Non-structured Model Research Articles

Two General Metapopulation Models and the Core-Satellite Species Hypothesis

This article describes two general metapopulation models with spatial variation in the sizes of habitat patches. The first model is a simple, nonstructured model that includes the mainland-island and Levins models as two limiting cases. The second model is a structured model explicitly including the size distribution of habitat patches, the size distribution of local populations, and migration among local populations. The models may have up to four equilibria, including two stable, positive equilibria. We discuss the core-satellite species hypothesis in light of these models. This hypothesis predicts that the distribution of patch-occupancy frequencies is bimodal in many species assemblages. We extend the original concept by demonstrating that the bimodal distribution of patch-occupancy frequencies can be generated by structurally more complex and more realistic metapopulation models than the original one; that the bimodal distribution is predicted by deterministic models, with no or infrequent switches of species between the core and the satellite state; and that metapopulation extinctions of rare species may be compensated by migration from outside the metapopulation (from a mainland), or metapopulation extinction may be prevented by low extinction probabilities of local populations in large or high-quality habitat patches. In every case the bimodal core-satellite distribution is due to the rescue effect, that is, the increasing migration rate and hence the decreasing probability of local extinction with an increasing fraction of patches occupied. We discuss how the metapopulation dynamic mechanisms described in this article may generate the bimodal core-satellite distribution in different kinds of communities.

Modeling and static optimization of the ethanol production in a cascade reactor. I. Modeling

Let us consider the modeling of a cascade reactor for the production of ethanol. The rates of reaction in alcoholic fermentation are modeled so that it can assume both ethanol and substrate inhibition, in relation to the observed results.A nonstructured model, based on biomass, substrate, and ethanol concentrations, is developed and identified. It is a complex model, this being due to the nonlinearity between the specific rate of ethanol production and the growth rate and, on the other hand, the study of the static optimization of ethanol fermentation is performed.