Kin selection and your toilet bowl

Altruism is a catastrophe for Darwinism.


Darwinism posits that adaptations are the consequence of heritable undirected variation and natural selection, which is differential reproduction, generally on the basis of competition for resources.

Altruism is cooperation that is based on self-sacrifice, the antithesis of natural selection by competition.

So how could altruism have evolved by natural selection?

For any real scientific theory, a contradiction of this magnitude would have killed the theory in its cradle. But Darwinism serves purposes far removed from science, so it limps on.

Darwin and his descendants understood the problem, and there is considerable stammering in the literature over the past century and an half about the problem altruism poses for Darwinian theory.

The original efforts to explain the evolution of altruism invoked sacrifice that would aid dissemination of an altruistic individual's genes via relatives. As Haldane famously quipped,

Would I lay down my life to save my brother? No, but I would to save two brothers or eight cousins.

This  pseudo-science was given a mathematical imprimatur by W.D. Hamilton in 1964, with his theory of kin selection. Hamilton observed that in the struggle for reproduction there are sources of the individual's genes other than the individual-- the kin. In sexually reproducing organisms (e.g. humans), offspring share 50% of genes with each parent, ditto with siblings, 25% with grandparents and aunts and uncles, 12.5% with cousins, etc. Hamilton defined fitness as the passage of one's alleles to the next generation, regardless of whether the alleles resided in the individual or the kin. He defined this "inclusive fitness' as the sum of the individual's own contribution and the contribution of relatives divided together by the average contribution of the population.

Hamilton observed that in this scheme an allele that diminished the fitness of a particular individual could still increase in the population if the same allele enhanced the reproduction of kin bearing the allele. Hamilton kept the math to rudimentary algebra (suited to a Darwinian audience), and gave "Hamilton's Rule" that states that an increase in frequency of an allele in a population as a result of an altruistic act will occur if:

r > C/B

where r is the degree of relatedness (0-1), C is the reproductive cost to the individual of the altruistic allele, and B is the reproductive benefit to the recipient(s) of the altruistic act associated with the allele.

Succinctly, if the cost to the altruist is smaller than the benefit to the kin by a factor less than the degree of relatedness, the altruistic trait will propagate. The difference between the degree of relatedness and the cost/benefit ratio is a measure of the strength of the kin selection.

If r is much larger than C/B, kin selection (altruism) is strong. If r is only slightly greater than C/B, kin selection is weak.

That's kin selection, and that's a big part of the Darwinian explanation of altruism.

Does it make sense?

Let's see.

Take a simple comparison-- altruism of a (human) mother for her five children, and altruism of one bacteria for other bacteria.

Using Hamilton's Rule, now for human altruism

r > C/B

r is 0.5, the fraction of alleles that mother and her five children share. Let's postulate that the cost to the mother of an act (say, laboring to obtain good clothing for her children) is less than the benefit to the children (good clothing). Let's apply some kind of number to this (Hamilton's Rule is an equation after all), and say that the C/B ratio is 0.1 for each child. The reproductive benefit to the children of good clothing is ten times the reproductive cost to the mother of obtaining good clothing, multiplied by five (for the five children who will carry the altruistic alleles).

Thus r > C/B is 0.5 > 0.02, which is true. r is 25 times the cost/benefit ratio. The altruistic allele for the mom to buy good clothes for her kids will increase in the population. Altruism spreads. The strength of the kin selection for the spread of this altruistic trait would be 25.

So far so good.

Now compare this kin selection explanation for altruism between a mother and child with the kin selection explanation for altruism between... bacteria.

Consider a colony of bacteria in your toilet bowl. For simplicity, assume it's a clonal colony of e. coli (you missed one little bug with the brush.) He rapidly proliferates, and in a few days there are a billion e. coli in the little colony.

Using Hamilton's Rule, now for bacterial altruism

r > C/B

Remember that the bacteria are clones, so r is 1. They are related as identical twins-- a relationship twice as close as that of a mother and a child. Let's postulate that the cost to one bacterium of an altruistic act (say, sharing a little plasmid or extending a pseudopod to the daughters) is less than the benefit to the daughters (a handy plasmid or a helpful pseudopod). And let's again apply some kind of number to this (Hamilton's Rule is an equation after all). Let's assume that the effect of the altruistic allele of the bacterium  is of the same magnitude as that of the human mother of the children-- the cost/benefit ration for the altruistic bacterium and one daughter is 0.1. 

But the original bacterium now has 1,000,000,000 daughters, each of whom is an identical twin and each of whom will carry the altruistic allele. 

An altruistic perfect storm. 

So the C/B ratio is 0.0000000001. Hamilton's rule for the bacterial colony, which measures the strength of kin selection, is 

r > C/B

r is ten billion times greater than the cost/benefit ratio, so by Hamilton's Rule the altruism (the strength of the kin selection) in the e. coli in your toilet bowl is 400 million times stronger than the altruism between a mother and her children. 




:O


Kin selection is not an explanation for altruism. Kin selection is pseudoscience with a mathematical patina.

Altruism is a catastrophe for Darwinism.