Until recently, my usual reaction to seeing the flood of papers on Arxiv about cooperation on complex networks was that “most people were reinventing the wheel” and hadn’t read the already vast literature on the subject. Nowak and team, as well as other folks centered more in the network science community, had already figured out the basics.
I think my former reaction on this was wrong. Nowak’s team, in particular, really has been focused less on networks, and more on the effects of graph motifs on evolutionary dynamics. Much of Nowak’s work has been focused, from the book onward, upon how a well-mixed selection coefficient is rescaled given the local effect of graph motifs, and the consequent effect on the long-run selection force. This is brilliant and foundational stuff, and it’s paralleled by some of Keeley’s work in epidemiology on epidemic thresholds given different pair and triplet motif distributions, but it misses the full picture of network science.
It misses the “long run effects” of having both micro and mesoscale motif and ultimately, community structure.
I think that the mesoscale structure, in particular, that means that we all need to pay close attention to the flood of papers coming through Arxiv, because we’re not done yet learning all we can learn about the dynamics of spreading processes on arbitrary networks. Not by a long shot. Not to say that a significant fraction of papers aren’t partially or completely duplicative, but most will need some care to determine where they overlap, if at all.
This fact is virtually guaranteed by the fact that we have explored a tiny fraction of the space of complex networks. Mainly we’ve explored complex, heterogeneous graphs with properties that are “fairly close” to tractable. Departures from E-R graphs are controlled as much as possible so that we can make analytical progress. But we must always remember that large finite or infinite networks can have connectivity structures that go well beyond various exponential or power-law functions. Despite the generality of the Molloy-Reed configuration model, we mostly generate density functions for use in the configuration model which are relatively well behaved.
And even if we explore the parts of the network phase space relevant to biological populations, the space of square-integrable functions which can describe stochastic processes on those networks is infintely larger than we’ve studied to date. And always will be. The space of networks and their effects on evolutionary dynamics is forever uncharted, however deeply we probe….