No abstract

The study of the Allee effect on the stability of equilibria of predatorprey systems is of recent interest to mathematicians, ecologists, and conservationists. Many theoretical models that include the Allee effect result in an unstable coexistence equilibrium. However, empirical evidence suggests that predator-prey systems exhibiting densitydependent growth at small population densities still can achieve coexistence in the long term. We review an often cited model that incorporates an Allee effect in the predator population resulting in an unstable coexistence equilibrium, and then present a novel extension to this model which includes a term modeling intraspecific competition within the predator population. The additional term penalizes predator population growth for large predator to prey density ratios. We use equilibrium analysis to define the regions in the parameter space where the coexistence equilibrium is stable, and show that there exist biologically reasonable parameter sets which produce a stable coexistence equilibrium for our model.

In the early 1990s, the island of Santa Cruz off the coast of California experienced a rapid decline of the canid Urocyon littoralis santacruzae. The reasons behind this decline included disease, predation, competition with other species, and genetic bottlenecking. We present an individual-based model that simulates the population of Santa Cruz island foxes. Through our model we provide evidence of the Allee effect in the Santa Cruz island fox population which is exacerbated by selection for reduced reproductive probability.

No abstract

Antibiotic resistance is a capacious and global problem, considered to be one of the most important public health threats of the 21st century. In our proposed chapter, we review the basic biological and mathematical concepts underlying the phenomenon. We then provide tutorial-type instruction to build agent-based modeling skills, ultimately to simulate and analyze antibiotic resistance and its effect on the planet. In this talk, we will summarize the content of our proposed chapter on undergraduate research that outlines how students can use agent-based models together with laboratory experiments to explore bacteria growth, competition, and resistance. Then, we'll provide explicit examples of problems and projects posed throughout the chapter. We will discuss how both simulation and laboratory-based exercises can be used to deepen student understanding and provide richer research experience.