  Selection on the level of loosely associated groups has been suggested as a
route towards the evolution of cooperation between individuals and the
subsequent formation of higher-level biological entities. Such group selection
explanations remain problematic, however, due to the narrow range of parameters
under which they can overturn within-group selection that favours selfish
behaviour. In principle, individual selection could act on such parameters so
as to strengthen the force of between-group selection and hence increase
cooperation and individual fitness, as illustrated in our previous work.
However, such a process cannot operate in parameter regions where group
selection effects are totally absent, since there would be no selective
gradient to follow. One key parameter, which when increased often rapidly
causes group selection effects to tend to zero, is initial group size, for when
groups are formed randomly then even moderately sized groups lack significant
variance in their composition. However, the consequent restriction of any group
selection effect to small sized groups is derived from models that assume
selfish types will competitively exclude their more cooperative counterparts at
within-group equilibrium. In such cases, diversity in the migrant pool can tend
to zero and accordingly variance in group composition cannot be generated. In
contrast, we show that if within-group dynamics lead to a stable coexistence of
selfish and cooperative types, then the range of group sizes showing some
effect of group selection is much larger.
