Model of population migration in a changing habitat

We propose a model describing the colonization process of empty ecological niches. The members of the population are characterized by a single trait (phenotype). The fitness of an individual is measured as the difference between the value of its trait and the optimal phenotype characterizing the environment. We show, via Monte Carlo simulations, that when the difference between the optimal phenotypes of the original habitat and the new colonized one, are too large, migration is in general unsuccessful. The difference in the concentrations in the two regions shows a very sharp transition depending on the difference in the respective phenotypes. We show also that when a population has a choice, it follows rather the old climate and migrate into a new territory rather than adapting to a new climate in the old region.