Exercises:

In an experimantal farm a large population of flowers consist of all possible genotypes AA, Aa, and aa with the initial distribution of $a_0, b_0$ and $c_0$.( that is $x_0 = \left[ \begin{array}{r} a_0\\ b_0\\ c_0\\ \end{array}\right]$)

Suppose that each flower in the population is fertilized with a flower of genotype $AA$.

a) Find an expression $x_n$ for the distribution of the possible genotypes of the population after n-generations.

b) Repeat part (a) with the assumpsion that each flower is fertilized by a flower of genotype $Aa.$

c) Repeat part (a) with the assumpsion that each flower is fertilized by a flower of genotype of its own.

d) Repeat part (a) with the assumpsion that each flower in the initial generation is fertilized by a flower of genotype Aa, each flower in the first generation is fertilized by a flower of genotype AA, each flower in the second generation is fertilized by a flower of genotype aa, and this pattern of fertilization continues.