiting phototrophic growth or providing protection against excessive exposure. These findings offer valuable insights into biofilm behavior in natural environments and can guide the optimization of biofilm-based processes in fields like wastewater treatment and bioremediation.
12. Marwa Tuffaha York University
    "The Role of Environmental Stress in Promoting Mutators Through Evolutionary Rescue"
Evolutionary rescue occurs when a population facing environmental stress avoids extinction by rapidly acquiring beneficial mutations. While higher mutation rates can enhance rescue, the role of mutators—genotypes with elevated mutation rates—remains unclear. We develop a theoretical framework and use stochastic simulations to investigate how mutators emerge and fix under selective pressure. Our results show that mutators cannot persist in stable environments but are favored when environmental deterioration occurs, with their fixation probability influenced by the speed of environmental change and wildtype mutation rates. Pre-existing mutators further increase rescue likelihood, particularly under rapid environmental shifts. These findings provide insights into antibiotic resistance, cancer evolution, and adaptation to climate change by highlighting how environmental stress shapes mutation rate evolution.
13. Sureni Wickramasooriya Univeresity of California - Davis
    "Dynamical Analysis of Additional Food Models with Mutual Interaction in Predator-Prey Systems for Pest Control"
The supplementation of additional food (AF) to introduced predators has been explored as a strategy to enhance pest control. However, AF models with prey-dependent functional responses can lead to unbounded predator growth. To address this, an AF model incorporating mutual interference has been proposed, demonstrating that pest eradication is feasible when the AF quantity ξξ exceeds a threshold function of the interference parameter ϵϵ. In this study, we revisit and extend this model, uncovering novel dynamical behaviors. We show that pest eradication occurs within a narrower AF range and can be bi-stable or globally attracting, arising through a saddle-node bifurcation. Additionally, we identify Hopf and global homoclinic bifurcations, revealing a unique dynamic where the pest extinction state becomes an 'almost' global attractor. This is the first analytical proof of such a structure in AF models, providing insights into bio-control strategies under varying predator interference conditions.
14. Chris Baker The University of Melbourne
    "Estimating potential myrtle rust impacts to carbon sequestration in Australia"
The impacts of invasive alien pests and diseases are routinely estimated and measured in the context of agriculture, but less so in the context of biodiversity and ecosystem services. In this study, we developed a new 'contribution modelling' approach to systematically estimate the impacts of pests and diseases at a continent scale. We developed this method using a case study of myrtle rust in Australia. We estimated the potential reduction of carbon sequestration in Australia due to myrtle rust using various national and scientific ecological datasets. We found that myrtle rust could lead to over 3% loss in national annual carbon sequestration if it were to spread across Australia, or over $700 million AUD value loss. While developed using a case study, this model is designed to be readily adaptible to other species and their impact on other environmental assets. Our work shows the need to systematically compile the potential impacts and costs of invasive pests and diseases to the environment and ecosystem services globally, to support both biosecurity decision-making and climate-change related initiatives such as net-zero emissions targets and reforestation efforts.

1. Kim Cuddington University of Waterloo
   "Exploring the population impacts of climate change effects on the mean, variance and autocorrelation of temperature using thermal performance curves."
Climate change is altering the mean, variance and autocorrelation of temperature. However, linear approaches to incorporating these temperature impacts in simple population models do not provide realistic predictions regarding climate change impacts. For example, simple degree days approaches or using a linear function of temperature to alter the density-independent population growth rate will not account for the sometimes catastrophic decrease in performance with high temperatures. We use an extremely simple population model coupled to nonlinear thermal performance curves to explore the simultaneous impact of changes to temperature mean, variance and autocorrelation. The realized density-independent population growth rate is given by three types of thermal performance curves that correspond to published data. We find relatively small impacts on established population dynamics when realistic changes in temperature sequences are used, suggesting that many populations may be quite robust to temperature-driven climate change impacts in the near term. The most extreme right-skewed performance curves are most likely to result in species extinctions, even though these curves have higher optimal temperatures.
2. Yves Dumont CIRAD/University of Pretoria
   "About the fight against the oriental fruit fly using a combination of non-chemical control tools - Mathematical strategy versus field strategy"
The oriental fruit fly, Bactrocera dorsalis, is a serious threat to crops and orchards in many places around the World, and in particular in Réunion island, where it was first detected in 2017. Since then, this pest has invaded the whole island and displaced established fruit fly populations. Since Réunion island is a hot spot of diversity, appropriate control tools have to be deployed to eliminate or reduce the wild population. I will present recent results that study the combination of the Sterile Insect Technique, entomopathogen fungi, and also pheromone traps. In particular, we will show how the spatial component and the orchards connectivity can drastically change the releases strategy, as well as the critical amount of sterile insects to release. We discuss (optimal) strategies obtained with our models versus realistic strategies that can actually be developed in the field. Our approach being generic, it can be adapted to other pests and disease vectors, such as mosquitoes. This works stands within the AttracTIS project, funded by Ecophyto 2021-2022.
3. Frank Hilker Osnabrueck University
   "A simple host-parasitoid model with Arnold tongues and shrimp-shaped periodic structures"
As parasitoids are the most frequently used biocontrol agents, especially in agriculture and forest ecosystems, they have become a cornerstone in mathematical biology. They are also a prototypical example of discrete-time systems. Here we consider a simple host-parasitoid model that is based on the classical Nicholson-Bailey model, but includes two extensions that are ecologically plausible: (1) density-dependent host growth (of Beverton-Holt type) and (2) a functional response of type III. The latter can be caused by a number of ecological mechanisms and is key in driving a rich dynamical behavior. While the system admits at most one nontrivial fixed point, we observe up to four coexisting non-equilibrium attractors. They can be periodic, quasi-periodic, or chaotic. They emerge in a quasi-periodic route to chaos and exhibit frequency-locking phenomena. We find different regular organized structures in the two-dimensional parameter plane that describe periodic oscillations surrounded by chaos. Among these structures are Arnold tongues (which have been previously reported in related models) and shrimp-shaped domains, which are little known in ecological models. Our results demonstrate that a type III functional response of parasitoids induces many new complex phenomena. While in continuous-time models the type III functional response tends to be stabilizing, in discrete-time models it can have very contrasting effects. The ecological implications are a high sensitivity not only to parameters but also to the initial condition.
4. Einar Bjarki Gunnarsson Science Institute, University of Iceland
   "The site frequency spectrum of an exponentially growing population: Theory and evolutionary history inference"
The site frequency spectrum (SFS) is a popular summary statistic of genomic data. In population genetics, the SFS has provided a simple means of inferring the rate of adaptation of a population and for distinguishing between neutral evolution and evolution under selection. The rapidly growing amount of cancer genomic data has attracted interest in the SFS of an exponentially growing population. In this talk, we discuss recent results on the expected value of the SFS of a population that grows according to a stochastic branching process, as well as (first-order) almost sure convergence results for the SFS in the large-time and large-population limits. Our results show that while the SFS depends linearly on the mutation rate, the branching process parameters of birth and death control the fundamental shape of the SFS at the low-frequency end. For the special case of a birth-death process (binary branching process), our results give rise to statistically consistent estimators for the mutation rate and extinction probability of the population, which stands in contrast to previous work which has indicated the need for additional data to decouple these two parameters. Overall, our work shows how single timepoint data on the SFS of an exponentially growing population can be used to infer important evolutionary parameters.
5. Axa-Maria Laaperi Newcastle University
   "Quantifying the fires of the future: Modelling and inference of wildfire spread dynamics."
Wildfires disrupt ecosystems, with climate change exacerbating vulnerability in regions poorly adapted to such disturbances. These events are driven by complex, multi-scale interactions where small perturbations in environmental factors can trigger large-scale shifts, complicating prediction efforts. We propose a coupled convection-reaction-diffusion system as a framework for modelling wildfire spread dynamics. This system integrates spatial and temporal variability to identify thresholds for spread and quantify the impact of abrupt environmental changes on burnt areas and rates of propagation. Incorporating environmental, meteorological, and historical fire record data from the Global Wildfire Information System, the Department for Environment, Food and Rural Affairs (UK), and drone footage of heather burning. Bayesian inference and Monte Carlo methods are employed for parameter estimation and uncertainty quantification, ensuring robust model validation against unseen data. Recent wildfire events around the globe highlight the need for actionable insights into environmental vulnerability, property loss, and infrastructure risk. By enabling near-real-time simulations, this model aims to provide a computational tool for emergency response, long-term management strategies, and assessments of climate change-induced outlier weather patterns influencing fire behaviour. This work highlights the potential of mathematical modelling to advance understanding and management of critical ecological disturbances.
6. Kaan Öcal University of Melbourne
   "Two sides of the same coin: Euler-Lotka and R0"
Two fundamental quantities in population biology, the reproductive number R0 and the growth rate, are intimately linked, but the exact nature of their relationship is somewhat obscure. Models of microbial growth typically have R0=2, but estimating their growth rate, and hence fitness, requires solving the famous Euler-Lotka equation. Conversely, in epidemiology one typically measures how quickly the infected population grows, but it is the reproductive number R0 that sets the threshold for an epidemic breakout and for herd immunity. In this talk, we use statistical techniques based on large deviations theory to clarify how exactly the population growth rate and R0 are connected. Building an analogy to classical thermodynamics, we show that the long-term behaviour of a population is encoded in a single convex function that relates growth rate, R0, and the statistics of intergeneration times in lineages. As an application, we derive a general formulation of the Euler-Lotka equation and explain why it is almost always appears as an implicit equation.
7. Swati Patel Oregon State University
   "Epistasis and the Emergence of Evolutionary Capacitance"
In the 90s, several experiments suggested a hypothesis that certain genes function to mask or buffer the effects of mutations, thereby allowing them to accumulate and be stored. These were termed evolutionary capacitors and addressed the fundamental evolutionary problem of how populations optimize fitness in one environment while maintaining variation to adapt to another. However, more recent experiments support an alternative hypothesis that such buffering of mutations is a natural and unsurprising outcome of epistasis and the mutation-selection process. To quantitatively test this hypothesis, we develop a mathematical framework that extends a classical partial differential equation of the mutation-selection process to account for epistasis. Using a perturbation method on steady state solutions, we show that certain types of epistatic interactions and selection pressures will lead to the emergence of the evolutionary capacitance phenomena.
8. Pranali Roy Chowdhury University of Alberta, Edmonton, Canada
   "A Qualitative Analysis Exploring the Hidden Threats of Methane to Ecosystems."
Methane, a potent greenhouse gas (GHG), is now driving climate change at an unprecedented rate. With a warming potential greater than carbon dioxide, it poses a substantial threat to the functioning of ecosystems. Despite its importance, studies investigating its direct impact on species interactions within ecosystems are rare. This growing concern highlights the need for a comprehensive understanding of the factors that could disrupt food chains, ultimately impacting ecosystem stability and resilience. In this talk, I will address this gap by developing a mechanistic model that integrates methane dynamics with the populations of species and detritus. This novel approach offers a framework for understanding how gaseous pollutants like methane influence trophic interactions. The model is studied for a range of concentrations of methane. Our findings reveal that low concentrations of methane can benefit species growth as an alternative carbon source. However, moderate to high levels induce sub-lethal to lethal effects. Further, analyzing the mechanisms for long transients in the fast-intermediate-slow formulation of the model, I will discuss how faster methane accumulation in water can result in slower species growth.
9. Fabiana Russo University of Naples Federico II
   "Modeling biofilm growth and microbially induced corrosion in wastewater concrete pipes: a double free boundary problem"
Microbially induced corrosion (MIC) is a significant global issue impacting infrastructure, economies, and environment. In wastewater systems, MIC is primarily associated with biofilm formation on concrete sewer pipes, leading to severe degradation due to microbial metabolic activity. The proliferation of sewer biofilms occurs in both submerged and unsubmerged conditions, leading to distinct microbial communities. Commonly, these biofilms host microorganisms such as fermentation bacteria, hydrogen-producing acetogens, denitrifying bacteria, sulfate-reducing bacteria, sulfur-oxidizing bacteria, and methanogens. In particular, sulfur-oxidizing bacteria play a crucial role in corrosion, as they oxidize hydrogen sulfide from wastewater effluents, generating sulfuric acid that accelerates concrete deterioration. A one-dimensional model with double free boundaries has been developed to investigate the proliferation of biofilms and the related corrosion process in wastewater concrete pipes. The domain is composed of two free boundary regions: a biofilm that grows towards the interior cavity of the pipe, sitting on a gypsum layer formed by corrosion, which penetrates the concrete pipe. Diffusion-reaction equations govern the transport and the metabolic production or consumption of dissolved substances, such as hydrogen sulfide, oxygen, and sulfuric acid within the biofilm layer. The biofilm free boundary tracks the growth of the microbial community, regulated by microbial metabolic activity and detachment phenomena. The corrosion process is incorporated into the model through a Stefan-type condition, which drives the advancement of the gypsum free boundary into the concrete pipe, governed by microbial production of sulfuric acid. Numerical simulations have been carried out to investigate the model behavior, encompassing the development and progression of the biofilm as well as the corrosion advancement, with the aim of elucidating the key factors governing both phenomena.
10. Anuraj Singh ABV-IIITM Gwalior, India
    "A modified May Holling Tanner Model: the role of dynamic alternative resources on species' survival"
The present paper investigates the dynamical behavior of the modified May Holling Tanner model in the presence of dynamic alternative resources. We study the role of dynamic alternative resources on the survival of the species when there is prey rarity. Detailed mathematical analysis and numerical evaluations, including the situation of ecosystem collapsing, have been presented to discuss the coexistence of species', stability, occurrence of different bifurcations (saddle-node, transcritical, and Hopf) in three cases in the presence of prey and alternative resources, in the absence of prey and in the absence of alternative resources. It has been obtained that the multiple coexisting states and their stability are outcomes of variations in predation rate for alternative resources. Also, the occurrence of Hopf bifurcation, saddle-node bifurcation, and transcritical bifurcation are due to variations in the parameters of dynamic alternative resources. The impact of dynamic alternative resources on species' density reveals the fact that if the predation rate for alternative resources increases, then the prey biomass increases (under some restrictions), and variations in the predator's biomass widely depend upon the quality of food items. This study also points out that the survival of predators is possible in the absence of prey. In the theme of ecological balance, the present study suggests some theoretical points of view for the eco-managers.
11. Beth Stokes University of Bath
    "Should I stay, or should I go: Sex ratio response drives a diverse range (anti-)correlated intra-species behaviours"
The decision of an individual or group to leave its current environment may be influenced by various factors. These include external or inter-species factors such as the presence of predators or food availability, and also intra-species dynamics like mate searching or the strength of social ties within a group. Understanding the consequences of these behaviours on the population level dynamics is non-trivial. In this study, we explore a stochastic model describing the movement of males and females of a species between localised patches, in which the movement rates are dependent on the sex ratio within the patch. By deriving a system of stochastic differential equations governing the fluctuations in these patches we can model a diverse range of intra-species behaviours driven solely by an individual's response to local sex ratio. We subsequently uncover and explore how different individual behaviours can give rise to large scale (anti-)correlated movements between the sexes.
12. Shohel Ahmed University of Alberta
    "Personality-Driven Consumer-Resource Dynamics"
To comprehend the mechanisms driving biodiversity and ecosystem resilience in a rapidly changing world, it is essential to explore the behavioral diversity among individuals in greater depth. Consistent individual differences in behavior, often referred to as animal personality, play a crucial role in shaping ecological and evolutionary dynamics, particularly in foraging behavior. Traditional approaches in behavioral and evolutionary ecology typically focus on average behavior, neglecting the significance of individual variability. This study explores the influence of consumer personality on ecological dynamics, specifically examining how variations in food availability affect behavioral strategies and ecosystem functioning. We develop a resource-consumer model that incorporates personality-dependent saturating attack rates based on the mean-field ratio of resources to consumers. The well-posedness of the model is established, and we analyze the existence and stability of all steady-state solutions. Through bifurcation analysis, we identify critical transition parameters and describe the nonlinear phenomena induced by personality-dependent attack rates. Our findings demonstrate that boldness in consumers enhances their persistence, particularly under low levels of boldness, where populations can survive even with moderate or high food supply, which was not captured in classical frameworks.
13. Sandip Banerjee Indian Institute of Technology Roorkee
    "Effect of productivity and seasonal variation on phytoplankton intermittency in a microscale ecological study using closure approach"
A microscale ecological study using the closure approach to understand the impact of productivity controlled by geographical and seasonal variations on the intermittency of phytoplankton will be presented in this talk. Using this approach for a nutrient–phytoplankton model with Holling type III functional response, it has been shown how the dynamics of the system can be affected by the environmental fluctuations triggered by the impact of light, temperature, and salinity, which fluctuate with regional and seasonal variations. Reynold’s averaging method in space, which results in expressing the original components in terms of its mean (average value) and perturbation (fluctuation) has been used to determine the impact of growth fluctuation in phytoplankton distribution and in the intermittency of phytoplankton spreading (variance). Parameters are estimated from the nature of productivity and spread of phytoplankton density during field observation done at four different locations of Tokyo Bay. The model validation shows that our results are in good agreement with the field observation and succeeded in explaining the intermittent phytoplankton distribution at different locations of Tokyo Bay, Japan, and its neighboring coastal regions.