Are gender traits completely a result of societal expectations?
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Suppose that the proportion of the white crest alleles (r) is given by w and that of the Red crest allele (R) is given by p. We have that p+w=1. The probability that an individual has 2 r alleles is given by w*w since for each allele position the probability is w. Only these individuals have a White phenotype. Hence, we get that w^2=
; the right hand side is the proportion of white birds in the total population. Doing the calculations, this yields that w=0.37. From this, we calculate that p=0.63. The possible ways we have heterozygous individuals are the combinations Rr and rR. The probability for each of those is p*w. Thus, the total probability is 2pw. This is equal to 0.466=0.47. This is the fraction of the future population that is going to be heterozygous assuming the conditions of the Handy-Weinberg equilibrium like random reproductive matching etc.