Stochastic Diploid Model for Gene Frequency in a Population

fitness parameter K

-0.1

stochastic noise e

0.458258

random seed

1

initial

p

0

Imagine a single gene with two alleles

A

and

a

, where the frequency of the

A

allele in the gene pool of an entire population is

p

0

. Assume that this is a large and isolated population, that there is random mating, and that the fitness parameter

K

varies stochastically through the generations. One can then predict the frequency

p

n

of the

A

allele in the population after

n

generations.

This Demonstration gives the time series of

p

n

and lets you vary the fitness parameter

K

and the stochastic noise

e

. By moving the sliders, you can see that for a fixed

K

there is a critical value of

e

beyond which polymorphism (the existence of two or more different phenotypes in the population) occurs as a result of stochastic resonance. The dynamics does not depend on the initial condition

p

0

.