MS01 - ECOP-07

Exploring Heterogeneity in Mathematical Models: Methods, Applications, and Insights (Part 1)

Monday, July 14 at 10:20am

SMB2025 Follow

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

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

Description:

This minisymposium will focus on the mathematical modeling of heterogeneity across various biological systems. Heterogeneity often plays a critical role in shaping the dynamics and outcomes of biological processes. The session aims to: (i) Showcase advances in modeling techniques that capture heterogeneity; (ii) Explore the impact of heterogeneity on predictions and control strategies; (iii) Highlight applications spanning population dynamics, epidemiology, ecology and evolution; (iv) Encourage discussions on the integration of data-driven and theoretical approaches to address heterogeneity. We have confirmed 10 speakers, with 2 more awaiting confirmation (one pending administrative approval at the CDC). Among the confirmed speakers, half are female, and over half are junior researchers, including 1 PhD student and 2 postdocs. Please note that we are going to submit another proposal for the total of 12 speakers.

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.

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.

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.

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.

#SMB2025 Follow

Annual Meeting for the Society for Mathematical Biology, 2025.