untitled

of offspring produced per individual, the effective population size will be smaller than

the census size. In the unlikely event of variance being less than the mean the

effective population size is greater than the census size and the population is coping

better genetically than one might naively have expected. The effective population size

Necorrected for this demographic character can be calculated as:

Ne=(NF−1)/[F+(s^2 /F) −1]

where Fis the mean lifetime production of offspring per individual and s^2 is the vari-

ance of production between individuals. It indicates that when mean and variance

are equal, Neapproximates to N. Since males and females sometimes differ in mean

and variance of offspring production, this equation is often solved for each sex sep-

arately and the sex-specific Nevalues summed.

Genetic drift is minimized when sex ratio is 50 : 50. Effective population size (genetic)

in terms of sex ratio is given by:

Ne=4/[(1/Nem) +(1/Nef)]

where Nemand Nefare the effective numbers of males and females as corrected

above for variation in production of offspring. The series below shows the relation-

ship numerically:

Sex ratio 50 : 50 60 : 40 70 : 30 80 : 20 90 : 10

Ne N 0.96N 0.84N 0.64N 0.36N

Further corrections can be made for other sources of disparity between real and ideal

populations. These considerations are often important in Drosophilaresearch and in

managing the very small populations in zoos, but they have little utility in conserva-

tion. Rather than attempting to estimate Nefor a threatened population you should

simply assume as a rule of thumb that Ne=0.4N, and that the censused population

is losing genetic variability at a rate appropriate to an ideal population less than half

its size.

The effective population size (demographic)is the size of a population with an even

sex ratio and a stable age distribution that has the same net change in numbers over

a year as the population of interest.

If a species is polygamous, and most species of wildlife are, a disparate sex ratio may

have a large effect upon net change in numbers over a year and hence effective

population size (demographic) at the beginning of that year. Net change in numbers

over a year can be calculated as:

∆N=NpbPf−N(1 −p)

where Pfis the proportion of females in the population, pis the probability of sur-

viving the year averaged over individuals of all ages within a stable age distribution,

and bis the number of live births produced per female at the birth pulse terminating

the year. It indicates that net change in numbers in a population of any given size

298 Chapter 17

17.5 Effective population size (demographic)

17.5.1Effect of sex
ratio