ECOP-05 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.

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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.

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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.

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