Population dynamics of interacting species

Tuesday, June 15 at 11:30am (PDT)
Tuesday, June 15 at 07:30pm (BST)
Wednesday, June 16 03:30am (KST)

SMB2021 SMB2021 Follow Tuesday (Wednesday) during the "MS08" time block.
Note: this minisymposia has multiple sessions. The second session is MS07-ECOP (click here).

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Rebecca Tyson (University of British Columbia, Canada), Maria Martignoni (Memorial University of Newfoundland, Canada), Frithjof Lutscher (University of Ottawa, Canada)


A clear understanding of the dynamics of interacting species is of crucial importance as researchers try to predict the effects of invasive species and climate change on population persistence, diversity, and spread. Without such understanding, it is easy for managers to implement actions that may seem appropriate based on past knowledge, but that turn out to be potentially disastrous given new, emerging understanding of interacting populations. For example, the use of mycorrhizae as a biofertilizer is seen to be of high benefit to growers, but field studies have generated conflicting results. Recent mathematical work shows that the fungi can ultimately be detrimental or beneficial, depending on the nature of the nonlinear interactions between plant and fungi. This example is an illustration of the importance of mathematical work on the nonlinear interactions between species in order to untangle the population dynamics that result. This mini-symposium will gather together talks covering a wide range of interacting species models, creating an environment where there is maximum likelihood that ideas from one speaker will be entirely novel to another speaker, and generate new ideas for future research and collaboration.

Juliana Berbert

(Universidade Federal do ABC, Brazil)
"Dessication-rehydration stress revealed by sugar-metabolite-reserve model"
We focus on the evaluation of photosynthetic organisms. Some species and tissues can endure periods of the dry season because they rely on robust dynamics of metabolites. The metabolic dynamics are complex and challenging to address because the system involves several steps, usually with hundreds of metabolites. The metabolite densities vary among species and tissues and respond to external conditions, such as an environmental stimulus like water supply. Understanding these responses, particularly the dessication-rehydration processes, are important both economically and evolutionarily, especially in the presence of climate change. Therefore, we propose a new way to analyze the dynamics of metabolites with a compartmental model which explores the metabolites’ density-dependence on water explicitly. We use a mathematical formulation to model the dynamics among three essential metabolite classes: sugar (S), active metabolite (A), and reserve accumulation (R). Through stability analysis and numerical solutions, we characterize regions on the phase space, defined by the transition rates between the classes S to A and S to R, where the system diverges or approaches zero. We show that different species and tissues respond distinctly to dessication processes, being more or less resilient according to the transition rates between the compartments of the model. Furthermore, the effects of water supply fluctuation, due to the dessication-rehydration processes, show that unless the organism has a robust reservoir for metabolism, the system cannot support itself for a long time. Many results corroborate experimental observations, and others provide a new perspective on the studies of metabolic dynamics, such as the significance of the metabolism reservoir. We understand that knowing the organism’s response to abiotic changes, particularly that of the water supply, may improve our management of the use of these organisms, for example, in the crop field during climate changes.

Chris Heggerud

(University of Alberta, Canada)
"Niche differentiation in the light spectrum promotes coexistence of phytoplankton species: a spatial modeling approach."
The paradox of the plankton highlights the contradiction between Gause's law and the observed diversity of phytoplankton. It is well known that phytoplankton dynamics depend heavily on two main resources; light and nutrients. Here we consider light as a continuum of resources rather than a single resource. We propose a spatially explicit RD model to explore under what circumstance coexistence is possible from a mathematical and biological perspective. Furthermore, we provide biological context as to when coexistence is expected based on the degree of niche differentiation within the light spectrum and overall turbidity of the water.

Pau Capera Aragones

(University of British Columbia Okanagan, Canada)
"Differential equation model for central-place foragers with memory: Implications for bumble bee crop pollination"
Bumble bees provide valuable pollination services to crops around the world. However, their populations are declining in intensively farmed landscapes. Understanding the dispersal behaviour of these bees is a key step in determining how agricultural landscapes can best be enhanced for bumble bee survival. In our work, we develop a partial integro-differential equation model to predict the spatial distribution of foraging bumble bees in dynamic heterogeneous landscapes. In our model, the foraging population is divided into two subpopulations, one engaged in an intensive search mode (modeled by diffusion) and the other engaged in an extensive search mode (modeled by advection). Our model considers the effects of resource-dependent switching rates between movement modes, resource depletion, central-place foraging behaviour, and memory. We use our model to investigate how crop pollination services are affected by wildflower enhancements. We find that planting wildflowers adjacent to a crop can increase the pollination services to the crop, and we quantify this benefit as a function of the location, quantity, and quality of the planted wildflowers.

Rebecca Tyson

(University of British Columbia Okanagan, Canada)
"Phase-sensitive tipping: Cyclic ecosystems subject to contemporary climate"
Global change is expected to lead to increased reddening and amplitude of climate noise. In this paper we explore how these changes in climate variability could interact with systems that are already oscillating, namely, predator-prey systems. We include an Allee effect in the prey equation so that we can determine whether or not extinction is deterministically possible. We identify the phase of the predator-prey cycle as a new critical factor for tipping points (critical transitions) in cyclic systems subject to time-varying external conditions. Our analysis of these examples uncovers a counter-intuitive behaviour, which we call phase-sensitive tipping (or P-tipping), where tipping to extinction occurs only from certain phases of the cycle. We find that P-tipping can occur in both the Rosenzweig-MacArthur (RM) and Leslie-Gower-May (LGM) model systems, and for realistic parameter values for the Canada lynx and snowshoe hare. Our work identifies a new mechanism for climate-induced extinction.

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Virtual conference of the Society for Mathematical Biology, 2021.