# How to understand relatedness in an infinite island model?

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 $\beta_{G'G}$, 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, $$\beta_{G'G} = \frac{E(G'\mid G) - E(G')}{G - E(G)}$$

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?