The viscosity of a population is the tendency of offspring to remain near their place of birth. Taylor 1992 ("Altruism in viscous populations") provides a model to study how viscosity affects the evolution of altruism in a patch-structured population. In Taylor's model, the marginal inclusive fitness is given by \begin{equation} W = bR -c - s^{2}(b-c)R \end{equation} where $R$ is the relatedness of a mother to random offspring born on her breeding patch and $s$ is the probability the offspring will remain on the natal patch. The altruistic act creates $b$ offspring with average relatedness $R$ and $-c$ offspring with relatedness 1.
My question is about the term $s^{2}(b-c)R$. Taylor explains this term as follows:
these b - c extra offspring remain on the natal patch with probability s and will therefore displace s(b - c) random individuals competing for the next generation breeding spots on that patch, and these will be native to that patch with probability s and in this case will have average relatedness R to the actor. Thus these displaced individuals will have average relatedness sR (p. 353)
My question is: Why is the average relatedness $sR$ (as opposed to $R$)? In other words, why is the term that accounts for competition among relatives $s^2(b-c)R$---as opposed to $s(b-c)R$?