untitled

quantitative phenotypic variation is inherited and 50% is environmentally induced).

The figure of 0.5 is the heritability coefficient for bristle number in Drosophila, and

quantitative characters in farm animals often have a heritability coefficient of that

general magnitude. The assumption is that such a level of heritability reflects a genet-

ically healthy population. The genetic variance needed to enforce such a heritability

coefficient has an equilibrium (where loss by genetic drift is balanced by gain from

mutation) of Ne=500 in the absence of selection, and that is taken as a safe lower

limit for population size.

The estimate of 50 comes from the observation of animal breeders that a loss of

genetic variance of 1% per generation causes no genetic problems. Since that rate is

1/(2Ne) we can write 0.01 =1/(2Ne), rearrange it to Ne=1/(2 ×0.01), and solve it

as Ne=50.

The arbitrary nature of both estimates of minimum viable population size will be

readily apparent. Neither should be accepted as anything more than general specula-

tion. No single number estimates have been offered for minimum viable population

size (demographic). It is clearly a function of Var(r) 1 interacting with Var(r)e(see

Sections 17.2.1 and 17.2.2) and so will vary among species and among populations

within species. However, for most populations it is likely to be higher than the cor-

responding minimum viable population size (genetic).

Population viability analysis (PVA) is a procedure by which we estimate the pro-

bability of persisting (or its converse, extinction) over a specified time interval

(Boyce 1992). Depending on the biological facts known for the population in question,

PVAs can be based on exponential, density-dependent, interactive predator–prey,

metapopulation, or even age- or stage-dependent models (Boyce 1992; Morris and

Doak 2002). Regardless of structural details, all PVAs use estimated variation in demo-

graphic parameters to add noise to simulated populations. By repeating such Monte

Carlo models many times, one can assess the probability of falling below an arbi-

trary critical value (termed a quasi-extinction threshold). Why is this critical level

not set at zero? First, many otherwise useful models do not have reliable behavior

as density approaches zero (for example, in the logistic model a population always

increases near zero). Second, we know that demographic stochasticity would often

doom any population that spent too long at “too low” a density. Third, we might

feel that crisis management is called for below this arbitrary threshold.

Some populations are so small that they are unlikely to experience any major

changes in net recruitment due to increasing density. If so, we would expect the

population to grow according to an exponential population model, such as:

Nt+ 1 =erNt

To make this more realistic we shall look at a real example (Fig. 17.2), the Yellow-

stone population of grizzlies, which is the largest remnant population left in the con-

tinental USA.

For the period 1959 – 82, the Yellowstone grizzly population hovered around

35– 40 female bears (Eberhardt et al. 1986). Such small population levels are often

considered dangerously low, due to the risk of demographic stochasticity or Allee

effects. This has raised conservation concerns for the long-term viability of grizzlies

300 Chapter 17

17.7 Population viability analysis

17.7.1PVA based on
the exponential
growth model