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Keywords:

  • hyperbolic discounting;
  • relatedness;
  • social discounting;
  • spatially structured population

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 group-wide effects.