The Limits of Complex Adaptation: An Analysis Based on a Simple Model of Structured Bacterial Populations
Douglas Axe
Abstract
To explain life's current level of complexity, we must first explain genetic innovation. Recognition of this fact has generated interest in the evolutionary feasibility of complex adaptations--adaptations requiring multiple mutations, with all intermediates being non-adaptive. Intuitively, one expects the waiting time for arrival and fixation of these adaptations to have exponential dependence on d, the number of specific base changes they require. Counter to this expectation, Lynch and Abegg have recently concluded that in the case of selectively neutral intermediates, the waiting time becomes independent of d as d becomes large. Here, I confirm the intuitive expectation by showing where the analysis of Lynch and Abegg erred and by developing new treatments of the two cases of complex adaptation--the case where intermediates are selectively maladaptive and the case where they are selectively neutral. In particular, I use an explicit model of a structured bacterial population, similar to the island model of Maruyama and Kimura, to examine the limits on complex adaptations during the evolution of paralogous genes--genes related by duplication of an ancestral gene. Although substantial functional innovation is thought to be possible within paralogous families, the tight limits on the value of d found here (d ≤ 2 for the maladaptive case, and d ≤ 6 for the neutral case) mean that the mutational jumps in this process cannot have been very large. Whether the functional divergence commonly attributed to paralogs is feasible within such tight limits is far from certain, judging by various experimental attempts to interconvert the functions of supposed paralogs. This study provides a mathematical framework for interpreting experiments of that kind, more of which will needed before the limits to functional divergence become clear.
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