Effects of environmental colored noise in the contact process and its implications on bet-hedging

The contact process is one of the simplest models for studying population dynamics on a lattice, whose properties have been well studied when birth and death rates are constant in time. However, non-trivial effects arise when such rates fluctuate, as for instance due to environmental variability. In this work we develop a general framework to analyze the case of colored (i.e. temporally correlated) environmental noise; by means of the well-established "unified colored noise approximation" and a path-integral approach, we calculated the stationary density distributions as well as the asymptotic extinction time behavior. At the same time, we implemented exact simulation techniques which proved to be a robust tool to check our analytical results. Finally we apply our results to a topic of interest in the context of living systems. We focus on the problem of bet-hedging in population dynamics, in which a community of individuals reproduces through to two different spreading strategies: a constant one with a low benefit and a more risky one which depends on the external environmental conditions. In particular we study the role that temporal correlations of such environmental conditions may have on the overall dynamics, since they are an intrinsic characteristic of every real system.