Question Solved1 Answer As a result of mutation, the number of individuals in a population carrying allele A and allele B changes in a way described by the equation [0.95 0 Yi+1 = 0.05 1 where y; is the vector whose components are the numbers of individuals carrying each allele at time t. An equilibrium is a value of the vector for which no change occurs, i.e. vectors y which satisfy the equation. [0.95 y = 0.05 y Find all possible equilibrium values.

4R95L9 The Asker · Advanced Mathematics

Transcribed Image Text: As a result of mutation, the number of individuals in a population carrying allele A and allele B changes in a way described by the equation [0.95 0 Yi+1 = 0.05 1 where y; is the vector whose components are the numbers of individuals carrying each allele at time t. An equilibrium is a value of the vector for which no change occurs, i.e. vectors y which satisfy the equation. [0.95 y = 0.05 y Find all possible equilibrium values.
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Transcribed Image Text: As a result of mutation, the number of individuals in a population carrying allele A and allele B changes in a way described by the equation [0.95 0 Yi+1 = 0.05 1 where y; is the vector whose components are the numbers of individuals carrying each allele at time t. An equilibrium is a value of the vector for which no change occurs, i.e. vectors y which satisfy the equation. [0.95 y = 0.05 y Find all possible equilibrium values.
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Solution:Consider that the population carrying allele A and allele B changes by the equation.y_(t+1)=[[0.95,0],[0.05,1]]y_(t)As equilibrium occurs when hat(y)=[[0.95,0],[0.05,1]] hat(y)Solve the above equalibrieum equation as shown below.{:[ hat(y)=[[0.95,0],[0.05,1]] hat(y)],[ hat(y)-[[0.95,0],[0.05,1]] hat(y)= hat(0)],[[[1,0],[0,1]] hat(y)-[[0.95,0],[0.05,1]] hat(y)=[[0],[0]]]:}{:[ ... See the full answer