ECOP Subgroup Contributed Talks

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.

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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.

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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.

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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.

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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.

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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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