Background: The Central Limit Theorem (CLT) is a statistical principle that states that as the number of repeated samples from any population increase, the variance among sample means will decrease and means will become more normally distributed. It has been conjectured that the CLT has the potential to provide benefits for group living in some animals via greater predictability in food acquisition, if the number of foraging bouts increases with group size. The potential existence of benefits for group living derived from a purely statistical principle is highly intriguing and it has implications for the origins of sociality.
Results: Here we show that in a social allodapine bee the relationship between cumulative food acquisition (measured as total brood weight) and colony size accords with the CLT. We show that deviations from expected food income decrease with group size, and that brood weights become more normally distributed both over time and with increasing colony size, as predicted by the CLT. Larger colonies are better able to match egg production to expected food intake, and better able to avoid costs associated with producing more brood than can be reared while reducing the risk of under-exploiting the food resources that may be available.
Conclusion: These benefits to group living derive from a purely statistical principle, rather than from ecological, ergonomic or genetic factors, and could apply to a wide variety of species. This in turn suggests that the CLT may provide benefits at the early evolutionary stages of sociality and that evolution of group size could result from selection on variances in reproductive fitness. In addition, they may help explain why sociality has evolved in some groups and not others.