Human activity and other events can cause environmental changes to the habitat of organisms. The environmental changes effect the vital rates for a population. In order to predict the impact of these environmental changes on populations, we use two different models for population dynamics. One simpler linear model that ignores environmental competition between individuals and another model that...

In the past, ecologists have been debating about the relative importance of density-dependent versus density-independent factors in determining population dynamics. Between 1989 and 1992, an experiment was conducted at the University of Reading for studying how both densityindependent and density-dependent factors affect greenbottle blowfly population dynamic structure. See Daniels (1994). Taki...

In this paper, we consider a stoichiometric population model of two producers and one consumer. It is a generalization of the Rosenzweig-MacArthur population growth model, which is a one-producer, one-consumer population model without stoichiometry. The generalization involves two steps: 1) adding a second producer which competes with the first, and 2) introducing stoichiometry into the system....

Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete evolutionary time step. The theory is applied to population dynamics of natural rotifer populations. We show that under particular conditions the behavior of the inhom...

In this paper theory from population biology is combined with stochastic differential equations. The aim is to compare previously studied deterministic population models with corresponding stochastic population models. As an illustrative example the models are applied to a classical dataset (Gause, 1934). The first half of the paper gives a brief review of the theoretical background needed in o...

We study a population model in which there are two species, one of which has a juvenile and adult life stage. The adults of the first species prey on the second species, which in turn preys on the juveniles of the first. One version of the model represents systems where neither species can survive on its own, although we find that both can survive through mutual predation. To avoid extinction, ...

Motivated by issues arising in population dynamics, we consider the problem of iterating a given analytic function a number of times. We use the celebrated technique known as Carleman linearization that turns (for a certain class of functions) this problem into simply taking the power of a real number. We expand this method, showing in particular that it can be used for population models with i...

This study investigates the effect of competition between individuals on population dynamics when they compete for different resources during different seasons or during different growth stages. Individuals are assumed to compete for a single resource during each of these periods according to one of the following competition types: scramble, contest, or an intermediate between the two. The effe...

Fleming-Viot processes are a wide class of probability-measure-valued diffusions which often arise as large population limits of so-called particle processes. Here we invert the procedure and show that a countable population process can be derived directly from the neutral diffusion model, with no arbitrary assumptions. We study the atomic structure of the neutral diffusion model, and elicit a ...