ECOP-07 Contributed Talks

Femke Reurik

Osnabrueck University

"Connectivity, conservation, and catch: understanding the effects of dispersal between harvested and protected patches"

Overharvesting is a pressing global problem, and spatial management, such as protecting designated areas, is one proposed solution. This talk examines how dispersal between protected and harvested areas affects the asymptotic total population size and the asymptotic yield, which are key questions for conservation management and the design of protected areas. We utilize a two-patch model with heterogeneous habitat qualities, symmetric dispersal and density-dependent growth functions in both discrete and continuous time. One patch is subject to proportional harvesting, while the other one is protected. Our results demonstrate that increased dispersal does not always increase the asymptotic total population size or the asymptotic yield. Depending on the circumstances, dispersal enables the protected patch to rescue the harvested patch from overexploitation, potentially increasing both total population size and yield. However, high levels of dispersal can also lead to a lower total population size or even cause extinction of both patches if harvesting pressure is strong. The population in the protected patch needs to have high reproductive potential and the patch needs to be the effectively larger patch in order to benefit monotonically from increased dispersal. These findings provide a fundamental understanding of how dispersal influences dynamics in fragmented landscapes under harvesting pressure.

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Shohel Ahmed

University of Alberta

"Stoichiometric theory in optimal foraging strategy"

Understanding how organisms make choices about what to eat is a fascinating puzzle explored in this study, which employs stoichiometric modeling and optimal forag- ing principles. The research delves into the intricate balance of nutrient intake with foraging strategies, investigating quality and quantity-based food selection through mathematical models. The stoichiometric models in this study, encompassing pro- ducers and a grazer, unveils the dynamics of decision-making processes, introducing fixed and variable energetic foraging costs. Analysis reveals cell quota-dependent pre- dation behaviors, elucidating biological phenomena such as “compensatory foraging behaviors” and the “stoichiometric extinction effect”. The Marginal Value Theorem quantifies food selection, highlighting the profitability of prey items and emphasizing its role in optimizing foraging strategies in predator–prey dynamics. The environ- mental factors like light and nutrient availability prove pivotal in shaping optimal foraging strategies, with numerical results from a multi-species model contributing to a comprehensive understanding of the intricate interplay between organisms and their environment.

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Alberto Tenore

Department of Mathematics and Applications, University of Naples Federico II, Italy

"Phototaxis-Driven Dynamics in Phototrophic Biofilms: Modeling Invasion and Light-Dependent Behavior of Planktonic Cells"

Phototaxis, the ability of microorganisms to move in response to light, plays a crucial role in shaping the dynamics of phototrophic biofilms. While sessile cells remain typically embedded within the extracellular polymeric matrix, planktonic cells can navigate through the biofilm’s porous structure, adjusting their position in response to light cues. This directed movement optimizes exposure to favorable light conditions while avoiding harmful intensities, influencing the spatial organization and development of the biofilm community. In this talk, I will present a mathematical model for planktonic cell invasion in biofilms, where phototaxis acts as a driver of directed motility. The model incorporates a volume-filling term into the transport equation for planktonic cells, enabling the representation of phototactic behavior. A light-dependent sensitivity function captures both positive and negative phototaxis, governing cell movement toward favorable light conditions and away from excessive illumination. The biofilm is modeled as a homogeneous, viscous, incompressible fluid, with velocity described by Darcy’s law. The governing equations are solved numerically to explore the role of phototaxis in shaping biofilm dynamics. Numerical simulations reveal that motile cells accumulate in well-lit regions, enhancing sessile phototrophic growth and promoting biofilm development. The distribution of phototrophic biomass results from the interplay between random diffusion and phototactic movement. Under high-light stress conditions, photoinhibition reduces phototrophic growth and reverses phototaxis, slowing overall biofilm growth. Additionally, biofilm density modulates light penetration, either limiting phototrophic growth or providing protection against excessive exposure. These findings offer valuable insights into biofilm behavior in natural environments and can guide the optimization of biofilm-based processes in fields like wastewater treatment and bioremediation.

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