Frozen Evolution. Or, that’s not the way it is, Mr. Darwin. A Farewell to Selfish Gene.

- Biological evolutionis a process that is substantially governed by chance. Neither its result nor the actual course can be estimated in advance as unique random events are constantly occurring. Because of the lack of predictability of these events, e.g. collision of the Earth with cosmic bodies, the progress of evolution cannot be described by a deterministic model. However, a great many random processes occurring in the evolution of living systems can be successfully described by a stochastic model. For one of the best known and, according to a number of authors, the most important of these processes, genetic drift, this model permits prediction of the character of the evolutionary processes that will accompany its action. It has been found that, under certain circumstances, genetic drift can very substantially affect the progress of biological evolution in some systems to such a degree that it can reverse or at least substantially reduce the effect of such an important evolutionary factor as, for example, natural selection. Similar to practically all the important ideas of theoretical biological evolution, R.A. Fisher (Fisher 1958)outlined the basic principles of the action of genetic drift in his main work on evolution. However, the American S. Wright (Wright 1931) and the Japanese scientists M. Kimura (Kimura 1983b) and T. Ohta (Ohta 1993) were responsible for the greatest developments in this area.

Genetic driftrefers to random shifts in the frequency of the individual alleles in the gene pool of a certain population (Fig. V.1). Simultaneously, these shifts are not caused by differences in the selection values of the relevant alleles. They exist because of discrepancy amongst the almost infinite number of different genotypes that can theoretically be formed through random combination of the individual alleles contained in the gene pool and the incomparably smaller number of actually formed genotypes, which is maximally equal to the number of individuals in a given generation. As, in each generation, of the total set of gametes, only a very limited sample of randomly selected zygotes develop, it must necessarily happen that the presence of the individual alleles in the gene pool changes randomly from one generation to the next. In addition, changes caused by genetic drift have a highly accumulative character. If a five-membered population of diploid organisms originally contained the same contents of allele A and allele a, then there is only 25% probability that this ratio will be retained in the first generation. The change in the content of alleles from one generation to the next depends on chance and on the contents of alleles in the previous, but not in the zero generation. As a consequence, in the second generation, the probability of the same contents of both alleles will be, not 25%, but only 18% and, in the tenth generation, this will decrease to only 5%.

There is the same probability that, through genetic drift, the frequency of certain alleles will increase or decrease from one generation to the next.In an infinitely large population, genetic drift would thus lead to regular reversible fluctuations in the frequency of the individual alleles.From the standpoint of evolutionary processes, these random fluctuations should be of relatively small importance.

However, the situation is different in real populations.The sizes of the populations of fauna and flora are always finite and are frequently greatly limited.Species living permanently in relatively isolated populations (domains) containing only several dozen individuals are not exceptional amongst mammals.Genetic driftmust necessarily lead to fixation of alleles in small populations.It is irrelevant how many various alleles were present in the population in the beginning.Following a sufficiently large number of generations, the bearers of only one of them will remain in the population (Fig. V.2).

Fixation of alleles occurs when their frequency reaches 100 %, i.e. when the frequencies of the other alleles of the relevant gene decrease to zero for some reason.There can be various reasons for a similar decrease in frequency, such as natural selection acting against the bearers of certain alleles.However, it is most probable that the process leading to fixation of the greatest number of mutations will be genetic drift or a process whose biological consequences are very similar (i.e. fixation of neutral mutations) – genetic draft (see IX.5.2).

The mechanism of fixation of alleles through the action of genetic drift in individual populations can best be demonstrated on the example of a large number of small populations in which alleles A and a are present in the same frequencies at the beginning of the experiment (Fig. V.3).The set of these populations at the individual moments in time can always be depicted by the relevant histogram, expressing the frequency of populations with frequency of allele A lying in the intervals 0-0.1; 0.1–0.2; 0.2–0.3; ... 0.9–1At time t₀ all the populations lie within a single frequency interval as the initial frequency of alleles A in all the populations equals 0.5.Following a certain number of generations, populations begin to occur increasingly often in which the frequency of allele A deviates ever more from value 0.5.The histogram begins to approach the histogram of normal distribution, where the standard deviation of the set increases constantly with time and the histogram thus becomes flatter.An important difference in the shape of the histogram or the normal distribution begins to appear when some populations begin to reach extreme positions through the effect of genetic drift, i.e. when populations with frequency of allele A equal to 1.0 to 0.0 appear in the population.If the individual populations are mutually isolated and if alleles A and a can change one into the other through the effect of mutation within the time horizon of our experiment, these states are irreversible for the given population and one or the other allele becomes fixed.As time progresses, additional populations will be in this state so that, after a sufficiently long time, only the two extreme columns will be present in the histogram.Approximately half the population will have a frequency of allele A equal to 1.0 and the other half will have frequency equal to 0.0.

The probability that certain alleles will become fixed is equal to their frequency in the population. If a new mutation is formed in the population, its original frequency in the gene pool of diploid organisms (containing two copies of each allele) is equal to 1/2N, where N is the number of individuals in the population. Thus, in a population with a size of 100, approximately each two-hundredth selectionally neutral mutation will be fixed by drift. There is substantial probability that a new selectionally neutral mutation will become fixed in a small population. This probability is much smaller in a large population.

The probability that a new mutation will be eliminated from the population through genetic drift immediately after its formation is very high and is basically not connected with its advantageousness from the standpoint of the biological fitness of the organism (Fisher 1958). In a size-stabilized population of sexually reproducing organisms, each parental pair leaves an average of two progeny and each individual passes two alleles of each gene down to the gene pool of the following generation. These two alleles can have both copies of the mutated alleles (probability p = 0.25) or both copies of the original alleles (p = 0.25), or one copy of the original allele and the second is a copy of the mutated allele (p = 0.5). This means that, in one quarter of cases, the mutated allele disappears from the population before it can even become an object of natural selection. If the mutated allele is not eliminated, its frequency is increased somewhat in the population as there is a probability of 1/3 that both progeny will have the mutated allele – the number of mutated alleles is doubled. Thus, the probability that the mutated allele will disappear from the second generation will be somewhat smaller than 0.25 and will equal approximately 0.18. The probability of disappearance of a mutated allele in subsequent generations is additive, so that, after 5-6 generations, any new allele will disappear from the population simply as a consequence of random processes without much reference to its selectional advantage. This is absolutely true for recessive mutations as the selectional advantage or disadvantage of the mutation can apply only to a homozygote with both alleles mutated. If the mutated allele is present in the population with only small frequency, the probability of the formation of these homozygotes in a panmictic population is almost negligible. This phenomenon (disadvantage for recessive mutations) is sometimes termed Haldane’s seive (Noor 1999)and this is discussed in a slightly different context in Section II.4.1.1. If an advantageous dominant mutation is involved, the situation will be somewhat more favourable for the fate of the new mutation; however, even here, random genetic drift will probably play the most important role in the first generations.s

The processes of fixation of alleles through the action of genetic drift are random from the standpoint of the moment when they occur and also to a substantial degree from the standpoint of which of the alleles will be fixed in the given population and which will be eliminated. The probability that the individual alleles will be fixed or eliminated differs for these individual alleles. For most alleles, these probabilities depend primarily and, in many alleles, exclusively on their momentary frequency in the population. If the population contains two alleles with the same frequency, then they both have the same probability of becoming fixed in the population. If the frequency of one of the alleles is, for example, ten times greater, then it also has ten times the probability of becoming fixed. If a population of organisms containing allele A with a frequency of 0.9 and allele a with a frequency of 0.1 is divided into one hundred smaller populations, then, after a sufficiently long period of time, allele A will become fixed in approximately 90 of them and allele a in approximately 10.