Measuring selection when parents and offspring interact

Non-social and social selection gradients are key evolutionary parameters in systems where individuals interact. They are most easily obtained by regressing an individual's fitness on the trait values of the individual and its social partner.
In the context of parental care it is more common to regress the trait value of the parents (i.e. the social partner) on a ‘mixed’ fitness measure that is a function of the parent's and offspring's fitness (for example, the number of recruits, which equals parental fecundity multiplied by offspring survival).
For such an approach to yield correct estimates of net-selection, the trait must be sex-limited and not affect the parents’ own survival.
When a trait is not sex-limited, the non-social selection should be weighted by one (because all individuals express the trait) and social selection should be weighted by a half (because the relatedness between parents and the offspring they care for is a half, usually). The ‘mixed’ fitness approach does not give estimates of both components of selection and so they cannot be weighted appropriately.
We show that mixed fitness components are frequently used in place of direct fitness measures in the literature (37% of fecundity selection estimates use a mixed fitness approach), but that the frequency is much higher in some taxa, such as birds and mammals.
We suggest alternative methods that could be used to estimate both social and non-social selection gradients, while at the same time assessing the importance of unmeasured traits.