ECOP Subgroup Contributed Talks

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.

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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.

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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.

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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.

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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.

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