Survival cost sharing among altruistic full siblings in Mendelian population

Background: We focus on familial selection of Haldane in monogamous families in a diploid population, where the survival probability of each sibling is determined by altruistic food sharing with its siblings during starvation. An autosomal recessive-dominant or intermediate allele pair uniquely determines the altruistic or selfish behavior, which are coded by homozygotes. We focus on the case when additive cost and benefit functions determine the survival probability of each full sibling. Results: We provide conditions for the existence of the altruistic and selfish homozygote. We show that the condition of evolutionary stability of altruism depends on the genotype-phenotype mapping. Furthermore, if the offspring size increases then the condition of evolutionary stability of altruism becomes stricter. Contrary to that, for the evolutionary stability of selfish behavior it is enough if the classical rule of Hamilton does not hold. Moreover, when the classical rule of Hamilton holds and the condition of evolutionarily stability of altruism does not hold, then the selfish and altruistic phenotypes coexist. Conclusions: In summary, the classical rule of Hamilton is a sufficient condition for the existence of altruism, but it alone does not imply the evolutionary stability of the pure altruistic homozygote population when the altruistic siblings share the cost of altruism.