We study a model for the evolutionarily stable strategy (ESS) used by biological populations for choosing the time
of life-history events, such as migration and breeding. In our model
we accounted for both intra-species competition (early individuals have a competitive advantage) and a disturbance
which strikes at a random time, killing a fraction 1-p of the population.
Disturbances include spells of bad weather, such as freezing or heavily raining days
It has been shown by Iwasa and Levin (1995), that when p=0, then
the ESS is a mixed strategy, where individuals wait for a certain time and afterwards
start arriving (or breeding) every day. We remove the constraint $p=0$ and show that if 0
then the ESS still implies a mixed choice of times, but strong competition may lead to a massive arrival
at the earliest time possible of a fraction of the population, while the rest
will arrive throughout the whole period during which the disturbance may occur.
More precisely, given "p", there is a threshold for the competition
parameter "a", above which massive arrivals occur and below which there is a behaviour as in Iwasa and Levin (1995). We study the behaviour of the ESS and of the average fitness of the population, depending on the parameters
involved. We also discuss how the population may be affected by climate change, in two respects:
first, how the ESS should change under the new climate and whether this change implies
an increase of the average fitness; second, which is the impact of the new climate on a population
that still follows the old strategy. We show that, at least under some conditions, extreme weather
events imply a temporary decrease of the average fitness (thus an increasing mortality).
If the population adapts to the new climate, the survivors may have a larger fitness.