  In this work we study the process of mutant invasion on an example of a
consumer-resource system with annual character of the behavior. Namely,
individuals are active during seasons of fixed length separated by winter
periods. All individuals die at the end of the season and the size of the next
generation is determined by the number of offspring produced during the past
season. The rate at which the consumers produce immature offspring depends on
their internal energy which can be increased by feeding. The reproduction of
the resource simply occurs at a constant rate. At the beginning, we consider a
population of consumers maximizing their common fitness, all consumers being
individuals having the same goal function and acting for the common good. We
suppose that a small fraction of the consumer population may appear at the
beginning of one season and start to behave as mutants in the main population.
We study how such invasion occurs.
