Question

) Consider the simple model of mutation we discussed in class in which pt is the frequency of allele A in generation t and μ is the probability that A mutates to a when producing the gametes that form the next generation. The recursion equation is therefore: p_(t+1) = p_t - μp_t

Assuming a non-zero mutation rate (i.e. μ > 0), what is the equilibrium values of p in this model? Is this equilibrium stable or unstable? Explain.

Given: p_(t+1) =0.95; p_t= 1

Answer 1

Answer:

Given,

p(t+1) =0.95; pt= 1

At non zero mutation state, if >0 ,

so at equilibrium state,

p_t+1 = p_t - p_t

_{Substitute the given values in the above equation then we get}

_0.95=1-

   =1-0.95

  =0.05

So here the system is unstable because the is greater than zero

• if > 0, then p_t+1 will be a negative value. ( unstable state),
• to set at equilibrium state must be equal to zero.

so, p_t+1 = p_t.   (equilibrium state)