OK. Let me try to explain a bit more... [And, yes, I'm simplifying, but I think this is a sufficient exposition for the purpose of the problem.] There are a fixed number of types of sexually hereditable objects ("chromosomes"). A chromosome of a given type can come in many versions. A given individual has exactly two chromosomes of each type, one chosen randomly from its mother's corresponding pair and one chosen randomly from its father's pair. There is one gender-determining chromosome type with two subtypes, X and Y. A male individual has one X and one Y; a female has two Xs. So, for this pair, the gender of the offspring is determined by the chromosome subtype inherited from the father. (The father can contribute either his X or his Y, the mother always contributes one of her Xs.) [Since males inherit their Y chromosome from their fathers, this genetic information can be used to trace paternal ancestry.] There is a small amount of additional hereditable information that is passed from mother to child, her mitochondrial genome, which also comes in many versions. [So this can be used to trace maternal ancestry.] I'll call an individual's specific combination of chromosomes and mitochondrial genome its Hereditable Information (HI). The actual traits of an individual are determined by its HI. Simple exercise: Prove that the proportion of a given chromosome version in the population remains the same in future generations. Assume that no particular combination of chromosome versions has any survival advantage. Now, for a given couple, what would determine the probability of having a boy? From the above, it would seem that boys and girls are equally likely. It must be that one of the genders is more likely to be conceived (conception being the process that combines the father's and mother's hereditable contributions) or to survive to birth, and this would be determined by the specific pair of HIs possessed by the couple. (It might also depend on the specific HI being contributed by each parent for the potential offspring in question, what follows can be easily extended to include this as well.) So, can we invent a universe of HIs and a mapping from father-mother pairs of HIs to gender probabilities (at birth) that produces Andy's hypothesized bimodal gender ratio AND continues to produce it in succeeding generations? Or perhaps more easily, can we invent a universe and mapping that produces a stable overall gender ratio in the absense of termination rules, AND where application of the gender termination rules alters that steady state. Note that we may also have to specify coupling rules (i.e. how coparents are paired). --ms On Thursday 08 July 2010 12:42:31 Dan Asimov wrote:

Mike Speciner wrote:

<< OK, but what are the plausible heredity rules that preserve the relevant ratios in the steady state (i.e., without the termination rule)? (By "plausible", I mean conforming to standard human genome kinds of things--gender determination from XvY sperm, mitochondrial genome from mother, mother-father gene pairs for everything else.) Presumably, the children of the two kinds of couples are genetically different in some way. What are the coupling rules that preserve the ratios, remembering that you need a boy to couple with a girl, and we probably need to assume monogamy to apply the "stop at first boy" rule (although it could be applied to just one parent, taking just that parent out of the reproducing pool). Assume a finite population, so at least some "interracial" coupling is required in the steady state.

I just don't know enough biology to translate this question into a mathematical one.

But if you restated it in math language, that would help (at least) me.

--Dan

I sleep as fast as possible so I can get more rest in the same amount of time.

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