A Generalization of Hamilton’s Rule for the Evolution of Microbial Cooperation

Abstract

Hamilton’s rule states that cooperation will evolve if the fitness cost to actors is less than the benefit to recipients multiplied by their genetic relatedness. This rule makes many simplifying assumptions, however, and does not accurately describe social evolution in organisms like microbes where selection is both strong and nonadditive. We derived a generalization of Hamilton’s rule and measured its parameters in Myxococcus xanthus bacteria. Nonadditivity made cooperative sporulation surprisingly resistant to exploitation by cheater strains. Selection was driven by higher-order moments of population structure, not relatedness. These results provide an empirically testable cooperation principle applicable to both microbes and multicellular organisms and show how nonlinear interactions among cells insulate bacteria against cheaters.

Cutting through the complexity of cell collectives

“…Analytical methods for studying collective behaviour often focus either on heterogeneities in structure [4,[20][21][22] or on heterogeneities in cell group composition [23][24][25], but rarely on both. Similarly, powerful theory has been developed for understanding the evolution of social interaction [26][27][28][29][30], but this theory is often difficult to apply directly to cell groups in realistic contexts (but see [31][32][33]). Computational individual-based modelling offers an alternative approach, implementing cells in two-or threedimensional space that behave independently in response to their local microenvironments [34,35].…”

Queller’s Separation Condition Explained and Defended

“…In either case, the way to overcome the problem is to add more predictors to the regression model in order to take deviations from additivity explicitly into account (Queller 1992b;Smith et al 2010;Cornforth et al 2012). …”

“…These extended formulations have already proved invaluable in lab studies of microbial cooperation, a context in which accounting for deviations from additivity turns out to be particularly important (Smith et al 2010;Cornforth et al 2012).…”

“…This result has led to the development of extended formulations of inclusive fitness theory in which deviations from additivity are explicitly represented and analysed (Smith et al 2010;Queller 2011;Cornforth et al 2012). These extended formulations have already proved invaluable in lab studies of microbial cooperation, a context in which accounting for deviations from additivity turns out to be particularly important (Smith et al 2010;Cornforth et al 2012).…”

“…In a recent critique, M. van Veelen et al (2012) argue (by means of a simple game-theoretic model) that the separation condition is irrelevant to the question of the comparative generality of inclusive fitness and multi-level selection, and that, moreover, the two approaches are not equally general after all. If these new results were valid, they would have far reaching implications for social evolution theory; for in addition to challenging conventional wisdom about the relationship between inclusive fitness and multi-level selection, they would also vitiate the program (pursued by Smith et al 2010 andQueller 2011) of using the separation condition to develop extended, more general formulations of Hamilton's rule. In this note, however, we come to Queller's defence.…”