Ariel Fernandez and Michael Lynch have published the paper “Non-adaptive origins of interactome complexity”. The paper is open access, in short it argues that the complexity of our (i.e., of multicellular eukaryotes) protein-protein interaction networks is due to the random non-adaptive processes, which are so important because of our small effective population size. This paper is in line with the book “The origins of genome architecture” by Michael Lynch. In this book Lynch conjectures (and gives ample evidence) that many features of our genome can be explained by non-adaptive processes. The book is a wonderful read, it is deceptively simple and convincing, and I really recommend it to anyone interested in evolutionary theory (and, btw, in application of mathematical models to biological data, Lynch is one of the best in this department). All this said, I still feel some uneasiness when Lynch describes the concept of the effective population size. It is difficult to formulate the sources of my discontent (obviously, if I could rigorously state my questions to Lynch’s theories, I would write to Nature, not in my blog). One of the problems that I can state exactly is the following: what is the relation between the effective population size (how it is defined by Lynch) and the probability of fixation of a mutant allele. I could not find any proof that the formula from the Fisher-Wright model can be used for any population, if we replace the constant population size with the effective population size of the population in question. In my opinion, this is one of the big questions of the modern mathematical genetics.

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