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The process of consanguineous mating is associated with changes in the mean phenotype within a population. These changes arise from two general causes: changes in genotype frequencies in a population per se and fitness effects associated with changes in genotype frequencies.

The mean phenotype of a population will be impacted by any changes in genotype frequency. To show this, it is necessary to introduce terminology to express the phenotype associated with a given genotype, a topic covered in much greater detail and explained more fully in Chapters 9 and 10. We will assign AA genotypes the phenotype +a, heterozygotes the phenotype d, and aa homozygotes the phenotype −a. Each genotype contributes to the overall phenotype based on how frequent it is in the population. The mean phenotype in a population is then the sum of each genotype‐frequency‐weighted phenotype (Table 2.10). When there is no dominance, the phenotype of the heterozygotes is exactly intermediate between the phenotypes of the two homozygotes and d = 0. In that case, it is easy to see that mating among relatives will not change the mean phenotype in the population since both homozygous genotypes increase by the same amount and their effects on the mean phenotype cancel out (mean = ap² + aFpq + d2pq − dF2pq − aq² − aFpq, where the heterozygote terms are crossed out since d = 0). When there is some degree of dominance (positive d indicates the phenotype of Aa is like that of AA while negative d indicates the phenotype of Aa is like that of aa), then the mean phenotype of the population will change with consanguineous mating since heterozygotes will become less frequent. If dominance is in the direction of the +a phenotype (d > 0), then mating among relatives will reduce the population mean because the heterozygote frequency will drop. Similarly, if dominance is in the direction of −a (d < 0), then mating among relatives will increase the population mean again because the heterozygote frequency decreases. It is also true in the case of dominance that a return to random mating will restore the frequencies of heterozygotes and return the population mean to its original value mating among relatives. These changes in the population mean phenotype are simply a consequence of changing the genotype frequencies when there is no change in the allele frequencies.

There is a wealth of evidence that the increase of homozygosity caused by mating among relatives has deleterious (harmful or damaging) consequences and is associated with a decline in the average phenotype in a population, a phenomenon referred to as inbreeding depression. Since the early twentieth century, studies in animals and plants that have been intentionally inbred provide ample evidence that decreased performance, growth, reproduction, viability (all measures of fitness), and abnormal phenotypes are associated with consanguineous mating. A related phenomenon is heterosis or hybrid vigor, characterized by beneficial consequences of increased heterozygosity such as increased viability and reproduction, or the reverse of inbreeding depression. One example is the heterosis exhibited in corn, which has led to the widespread use of F1 hybrid seed in industrial agriculture.

Table 2.10 The mean phenotype in a population that is experiencing consanguineous mating. The fixation index quantifying deviation from Hardy–Weinberg expected genotype frequencies is F, and d = 0 when there is no dominance.

Genotype	Phenotype	Frequency	Contribution to population mean
AA	+a	p2 + Fpq	ap2 + aFpq
Aa	D	2pq – F2pq	d2pq – dF2pq
aa	−a	q2 + Fpq	−aq2 – aFpq

population mean: ap² + d2pq – dF2pq ‐ aq² = a(p‐q) + d2pq(1‐F)

Heterosis: The increase in performance, survival, and ability to reproduce of individuals possessing heterozygous loci (hybrid vigor); increase in the population average phenotype associated with increased heterozygosity.

Inbreeding depression: The reduction in performance, survival, and ability to reproduce of individuals possessing homozygous genotypes; decrease in the population average phenotype associated with mating among relatives that increases homozygosity.

There is evidence that humans possess homozygosity because of mating among relatives and also experience inbreeding depression. Genome‐scale genetic marker data in humans has revealed stretches of the genome where both chromosomes possess identical alleles called runs of homozygosity that are explained by both recent family members being related as well as by the history of population size and mixing (reviewed by Ceballos et al. 2018). There is also evidence for inbreeding depression in humans based on observed phenotypes in the offspring of couples with known consanguinity. For example, mortality among children of first‐cousin marriages was about 3.5% greater than for marriages between unrelated individuals measured in a range of human populations (Bittles and Black 2010). Human studies have utilized existing parental pairs with relatively low levels of inbreeding, such as uncle/niece, first cousins, or second cousins, in contrast to animal and plant studies where both very high levels and a broad range of coancestry coefficients are achieved intentionally. Drawing conclusions about the causes of variation in phenotypes from such observational studies requires caution, since the prevalence of consanguineous mating in humans is also correlated with social and economic variables such as illiteracy, age at marriage, duration of marriage, and income. These latter variables are therefore not independent of consanguinity and can themselves contribute to variation in phenotypes such as fertility and infant mortality (see Bittles and Black 2010).

The Mendelian genetic causes of inbreeding depression have been a topic of population genetics research for more than a century. None other than Charles Darwin carried out experimental pollinations in numerous plant species and observed that progeny of self‐fertilization were shorter and produced fewer seeds than outcrossed progeny (Darwin 1876). There are two classical hypotheses to explain inbreeding depression and changes in fitness as the fixation index increases (Charlesworth and Charlesworth 1999; Carr et al. 2003). Both hypotheses predict that levels of inbreeding depression will increase along with consanguineous mating that increases homozygosity, although for different reasons (Table 2.11). The first hypothesis, often called the dominance hypothesis, is that increasing homozygosity increases the phenotypic expression of fully and partly recessive alleles with deleterious effects. The second hypothesis is that inbreeding depression is the result of the decrease in the frequency of heterozygotes that occurs with consanguineous mating. This explanation supposes that heterozygotes have higher fitness than homozygotes (heterosis) and is called the overdominance hypothesis. In addition, the fitness interactions of alleles at different loci (epistasis; see Chapter 9) may also cause inbreeding depression, a hypothesis that is particularly difficult to test (see Carr and Dudash 2003). These causes of inbreeding depression may all operate simultaneously.

Table 2.11 A summary of the Mendelian basis of inbreeding depression under the dominance and overdominance hypotheses along with predicted patterns of inbreeding depression with continued consanguineous mating.

Hypothesis	Mendelian basis	Low fitness genotypes	Changes in inbreeding depression w/ continued consanguineous mating
Dominance	recessive and partly	only homozygotes for	purging of deleterious alleles that
	recessive deleterious alleles	deleterious recessive	is increasingly effective as degree of
		alleles	recessiveness increases
Overdominance	heterozygote advantage	all homozygotes	no changes as long as consanguineous mating keeps heterozygosity low
	or heterosis

These dominance and overdominance hypotheses make different testable predictions about how inbreeding depression (measured as the average phenotype of a population) will change over time with continued consanguineous mating. Under the dominance hypothesis, recessive alleles that cause lowered fitness are more frequently found in homozygous genotypes under consanguineous mating. This exposes the deleterious phenotype and the genotype will decrease in frequency in a population by natural selection (individuals homozygous for such alleles have lower survivorship and reproduction). This reduction in the frequency of deleterious alleles by natural selection is referred to as purging of genetic load. Purging increases the frequency of alleles that do not have deleterious effects when homozygous, so that the average phenotype in a population then returns to the initial average it had before the onset of consanguineous mating. In contrast, the overdominance hypothesis does not predict a purging effect with consanguineous mating. With consanguineous mating, the frequency of heterozygotes will decrease and not recover until mating patterns change (see Figure 2.12). Even if heterozygotes are frequent and have a fitness advantage, each generation of mating and Mendelian segregation will reconstitute the two homozygous genotypes so purging cannot occur. These predictions highlight the major difference between the hypotheses. Inbreeding depression with overdominance arises from genotype frequencies in a population, while inbreeding depression with dominance is caused by the frequency of deleterious recessive alleles in a population. Models of natural selection that are relevant to inbreeding depression on population genotype and allele frequencies receive detailed coverage in Chapter 6.

Inbreeding depression in many animals and plants appears to be caused, at least in part, by deleterious recessive alleles consistent with the dominance hypothesis (Byers and Waller 1999; Charlesworth and Charlesworth 1999; Crnokrak and Barrett 2002). A classic example of inbreeding depression and recovery of the population mean for litter size in mice is shown in Figure 2.17. Model research organisms such as mice, rats, and Drosophila, intentionally bred by schemes such as full sibling mating for 10s or 100s of generations to create highly homozygous, so‐called pure‐breeding lines, are also not immune to inbreeding depression. Such inbred lines are often founded from multiple families, and many of these family lines go extinct from low viability or reproductive failure with habitual inbreeding. This is another type of purging effect due to natural selection that leaves only those lines that exhibit less inbreeding depression, which could be due to dominance, overdominance, or epistasis.

There is evidence that inbreeding depression exhibits environmental dependence due to variation among environments in phenotypic expression, dominance, and natural selection (Armbruster and Reed 2005; Cheptou and Donohue 2011). The social and economic correlates of inbreeding depression in humans mentioned above are a specific example of environmental effects on phenotypes. Inbreeding depression can be more pronounced when environmental conditions are more severe or limiting. For example, in the plant rose pink ( Sabatia angularis ) progeny from self‐fertilizations showed decreasing performance when grown in the greenhouse, a garden, and their native habitat, consistent with environmental contributions to the expression of inbreeding depression (Dudash 1990). In another study, the number of surviving progeny for inbred and random‐bred male wild mice (Mus domesticus) was similar under laboratory conditions, but male progeny of matings between relatives sired only 20% of the surviving progeny that males from matings between unrelated individuals did when under semi‐natural conditions due to male–male competition (Meagher et al. 2000). However, not all studies show environmental differences in the expression of inbreeding depression. As an example, uniform levels of inbreeding depression were shown by mosquitoes grown in the laboratory and in natural tree holes where they develop as larvae and pupae in the wild (Armbruster et al. 2000).

Figure 2.17 A graphical depiction of the predictions of the dominance and overdominance hypotheses for the genetic basis of inbreeding depression. The line for dominance shows purging and recovery of the population mean under continued consanguineous mating expected if deleterious recessive alleles cause inbreeding depression. However, the line for overdominance as the basis of inbreeding depression shows no purging effect since heterozygotes continue to decrease in frequency. The results of an inbreeding depression experiment with mice show that litter size recovers under continued brother–sister mating as expected under the dominance hypothesis (Lynch 1977). Only two of the original 14 pairs of wild‐caught mice were left at the sixth generation. Not all of the mouse phenotypes showed patterns consistent with the dominance hypothesis.

The degree of inbreeding depression also depends on the phenotype being considered. In plants, traits early in the life cycle such as germination less often show inbreeding depression than traits later in the life cycle such as growth and reproduction (Husband and Schemske 1996). A similar pattern is apparent in animals, with inbreeding depression most often observed for traits related to survival and reproduction.

Inbreeding depression is a critical concept when thinking about the evolution of mating patterns in plants and animals. Suppose that a single locus determines whether an individual will self or outcross and the only allele present in a population is the outcrossing allele. Then imagine that mutation produces an allele at that locus, which, when homozygous, causes an individual to self‐fertilize. Such a selfing allele would have a transmission advantage over outcrossing alleles in the population. To see this, consider the number of allele copies at the mating locus transmitted from parents to progeny. Parents with outcrossing alleles mate with another individual and transmit one allele to their progeny. Self‐fertilizing parents, however, are both mom and dad to their offspring and transmit two alleles to their progeny. In a population of constant size where each individual contributes an average of one progeny to the next generation, the selfing allele is reproduced twice as fast as an outcrossing allele and would rapidly become fixed in the population (see Lande and Schemske 1985; Fisher 1999). Based on this twofold higher rate of increase of the selfing allele, complete self‐fertilization would eventually evolve unless some disadvantage counteracted the increase of selfed progeny in the population. Inbreeding depression where the average fitness of outcrossed progeny exceeds the average fitness of selfed progeny by a factor of two could play this role. If outcrossed progeny are at a twofold advantage due to inbreeding depression, then complete outcrossing would evolve. Explaining the existence of populations that engage in intermediate levels of selfing and outcrossing, a mating system common in plants, remains a challenge under these predictions (Byers and Waller 1999).