We approximate the Bolker-Pacala model of population dynamics with the logistic Markov chain and analyze the latter. We find the asymptotics of the degenerated hypergeometric function and use these to prove a local CLT and large deviations result. We also state global limit theorems and obtain asymptotics for the first passage time to the boundary of a large interval.

Understanding under what conditions populations, whether they be plants, animals or viral particles, persist is an issue of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations are key factors that can facilitate or disrupt persistence. One approach to examining the interplay between these deterministic and stochastic forces is the ...

The local stability of a quasi-linear age-size structured population model studied in Tchuenche (2007) is analysed. If a certain threshold parameter known as the basic reproductive rate is less than unity, then the trivial steady state is locally asymptotically stable. Also, it is shown that if the only real root of the equation R(m′) = 1 is negative, then, the non trivial steady state is local...

Libraries of stellar spectra are fundamental tools in the study of stellar populations and in automatic determination of atmospheric parameters for large samples of observed stars. In the context of the present volume, here I give an overview of the current status of stellar spectral libraries from the perspective of stellar population modeling: what we have currently available, how good they a...

Leslie matrices are taught as a method of modeling populations in a discrete-time fashion with more detail in the tracking of age groups within the population. Leslie matrices have limited use in the actual modeling of populations, since when the age groups are summed, it is basically equivalent to discrete-time modeling assuming exponential population growth. The logistic model of population g...

The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton communities, which has been observed to be patchy over a wide range of spatial and temporal scales. Here, we use plankton communities as prototype systems to...

We survey recent results in one-dimensional dynamics, and as an application, we derive rigorous basic dynamical facts for two standard models in population dynamics, the Ricker and the Hassell families. We also informally discuss the concept of chaos in the context of one-dimensional discrete time models. First we use the model case of the quadratic family for an informal exposition and then we...

Abstract. We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their lo...

A growing body of research focuses on computationally detecting controversial topics and understanding the stances people hold on them. Yet gaps remain in our theoretical and practical understanding of how to define controversy, how it manifests, and how to measure it. In this paper, we introduce a novel measure we call “contention”, defined with respect to a topic and a population. We model co...