Double decomposition: decomposing the variance in subcomponents of male extra-pair reproductive success

1. Extra-pair reproductive success (EPRS) is a key component of male fitness in socially monogamous systems and could cause selection on female extra-pair reproduction if extra-pair offspring (EPO) inherit high value for EPRS from their successful extra-pair fathers. However, EPRS is itself a composite trait that can be fully decomposed into subcomponents of variation, each of which can be further decomposed into genetic and environmental variances. However, such decompositions have not been implemented in wild populations, impeding evolutionary inference. 2. We first show that EPRS can be decomposed into the product of three life-history subcomponents: the number of broods available to a focal male to sire EPO, the male's probability of siring an EPO in an available brood and the number of offspring in available broods. This decomposition of EPRS facilitates estimation from field data because all subcomponents can be quantified from paternity data without need to quantify extra-pair ma...