While it might seem that a random force would be of little significance to evolutionary "progress" we'' confront this loaded term later , genetic drift is an extremely important force in evolution.
However, its strength depends on the size of the population, as a simple exercise in coin tossing will illustrate. In ten tosses you might easily get seven heads; in tosses, however, you would never get heads with a "fair" coin.
The same sort of random fluctuation in allele frequencies can occur in small populations : consider a bag full of red and green marbles each in equal frequency; pull out a small handful and the frequency in your hand will probably not equal the frequency in the original bag.
Let that handful determine the frequency in a new population that grows back to the original population size. A second small handful will randomly shift the frequency to yet another frequency.
Genetic drift is not a potent evolutionary force in very large randomly mating populations. To illustrate the consequences of genetic drift we will consider what happens when drift alone is altering the frequencies of alleles among many small populations. To illustrate this we need to understand Population structure , which describes how individuals or allele frequencies in breeding populations vary in time and space.
This structure is determined by the combined effect of deterministic and stochastic forces. We will introduce the idea of population structure by showing how genetic drift and inbreeding can change the frequencies of genotypes in populations.
Consider a grid of small populations e. Through time each population will experience genetic drift due to random sampling and the frequencies in each population will diverge.
The distribution of frequencies changes over time from a tight distribution all 0. Fixation is when all alleles in the population are A; this necessarily implies loss of the a allele "fixation" or "loss" should only be used with reference to a specific allele.
Main Points: 1 total variation does not change; variation goes from within populations no variation between populations to between populations no variation within populations.
This is why genetic drift can be an important force in evolution. When all populations in the array have fixed or lost the allele, there can be no heterozygotes i. This shows that the proportion of heterozygotes decreases as drift proceeds this also occurs when there is inbreeding which can also be thought of as a sampling error phenomenon.
Looking at these equations it is clear that with small population sizes, heterozygosity will be lost quickly drift will proceed quickly , whereas in large populations there will be little loss of heterozygosity. Like the loss of heterozygosity due to drift, the increase in the variation among demes depends on the population size.
As the number of generations proceeds, the variation among populations V t increases rapidly if N is small, but slowly if N is large. A general result as drift proceeds in small populations is a deficiency of heterozygotes, and reciprocally, an excess of homozygotes. In fact genetic drift and inbreeding are related phenomena. One effect of inbreeding is to increase the frequency of homozygotes and thus, necessarily, decrease the frequency of heterozygotes.
Does it really matter whether a species has low or high levels of genetic variation? Biologists, conservationists, environmentalists, and informed citizens all worry about the impact of environmental change on the ecosphere. Although organisms cannot plan for environmental change, the more variation that exists in a population , the better prepared that population will be to adapt to change when it does occur. Note that the level of genetic variation within a population is dynamic: It reflects an ever-changing balance between processes, both random and nonrandom, which remove variation.
Sometimes, the latter can overwhelm the former, leading to low levels of variation that cannot be reconstituted over ecological time scales. Researchers understand that variation arises through mutation and recombination , and they also know that natural selection can remove variation from a population.
Moreover, scientists are well aware of the fact that real-life populations are not infinite, as the Hardy-Weinberg model requires us to assume. Together, these factors lead to a relentless loss of variation, a process referred to as genetic drift.
Genetic drift is the reason why we worry about African cheetahs and other species that exist in small populations. Drift is more pronounced in such populations, because smaller populations have less variation and, therefore, a lower ability to respond favorably — that is, adapt — to changing conditions. Thus, it's not just the number of cheetahs that worries us—it's also the decreased variation in those cheetahs. To get a feel for genetic drift, consider a population at Hardy-Weinberg equilibrium for a gene with two alleles , A and a.
For no drift to occur, the frequencies of the alleles in successive generations must remain at 0. If N is the population size of diploid organisms, then the number of A alleles denoted k is equal to 2 pN. Given this information, how can we calculate the exact probability that k remains equal to 2 pN after a generation of random sampling?
To do so, we begin with the general formula for the binomial distribution:. The binomial distribution is used when a there are two possible outcomes of a trial, b the probability of each outcome remains the same across all trials, and c all trials are independent of each other. Here, the two possible outcomes i.
The term [ n! The term p k 1- p n - k is the exact probability of observing any given order of k "successes" and n - k "failures. Doing so yields the following results:. At first glance, these results might seem backward. According to the table, the probability that the allele frequencies will remain unchanged is higher for the smaller populations! However, that's only part of the story. In all of these cases, it's more likely that the allele frequencies will change, and it is actually the magnitude of the change that matters.
Figures 1 through 3 show the probabilities of allele frequencies in the next generation of each of these populations. When looking at these figures, it should be evident that the breadth of the distribution narrows as population size increases. This is due to a decrease in sampling error. So, while allele frequencies are almost certain to change in each generation, the amount of change due to sampling error decreases as the population size increases.
Perhaps the most important point is that the direction of the change is unpredictable; allele frequencies will randomly increase and decrease over time. Furthermore, when change does occur, sampling to produce the next generation will center on the new value of p. Thus, given enough time, in the absence of factors that maintain both alleles e. The time that it takes for this to occur depends on the starting frequencies of the alleles and, of course, the population size see below under "The Population Genetic Consequences of N e ".
Figure 4: The relationship between Ne and Nf in a population of mating individuals. Because most populations are large, it seems fair to ask whether genetic drift is really all that important. It's true that most populations are large, but they don't necessary act large. Thus, the rate of genetic drift is not really proportional to census population size N c. Rather, it's proportional to something more abstract — specifically, the effective population size N e. In an ideal population of sexually reproducing individuals , N e will equal N c.
An "ideal" population has the following characteristics, and most deviations will decrease the effective population size :. Essentially, anything that increases the variance among individuals in reproductive success above sampling variance will reduce N e the size of an ideal population that experiences genetic drift at the rate of the population in question.
For example, consider the effect of unequal numbers of mating males and females. In an ideal population, all males and all females would have an equal chance of mating. However, in situations in which one sex outnumbers the other, an individual's chance to mate is now affected by its sex, even if all individuals within each sex have an equal chance to mate. Figure 4 shows the relationship between N e and N f in a population of 1, mating individuals. In an ideal population, all individuals have an equal opportunity to pass on their genes.
In real life, however, this is rarely the case, and N e is particularly sensitive to unequal numbers of males and females in the population. Within prime-aged females, normalised HL explains the least amount of variation in contributions to population growth out of all the traits, except for when it is considered in an interaction with year, where it explains slightly more approx. When we grouped individual contributions to population growth explained by individual traits within each age-class according to sex Figure 2 and Table 5 , normalised HL in an interaction with year explains approximately four times the amount of variation in both male p t i and fecundity compared to the variation explained in female survival.
When it is considered on its own, it explains double the amount. Albeit more important in males, normalised HL still explains a minimal amount. Within male p t i and F t i , normalised HL explains approximately the same amount approx. In an interaction with year, normalised HL explains approximately the same amount of variation in male p t i as FEC in an interaction with year approx.
Within the contributions via male fecundity, normalised HL in an interaction with year accounts for approximately the same amount of variation as weight in an interaction with year approx. The bars represent the total explained variation within p t i , S t i and F t i across different sections of the population in the population as a whole, within females and within males.
The different colours represent the proportion explained by individual covariates on their own or in an interaction with year. The colon between covariate terms indicates that their effects are being considered in an interaction with one another. When the explanatory power of normalised H is grouped within females Figure 2 and Table 5 , it accounts for a minimal amount of variation in survival when analysed in an interaction with year 1. When normalised HL is considered on its own it explains an even more negligible amount of variation within female survival 0.
Although differences in individual weight and FEC on their own explain eight and twelve times more of the variation in female contributions via survival than normalised HL , their explanatory power is also very low i. At the population level, normalised HL explains approximately the same low amount of variation in overall individual contributions to population growth p t i as that accounted for via survival and fecundity approx.
When considered in an interaction with year, normalised HL explains slightly more variation. Specifically, it accounts for about the same amount of variation in p t i and via fecundity approx. Compared to the amount of variation explained by the other traits, normalised HL explains the least in p t i and via survival, both on its own and in an interaction with year.
In this article, we put forward two key findings. First of all, we demonstrate how the choice of method used to calculate multi-locus heterozygosity can influence ones results. We improve on previous methods by providing a normalising technique, which controls for variation in the number of loci genotyped between individuals.
Secondly, we demonstrate that although heterozygosity influences some fitness components, most notably male reproductive success, in general it contributes very little to population growth in the Soay sheep of St. We achieve this insight by extending a univariate approach, linking trait variation to individual contributions to population growth [13] into a multivariate framework. Multi-locus heterozygosity quantities are frequently used to estimate how inbred or outbred an individual is, although recent research has queried how well they correlate with inbreeding coefficients [35] , [36].
Nonetheless, multi-locus heterozygosity has been widely reported to influence fitness e. A range of multi-locus estimators have been developed, and although they are strongly correlated, the choice of estimator can influence results.
We chose to work with HL as it determines the probability an individual is heterozygous given the alleles it carries and the frequency of those alleles within the population. Despite this, we still identified a problem with HL , and other measures of heterozygosity, as they all exhibit substantial heteroscedasticity as a function of the number of loci individuals are genotyped at, with much lower variation in heterozygosity among those individuals genotyped at a larger number of loci.
Such heteroscedasticity could influence results, especially if the number of loci routinely genotyped increases with time within a study. We corrected for this heteroscedasticity by normalising the HL score within individuals genotyped at the same number of loci. This finding is crucial as it suggests that studies where individuals are genotyped at different numbers of loci across a population may be reporting biased mean heterozygosity values.
If we did not normalise HL in this study, heterozygosity values from different individuals would not have been statistically comparable under the assumptions of normality. As a consequence, our understanding of the contribution of heterozygosity to population growth would have been flawed.
To our knowledge, we are the first to consider this source of bias within heterozygosity calculations. The second main finding of this study is that although heterozygosity has a weak role in population growth, there is considerable variation in the impact of heterozygosity on population dynamics within different gender and age groups. This is related to disparities in the importance of individual traits across population stages.
Albeit weak, we found that individual traits explain approximately 2. This difference is even more pronounced in the recruitment component F t i of contributions to population growth, where male individual differences account for approximately four times as much variation as in females. These results can be explained by the fact that individual traits are important in defining which males breed as they influence mating success during the rut [21].
In contrast, in prime-aged females, variation in size and FEC are of greater influence to their survival than reproduction. Since they do not need to compete for mates, females will invest more heavily in traits allowing them to survive the winter months, as well as over their pregnancy period [21].
This highlights the importance of local environmental stochasticity within the dynamics of this population. The components of the population where we find heterozygosity defined by normalised HL most strongly influences individual contributions to population growth are prime-aged females, male lambs, and adult males composed of prime-aged and senescents.
Of these, normalised HL accounts for approximately twice as much within male contributions to population growth as in females, specifically via adult reproductive success. Despite the relative importance of normalised HL in adult males, this effect does not leave a large signature on the population dynamics because it constitutes such a small fraction of the population.
Heterozygosity in males determines which males successfully mate in some years even if this has no effect on the number of females that would become pregnant in the absence of heterozygous males.
The importance of heterozygosity in reproductive success may differ between years on account of fluctuating selection, countervailing selection for different fitness components or frequency-dependent selection [19] , [27].
Within females, normalised HL contributed little to population growth and typically much less than other measures of individual variation, such as body weight and FEC. As with all individual traits, when all females are considered together, normalised HL only contributes to survival. When each female age-class is considered separately, we find that this effect is experienced solely via prime-aged females.
Our findings add to the growing number of studies on heterozygosity-fitness correlations that show considerable variation in the strength of this relationship across species, populations and even between gender and age groups within a population.
First of all, there has been evidence supporting class-specific effects of heterozygosity in populations of alpine marmots Marmota marmota and roe deer Capreolus capreolus , with similarly low effect sizes [38] , [39]. Previous studies of the Soay sheep population of Hirta have also found that heterozygosity explained little variation in parasite resistance [7] and neonatal birth weight and survival [32].
In contrast, Sneddon et al. We propose that the range of discrepancies in the importance of heterozygosity for survival and breeding success across HFC analyses may reflect differences in recent immigration and mixing between populations as well as variation in selection pressures [40].
We extend a recently developed method [13] for linking individual and population level processes to gain insight into the role of heterozygosity in population dynamics. Using a statistical transformation of the homozygosity weighted by loci HL index, we show that the relative importance of heterozygosity in Soay sheep population growth differs markedly between sexes and age-classes.
Overall, we find little evidence that heterozygosity influences population growth. Summary of linear models describing the association between normalised and non-normalised heterozygosity measures estimated using the selected panel of loci. Kilda and Benbecula for logistical support. Pilkington and many volunteers have collected field data and D.
Bancroft, J. Slate, J. Smith, K. Byrne, F. Jones, M. Robinson and A. Bento contributed to the genotyping. Ezard provided helpful comments on an earlier version. Conceived and designed the experiments: FP TC.
Browse Subject Areas? Click through the PLOS taxonomy to find articles in your field. Abstract Heterozygosity has been associated with components of fitness in numerous studies across a wide range of taxa. Funding: The authors have no support or funding to report.
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