In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertaint...

Two conceptually different approaches to incorporate growth uncertainty into sizestructured population models have recently been investigated. One entails imposing a probabilistic structure on all the possible growth rates across the entire population, which results in a growth rate distribution model. The other involves formulating growth as a Markov stochastic diffusion process, which leads t...

Weekly abundances of 2 salp populations (Salpa fusiformis and Thalia democratica) were determined for the period from 1967 to 1990 at a coastal station in the Western Mediterranean using a discrete abundance scale. A previous analysis modeled these data as a Markov chain with ordered states and found a significant effect of stratification on the Markov transition probabilities. An alternative a...

Increasing pressures on the environment are generating an ever-increasing need to manage animal and plant populations sustainably, and to protect and rebuild endangered populations. Effective management requires reliable mathematical models, so that the effects of management action can be predicted, and the uncertainty in these predictions quantified. These models must be able to predict the re...

Finite mixtures are widely used in applications to model data coming from different populations. Let X be the latent random variable whose value is the label of the population the observation comes from, and let Y be the observed random variable. With finitely many populations, X takes values in {1, . . . , k} for some fixed integer k, and conditionally to X = j, Y has distribution μj. Here, μ1...

In this paper we propose a probabilistic approach to synthesize an agent-based heterogeneous population interaction model to study the spatio-temporal dynamics of an air-born epidemic, such as influenza, in a metropolitan area. The methodology is generic in nature and can generate a baseline population for cities for which detailed population summary tables are not available. The joint probabil...

The results obtained by two estimators of population sizes, MNKA and Mh, were compared for four species of sma ll mammmais Didelphis ol/rito Wied, 1826, Philollder /relloto (Oilers, 1818), NectolllYs sql/olllipes (Brants, 1827) and Akodon cursor (Wi nge, 1887) during a long-te rm population study. The MNKA estimator consistently underestimated the population sizes in relation to Mh. On the othe...

In this paper we deal with a model describing the evolution in time of the density of a neural population in a state space, where the state is given by Izhikevich’s two dimensional single neuron model. The main goal is to mathematically describe the occurrence of a significant phenomenon observed in neurons populations, the synchronization. To this end, we are making the transition to phase den...

In recent years fluid approaches to the analysis of Markov populations models have been demonstrated to have great pragmatic value. Initially developed to estimate the behaviour of the system in terms of the expected values of population counts, the fluid approach has subsequently been extended to more sophisticated interrogations of models through its embedding within model checking procedures...

The multilevel model of change and the latent growth model are flexible means to describe all sorts of population heterogeneity with respect to growth and development, including the presence of sub-populations. The growth mixture model is a natural extension of these models. It comes at hand when information about sub-populations is missing and researchers nevertheless want to retrieve developm...