1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of ...

Similar to the model studied in [11], it is assumed that the parasite under consideration is a microparasite so that the parasite population is not explicitly modeled in the interaction. There are only two interacting species prey and predator in the model. Individuals in each species are classified as either infected or uninfected. Let x1 and x2 denote the uninfected and infected prey populati...

Predator-prey models with Hassell-Varley type functional response are appropriate for interactions where predators form groups and have applications in biological control. Here we present a systematic global qualitative analysis to a general predator-prey model with Hassell-Varley type functional response. We show that the predator free equilibrium is a global attractor only when the predator d...

Cannibalism is ubiquitous in natural communities and has the potential to alter the functional relationship of predator–prey interactions. Although cannibalistic species are frequently subject to predation, the consequences of cannibalism in the prey for predator–prey interactions are poorly understood. Using a dragonfly larvae system, I provide the first experimental evidence that cannibalism ...

In a recent paper, Brodie and Brodie provide a very detailed description of advances and counter-measures among predator-prey communities with a poisonous prey that closely parallel an arms race in modern society. In this work, we provide a mathematical model and simulations that provide a theory as to how this might work. The model is built on a two-dimensional classical predator-prey model th...

We formulate and study a three-species population model consisting of an endemic prey (bird), an alien prey (rabbit) and an alien predator (cat). Our model overcomes several model construction problems in existing models. Moreover, our model generates richer, more reasonable and realistic dynamics. We explore the possible control strategies to save or restore the bird by controlling or eliminat...

The dynamics of predator-prey pursuit appears complex, making the development of a framework explaining predator and prey strategies problematic. We develop a model for terrestrial, cursorial predators to examine how animal mass modulates predator and prey trajectories and affects best strategies for both parties. We incorporated the maximum speed-mass relationship with an explanation of why la...

The traditional Lotka-Volterra-type predator-prey model has received great attention from both theoretical and mathematical biologists, and has been well studied (see, e.g., [5, 8, 9]). It is assumed in the classical Lotka-Volterra predator-prey model that each individual predator admits the same ability to attack prey. This assumption seems not to be realistic for many animals. In the natural ...

We study a supply chain model which is based on Schnakenberg type kinetics. This model is realistic in a predator-prey context if cooperation of predators is prevalent in the system and if there is practically an unlimited pool of prey, i.e. the predators will not feel the impact of the limited amount of prey due to its large quantity. The system also serves as a model for a sequence of irrever...