Robert Stephen Cantrell
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Mean Field Games and Ideal Free Distribution Open
The ideal free distribution in ecology was introduced by Fretwell and Lucas to model the habitat selection of animal populations. In this paper, we revisit the concept via a mean field game system with local coupling, which models a dynami…
The Influence Of Corporate Governance On Investor Reactions To Layoff Announcements Open
Researchers in strategy often use agency theory to explain problems arising from the separation of ownership and management in corporations. These so-called agency problems occur when managerial activities fail to maximize shareholder valu…
Evolution of dispersal by memory and learning in integrodifference equation models Open
In this paper, we develop an integrodifference equation model that incorporates spatial memory and learning so that each year, a fraction of the population use the same dispersal kernel as the previous year, and the remaining individuals r…
Linking mathematical models and trap data to infer the proliferation, abundance, and control of Aedes aegypti Open
Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county…
What’s in a resource gradient? Comparing alternative cues for foraging in dynamic environments via movement, perception, and memory Open
Consumers must track and acquire resources in complex landscapes. Much discussion has focused on the concept of a ‘resource gradient’ and the mechanisms by which consumers can take advantage of such gradients as they navigate their landsca…
What’s in a resource gradient ? Comparing alternative cues for foraging in dynamic environments via movement, perception, and memory Open
Consumers must track and acquire resources in complex landscapes. Much discussion has focused on the concept of a ‘resource gradient’ and the mechanisms by which consumers can take advantage of such gradients as they navigate their landsca…
Memories of Migrations Past: Sociality and Cognition in Dynamic, Seasonal Environments Open
Seasonal migrations are a widespread and broadly successful strategy for animals to exploit periodic and localized resources over large spatial scales. It remains an open and largely case-specific question whether long-distance migrations …
Ideal Free Dispersal under General Spatial Heterogeneity and Time Periodicity Open
A population is said to have an ideal free distribution in a spatially\nheterogeneous but temporally constant environment if each of its members have\nchosen a fixed spatial location in a way that optimizes its individual fitness,\nallowin…
On the Evolution of Slow Dispersal in MultiSpecies Communities Open
For any $N \geq 2$, we show that there are choices of diffusion rates $\{d_i\}_{i=1}^N$ such that for $N$ competing species which are ecologically identical and having distinct diffusion rates, the slowest disperser is able to competitive …
Competitive exclusion in phytoplankton communities in a eutrophic water column Open
We analyze a reaction-diffusion system modeling the competition of multiple phytoplankton species which are limited only by light. While the dynamics of a single species has been well studied, the dynamics of the two-species model has only…
Persistence for a Two-Stage Reaction-Diffusion System Open
In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage structured population in a heterogeneous environment affect the model’s predictions of persistence or extinction for the population. In the case…
Populations with individual variation in dispersal in heterogeneous environments: dynamics and competition with simply diffusing populations Open
We consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior h…
View article: The total dispersal kernel: a review and future directions
The total dispersal kernel: a review and future directions Open
The distribution and abundance of plants across the world depends in part on their ability to move, which is commonly characterized by a dispersal kernel. For seeds, the total dispersal kernel (TDK) describes the combined influence of all …
View article: Advancing an interdisciplinary framework to study seed dispersal ecology
Advancing an interdisciplinary framework to study seed dispersal ecology Open
Although dispersal is generally viewed as a crucial determinant for the fitness of any organism, our understanding of its role in the persistence and spread of plant populations remains incomplete. Generalizing and predicting dispersal pro…
Rapid changes in seed dispersal traits may modify plant responses to global change Open
When climatic or environmental conditions change, plant populations must either adapt to these new conditions, or track their niche via seed dispersal. Adaptation of plants to different abiotic environments has mostly been discussed with r…
View article: Employing plant functional groups to advance seed dispersal ecology and conservation
Employing plant functional groups to advance seed dispersal ecology and conservation Open
Seed dispersal enables plants to reach hospitable germination sites and escape natural enemies. Understanding when and how much seed dispersal matters to plant fitness is critical for understanding plant population and community dynamics. …
Evolutionary stability of ideal free dispersal under spatial heterogeneity and time periodicity Open
Roughly speaking, a population is said to have an ideal free distribution on a spatial region if all of its members can and do locate themselves in a way that optimizes their fitness, allowing for the effects of crowding. Dispersal strateg…
Dynamics of populations with individual variation in dispersal on bounded domains Open
Most classical models for the movement of organisms assume that all individuals have the same patterns and rates of movement (for example, diffusion with a fixed diffusion coefficient) but there is empirical evidence that movement rates an…
A tridiagonal patch model of bacteria inhabiting a Nanofabricated landscape Open
In this paper we employ a discrete-diffusion modeling framework to examine a system inspired by the nano-ecology experiments on the bacterium Escherichia coli reported upon in Keymer et al. (2006). In these experiments, the bacteria inhabi…
View article: A PDE model of intraguild predation with cross-diffusion
A PDE model of intraguild predation with cross-diffusion Open
This note concerns a quasilinear parabolic system modeling an intraguild predation community in a focal habitat in $\mathbb{R}^n$, $n ≥ 2$. In this system the intraguild prey employs a fitness-based dispersal strategy whereby the intraguil…
Modeling and control of local outbreaks of West Nile virus in the United States Open
West Nile virus (WNV) was first detected in the United States (U.S.) during an outbreak in New York City in 1999 with 62 human cases including seven deaths. In 2001, the first human case in Florida was identified, and in Texas and Californ…
Evolution of Natal Dispersal in Spatially Heterogenous Environments Open
Understanding the evolution of dispersal is an important issue in evolutionary ecology. For continuous time models in which individuals disperse throughout their lifetime, it has been shown that a balanced dispersal strategy, which results…
Transmission Dynamics of Rift Valley Fever Virus: Effects of Live and Killed Vaccines on Epizootic Outbreaks and Enzootic Maintenance Open
Rift Valley fever virus (RVFV) is an arthropod-borne viral pathogen that causes significant morbidity and mortality in small ruminants throughout Africa and the Middle East. Due to the sporadic and explosive nature of RVF outbreaks, vaccin…