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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 $lambda^{-1}$.
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species colonization and local extinction in a given g
The competitive exclusion principle asserts that coexisting species must occupy distinct ecological niches (i.e. the number of surviving species can not exceed the number of resources). An open question is to understand if and how different resource
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 resou
It is well-established that including spatial structure and stochastic noise in models for predator-prey interactions invalidates the classical deterministic Lotka-Volterra picture of neutral population cycles. In contrast, stochastic models yield lo
We investigate the competing effects and relative importance of intrinsic demographic and environmental variability on the evolutionary dynamics of a stochastic two-species Lotka-Volterra model by means of Monte Carlo simulations on a two-dimensional