Ignacio Barradas

Disturbances allow coexistence of competing species

We give the first mathematically rigorous proof that disturbances allow competing species to coexist. This work provides a mathematical framework to explain the existence of fugitive species and the role played by disturbances in increasing or decreasing the biodiversity of ecosystems. We study modifications of the metapopulation model for patchy environments proposed by Caswell and Cohen (1990, 1991). For the one- and two-species models we give necessary and sufficient conditions on the parameters for the existence of a non-trivial equilibrium solution, which is shown to be always globally stable.

Competition during colonization vs competition after colonization in disturbed environments: A metapopulation approach

How two species interact during and after colonization influences which of them will be present in each stage of succession. In the tolerance model of ecological succession in a patchy environment, empty patches can be colonized by any species, but the ability to tolerate reduced resource levels determines which species will exclude the other. Here, we analyze a meta-population model of the possible roles of competition in colonization and succession, using non-linear Markov chains as a mathematical framework. Different kinds of competition affect the final equilibrial, abundances of the species involved in qualitatively different ways. An explicit criterion is given to determine which interactions have stronger effects on the final equilibrial levels of the weaker, species. Precise conditions are stated for the co-existence of both species. Both species are more likely to co-exist in the presence of an intermediate disturbance frequency.

A MATHEMATICAL MODEL FOR HUMAN AND ANIMAL LEPTOSPIROSIS

In this paper, we propose a SI model for the study of human and animal leptospirosis. Unlike other models for leptospirosis which consider only rodents as infection vectors, we consider that humans can be infected not only through contact with rodents, but also through any other animal that serves as a reservoir for the bacteria, and through contact with bacteria that are free in the environment. We calculate the basic reproductive number for this model, which is given in terms of the basic reproductive numbers of simpler subsystems of the original model, and propose some intervention techniques for controlling the disease based on our results.

Deceptive pollination and insects’ learning: a delicate balance

ABSTRACT In this paper we propose and discuss a simple two-dimensional model describing the interaction between two species: a plant population that gets pollinated by an insect population. The plants attract the insects deceiving them and not delivering any reward. We are interested in analysing the effect of learning by the insect population due to unsuccessfully visiting the deceiving plants. We are especially interested in three elements: conditions for the simultaneous coexistence of both species, their extinction as a function of the biological cost of the deceptiveness for the pollinator, and the appearance of oscillations in the dynamics. We also look for conditions under which plants would be better off by switching to different strategies, in particular, we look for conditions for the existence and stability of the equilibria of the corresponding differential equations system, and the conditions for the existence of periodic solutions.

A plant–pollinator system: How learning versus cost-benefit can induce periodic oscillations

In this paper, we propose a model describing the interaction between two species: a plant population that gets pollinated by an insect population. We assume the plant population is divided into two...

IMPROVING POLLINATION THROUGH LEARNING

In this paper we present a mathematical model describing the interaction of two species, a plant population and an insect population, the latter being divided in two subgroups: novice and expert pollinators. We analyze the system and show the existence of a single nontrivial equilibrium, which is stable and represents a state of mutual benefit for all species involved. We show some numerical simulations of the global stability.

Control Strategies in Multigroup Models: The Case of the Star Network Topology

In this paper, we propose control strategies for multigroup epidemic models. We use compartmental

On the Calculation of R_0 Using Submodels

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