***post updated below.***

now here’s something i hadn’t thought of! [pgs. 97-100]:

*“Idle in my bag stayed also the notes I had prepared for the defence of my formulas of relatedness against Rick [Michod] — that is, my struggles yet again through all that logic about how knowing that either he or that other are inbred should change, for example, how Henry IV felt about his cousin, Richard II, or how Henry’s son, soon to be Henry V, felt about his cousin (second cousin actually in this cast), Edmund Mortimer, and how Edmund Mortimer about him.*

“Usually when explaining to non-biologists how kin are to be valued in the evolutionary calculations, I start with a deliberate vagueness about what might be meant by such a phrase as ‘the proportion of genes in common’ between two relatives and I concentrate on the obvious importance of the probabilities of gene survival. What ‘genes in common’ means it takes too long to explain and perhaps even at the end I don’t completely understand the matter myself … **Suppose Harry Plantagenet, Prince of Wales, is inbred and hence has two copies, aa say, of some altruism-determining gene, while his second cousin Edmund Mortimer (who, as it happens, was another very plausible contender for the throne) happens to have one only — his genotype is ab let us say.** What proportion at this locus do we say the two have in common? Obviously the question hardly makes sense or at least doesn’t unless one says a lot more first. Had they been haploid like two moss plants who were cousins all would be easy; either plant X would have the altruism gene possessed by plant Y or it wouldn’t: one could give a probability and then simply average such chances for all the gene loci. But notwithstanding the thoughts given in the introduction to Chapter 2, most of the socially most interesting organisms are diploid. As I have pointed out, diploids have two copies of every kind of chromosome, one from their mother and one from their father. And in fact this problem about ‘genes in common’ was an old chestnut for me and I had pricked fingers on it from the very earliest days of my ‘altruism’ obsession. I had dealt in outline with questions of relatedness when one or both of two relatives could be inbred in some of my recent papers (see Chapters 5 and 8 of Volume 1) but I was very much aware of various issues still unresolved or remaining unpublished.

“About the time of my first invitation from Rick Michod, Nathan Flesness, for example, had published in Nature a paper entitled ‘Kinship asymmetry in diploids’. He showed clearly that **if one relative was inbred and another not or less so, as in my example of the first two pretenders to the English throne above, the coefficient of relatedness that the inbred should use when deciding how to behave towards the outbred relative (a cousin once again, let us say) was not the same as the coefficient that the outbred cousin should apply if making the reciprocal decision. The theory says that the outbred person in fact, to a slight degree, should tolerate the unfairness in the interest of his genes, or, to put it more properly, his genes should even see to such an unfairness coming about: he should behave more generously towards the inbred than he would expect the inbred to reciprocate.** The key to my understanding this had come when I realized, a year or two after my paper of 1964, that Sewall Wright’s correlation concept of relatedness hadn’t been quite what I needed for my own calculus of relatedness. For a Machiavellian world of pure gene-controlled behaviour I saw that what Henry IV and Henry V need to do to decide their cousinly status with regard to their respective copretenders to the throne is to predict the genotypes of Richard II and cousin Mortimer with reference to their own, and to do so by the best possible statistical reasoning. Just as a statistically minded agronomist uses a regression coeffficient based on his knowledge of responses to fertilizer to predict as best he can the yield of crop, so must the Henrys use regression coefficients of genes to be predict how genes in common may have descended to the cousin. This, of course, is not an adequate explanation but it gives the idea. The upshot was that I, too, needed the regression coefficient, not the correlation one of Wright.

*“Wright had practically provided both of them but the one he himself had used had been the correlation. It is well known that if a bivariate scatter of values in not a straight line, the regression of Y on X is not the same as the regression of X on Y. The simplest ‘regression’ relatedness formula is b _{XY} = 2r_{XY} / (1 + F_{X}) where F_{X} is a measure of individual X’s inbreeding: this formula had been given in my papers of 1970 and 1971. The consequence for asymmetry of altruism was left implicit in the formula at that time — increase F_{X} and the value of the formula is obviously reduced.“*

so, if your cousin is more inbred than you, you should (would) be more altrustic towards him than he to you because he has *more* of the genes which you share in common.

heh. i love it!

in a similar vein, fox et. al. found that, due to the differential inheritance of the x- and y-chromsomes, not all grandmas are equally related to their grandkids and that they are, therefore, more altruistic to some of the kiddies than others.

meanwhile, i’ve been calculating the different coefficients of relatedness for family members based on the differential inheritance of the sex chromosomes. how was i supposed to know all i needed was a nice regression coefficient formula? (~_^)

**update 10/29:** i forgot to give you the punchline to the henry vs. mortimer story! [pg. 106]:

*“Edmund Mortimer, already mentioned, by my data he has F = 0* [in other words, he was not inbred – hbd chick]*. In this light it fits again that (a) he joined the rebellious faction of Hotspur and Glendower as its ‘pretender’ only by their persuasion; (b) after his capture, by henry iv, he stayed tamely (and was tolerated) for the rest of his life as a semi-prisoner at Windsor; and (c) my EB source (Vol. 15, pp. 867-8) tells us that ‘Edmund seems to have rewarded Henry V with persistent loyalty’, including informing him of a plot by others to depose the king and put him (Edmund) on the throne. All this has the expected slant of the theory. The man to whom he gave loyalty, as noted, was seemingly no more inbred than he was; however, his pattern of behavior was probably set during the reign of his relative’s inbred and doubtless (to the youth) dominating and awesome father.”*

**update 09/12/12:** see also the asymmetry of altruism again

_{(note: comments do not require an email. asymmetrical altruism.)}

“how was i supposed to know all i needed was a nice regression coefficient formula?”

should be all downhil now :)

@g.w. – (^_^) (^_^) (^_^)