Detecting kin selection at work using inclusive fitness

Abstract

A recent model shows that altruism can evolve with limited migration and variable group sizes, and the authors claim that kin selection cannot provide a sufficient explanation of their results. It is demonstrated, using a recent reformulation of Hamilton's original arguments, that the model falls squarely within the scope of inclusive fitness theory, which furthermore shows how to calculate inclusive fitness and the relevant relatedness. A distinction is drawn between inclusive fitness, which is a method of analysing social behaviour; and kin selection, a process that operates through genetic similarity brought about by common ancestry, but not by assortation by genotype or by direct assessment of genetic similarity. The recent model is analysed, and it turns out that kin selection provides a sufficient explanation to considerable quantitative accuracy, contrary to the authors' claims. A parallel analysis is possible and would be illuminating for all models of social behaviour in which individuals' effects on each other's offspring numbers combine additively.

Figure 1

The probability of migration (d) on the x-axis affects the relatedness (r) of an individual to her whole group (including herself). The theoretical value in the monomorphic model given in equation (A 2), r_anc, is shown with an open rectangle. The measured values in the polymorphic model are shown for k_anc (filled rectangle), 0.99×k_anc (triangle) and 1.01×k_anc (cross). The values are too close together to be graphically distinguished. The data are provided in the electronic supplementary material.

Figure 2

The probability of migration (d) on the x-axis is related to the fractions of emigrants that are type 2 on the y-axis. The immigrants have a fraction of 0.4, so values above (below) 0.4 indicate selection for higher (lower) x. The cases are 0.99×k_anc (diamond), k_anc (cross), 1.01×k_anc (open square) and the null case with x¹=x²=0 (filled square). For clarity across the range of d, the deviations from 0.4 are shown as relative to the discrepancy of the 1.01×k_anc case, whose values are therefore all +1. The deviations of the k_anc case from zero are caused by (i) slight deviations of r_anc in the selection model compared with the monomorphic model arising from the difference between x¹ and x², (ii) numerical inaccuracies in the calculation of r_anc; and deviations in both the k_anc and null cases, (iii) the restriction of the calculation to a finite grid when in theory groups are of unlimited size as well as, (iv) general numerical accuracy issues in computer programs. The figure shows that within high numerical accuracy, the critical value of k at which selection is neutral is k_anc. The relative and absolute discrepancies are provided in the electronic supplementary material.