Theoretical models of animal movement and foraging

Sarah MacQueen

University College Dublin (School of Agriculture and Food Science)

"Model mechanism for choice of foraging site affects predicted pollination services"

Foraging constancy, or repeated return to the same foraging location, is an important aspect of bumble bee behaviour, and should therefore be an important consideration when using modeling to predict the pollination services provided by bumble bees.  However, it is unknown exactly how bumble bees select their foraging sites, and most modelling studies do not account for this uncertainty.  We use an individual based model to explore how predicted pollination services and bee fitness change under different foraging site selection mechanisms.  We considered two different site-searching methods (random and more realistic exploration behaviour) and four different site-selection metrics (random, minimal distance, maximal wild flower density, maximal net rate of energy return) in an agricultural landscape containing wildflower, crop (in bloom), and empty (no resource) patches.  We find that site-selection metric has a greater impact on crop pollination services and bee fitness than either site-searching method or landscape characteristics.  Site-selection based on maximising the net rate of energy return leads to both the highest crop pollination services and the longest foraging trips.  We find that the percent of crop fields visited, amount of time spent foraging, number of foraging sites located in crops, and the number of flowers visited may be used to determine how real bees select their foraging sites.
Additional authors: W. John Braun, University of British Columbia Okanagan; R.C. Tyson, University of British Columbia Okanagan

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Laurence Ketchemen Tchouaga

McGill University (Mathematics and statistics)

"Spatial steady states in fragmented landscapes under monostable and bistable growth dynamics"

Many biological populations reside in increasingly fragmented landscapes, where habitat quality may change abruptly in space. A reaction-diffusion model for a single species population which propagates in a heterogeneous landscape in a one-dimensional space is presented. The landscape is composed of two homogeneous adjacent patches with different diffusivities and net growth functions (monostable and bistable). A coupling interface condition between the two patches is involved. We consider various combinations of the reaction term and establish the existence, uniqueness and—in some cases—global asymptotic stability of a positive steady state. We classify the shape of these states depending on movement behaviour and clarify the role of movement in this context. We also give an answer to the following ecological question: how can the total population abundance at a steady state exceed the total carrying capacity? The analysis of the model with a bistable net growth function on one of the two patches yields a rich and interesting structure of steady states. Under certain parameter conditions, some of these states are amenable to explicit stability calculations. These yield insights into the possible bifurcations that can occur in our system. Numerical simulations reveal fold bifurcations.
Additional authors: Frithjof Lutscher - University of Ottawa

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Katie Florko

 University of British Columbia ( Institute for the Oceans and Fisheries)

"Linking movement and dive data to prey distribution models: new insights in foraging behaviour and potential pitfalls of movement analyses"

Animal movement data are regularly used to infer foraging behaviour and relationships to environmental characteristics, often to help identify critical habitat. To characterize foraging, movement models make a set of assumptions rooted in theory, for example, time spent foraging in an area increases with higher prey density. We assessed the validity of these assumptions by associating horizontal movement and diving of satellite-telemetered ringed seals (Pusa hispida)—an opportunistic predator—in Hudson Bay, Canada, to modelled prey data and environmental proxies. Modelled prey biomass data performed better than their environmental proxies (e.g., sea surface temperature) for explaining seal movement; however movement was not related to foraging effort. Counter to theory, seals appeared to forage more in areas with relatively lower prey diversity and biomass, potentially due to reduced foraging efficiency in those areas. Our study highlights the need to validate movement analyses with prey data to effectively estimate the relationship between prey availability and foraging behaviour.
Additional authors: Courtney Shuert, William Cheung, Steven Ferguson, Ian Jonsen, David Rosen, U Rashid Sumaila, Travis Tai, David Yurkowski, Marie Auger-Methe

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Mennatallah Gouda

Utah State University (Mathematics and Statistics Department)

"Characterization of the long-distance dispersal kernel of white-tailed deer and evaluating its impact on chronic wasting disease spread in Wisconsin"

Chronic Wasting Disease (CWD) is a fatal untreatable neurodegenerative disease that infects cervids. It is highly contagious and caused by abnormal malfunction and assembly of the normal cellular prion proteins (PrPC) into aggregation-prone prions (PrPSc). Centers for Disease Control and prevention (CDC) report that the prevalence of CWD in free-ranging deer in the US is still relatively low. However, in several states the infection rates exceed 1 deer in 10. Cervids may uptake CWD prions from direct interaction with infected individuals or from the environment. Infected individuals shed prions into the environment through feces, urine, saliva or carcass, and long-distance dispersal of infected deer poses a danger of spreading CWD to new regions. We propose an Integrodifference Model (IDE) to capture CWD dynamics and the consequences of long-distance dispersal behavior of White-Tailed Deer (WTD, Odocoileus virginianus). Currently there are no dispersal kernels available to describe the long-distance dispersal behavior of WTD juveniles. Our aim is to characterize long-distance dispersal of WTD juveniles and assess how it may affect CWD spread. We introduce a long-distance dispersal model, based on a diffusion-settling seed transport by vertebrates, accommodating a variety of hypothetical dispersal behaviors of WTD. Four kernels were obtained by solving 2D diffusion-settling Partial Differential Equation (PDE) models and approximating using Laplace’s method. We parameterized the kernels with GPS collar data collected in Wisconsin, US. Using a Maximum Likelihood Estimation (MLE) approach, we fitted the model parameters, and assessed model fits using the Bayesian Information Criterion (BIC). Sensitivity of results was determined using nonparametric bootstrapping and the impact of long-distance dispersal on CWD spread was quantified using the IDE model. A Holling type III settling rate function resulted in the most supported long-distance dispersal kernel reflecting deer preference to not settle down soon after they start dispersal. Our results will assist CWD management facilities in controlling disease spread.
Additional authors: Jim Powell, Utah State University; Jake McClure, Utah State University

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