Spatial patterns of extra-pair paternity: beyond paternity gains and losses.

Most studies on extra-pair paternity (EPP) focus either on a specific male's extra-pair gains or his extra-pair losses. For an individual bird however, mate choice or mate availability may underlie strong spatial restrictions. Disregarding this spatial aspect may underestimate or mask effects of parameters influencing observed EPP patterns. Here, we propose a spatially explicit model for investigating the probability of having extra-pair offspring (EPO) within local networks of breeding pairs. The data set includes all realized and unrealized potential extra-pair matings. This method is biologically meaningful because it allows (a) considering both members of an extra-pair mating and their social mates, and (b) direct modelling of the spatial context in which extra-pair behaviour occurs. The method has the advantage that it can provide inference about the relative contribution of spatial and non-spatial parameters, and about the relative importance of male and female neighbourhoods. We apply this method to parentage data from 1025 broods collected over 12 breeding seasons in two independent study populations of blue tits (Cyanistes caeruleus). We investigate a set of predictions based on the EPP literature, namely that EPP depends on male age and body size, breeding density and breeding synchrony. In all analyses, we control for breeding distance, a parameter that is expected to influence EPP even under random mating. The results show that older and larger males were more likely to sire EPO, but both effects decreased with increasing breeding distance. Local breeding density but not synchrony predicted whether a particular male-female combination had EPO, at least in one of the study areas. Apart from breeding distance, male age had the strongest effect on EPP, followed by a measure of breeding density. The method thus allows a comprehensive assessment of the relative importance of different types of spatial and non-spatial parameters to explain variation in the occurrence of EPP, while controlling for the fact that individuals that breed further apart are less likely to have EPO. The proposed approach is not limited to investigate EPP, but can be applied to other behavioural interactions between two individuals, such as dominance, competition and (social) mating.