Removing Lewontin's Fallacy From Hamilton's Rule

Lewontin's Fallacy has weakened the foundation of behavioral ecology by ignoring genetic correlation structures that allow us to accurately discern, and rationally weight the significance of, phylogenetic groups such as clans, subspecies or races.

It is my hope that providing a definition of "particle", as correlation structures of nucleotides, will clarify the application of Price's equations in W. D. Hamilton's paper Innate Social Aptitudes of Man and a bioinformatic direction will emerge for behavioral ecology. As this direction emerges many critiques of behavioral ecology theory will be exposed as semantic confusion arising from the historic definitions of heritable particles -- such as genes or alleles -- definitions that lack sufficient bioinformatic rigor. This will be hard work. For the usual reasons, we cannot expect government-funded scientists to be very cooperative. Behavioral ecology, by focusing on sums of differences in individual genes rather than focusing on the differences in phylogenetic correlation structure of genes, seems to be suffering from a kind of "Lewontin's Fallacy", as described by A. W. F. Edwards in his paper by that name. The question is, how can we generalize behavioral ecology's equations to look at the correlation structures so that Hamilton's equations fall out as a special case? Another way of asking this might be: How can we generalize the definition of "gene", or more accurately "allele", so that what we now think of as alleles are  degenerate correlation structures? In "Innate Social Aptitudes of Man" Hamilton introduces us to his concept of group selection he writes:

Consider a population consisting of a mixture of particles, and suppose we are interested in the frequency of a certain kind of particle G. Suppose the particles are grouped.

What are the most fundamental particles of all -- from which all other groups of particles are composed? The answer seems to be nucleotides rather than "genes" for not even "genes" are "atomic". So here's an approach to our new bioinformatic sociobiology: First, look at populations of genomes as sets of (nucleotide,locus) pairs. This is a standard way of viewing sequenced genomes within bioinformatics. Next, find all the correlation structures that are nearly perfect across the population. Those are "alleles" in the current molecular biological sense. From this perspective it should be obvious that there is no fundamental distinction between alleles and other correlation structures. We can't ignore the other structures just because they have a (Pearson's correlation coefficient) r<1 -- particularly where we can impute them as being due to phylogeny. Rewriting Hamilton's Rule, as represented in Innate Social Aptitudes of Man, in terms of these correlation structure "particles" will yield identical predictions to current theory if we restrict ourselves to r~1 but very different predictions if we allow ourselves access to the lesser bioinformatic correlation structures. I've now put forth a proposal for how one can clarify the definition of heritable "particles" which should provide more rigor to definitions of "gene" such as Richard Dawkins provided in "The Extended Phenotype":

'that which segregates and recombines with appreciable frequency' ... 'any hereditary information for which there is favorable or unfavorable selection bias equal to several or many times its rate of endogenous change'

...replacing phrases like "appreciable" and "several or many" with actual bioinformatically-derived numbers. Beyond that this reformulation also provides bioinformatiac numbers for correlation structures other than the allele, such as those referenced by Edwards and as are being discovered in bioinformatic projects such as the International Hapmap Project.