The components of directional and disruptive selection in heterogeneous group-structured populations

Abstract

We derive how directional and disruptive selection operate on scalar traits in heterogeneous groupstructured populations for a general class of models. In particular, we assume that each group in the population can be in one of a finite number of states, where states can affect group size and/or other environmental variables, at a given time. Using up to second-order perturbation expansions of the invasion fitness of a mutant allele, we derive expressions for the directional and disruptive selection coefficients, which are sufficient to classify the singular strategies of adaptive dynamics. These expressions include first-and second-order perturbations of individual fitness (expected number of settled offspring produced by an individual, possibly including self through survival); the first-order perturbation of the stationary distribution of mutants (derived here explicitly for the first time); the first-order perturbation of relatedness; and reproductive values, pairwise and third-order relatedness evaluated under neutrality.We introduce the concept of the individual k-fitness (defined as the expected number of settled offspring for which k − 1 randomly chosen neighbors are lineage members) and show its usefulness for calculating relatedness and its perturbation. We then show that the directional and disruptive selection coefficients can be expressed in terms individual k-fitnesses with k = 1, 2, 3 only. This allows for both a significant reduction in the dimensions of the system of equations describing population dynamics that needs to be solved to evaluate explicitly these selection coefficients and a biologically meaningful interpretation of their components. As an application of our methodology, we analyze directional and disruptive selection

Metacommunities, fitness and gradual evolution

“…Conditional fitness. The concept of individual fitness (16) has been considered in the previous literature for discrete time processes (Lehmann et al, 2016;Ohtsuki et al, 2020) and could generically be called unconditional individual fitness because it is evaluated unconditionally on whether or not a group transition occurs. We can distinguish its dispersal and philopatric components, as discussed in Section 3.3, by writing Lehmann and Rousset (2010), which hold as the conditional fitnesses for the model of Alizon and Taylor (2008).…”

“…We note that many closely connected ecological or evolutionary models allowing for various heterogeneities within and/or between groups have been considered before for both continuous or discrete time processes e.g. by Chesson (1981Chesson ( , 1985; Grey et al (1995); Frank (1998); Gandon and Michalakis (1999); Ronce et al (2000); ; Arrigoni (2003); Cadet et al (2003); Barbour and Pugliese (2004); Rousset (2004); Rousset and Ronce (2004); Martcheva and Thieme (2005); Lehmann et al (2006); ; ; Alizon and Taylor (2008); Wild et al (2009); Ronce and Promislow (2010); Wild (2011);Peña (2011);Rodrigues and Gardner (2012); Parvinen (2013); Massol and Débarre (2015); Lehmann et al (2016); Rodrigues (2018); Parvinen et al (2018); Kuijper and Johnstone (2019); Ohtsuki et al (2020). No prior model has however considered metacommunities with multiple interacting species where individuals and groups are characterized by arbitrary states and as such all these previous models, as well as models with finite class-structure in panmictic populations, can be conceptually subsumed to the present analysis.…”