The use of parallel and distributed models of evolutionary algorithms (EAs) is widespread nowadays as a means to improve solution quality and reduce computational times when solving hard optimization problems. For this purpose, emergent computational environments such as P2P networks and desktop grids are offering a plethora of new opportunities but also bring new challenges: functioning on a computational network whose resources are volatile requires fault tolerance and resilience to churn. In this work we analyze these issues from the point of view of island-based EAs. We consider two EA variants, genetic and multimemetic algorithms, and analyze the impact on them of design decisions regarding the logical interconnection topology among islands and the particular fault-management policy used. To be precise, we have conducted an extensive empirical evaluation of five topologies (ring, von Neumann grid, hypercube and two kinds of scale-free networks) and four policies (including checkpoint creation and population reinitialization variants) on four benchmark problems, considering three different scenarios of increasing resource volatility. The statistical analysis of the results underlines the inherent fault-tolerance of these EAs and indicates that, while checkpointing is the most robust strategy and is superior in the most fragile topologies, a seemingly simpler guided reinitialization strategy provide statistically comparable results on the top-performing topologies, namely von Neumann grids and hypercubes.