is a linear function of the proportion of females in the population. The regression
of ∆Non Pfhas a slope of Npband an intercept (i.e. the value of ∆Nwhen Pf=0)
of −N(1 −p).
The hypothetical example in Section 17.2.1 had a population size of N=1000,
a probability of survival per individual per year of p=0.9, and a fecundity rate of
b=0.95 live births per female per year. Those values fed into the above equation
yield ∆Nas 541 when Pf=0.75, as 328 when Pf=0.5, and as 114 when Pf=0.25.
The relationship can be rearranged to estimate Ne, the effective population size (demo-
graphic), as:Ne=N(pbPf+p−1)/(0.5pb+p−1)For the above example, Neis solved as 1653 when Pf=0.75, as 1000 when Pf=0.5,
and as 347 when Pf=0.25. Thus a disparate sex ratio may have a significant effect
on a population’s ability to increase from low numbers, enhancing that ability when
females predominate and depressing it when males dominate. Ungulate populations
that have crashed because they have eaten out their food, or because a drought has
cut their food from under them, often end the population slide with a preponder-
ance of females. They are thus in better shape demographically to recover from the
decline than if parity of sex ratio had been retained. Note here an important point:
the sex ratio minimizing genetic drift (50 : 50) is not that maximizing rate of
increase (disparity of females). Hence the appropriate “effective population size” depends
on context. The genetic version is appropriate for a small, capped population in a
zoo. The demographic version is often more appropriate in the wild where the aim
is usually to stimulate the growth of an endangered species.Similarly, an equation for effective population size (demographic) can be written to
correct for the effect of an unstable age distribution. It requires knowledge of the age
distribution, population size, age-specific fecundity, and age-specific mortality (see
Sections 6.3 and 6.4 for calculating these). However, these estimates are difficult to
obtain in practice, particularly for a small population. When faced by the urgent task
of diagnosing the cause of the decline of an endangered species, instead of wasting
valuable research time on estimating its age-distribution version of effective popula-
tion size (demographic) you should simply understand the principle and appreciate
that, because of instability of age distribution, the population’s rate of change may
be higher or lower than would be expected from a simple tallying of numbers. Suppose
the population experienced a severe drought in the previous year that killed off the
vulnerable young and old animals. The age distribution will now be loaded with
animals of prime breeding age, and the birth rate, measured as offspring per indi-
vidual, will therefore be much higher than usual. In consequence, rate of increase
will be higher than usual. Alternatively the population may have experienced a mild
winter such that the age distribution is loaded with young animals below breeding
age. Birth rate at the next birth pulse is then lower than usual and so is rate of increase.Two values for minimum viable population size (genetic) are commonly quoted: 500
and 50. The difference between them reflects the differing assumptions upon which
they are based. The 500 figure (Franklin 1980) is the effective population size at which
the heritability of a quantitative character stabilizes at 0.5 on average (i.e. 50% ofCONSERVATION IN THEORY 299
17.5.2Effect of age
distribution