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My understanding is that the relatedness coefficient in kin selection models measures *positive assortment*. That is, altruism is more likely to evolve if altruists tend to interact with other altruists. As an example, consider a general model of kin selection due to Queller (Queller 1992 "A general model of kin selection"). According to this model, relatedness is viewed as the regression coefficient $eta_{G'G}$, where $G$ is the individual's frequency of the altruism allele and $G'$ is the average value of $G$ of an individual's neighbors. Queller's definition of relatedness is a measure of positive assortment because, by definition, $$eta_{G'G} = frac{E(G'mid G) - E(G')}{G - E(G)}$$

If relatedness is positive, if the focal individual is more altruist than average ($G-E(G)>0$), then this individual will tend to interact with individuals that are more altruist than average ($E(G'mid G) - E(G')>0$).

Now, in Taylor's 1992 kin selection model in patch-structured populations with asexual reproduction ("Altruism in viscous populations"), relatedness $R$ is defined as the recursion (p. 354): $$ R' = frac{1}{N} + frac{N-1}{N}s^2R$$ where $N$ is the number of individuals in each patch and $s$ is the probability the offspring will remain on the natal patch (link to a question about $s$). Here $R$ doesn't seem to be a measure of positive assortment, but simply the chance that two alleles picked *at random* within the patch will be of the same type.

On one hand, $R$ in standard models of kin selection (e.g., Queller's) measures positive assortment. On the other hand, Taylor's kin selection model for patch-structured populations $R$ does not seem to measure positive assortment within a group but the chance that two random individuals share the same allele.

I tended to think of Queller's model as a general formulation of kin selection (accordingly, Taylor's model would be a particular instance of Queller's model). But, as I tried to explain above, my impression is that Taylor's model is an entirely different way of modeling kin selection ($R$ does not measure positive assortment). Am I missing some connection between Queller's and Taylor's models of kin selection? Or is there any way of connecting the two definitions of relatedness mentioned above?