Research Symposium

BIO

Elle Daily is a senior majoring in Biomathematics and Environmental Science interested in theoretical ecology. She is currently in two research labs: one with Dr. Micheal Cortez studying optimal inducible defenses and another with Dr. Emily Duval studying coordination in Lance Tailed Manakins. She will be pursuing a PhD in Biology after she graduates.

Modeling the Optimal Reaction Norm for Inducible Defenses

Abstract

Inducible defenses are defense mechanisms that prey species deploy when they sense predators and do not deploy when predators are absent, which often comes at a cost to the prey's reproduction. The prey’s reaction norm determines how much prey defend themselves as predator densities increase. The main goal of this paper was to derive the shapes of prey reaction norms using calculus of variation where it is assumed the induced responses of the prey maximize prey fitness. I first analyzed the Lotka-Volterra predator-prey model 𝑑𝑥/𝑑𝑡=𝑥[𝑟(𝛼)−𝑎(𝛼)𝑦] where x is prey density, α is rate of induction, y is predator density and r and a are functions that represent reproductive success and predator attack success respectively, both of which decrease as prey defense increases. I find that the optimal reaction norm is either (a) a step function where defense switches from no defense to maximum defense when predator density surpasses a threshold value or (b) a nonlinear function where defense gradually increases with predator density. I show that the specific shape of the reaction norm depends on how the prey’s reproduction rate (r) and the predator’s attack rate (a) decrease with prey defense. My results help explain how prey respond to predators and provide tools for making more accurate predictions about the dynamics of predator-prey systems. Other models that will be analyzed to represent other types of functional responses and compared include exponential and logistic forms for each term.

Keywords: inducible defenses