Paper: Hamilton's r vs. Ohtsuki's k

A recent paper by Wolf et al. in The American Naturalist looks at the relation between genetic relatedness and social structure from a new angle. The authors compare two parameters that should predict the level of cooperation in a society. Hamilton's rule of kin selection (1964) suggests that an individual A should cooperate with B if the benefit to B, relative to the cost to A, is more than the inverse of the genetic relatedness between them (b/c > 1/r), i.e. that you'll have a stronger will to help a closer relative. Studying (rather simple) model networks, Ohtsuki et al. (2006) suggested that cooperation is favorable when b/c > k, k being the average number of neighbors in the network, meaning you'll have a stronger will to help someone if the network is more sparse.

In a study of sea lions in the Galapagos, they compared r and k in different social levels: individual, clique, and community. They found a strong negative correlation between r and k in all social levels, meaning that k and r capture similar structural information in the population.
It is suggested that individuals may prefer associating with their relatives, although it's hard to understand how they "know" their relatedness to any other individual (I can think of some olfactory mechanisms that may facilitate this).

The  authors raise the concern that k may not reliably represent K, the "real" average for the population over longer timeframes (data was collected over a 3-month period). I also share this concern, especially since only one population was used. However, from my experience, if three months are enough for getting a "saturated" network in the sea lions, then more observations would contribute little to the analysis. One more concern considers their use of filtered binary networks, where a lot of information is lost, especially about weaker associations. This analysis seems like one that could gain more power from a weighted network, where the strength of each tie is taken into account.