  We consider the problem of explaining the emergence and evolution of
cooperation in dynamic network-structured populations. Building on seminal work
by Poncela et al, which shows how cooperation (in one-shot prisoner's dilemma)
is supported in growing populations by an evolutionary preferential attachment
(EPA) model, we investigate the effect of fluctuations in the population size.
We find that the fluctuating model is more robust than Poncela et al's in that
cooperation flourishes for a wide variety of initial conditions. In terms of
both the temptation to defect, and the types of strategies present in the
founder network, the fluctuating population is found to lead more securely to
cooperation. Further, we find that this model will also support the emergence
of cooperation from pre-existing non-cooperative random networks. This model,
like Poncela et al's, does not require agents to have memory, recognition of
other agents, or other cognitive abilities, and so may suggest a more general
explanation of the emergence of cooperation in early evolutionary transitions,
than mechanisms such as kin selection, direct and indirect reciprocity.
