In this survey, we briefly review some of our recent studies on predator-prey models with discrete delay. We first study the distribution of zeros of a second degree transcendental polynomial. Then we apply the general results on the distribution of zeros of the second degree transcendental polynomial to various predator-prey models with discrete delay, including Kolmogorov-type predator-prey m...

Predator switching is often assumed to be a stabilizing force in predator–prey interactions. Recent models, however, have shown that predator switching can have a destabilizing effect on populations, creating cycles or even extinctions of predators and prey. However, most of these models have been traditional top-down mathematical models that do not incorporate individual variability or evoluti...

In this work we present a predator–prey model that incorporates individual behavior of the predators. A classical Lotka–Volterra model with self-limiting prey describes the predator–prey interaction. Predator individuals can use two behavioral tactics to dispute a prey when they meet, the classical hawk and dove tactics. Each individual can use both tactics along its life. The predator behavior...

study of the spatial distribution of a pest and its natural enemies provides better decision tool for integrated pest management. the spatial distribution and seasonal activity of panonychus ulmi (koch) and its predator zetzellia mali (ewing) were studied in an apple orchard in khoramdareh (zanjan province, iran) during 2007. the interaction (density dependence) between the prey and its predato...

Traditionally, predator switching has been assumed to be a stabilizing force in ecological systems. Recent work, however, has shown that predator switching can be either stabilizing or destabilizing. Most models of predator switching, to date, assume that prey are behaviorally passive and do not respond to predators. We allowed prey to respond behaviorally to predators, so as to avoid capture, ...

In this work we present a predator-prey model that incorporates individual behavior of the predators. A classical Lotka-Volterra model with self-limiting prey describes the predator-prey interaction. Predator individuals can use two behavioral tactics to dispute a prey when they meet, the classical hawk and dove tactics. Each individual can use both tactics along its life. The predator behavior...

Predators can affect prey populations and, via trophic cascades, predators can indirectly impact resource populations (2 trophic levels below the predator) through consumption of prey (density-mediated indirect effects; DMIEs) and by inducing predator-avoidance behavior in prey (trait-mediated indirect effects; TMIEs). Prey often employ multiple predator-avoidance behaviors, such as dispersal o...

Predator-prey systems have been studied extensively. See, for instance, [1, 6, 8–10] and the references cited therein. Most of the previous papers focused on the predator-prey systems without stocking. Brauer and Soudack [2, 3] studied some predator-prey systems under constant rate stocking. To our knowledge, few papers have been published on the existence of positive periodic solutions for del...

Hundreds of studies exist on predator foraging behaviour, and the same holds for anti-predator behaviour in prey. However, despite these many studies, almost nothing is known about diet choice by predators that feed on prey with anti-predator behaviour. We addressed this problem theoretically by incorporating anti-predator vigilance into two classical models of diet choice by predators. Vigilan...

Predator-prey interactions often vary on the basis of the traits of the individual predators and prey involved. Here we examine whether the multidimensional behavioral diversity of predator groups shapes prey mortality rates and selection on prey behavior. We ran individual sea stars (Pisaster ochraceus) through three behavioral assays to characterize individuals' behavioral phenotype along thr...