  Frequency dependent selection and demographic fluctuations play important
roles in evolutionary and ecological processes. Under frequency dependent
selection, the average fitness of the population may increase or decrease based
on interactions between individuals within the population. This should be
reflected in fluctuations of the population size even in constant environments.
Here, we propose a stochastic model, which naturally combines these two
evolutionary ingredients by assuming frequency dependent competition between
different types in an individual-based model. In contrast to previous game
theoretic models, the carrying capacity of the population and thus the
population size is determined by pairwise competition of individuals mediated
by evolutionary games and demographic stochasticity. In the limit of infinite
population size, the averaged stochastic dynamics is captured by the
deterministic competitive Lotka-Volterra equations. In small populations,
demographic stochasticity may instead lead to the extinction of the entire
population. As the population size is driven by the fitness in evolutionary
games, a population of cooperators is less prone to go extinct than a
population of defectors, whereas in the usual systems of fixed size, the
population would thrive regardless of its average payoff.
