Effective Population Size Problem 3
Tutorial to help us answer problem 3.
In this population of elephant seals, one male mates with all the females (Nm). We can write the equation for Ne as,
Now we have Ne as a function of a single variable, Nf . What happens as we let Nf → ∞? Notice that Ne is a rational function where the degree of the numerator equals the degree of the denominator. In this case, Nf → ∞ implies Ne → a/b where a is the leading coefficient of the numerator and b is the leading coefficient of the denominator. The leading coefficient of the numerator is a = 4, and the leading coefficient of the denominator is b =1, and we have Ne → 4 as Nf → ∞. Therefore, we have shown that no matter how many breeding females there are, the effective population is less than 4 with one breeding male.