Population Genetics for Small Populations

Whenever a gene has more than one allele, we have to consider the distribution of these alleles over the whole population. This conventionally is being calculated by means of the Hardy-Weinberg law, which states that, with p = frequency of allele ai, q = frequency of allele a2, the genotype frequencies are constant over generations at

However, the Hardy-Weinberg law only applies to the so-called ideal populations. And these ideal populations have several preconditions which in reality can rarely be met: they have to be infinitely large, there has to be panmixia (i.e., every member of one sex can mate with every member of the other sex with the same probability), and there must not be any selection. In most populations, especially of rare species in management and conservation programs, these conditions do not apply. These populations are small, often fractured, they often occur only in some remnants of their earlier habitat (i.e., selective pressures are to be expected; see below), and there is no panmixia. Even in the absence of habitat fragmentation or other environmental effects, panmixia is often prevented by behavioral aspects, such as assortive mating (preferring certain members of the available ones, e.g., regarding their immunotype), hierarchies and other social factors monopolizing mating privileges, polygamous mating systems, etc. The influence of some of these social factors shall be discussed below (cf.effective population size).

Selection, in a population of partly homozygous, partly heterozygous members, can principally be of one of three possible types: should, for some reason or other, the heterozygous genotype have some advantages, we get stabilizing selection. In this case, the Gaussian distribution of allele frequencies essentially will remain in place, but the apex of the curve will become higher over generations, which means that we can expect to get more heterozygous individuals. On the other hand, if one homozygous genotype has advantages (see above - roving Drosophila larvae under crowded conditions), this will lead to directional selection, and over generations the curve is going to be shifted toward more individuals of that type. Should, however, there be an advantage for both types of homozygous situations, over the heterozygous one, then disruptive or splitting selection is to be expected and this in turn can lead to a process of sympatric speciation.

Some important terms of population genetics are of particular relevance for conservation genetics. 'Founder effects' is one such term. Once we start a conservation program, be it in situ or ex situ, we must expect the allele frequencies of the animals that we use to start with, to differ already from those in the original population. Some rare alleles can be missing because we only get a tiny section of the overall population, some might even be overrepresented. These founder effects tend to be more pronounced the smaller the founder population is. After starting the program, from a genetical point of view, each founder should have the same number of offspring and further descendants - again a problem with mating systems (see below). If we start a breeding program with 20 founders, we must expect to have 2.5% of original H being lost already at the beginning. As the credo of conservation biology is to aim for the preserving of 90% of original variability over 200 years, this is already a bad start! Following the establishment of a conservation program, we have to expect loss of genetic diversity by gene drift, with heterozygosity after t generations as

where N = population size and H0 = original value of heterozygosity in founders.

One possibility to slow this process is to lengthen generation time; thus, letting animals breed for the first time later in life can be helpful. The most important confounding factor from the behavioral perspective is the dependence of the so-called effective population size on behavioral factors. Effective population size Ne is defined as that number of individuals of this real population, that is expected to lose genetic variability as quickly as an ideal population would do.

One of the social influences on Ne concerns the unequal number of males and females that in nonmono-gamous species tend to reproduce:

Ne = 4NmNf /Nm + Nf where Nm = number of reproducing males and Nf = number of reproducing females. This means that in a population of 100 zebra (40 stallions:60 mares, but only 12 stallions holding harem of 5 mares each), Ne = 40!

A second effect on effective population size is unequal family size (by which a population geneticist means unequal number of offspring, for example, lower-ranking mothers having a higher mortality of their young). This influences

with Vk being variance in offspring numbers.

And finally, fluctuating population sizes, be they due to management problems, natural and climatic factors, draft, etc., tend to reduce Ne by

with t = number of generations, N1, N2,..., Nt = population size per generation.

Again, taking a simple example, assume a population that over ten generations had 100 individuals per generation, except for one bottleneck of only 25. In this case, Ne already decreases to 77.

All these factors lead to a progressive decrease of genetic variability, that is, loss of heterozygosity, over generations, and rare alleles, of course, are the ones most susceptile to disappearance.

Beneath a constant loss of genetic diversity (and thus of adaptive potential for future, unexpected challenges such as climate change, emerging diseases, etc.), extinction risk is also increased by inbreeding. Inbreeding in a population genetic sense occurs whenever two individuals mate that are more closely related than the average of the population. (Note that this is a different definition from the one in laboratory animal science, which strictly crosses brothers with sisters over generations.) Inbreeding leads to an increase of homozygosity through descent - the inbreeding coefficient F is defined as the probability of any offspring to become homozygous for a certain gene by descent.

Inbreeding in a population reduces H, recessive alleles are increasingly expressed, and the increase of homozy-gous individuals can be calculated as

Inbreeding is being discussed with a certain controversy in conservation biology. Behavioral biologists tend to point out, as do many zoo population managers, that there are examples of wild species with a high degree of inbreeding without any obvious loss of overall fitness. Population geneticists tend to point to examples of inbreeding depression in wild populations, computer simulations that lead to exponential loss of genetic diversity in small inbred populations, and decreases in fertility, infant survival, sexual maturity, etc. Recent reviews and meta-analyses both from zoo and wild populations do indeed demonstrate a detrimental influence of a high degree of inbreeding on the overall reproductive performance of a population. This was about 7 times greater on wild than captive populations. Several laboratory studies and computer simulations could also link this to an increase in extinction risks. There are some examples that seem to contradict these findings, both from laboratory animal breeding (the lab/ pet golden hamsters, all descending from one female and her young, after almost 60 years do not significantly differ in behavior or physiology from recently wild-caught ones) or recently recovered populations of large mammals (e.g., the northern elephant seal), but in general there are more studies showing the other effect, for example, of inbred populations recovering after introduction or immigration of new animals from other populations even if they were themselves inbred. Such examples of gray wolves, deer mice, adders, and others also seem to resolve one of the other controversies of population management, which is called SLOSS (single large or several small), meaning there was a controversy over whether it would be better to manage all available individuals in one large population, or in several smaller populations. Obviously, due to random gene drift, different alleles tend to be retained in different populations and this could increase their chances. In order to avoid detrimental effects of inbreeding in fractured, intensively managed populations, MAI (maximum avoidance of inbreeding) schemes have been developed. Essentially, these consist of moving all offspring of one sex from subpopulation 1 to group 2, from group 2 to group 3, etc. In the next generation, offspring goes from group 1 to group 3, group 2 to group 4, etc. This ensures that for as many generations as there are participating groups, there will not be any increase of inbreeding.

Here again, behavioral biology meets population genetics, because age at natural dispersal, sex biases in dispersal, and other mechanisms of emigration and immigration in groups have to be considered.

This brief overview should only encourage students of behavioral biology and population genetics to cooperate more closely. More detailed information can be obtained from specific literature.

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