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1.
Linkage Disequilibrium in Growing and Stable Populations   总被引:23,自引:6,他引:17       下载免费PDF全文
M. Slatkin 《Genetics》1994,137(1):331-336
Nonrandom associations between alleles at different loci can be tested for using Fisher's exact test. Extensive simulations show that there is a substantial probability of obtaining significant nonrandom associations between closely or completely linked polymorphic neutral loci in a population of constant size at equilibrium under mutation and genetic drift. In a rapidly growing population, however, there will be little chance of finding significant nonrandom associations even between completely linked loci if the growth has been sufficiently rapid. This result is illustrated by the analysis of mitochondrial DNA sequence data from humans. In comparing all pairs of informative sites, fewer than 5% of the pairs show significant disequilibrium in Sardinians, which have apparently undergone rapid population growth, while 20% to 30% in !Kung and Pygmies, which apparently have not undergone rapid growth, show significance. The extent of linkage disequilibrium in a population is closely related to the gene genealogies of the loci examined, with ``starlike' genealogies making significant linkage disequilibrium unlikely.  相似文献   

2.
Two large, stable populations (Texas and Japan) of Drosophila melanogaster were surveyed at 21 allozyme loci on the second and third chromosomes and for chromosomal gene arrangements on those two chromosomes. Over 220 independent gametes were sampled from each population. The types and frequencies of the surveyed genetic variation are similar to those observed previously and suggest only slight differentiation among geographically distant populations. Linkage disequilibrium among linked allozymes loci is only slightly, if at all, detectable with these sample sizes. Linkage disequilibrium between linked inversions and allozymes loci is common especially when located in the same arm. These disequilibria appear to be in the same direction for most comparisons in the two population samples. This result is interpreted as evidence of similar selective environments (ecological and genetic) in the two populations. It is also noted that the direction of these linkage disequilibria appears to be oriented with respect to the gene frequencies at the component loci.  相似文献   

3.
M. Loukas  C. B. Krimbas    Y. Vergini 《Genetics》1979,93(2):497-523
Gametic frequencies were obtained in four natural populations of D. sub-obscura by extracting wild chromosomes and subsequently analyzing them for inversions and allozymes. The genes Lap and Pept-1, both located within the same inversions of chromosome O, were found in striking nonrandom associations with them of the same kind and degree in all populations studied. On the contrary, the gene Acph, also located within the previously mentioned inversions, was found in linkage disequilibrium with them only in two populations and of opposite directions. This is also the case for the genes Est-9 and Hk, both located within chromosome E inversions. While the gene Est-9 was in strong linkage disequilibrium with the inversions, of the same kind and degree in all populations studied, Hk was found to be in linkage equilibrium. Allele frequencies for the 29 genes studied do not show geographical variation except for the genes Lap, Pept-1 and Est-9, the ones found in linkage disequilibria with the geographically varying gene arrangements. Although mechanical or historical explanations for these equilibria cannot be ruled out, these data cannot be explained satisfactorily by the "middle gene explanation," which states that loci displaying such linkage disequilibria are the ones located near the break points of inversions, while the ones displaying linkage equilibria with them are located in the middle of them. There is no evidence for consistent linkage disequilibria between pairs of loci, except for the closely linked genes of the complex locus, Est-9. This would imply, if it is not a peculiarity of the Est-9 complex, that the linkage disequilibria are found only between very closely linked loci or that, for less closely linked genes, the associations are too weak to be detected by the usual samples sizes.  相似文献   

4.
Gametic disequilibria between second chromosome polymorphic arrangements and seven linked allozyme loci were estimated in seven populations of Drosophila buzzatii from Argentina. Significant and consistent associations across populations were detected for Est-1, Est-2, Aldox, and XDH: Phenograms based on Nei's genetic distance showed that chromosomes carrying the 2ST arrangement were more similar to each other, irrespective of the population from which they were extracted, than to chromosomes carrying the derived 2J and 2JZ3.Restriction of recombination in heterokaryotypes seems to be the best explanation for the significant linkage disequilibria between inversions and the loci located inside the rearranged segments, for example, Est-1 and Aldox, or close to the break points, for example, Est-2. However, epistatic interactions between Xdh, which is outside the inversions and not near the break points, and loci tightly linked to the inversions, is the most likely explanation for the association between Xdh and chromosomal arrangements. Some of the associations detected in endemic Argentinean populations are coincident with data obtained in colonizing populations of the Old World and Australia. Thus historical processes that took place in the original area of the species' distribution can account for these linkage disequilibria in colonized populations of D. buzzatii.  相似文献   

5.
The evolution of complex traits in heterogeneous environments may shape the order of genes within chromosomes. Drosophila pseudoobscura has a rich gene arrangement polymorphism that allows one to test evolutionary genetic hypotheses about how chromosomal inversions are established in populations. D. pseudoobscura has >30 gene arrangements on a single chromosome that were generated through a series of overlapping inversion mutations with >10 inversions with appreciable frequencies and wide geographic distributions. This study analyses the genomic sequences of 54 strains of Drosophila pseudoobscura that carry one of six different chromosomal arrangements to test whether (i) genetic drift, (ii) hitchhiking with an adaptive allele, (iii) direct effects of inversions to create gene disruptions caused by breakpoints, or (iv) indirect effects of inversions in limiting the formation of recombinant gametes are responsible for the establishment of new gene arrangements. We found that the inversion events do not disrupt the structure of protein coding genes at the breakpoints. Population genetic analyses of 2,669 protein coding genes identified 277 outlier loci harbouring elevated frequencies of arrangement‐specific derived alleles. Significant linkage disequilibrium occurs among distant loci interspersed between regions with low levels of association indicating that distant allelic combinations are held together despite shared polymorphism among arrangements. Outlier genes showing evidence of genetic differentiation between arrangements are enriched for sensory perception and detoxification genes. The data presented here support the indirect effect of inversion hypothesis where chromosomal inversions are favoured because they maintain linked associations among multilocus allelic combinations among different arrangements.  相似文献   

6.
A marker locus closely linked to a disease locus is often useful for genetic counseling provided that a counselee is heterozygous at both disease and marker loci. Furthermore, the linkage phase of these genes in the counselee must be known. When the linkage between the disease and marker loci is very close, one often finds linkage disequilibrium between the loci. To evaluate the effect of such nonrandom associations on the utility of linked marker genes for genetic counseling, the proportion of informative families is studied for X-linked recessive and autosomal dominant diseases. This proportion is higher for X-linked genes than for autosomal genes, if other factors are the same. In general, codominant markers are more useful than dominant markers. Also, under appropriate conditions, the proportion of informative families is higher when linkage disequilibrium is present. The results obtained in this paper are useful for evaluating the utility of polymorphic restriction endonuclease cleavage sites as markers in genetic counseling.  相似文献   

7.
Munté A  Rozas J  Aguadé M  Segarra C 《Genetics》2005,169(3):1573-1581
The adaptive character of inversion polymorphism in Drosophila subobscura is well established. The O(ST) and O(3+4) chromosomal arrangements of this species differ by two overlapping inversions that arose independently on O(3) chromosomes. Nucleotide variation in eight gene regions distributed along inversion O(3) was analyzed in 14 O(ST) and 14 O(3+4) lines. Levels of variation within arrangements were quite similar along the inversion. In addition, we detected (i) extensive genetic differentiation between arrangements in all regions, regardless of their distance to the inversion breakpoints; (ii) strong association between nucleotide variants and chromosomal arrangements; and (iii) high levels of linkage disequilibrium in intralocus and also in interlocus comparisons, extending over distances as great as approximately 4 Mb. These results are not consistent with the higher genetic exchange between chromosomal arrangements expected in the central part of an inversion from double-crossover events. Hence, double crossovers were not produced or, alternatively, recombinant chromosomes were eliminated by natural selection to maintain coadapted gene complexes. If the strong genetic differentiation detected along O(3) extends to other inversions, nucleotide variation would be highly structured not only in D. subobscura, but also in the genome of other species with a rich chromosomal polymorphism.  相似文献   

8.
The termite Incisitermes schwarzi has multiple sex chromosomes that have arisen by repeated translocations between autosomes and previously existing sex chromosomes. Two sex-linked allozyme loci--Acp-1 and Est-3--are holozygous, not hemizygous, in males (the heterogametic sex). Both loci show less than 1% crossing-over between X and Y chromosomes, and alleles of both are in marked disequilibrium with respect to X vs Y linkage. The two loci assort independently in female meiosis, indicating that they lie on different sex chromosomes. But they are tightly linked in male meiosis because of nonrandom assortment of the multiple X and Y chromosomes in males of this species. The findings of holozygosity and strong linkage disequilibrium suggest that differential selection in the two sexes at or near these loci may be responsible for the establishment of the translocations in this species. The existence of active Y-linked alleles also suggests that the translocations may have occurred recently.  相似文献   

9.
There is considerable evidence for an adaptive role of inversions, but how their genetic content evolves and affects the subsequent evolution of chromosomal polymorphism remains controversial. Here, we track how life‐history traits, chromosomal arrangements and 22 microsatellites, within and outside inversions, change in three replicated populations of Drosophila subobscura for 30 generations of laboratory evolution since founding from the wild. The dynamics of fitness‐related traits indicated adaptation to the new environment concomitant with directional evolution of chromosomal polymorphism. Evidence of selective changes in frequency of inversions was obtained for seven of 23 chromosomal arrangements, corroborating a role for inversions in adaptation. The evolution of linkage disequilibrium between some microsatellites and chromosomes suggested that adaptive changes in arrangements involved changes in their genetic content. Several microsatellite alleles increased in frequency more than expected by drift in targeted inversions in all replicate populations. In particular, there were signs of selection in the O3+4 arrangement favouring a combination of alleles in two loci linked to the inversion and changing along with it, although the lack of linkage disequilibrium between these loci precludes epistatic selection. Seven other alleles increased in frequency within inversions more than expected by drift, but were not in linkage disequilibrium with them. Possibly these alleles were hitchhiking along with alleles under selection that were not specific to those inversions. Overall, the selection detected on the genetic content of inversions, despite limited coverage of the genome, suggests that genetic changes within inversions play an important role in adaptation.  相似文献   

10.
Z. Smit-McBride  A. Moya    F. J. Ayala 《Genetics》1988,120(4):1043-1051
We have studied linkage disequilibrium in Drosophila melanogaster in two samples from a wild population and in four large laboratory populations derived from the wild samples. We have assayed four polymorphic enzyme loci, fairly closely linked in the third chromosome: Sod Est-6, Pgm, and Odh. The assay method used allows us to identify the allele associations separately in each of the two homologous chromosomes from each male sampled. We have detected significant linkage disequilibrium between two loci in 16.7% of the cases in the wild samples and in 27.8% of the cases in the experimental populations, considerably more than would be expected by chance alone. We have also found three-locus disequilibria in more instances than would be expected by chance. Some disequilibria present in the wild samples disappear in the experimental populations derived from them, but new ones appear over the generations. The effective population sizes required to generate the observed disequilibria by randomness range from 40 to more than 60,000 individuals in the natural population, depending on which locus pair is considered, and from 100 to more than 60,000 in the experimental populations. These population sizes are unrealistic; the fact that different locus-pairs yield disparate estimates within the same population argues against the likelihood that the disequilibria may have arisen as a consequence of population bottlenecks. Migration, or population mixing, cannot be excluded as the process generating the disequilibria in the wild samples, but can in the experimental populations. We conclude that linkage disequilibrium in these populations is most likely due to natural selection acting on the allozymes, or on loci very tightly linked to them.  相似文献   

11.
Kovacevic M  Schaeffer SW 《Genetics》2000,156(1):155-172
This article presents a nucleotide sequence analysis of 500 bp determined in each of five X-linked genes, runt, sisterlessA, period, esterase 5, and Heat-shock protein 83, in 40 Drosophila pseudoobscura strains collected from two populations. Estimates of the neutral migration parameter for the five loci show that gene flow among D. pseudoobscura populations is sufficient to homogenize inversion frequencies across the range of the species. Nucleotide diversity at each locus fails to reject a neutral model of molecular evolution. The sample of 40 chromosomes included six Sex-ratio inversions, a series of three nonoverlapping inversions that are associated with a strong meiotic drive phenotype. The selection driven by the Sex-ratio meiotic drive element has not fixed variation across the X chromosome of D. pseudoobscura because, while significant linkage disequilibrium was observed within the sisterlessA, period, and esterase 5 genes, we did not find evidence for nonrandom association among loci. The Sex-ratio chromosome was estimated to be 25,000 years old based on the decomposition of linkage disequilibrium between esterase 5 and Heat-shock protein 83 or 1 million years old based on the net divergence of esterase 5 between Standard and Sex-ratio chromosomes. Genetic diversity was depressed within esterase 5 within Sex-ratio chromosomes, while the four other genes failed to show a reduction in heterozygosity in the Sex-ratio background. The reduced heterogeneity in esterase 5 is due either to its location near one of the Sex-ratio inversion breakpoints or that it is closely linked to a gene or genes responsible for the Sex-ratio meiotic drive system.  相似文献   

12.
Chromosomal inversion polymorphism affects nucleotide variation at loci associated with inversions. In Drosophila subobscura, a species with a rich chromosomal inversion polymorphism and the largest recombinational map so far reported in the Drosophila genus, extensive genetic structure of nucleotide variation was detected in the segment affected by the O(3) inversion, a moderately sized inversion at Muller's element E. Indeed, a strong genetic differentiation all over O(3) and no evidence of a higher genetic exchange in the center of the inversion than at breakpoints were detected. In order to ascertain, whether other polymorphic and differently sized inversions of D. subobscura also exhibited a strong genetic structure, nucleotide variation in 5 gene regions (P236, P275, P150, Sxl, and P125) located along the A(2) inversion was analyzed in A(st) and A(2) chromosomes of D. subobscura. A(2) is a medium-sized inversion at Muller's element A and forms a single inversion loop in heterokaryotypes. The lower level of variation in A(2) relative to A(st) and the significant excess of low-frequency variants at polymorphic sites indicate that nucleotide variation at A(2) is not at mutation-drift equilibrium. The closest region to an inversion breakpoint, P236, exhibits the highest level of genetic differentiation (F(ST)) and of linkage disequilibrium (LD) between arrangements and variants at nucleotide polymorphic sites. The remaining 4 regions show a higher level of genetic exchange between A(2) and A(st) chromosomes than P236, as revealed by F(ST) and LD estimates. However, significant genetic differentiation between the A(st) and A(2) arrangements was detected not only at P236 but also in the other 4 regions separated from the nearest breakpoint by 1.2-2.9 Mb. Therefore, the extent of genetic exchange between arrangements has not been high enough to homogenize nucleotide variation in the center of the A(2) inversion. A(2) can be considered a typical successful inversion of D. subobscura according to its relative length. Chromosomal inversion polymorphism of D. subobscura might thus cause the genome of this species to be highly structured and to harbor different gene pools that might contribute to maintain adaptations to particular environments.  相似文献   

13.
Frankham R 《Heredity》2012,108(3):167-178
Levels of genetic diversity in finite populations are crucial in conservation and evolutionary biology. Genetic diversity is required for populations to evolve and its loss is related to inbreeding in random mating populations, and thus to reduced population fitness and increased extinction risk. Neutral theory is widely used to predict levels of genetic diversity. I review levels of genetic diversity in finite populations in relation to predictions of neutral theory. Positive associations between genetic diversity and population size, as predicted by neutral theory, are observed for microsatellites, allozymes, quantitative genetic variation and usually for mitochondrial DNA (mtDNA). However, there are frequently significant deviations from neutral theory owing to indirect selection at linked loci caused by balancing selection, selective sweeps and background selection. Substantially lower genetic diversity than predicted under neutrality was found for chromosomes with low recombination rates and high linkage disequilibrium (compared with 'normally' recombining chromosomes within species and adjusted for different copy numbers and mutation rates), including W (median 100% lower) and Y (89% lower) chromosomes, dot fourth chromosomes in Drosophila (94% lower) and mtDNA (67% lower). Further, microsatellite genetic and allelic diversity were lost at 12 and 33% faster rates than expected in populations adapting to captivity, owing to widespread selective sweeps. Overall, neither neutral theory nor most versions of the genetic draft hypothesis are compatible with all empirical results.  相似文献   

14.
The capacity of the usual tests (chi-square and related tests) to detect gametic disequilibrium between allozyme loci in natural populations of Drosophila has been investigated. We analyzed a large collection of previously reported gametic samples from natural populations involving a variety of loosely linked allozyme loci located along the O chromosome of Drosophila subobscura and the second chromosome of D. melanogaster. It is found that the statistical power of the individual tests to detect the sample disequilibria between allozyme loci is remarkably low, being the average (over pairs of loci) of power estimates close to 0.20 in both species. Moreover, the average minimum disequilibrium (D‘min) that would be required to reject (90% probability) the hypothesis of gametic equilibrium is higher than 0.50 given the observed degree of polymorphism and sample sizes used. This means that statistically significant associations between allozyme loci would rarely be detected by single-sample tests even when much disequilibrium is present in natural populations of Drosophila. However, an alternative approach based on the analysis of disquilibrium for large sets of gametic samples, combining probabilities from single independent tests and assessing significance by a bootstrap procedure, reveals that most of the locus pairs within segment I and II of the O chromosome of D. subobscura and left arm of the second chromosome of D. melanogaster present significant nonrandom associations. Within these chromosomal sections, the observed average absolute value of disquilibrium (D‘) between loci is around 0.25 (under the more conservative estimation). Also, a positive relationship between the magnitude of disequilibrium and linkage was detected. These findings suggest that weak or moderate values of disequilibrium between loosely linked allozyme loci are more frequent in natural populations of Drosophila than is currently believed.  相似文献   

15.
Seasonal variation (spring, early summer, late summer, and autumn) of gametic disequilibrium between gene arrangements (OST and O3+4) of the O chromosome and Lap, Pept-1, and Acph allozyme loci, located inside these inversions, has been recorded in a natural population of Drosophila subobscura during seven years over a 15-year period. The length of the study allowed us to investigate the temporal variation of the allozyme-inversion associations by statistical methods of time series analysis. Cyclic seasonal changes of allozyme-inversion associations for both Lap and Pept-1 are detected in the natural population. In both cases, the patterns of seasonal change are due to the seasonal change of frequency of Lap and Pept-1 allozymes occurring exclusively within the OST gene arrangement. In contrast, the allozyme frequencies at these loci within the O3+4 gene arrangement are stable along seasons. The patterns of temporal variation of allozyme-inversion associations for Lap and Pept-1 in the natural population are contrasted with those previously published that correspond to gene arrangements of the O chromosome and nucleotide polymorphism at the rp49 region located inside these inversions, suggesting that natural selection is operating on these allozyme-inversion associations.  相似文献   

16.
Satya Prakash 《Genetics》1974,77(4):795-804
The Standard and Sex Ratio gene arrangements of the X chromosome of D. pseudobscura differ from each other in allele frequencies at the four X chromosome loci, esterase-5, adult acid phosphatase-6, phosphoglucomutase-1 and octanol dehydrogenase-3. The Standard arrangement which is the common arrangement in all populations is polymorphic at these loci in varying degrees, the geographically less widespread Sex Ratio arrangement has little polymorphism and is genically predominantly E-5(1.04) AP-6(-) Pgm1(1.0) ODH-3(1.0). The Sex Ratio arrangement from different populations is alike at all of the four loci, the Standard arrangement shows some gene frequency differences among populations. The Standard and Sex Ratio arrangements differ from each other by three inversions which suggests that the two arrangements are "old". Gene differences between these two chromosome arrangements can be explained due to differential natural selection of alleles in the Standard and Sex Ratio arrangments.-The order and percent recombination among these four loci in the Standard arrangement are: E-5-.294-AP-6-.335-Pgm-1-.024-ODH-3. The Standard X chromosomes from four different wild populations were analyzed for evidence of linkage disequilibrium between pairs of loci at these four loci. No evidence of linkage disequilibrium between pairs of loci was obtained. However, when linkages involving simultaneously three loci, E-5, AP-6 and Pgm-1 are considered, then significant departure from linkage equilibrium is observed.  相似文献   

17.
The HLA system and the analysis of multifactorial genetic disease   总被引:4,自引:0,他引:4  
The human leukocyte antigen (HLA) system comprises closely linked genes controlling highly polymorphic proteins involved in the presentation of peptides to the T-cell receptor. Specific alleles at HLA loci are associated with diseases, often those suspected to be of autoimmune aetiology. Many of these associations result from linkage disequilibrium between the HLA gene studied and other HLA genes or non-HLA gebes close by. Owing to its high level of polymorphism and its candidate role in many diseases, HLA was the first system used in many techniques of genetic mapping, such as affected-sib-pair analysis and association (linkage disequilibrium) studies. Much remains unknown about the reasons why diseases are associated with HLA. Experience gained from HLA has, however, shown how other loci involved in complex traits can be identified by studying families with multiple affected cases or sib pairs, followed by linkage-disequilibrium mapping and then analysis of candidate genes.  相似文献   

18.
Although linkage maps are important tools in evolutionary biology, their availability for wild populations is limited. The population of song sparrows (Melospiza melodia) on Mandarte Island, Canada, is among the more intensively studied wild animal populations. Its long‐term pedigree data, together with extensive genetic sampling, have allowed the study of a range of questions in evolutionary biology and ecology. However, the availability of genetic markers has been limited. We here describe 191 new microsatellite loci, including 160 high‐quality polymorphic autosomal, 7 Z‐linked and 1 W‐linked markers. We used these markers to construct a linkage map for song sparrows with a total sex‐averaged map length of 1731 cM and covering 35 linkage groups, and hence, these markers cover most of the 38–40 chromosomes. Female and male map lengths did not differ significantly. We then bioinformatically mapped these loci to the zebra finch (Taeniopygia guttata) genome and found that linkage groups were conserved between song sparrows and zebra finches. Compared to the zebra finch, marker order within small linkage groups was well conserved, whereas the larger linkage groups showed some intrachromosomal rearrangements. Finally, we show that as expected, recombination frequency between linked loci explained the majority of variation in gametic phase disequilibrium. Yet, there was substantial overlap in gametic phase disequilibrium between pairs of linked and unlinked loci. Given that the microsatellites described here lie on 35 of the 38–40 chromosomes, these markers will be useful for studies in this species, as well as for comparative genomics studies with other species.  相似文献   

19.
Two-locus population genetic models are analyzed to evaluate the utility of restriction fragment length polymorphisms for purposes of genetic counseling. It is shown that the linkage disequilibrium between a neutral marker and a tightly linked overdominant mutant will increase rapidly as the mutant moves to its polymorphic equilibrium. The linkage disequilibrium decays for deleterious recessive mutants. Two measures involving the linkage disequilibrium are investigated to determine how much information the transmission of the neutral marker provides about the transmission of the selected gene. In certain kinds of matings, where the parental two-locus genotypes and linkage phases are known, it is possible to determine whether or not a progeny is homozygous for the selected gene on the basis of the fetal genotype at the marker locus. A quantity of primary interest is the fraction of matings between individuals heterozygous for the selected gene in which exact diagnosis can be made in this way. The expected proportion of such matings, taken over all two-locus matings involving heterozygotes at the selected locus, is calculated as a function of the gene frequencies at the two loci and the linkage disequilibrium between them. This expected value is maximized when the linkage disequilibrium is at its maximum in absolute value. Fewer than half of all matings are informative if the linkage disequilibrium is small in magnitude or if the gene frequencies at the two loci are quite different. Consideration is also given to various conditional measures of association that may be useful when the parental two-locus genotypes are unknown. The results suggest that the utility of tightly linked neutral marker genes in predicting the transmission of a selected gene is generally less when selection acts against a recessive gene than for overdominant selection.  相似文献   

20.
The sex‐ratio X‐chromosome (SR) is a selfish chromosome that promotes its own transmission to the next generation by destroying Y‐bearing sperm in the testes of carrier males. In some natural populations of the fly Drosophila neotestacea, up to 30% of the X‐chromosomes are SR chromosomes. To investigate the molecular evolutionary history and consequences of SR, we sequenced SR and standard (ST) males at 11 X‐linked loci that span the ST X‐chromosome and at seven arbitrarily chosen autosomal loci from a sample of D. neotestacea males from throughout the species range. We found that the evolutionary relationship between ST and SR varies among individual markers, but genetic differentiation between SR and ST is chromosome‐wide and likely due to large chromosomal inversions that suppress recombination. However, SR does not consist of a single multilocus haplotype: we find evidence for gene flow between ST and SR at every locus assayed. Furthermore, we do not find long‐distance linkage disequilibrium within SR chromosomes, suggesting that recombination occurs in females homozygous for SR. Finally, polymorphism on SR is reduced compared to that on ST, and loci displaying signatures of selection on ST do not show similar patterns on SR. Thus, even if selection is less effective on SR, our results suggest that gene flow with ST and recombination between SR chromosomes may prevent the accumulation of deleterious mutations and allow its long‐term persistence at relatively high frequencies.  相似文献   

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