A biologist discovers that a gene has a lethal allele 'a' that is not purely recessive: genotypes of the form aaall die before reproducing and one third genotypes of the form Aa also die before reproducing.
a) Show, that the difference equation describe the proportion xn of the lethal gene from one generation to the next is now given by the difference equation: xn+1 = 2xn / (3 + xn)
b) Calculate the first ten terms of the resulting sequence starting from x1 = 0.5.
c) Find all equilibrium solutions.
d) What do you notice about how rapidly the allele disappears?