Diego J. Rodríguez

Models of spatio-temporal dynamics in malaria

Abstract The development of mathematical models has been very useful in the study of the dynamics of infectious diseases. However, there is a scarcity of models which take into account the spatial heterogeneity of the environment. The few models developed indicate that, when the environment is fragmented, an increase in mobility between the patches enhances the persistence of the disease. We develop a model which describes the dynamics of malaria in time in a heterogeneous environment. As expected, fragmenting the environment decreases the likelihood of establishment of the disease in comparison with a homogeneous environment. Two types of mobility patterns are considered in the fragmented environment: migration between patches with no return, and visitation in which the individuals return to their patch of origin after visiting other patches. When compared with the fragmented environment without mobility, the time elapsed to reach the equilibrium decreases with both patterns of mobility; however, the chances of establishment and the equilibrium prevalence are the same with the migration pattern and higher with the visitation pattern. It is concluded that the effects of mobility in heterogeneous environments is not a simple matter, and depends on the patterns of mobility. The relevance of these findings to the design of control strategies is discussed.

Population dynamics of Oithona hebes (Copepoda: Cyclopoida) in a coastal estuarine lagoon of Venezuela: a stage-dependent matrix growth model

We study some aspects of the development and population dynamics of the copepod Oithona hebes. In this experiment, the number of individuals of different stages are monitored through 14 days. The data suggests the absence of density-dependence. A stage-dependent matrix model that predicts the number of the three stages, nauplii, copepodids, and adults, is constructed. Using experimental data we estimate the elements of the matrix model, by using regression as well as maximum likelihood methods. Finally the value of the asymptotic growth rate of the population is obtained with the eigenvalue with largest modulus of the transition matrix. We also estimate a confidence interval of the growth rate, which indicates that its difference from 1 is not statistically significant. The ecological and evolutionary implications of this finding are discussed. The predictions of a stochastic version of the model generally agree with the values experimentally obtained.

A method to detect higher order interactions in ecological communities

Abstract Higher order interactions are present in ecological communities when the effect of one species on the per capita growth rate of another depends not only on the first species. A method to detect such interactions in ecological communities is devised. As in a previous approach by Case and Bender (1981) , the method checks if the per capita growth rate of a species can be expressed as a sum of terms each one of which depends only on one species. If that expression is not possible there are higher order interactions. However Case and Bender (1981) , as well as other authors in subsequent studies, calculate the per capita growth rates with methods which can introduce errors. These methods also make assumptions about the mechanisms involved in the regulation processes which are not very realistic. The method proposed here alleviates these problems. It has the limitation, however, of needing short time intervals. The method is applied to experimental data of insect communities, and the results indicate that, in various analysis of 2-species communities, there are no reasons to suspect the existence of higher order interactions.