Competition for Limiting Resources, Hamilton’s Rule, and Chesson’s R*

Abstract

This chapter links Chesson’s R* with inclusive fitness theory, arguing that competition for limiting resources within and between groups underlies both formulations. Chesson’s R* determines the strengths of interspecific compared to intraspecific competition, the balance of which is determined by the species having the highest rate of increase when conditions are at their worst. The latter formulation is generalized to the within- and between-group levels, l*_within and l*_between, where types compete for the lowest l* values in the most severe regimes. Conditionally, entities with the highest growth (group, population) or reproductive (types) rates are, theoretically, the superior or dominant types. It is argued that l* values are linked to Hamilton’s rule via a formulation advanced in 2002 showing when kin should remain in groups and when they should leave, states determined by intensities of within-group compared to between-group competition.

“Competition is an interaction between individuals, brought about by a shared requirement for a resource in limited supply, and leading to a reduction in the survivorship, growth, and/or reproduction of the competing individuals concerned.” Begon et al. (1990)

“Social evolution is facilitated in proportion to the coincidence of fitness interests experienced, through sociality, by the component sub-units (partners). Such a coincidence may come about through two basic methods, namely shared genes (relatedness) or shared reproductive fate.” Bourke (2011)

“The expected evolution obeys an adaptive topography defined by the long-run growth rate of the population. The expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population.” Engen et al. (2009)