No Arabic abstract
The possible coexistence of one host, one aggressive parasite and one non-lethal parasite is simulated using the Penna model of biological ageing. If the aggressive parasites survive the difficult initial times where they have to adjust genetically to the proper host age, all three species may survive, though the host number may be diminished by increasing parasite aggressivity.
Spatial patterning can be crucially important for understanding the behavior of interacting populations. Here we investigate a simple model of parasite and host populations in which parasites are random walkers that must come into contact with a host in order to reproduce. We focus on the spatial arrangement of parasites around a single host, and we derive using analytics and numerical simulations the necessary conditions placed on the parasite fecundity and lifetime for the populations long-term survival. We also show that the parasite population can be pushed to extinction by a large drift velocity, but, counterintuitively, a small drift velocity generally increases the parasite population.
Cooperative interactions pervade the dynamics of a broad rage of many-body systems, such as ecological communities, the organization of social structures, and economic webs. In this work, we investigate the dynamics of a simple population model that is driven by cooperative and symmetric interactions between two species. We develop a mean-field and a stochastic description for this cooperative two-species reaction scheme. For an isolated population, we determine the probability to reach a state of fixation, where only one species survives, as a function of the initial concentrations of the two species. We also determine the time to reach the fixation state. When each species can migrate into the population and replace a randomly selected individual, the population reaches a steady state. We show that this steady-state distribution undergoes a unimodal to trimodal transition as the migration rate is decreased beyond a critical value. In this low-migration regime, the steady state is not truly steady, but instead fluctuates strongly between near-fixation states of the two species. The characteristic time scale of these fluctuations diverges as $lambda^{-1}$.
The outcome of competition among species is influenced by the spatial distribution of species and effects such as demographic stochasticity, immigration fluxes, and the existence of preferred habitats. We introduce an individual-based model describing the competition of two species and incorporating all the above ingredients. We find that the presence of habitat preference --- generating spatial niches --- strongly stabilizes the coexistence of the two species. Eliminating habitat preference --- neutral dynamics --- the model generates patterns, such as distribution of population sizes, practically identical to those obtained in the presence of habitat preference, provided an higher immigration rate is considered. Notwithstanding the similarity in the population distribution, we show that invasibility properties depend on habitat preference in a non-trivial way. In particular, the neutral model results results more invasible or less invasible depending on whether the comparison is made at equal immigration rate or at equal distribution of population size, respectively. We discuss the relevance of these results for the interpretation of invasibility experiments and the species occupancy of preferred habitats.
Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resources. We also present new results on spatial patterns of two populations, while modeling real distributions of anchovies and sardines. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. We find noise induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise delayed extinction, and noise induced pattern formation. In addition, our theoretical results are validated with experimental findings. Specifically the results, obtained by a coupled map lattice model, well reproduce the spatial distributions of anchovies and sardines, observed in a marine ecosystem. Moreover, the experimental dynamical behavior of two competing bacterial populations in a meat product and the probability distribution at long times of one of them are well reproduced by a stochastic microbial predictive model.
Population dynamics of a competitive two-species system under the influence of random events are analyzed and expressions for the steady-state population mean, fluctuations, and cross-correlation of the two species are presented. It is shown that random events cause the population mean of each specie to make smooth transition from far above to far below of its growth rate threshold. At the same time, the population mean of the weaker specie never reaches the extinction point. It is also shown that, as a result of competition, the relative population fluctuations do not die out as the growth rates of both species are raised far above their respective thresholds. This behavior is most remarkable at the maximum competition point where the weaker species population statistics becomes completely chaotic regardless of how far its growth rate in raised.