genetics--hardy-weinberg related question Assume a sex-linked trait that does not kill before mating. Using X for X-chromosomes and Y for Y chromosomes, x for an x chromosome bearing the trait in question; assuming also that all females mate with all males in their own generation only, if a female carrier (xX) mates with a normal male (XY), F1 looks like : XX, Xx, XY, xY. The male xY has the trait, so 1/4 of F1 has the phenotype. If F1 is allowed to mate randomly, F2 looks like: 4 xX, 3 XX, 1 xx, 6 XY, 2 xY, for 16 offspring. So two males express the trait in F2. Absent an arithmetic error, 46 males out of the 256 in F3 have the trait. My question is, does the proportion of afflicted males stabilize for F_n as n gets large? This seems related to H-W equilibrium or maybe fixed-point problems, but I don't see an obvious way to put the problem in simple mathematical terms. _______ Defining XX = a, Xx = b, xx = c, XY = d, xY = e, with the convention that a-e on the LHS have subscript _n+1 and on the RHS a-e have subscript _n. a = 2ad + bd b = 2ae + bd + be + 2cd + ce c = be + ce d = 2ad + 2ae + bd + be + ce e = bd + be + 2cd + ce If F_1 has cardinality xX = XX = xY = XY = 1 this iterative system seems to give the correct answers. I am cross-posting this question to Linear Algebra.