4 Let Us Assume That There Is A Species Of Mice That Has A Gene That Decides On Fur Colour This Gene Can Appear In Two 1 (82.18 KiB) Viewed 23 times
4. Let us assume that there is a species of mice that has a gene that decides on fur colour. This gene can appear in two different variations: W for white fur, and b for brown fur. Every mouse carries two versions of the gene, i.e. every mouse carries one of the following pairs: .WW-white fur ('dominant') . Wb=bW (order doesn't matter) - grey fur ('hybrid') .bb brown fur ('recessive') The offspring of a mouse inherits, from each parent, one of the two genes at random. This means for example that the offspring of a dominant mouse (WW) and a hybrid mouse (Wb) is dominant with probability and hybrid with probability, but it cannot be recessive (probability 0). This example is illustrated in the following table, where you can see that half of the possible outcomes for children are WW and the other half Wb: parent 1 W W 2 W WW WW b Wb Wb parent
Now assume that we start with a mouse with any given gene pair WW, Wb, or bb, and mate it in every generation with a hybrid mouse Wb. (a) Give the transition matrix and transition diagram for this Markov chain. (b) Assume we start with a recessive mouse (at generation 0). What is the probability of getting a hybrid after two generations (i.e. at generation 2)? Show your working. (c) Give the two-step transition matrix for this Markov chain.
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