ECOP Subgroup Contributed Talks

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

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.

---

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?

---