# Question on Effective Population Size

Daniel Weinreich dmw at MCZ.HARVARD.EDU
Thu Nov 30 12:14:15 EST 1995

```On Tue, 21 Nov 1995, Fred Bacon wrote:

> ... [Li and Graur]
> offer a formula to calculate N_e when the number of males and females
in a
> populations is different.
>
>                       4 N_m N_f
>               N_e = -------------
>                       N_m + N_f
>
> [How is this equation derived and what's it good for?]

> Fred Bacon

The derivation of this equation can be found in (among other places) Hartl
and Clark's _Principles of Population Genetics_ (p. 85), which I happen to
have in front of me.

You must further accept that N_m and N_f are the EFFECTIVE number of males
and females, respectively, and not the census numbers.  In a monoecious
population the effective number of individuals (N_e) is defined as the
census size of a theoretical population undergoing random mating which
exibits the "population genetical behavior" observed in the true
population.  "Population genetical behavior" could be rate of loss of
heterozygotes due to drift, or rate of increase of an allele confiring a
given selective advantage, or anything else population geneticists
estimate.

N_e is an empirical estimate made from observing the population genetical
behavior of a population, and is of a different dimension from population
census size.  Although N_e is sometimes described as the "breeding size"
of the population, it isn't correct to suppose that exactly N_e of the
individuals in the population are breeding.  (Although if a subset of the
population does all the mating AND these individuals all choose their mate
at random, then N_e is the number of mating individuals.)

What the equation tells us is that in a dioecious population with unequal
numbers of males and females, if the males and females are mating at
random with one another, then the population genetical behavior of the
population is as if it were a monoecious population of size
4*N_f*N_m/(N_f+N_m) undergoing random mating.

(By the way, could anyone suggest how to estimate N_m and N_f?)

Best regards,
Dan.

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