If n[t] is the probability that the microsatellite increases by one repeat in a generation and n[t] is the probability that the microsatellite decreases by one repeat in a generation, then

n[t+1] = n[t] + 1* n[t] - 1* n[t]

n[t+1] = n[t] (1+ - )

This is analogous to the model of exponential growth, with R = (1+ - ).

This tells us that the number of repeats will

• increase exponentially if (1+ - ) > 1, ie >
• decrease exponentially if (1+ - ) < 1, ie <
• remain constant if (1+ - ) =1.

Part 2:

If n[t] is the probability that the microsatellite increases by one repeat in a generation and n[t]² is the probability that the microsatellite decreases by one repeat in a generation, then

n[t+1] = n[t] + 1* n[t] - 1* n[t]²

n[t+1] = n[t] (1+ - n[t])

This is analogous to the model of logistic growth [n[t+1] = n[t] + r n[t] (1-n[t]/K)] in discrete time, with r = and K = /.

This tells us that the number of repeats will increase towards a "carrying capacity" if is positive.

The number of repeats will remain constant (at equilibrium) when n[t] = /, assuming that is positive.

Notice that there will only be more than one repeat at equilibrium if >