Abstract
Surprising invariance relationships have emerged from the study of social interaction, whereby a cancelling-out of multiple partial effects of genetic, ecological or demographic parameters means that they have no net impact upon the evolution of a social behaviour. Such invariants play a pivotal role in the study of social adaptation: on the one hand, they provide theoretical hypotheses that can be empirically tested; and, on the other hand, they provide benchmark frameworks against which new theoretical developments can be understood. Here we derive a novel invariant for dispersal evolution: the 'constant philopater hypothesis' (CPH). Specifically, we find that, irrespective of variation in maternal fecundity, all mothers are favoured to produce exactly the same number of philopatric offspring, with high-fecundity mothers investing proportionally more, and low-fecundity mothers investing proportionally less, into dispersing offspring. This result holds for female and male dispersal, under haploid, diploid and haplodiploid modes of inheritance, irrespective of the sex ratio, local resource availability and whether mother or offspring controls the latter's dispersal propensity. We explore the implications of this result for evolutionary conflict of interests--and the exchange and withholding of contextual information--both within and between families, and we show that the CPH is the fundamental invariant that underpins and explains a wider family of invariance relationships that emerge from the study of social evolution.