How bad is to be slow-reacting ? On the effect of the delay in response to a changing environment on a population's survival

We consider a simple-model population, whose individuals react with a certain delay to temporal variations of their habitat. We investigate the impact of such a delayed-answer on the survival chances of the population, both in a periodically changing environment, and in the case of an abrupt change of it. It is found that for population with low degree of mutation-induced variability, being "slow-reacting" decreases the extinction risk face to environmental changes. On the contrary, for populations with high mutation amplitude, the delayed reaction reduces the survival chances.