ECOP Subgroup Contributed Talks

Eduardo Colombo

Princeton Univeristy

"Taxis-induced mesoscale patchiness in plankton communities"

A fundamental problem in ecology is how individual-level behavior affects emergent macro-ecological patterns. In marine ecosystems, this issue is intimately related to the interaction between physical and biological forces. For example, while being advected by the turbulent ocean, plankton can actively move in search for resources, establishing a tug-of-war between behavior and turbulence. The spatial structures that emerge from this interplay, especially at small scales, are key to community diversity and stability. To further the understanding about this issue, we developed an agent-based model that keeps track of a grazer-resource community advected by a turbulent flow. Our model accounts for this flow by using the “seeded-eddy” model to generate a velocity vector field that mimics the main hydrodynamic signatures of turbulence. The ecological dynamics include reproduction, grazing, natural mortality, as well as grazer capabilities of swimming and sensing resources' hydrodynamic and chemical cues. We observe that, as the grazer shifts from a purely planktonic to an active behavior, mesoscale patchiness and a new phase portrait for the population dynamics emerge. In detail, we investigate how the grazer swimming velocity affects these outcomes.

Paulo Amorim

Federal University of Rio de Janeiro

"Predator-prey models with hunger structure"

We present, analyse and simulate a model for predator-prey interaction structured by hunger. The model consists of a nonlocal transport equation for the predator, coupled to an ordinary differential equation for the prey. We deduce a system of 3 ODEs for integral quantities of the transport equation, which generalises some classical Lotka-Volterra systems. By taking an asymptotic regime of fast hunger variation, we find that this system provides new interpretations and derivations of several variations of the classical Lotka-Volterra system, including the Holling-type functional responses. We next establish a well-posedness result for the nonlocal transport equation. Finally, we show that in the basin of attraction of the nontrivial equilibrium, the asymptotic behaviour of the original coupled PDE-ODE system is completely described by solutions of the ODE system.

Anna Sisk

University of Tennessee

"Linking Immuno-Epidemiology Principles to Violence"

Societies have always struggled with violence, but recently there has been a push to understand violence as a disease and public health issue. This idea has unified professionals in medicine, epidemiology, and psychology with a goal to end violence and help heal those exposed to it. Recently, analogies have been made between community-level infectious disease epidemiology and how violence spreads within a community. Experts in public health and medicine suggest an epidemiological framework could be used to study violence. Since mathematical modeling plays an important role in epidemiology and community level organizations have previously shown success in addressing violence using disease mitigating-like techniques, we see that mathematical modeling could be useful tool in violence prevention. In this talk I will expand on the analogy of violence as an infectious disease and show how mathematical epidemiology is a useful framework for understanding the dynamics of violence. Then we will examine a susceptible-exposed-infected mathematical model for violence spread in a community and explore its usefulness by looking at some example numerical simulations. To end we will explore some of the primary insight these simulations offer on the effectiveness of different potential violence prevention strategies that have been considered for deployment.

Adam Lampert

Arizona State University, Tempe, AZ, USA

"Combining multiple tactics over time for cost-effective eradication of invading insect populations"

Because of the profound ecological and economic impacts of many non-native insect species, early detection and eradication of newly founded, isolated populations is a high priority for preventing damages. Though successful eradication is often challenging, the effectiveness of several treatment methods/tactics is enhanced by the existence of Allee dynamics in target populations. Historically, successful eradication has often relied on the application of several tactics. We ask how to combine three treatment tactics in the most cost-effective manner, either simultaneously or sequentially in a multiple-annum process. We construct an optimal-control model that describes the population dynamics of the invading insect population and how it is affected by three types of treatments: pesticide cation, mating disruption, and sterile male release. Then, we use stochastic programming to find the optimal treatment over time. We show that each of the three tactics is most efficient across a specific range of population densities. Furthermore, we show that mating disruption and sterile male release inhibit the efficiency of each other, and therefore, they should not be used simultaneously. However, since each tactic is effective at different population densities, different combinations of tactics should be applied sequentially through time when a multiple-annum eradication program is needed.