The evolution of social discounting in hierarchically clustered populations

Abstract

The expression of a social behaviour may affect the fitness of actors and recipients living in the present and in the future of the population. When there is a risk that a future reward will not be experienced in such a context, the value of that reward should be discounted; but by how much? Here, we evaluate social discount rates for delayed fitness rewards to group of recipients living at different positions in both space and time than the actor in a hierarchically clustered population. This is a population where individuals are grouped into families, families into villages, villages into clans, and so on, possibly ad infinitum. The group-wide fitness effects are assumed to either increase or decrease the fecundity or the survival of recipients and can be arbitrarily extended in space and time. We find that actions changing the survival of individuals living in the future are generally more strongly discounted than fecundity-changing actions for all future times and that the value of future rewards increases as individuals live longer. We also find that delayed fitness effects may not only be discounted by a constant factor per unit delay (exponential discounting), but that, as soon as there is localized dispersal in a population, discounting per unit delay is likely to fall rapidly for small delays and then slowly for longer delays (hyperbolic discounting). As dispersal tends to be localized in natural populations, our results suggest that evolution is likely to favour individuals that express present-biased behaviours and that may be time-inconsistent with respect to their groupwide effects.

Inclusive fitness forces of selection in an age-structured population

“…Here, we focus on the effects of cooperative interactions between individuals and the corresponding forces of selection, but note that our model also has scope to consider other scenarios, such as cases of harm (see Discussion). Using an infinite island framework to describe a resident social population 16,20,[24][25][26][27][28][29][30][31][32][33][34] , we explore the fate of a mutant allele that alters (i) survival rate from age 𝑥 to age 𝑥 + 1 and (ii) reproduction at age 𝑥. We derive inclusive fitness forces of selection acting on these mutant alleles, which indicate how the efficacy of natural selection changes with age with respect to socio-demographic parameters.…”

“…We consider a population divided into an infinite number of patches, and model the population dynamics of a focal patch. This infinite island approach 16,20,[24][25][26][27][28][29][30][31][32][33][34] allows kin selection to be modelled while also considering the effects of demography, which is appropriate for considering an age-structured population in which individuals have effects on one another's fitness. Each patch, which could also be conceptualised as a territory, contains discrete groups of exactly 𝑁 individuals that are, for simplicity, haploid and asexual.…”

Relatedness and synergies of kind and scale in the evolution of helping

“…Dispersal between groups may follow a variety of schemes, including the island model of dispersal (Wright, 1931;Taylor, 1992), isolation by distance (Malécot, 1975;Rousset, 2004), hierarchical migration (Sawyer and Felsenstein, 1983;Lehmann and Rousset, 2012), a model where groups split into daughter groups and compete against each other (Gardner and West, 2006;Lehmann et al, 2006;Traulsen and Nowak, 2006), and several variants of the haystack model (e.g., Matessi and Jayakar, 1976;Godfrey-Smith and Kerr, 2009). We leave the exact details of the life history unspecified, but assume that they fall within the scope of models of spatially homogeneous populations with constant population size (see Rousset, 2004, ch.…”

Social systems: demographic and genetic issues

“…2012). These specific temporal and spatial aspects of social actions necessarily lead to complex discounting (Lehmann & Rousset 2012).…”