We know that once populations become small, they have a much higher, but very variable, risk of extinction. We also know that small population size in itself does not necessarily mean that extinction will occur - there are many examples of bottlenecks in nature. In New Zealand, for instance, an introduced population of 13 Himalayan tahr introduced in the early 1900s had increased to 30,000 to 40,000 animals by 1970. So small population size in itself is not a disaster. Remember also that the other aspect of small population size is speciation, so population declines do play an important part in evolutionary processes.
What is population viability analysis?
As a general rule, the size of isolated populations with little or no immigration affects viability. For example, a study of birds on islands around the British coastline showed that one to two pairs had a mean time to extinction of 1.6 years, three to five pairs had a mean time to extinction of 3.5 years, and populations of six to twelve pairs had a mean time to extinction of 7.5 years. Thus even among very small populations, the time to extinction will increase with very small increases in population size. So conservation biologists used to try to establish minimum viable population sizes for different species. However, intrinsically this is very difficult and fails to take account of population processes.
Clearly many factors can put a species at risk of extinction, and we need to have some means of assessing the magnitude of these risks. Models of the factors contributing to population viability are proving to be an invaluable tool for conservationists in that they provide some basic means of assessing risk by means of a population viability analysis (PVA). There are four issues to consider when compiling a PVA:-
1. Environmental uncertainty or stochasticity
2. Natural catastrophes
3. Demographic uncertainty or stochasticity
4. Genetic uncertainty or stochasticity
Obviously, habitat loss is often also an important factor to consider - is the habitat for the species itself also viable? So now people often talk about a PHVA - a population and habitat viability analysis.
Organisms with low population densities that are restricted to small geographic ranges (i.e. most endangered large vertebrates) require a population viability analysis that concentrates on the genetic and demographic factors that affect small populations, and especially those with less than fifty individuals, although small populations are also at risk from environmental uncertainty and natural catastrophes. Smaller organisms, such as most threatened invertebrates, have a different set of problems. They are frequently restricted to a few habitat patches, but within these patches small organisms can reach high population densities. For these species, population viability analyses will have to concentrate more on environmental uncertainty and catastrophic events.
How do environmental stochasticity and natural catastrophes lead to population declines?
Environmental stochasticity and natural catastrophes used to be considered to be different processes, with catastrophes being more important in leading to population declines than environmental stochasticity. Now it is generally believed that basically they both operate in the same way, and that one is no more important or disrupting than the other.
Unlike demographic stochasticity, the effect of environmental fluctuations and/or catastrophic events is largely independent of population size, and will lead to much the same proportionate effect on numbers irrespective of whether the population is large or small. Thus the impact can be dramatic on large populations, as well as small, and so all populations are susceptible to environmental stochasticity. However, other than that, we know little about the effects on populations.
How does demographic stochasticity lead to population declines?
Demography encompasses the intrinsic factors that contribute to population growth or decline, often referred to as the BIDE factors - birth, immigration, death and emigration. To understand the demographic risks, you need to understand basic population processes and a number of basic population parameters. The first is the carrying capacity of a particular environment for that particular species. In ecological terms, this is the natural limit of the population set by the resources in that environment and populations tend to fluctuate around this equilibrium due to density dependent effects due to lack of food or e.g. nest sites for birds, especially hole nesting species and others with specific requirements. Thus all populations fluctuate, even when at the carrying capacity, and populations are not stable.
How do populations grow?
With density-dependent mortality and birth rates, the rate of population growth follows a sigmoidal curve that is symmetrical around its inflection point. Growth rates are very slow over time at either end of the curve, with maximum rate of recruitment into the population occurring in the middle of the curve. This is because for small populations, the individual reproductive rate is high but numbers are low; for density-dependent populations, crowding lowers both individual and population reproductive rates. In this symmetrical growth curve, the maximum rate of recruitment occurs at the inflection point.
So the theory is simple. If a population has been reduced, so long as the habitat is right i.e. the reasons for its decline have been addressed, initial recovery should be slow, but this will be followed by a period of rapid escalation in numbers before the rate of population growth starts to decline again. The other thing to bear in mind is that populations are best able to sustain losses at the inflection point of the curve - this is at K/2 (K is the carrying capacity). Losses at the start of the curve will be very bad news and are unlikely to be sustainable,
whereas at the top of the curve losses will simply push you back into the period of rapid population growth, so although such losses lead to a population decline they are likely to be sustainable.
However, if you exceed the sustainable level of losses at K/2 - known as the maximum sustained yield - the population will inevitably decline to extinction, even if the mortality rate is only a fraction below the maximum sustained yield.
Predicting rates of population growth is particularly difficult if the population is subject to wide year-to-year variations in numbers. The problem is that the variance in r, the exponential rate of population increase, depends on population size, and a halving in population size leads to a doubling in the variance in r. The variance in r declines with increasing population size, such that by the time that population size exceeds 300, the effects of variance in r is negligible. Thus a small population is likely to suffer erratic swings in size under the influence of demographic stochasticity due e.g. to poor breeding by a number of individuals, or a drift in the sex ratio, and small numbers provide no buffer against a decrease leading to extinction. One of the classic examples is the kakapo, the nocturnal ground parrot found only in New Zealand. There were only two surviving populations. One had 18 individuals - unfortunately all male. They survived for ten years until this population finally disappeared.
The other problem is that many species show age-specific rates of mortality and fecundity. This means that you want to ensure that the population you are trying to conserve has the optimum age distribution i.e. a balance of age classes to ensure a constant rate of population increase. If the population drifts towards a high proportion of young or old animals, age-specific mortality rates exceed fecundity, and so the population inevitably declines to extinction. As an example of the sort of problems that occur with population management, male mortality rates are often greater than those for females, and so if a population crashes due e.g. to lack of food or over-hunting, you end up with a population that is highly skewed towards females. This is good news for polygynous species, where the potential for population increase would then be much higher than if the sex ratio is 50:50, but it is bad news if you are dealing with a monogamous species with pair bonds. However, for many species, an environmental perturbation, such as a drought or food shortage, leads to higher mortality rates for the younger and older age classes, and so the surviving individuals have the greatest potential for increase since they are the individuals with the highest fecundity levels and lowest rates of mortality. So populations can respond positively to bottlenecks.
Part of the reason for sudden population crashes is that populations do not change in a linear fashion. Many show a threshold response, and this makes it very difficult to design a conservation strategy for managing a particular population over time. Such catastrophic population collapses could apply in a variety of situations, including habitat loss, exposure to toxins and habitat fragmentation. For instance, let us assume a hypothetical population of birds that nests in pieces of woodland surrounded by agricultural land where there is a heavy use of pesticides. It is basically a woodland species that is suffering from habitat fragmentation. The birds that nest close to the agricultural land have a low reproductive success due to pesticide poisoning. Consequently, as the area of agricultural land increases, and a greater proportion of the remaining land abuts agricultural land, reproductive success of the whole population declines. When reproductive success declines to the threshold which is necessary to balance mortality, the fraction of the suitable habitat patches that are occupied (and hence the population size) declines abruptly, with the rapidity of the change depending on the dispersal abilities of the species.
Thus it is clear that we need to understand population processes much better, and should not rely simply on simple estimates of minimum viable population sizes.
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