Join forces or cheat: evolutionary analysis of a consumer-resource system

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.