Gene Conversion, Linkage, and the Evolution of Multigene Families

The evolution of the probabilities of genetic identity within and between the loci of a multigene family is investigated. Unbiased gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. The linkage map is arbitrary, and the location dependence of the probabilities of identity is formulated exactly. The greatest of the rates of gene conversion, random drift, and mutation is epsilon much less than 1. For interchromosomal conversion, the equilibrium probabilities of identity are within order epsilon [i.e., O(epsilon)] of those in a simple model that has no location dependence and, at equilibrium, no linkage disequilibrium. At equilibrium, the linkage disequilibria are of O(epsilon); they are evaluated explicitly with an error of O(epsilon 2); they may be negative if symmetric heteroduplexes occur. The ultimate rate and pattern of convergence to equilibrium are within O(epsilon 2) and O(epsilon), respectively, of that of the same simple model. If linkage is loose (i.e., all the crossover rates greatly exceed epsilon, though they may still be much less than 1/2), the linkage disequilibria are reduced to O(epsilon) in a time of O(-ln epsilon). If intrachromosomal conversion is incorporated, the same results hold for loose linkage, except that, if the crossover rates are much less than 1/2, then the linkage disequilibria generally exceed those for pure interchromosomal conversion.     

Intrachromosomal gene conversion, linkage, and the evolution of multigene families

The evolution of the probabilities of genetic identity within and between tandemly repeated loci of a multigene family is investigated analytically and numerically. Unbiased intrachromosomal gene conversion, equal crossing over, random genetic drift, and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Under the restriction that there is at most one crossover in the multigene family per individual per generation, the dependence on location of the probabilities of identity is treated exactly. In the "homogeneous" approximation to this "exact" model, end effects are disregarded; in the "exchangeable" approximation, to which all previous work was confined, all position dependence is neglected. Numerical results indicate that the exchangeable and homogeneous models are both qualitatively correct, the exchangeable model is sometimes too inaccurate for quantitative conclusions, and the homogeneous model is always more accurate than the exchangeable one and is always sufficiently accurate for quantitative conclusions.     

The Evolution of Multigene Families under Intrachromosomal Gene Conversion

A model for the evolution of the probabilities of genetic identity within and between loci of a multigene family in a finite population is formulated and investigated. Unbiased intrachromosomal gene conversion, equal crossing over between tandemly repeated genes, random genetic drift and mutation to new alleles are incorporated. Generations are discrete and nonoverlapping; the diploid, monoecious population mates at random. Formulas for the equilibrium values of the probabilities of identity and a cubic equation for the rate of convergence are deduced. Numerical examples indicate the following. The amount of homology at equilibrium generally decreases as the mutation rate, the population size and the number of repeats increase; it may increase or decrease with increasing crossover rate. The intralocus homology has an intermediate minimum, whereas the interlocus homology increases, as the rate of gene conversion increases. The intralocus homology decreases, whereas the interlocus homology increases, as the proportion of symmetric heteroduplexes increases. The characteristic convergence time can be sufficiently short to imply that intrachromosomal gene conversion may be an important mechanism for maintaining sequence homogeneity among repeated genes. The convergence time decreases as the conversion rate and the proportion of symmetric heteroduplexes increase; although exceptions occur, it generally increases as the population size and the number of repeats increase; it may increase or decrease with increasing crossover rate.     

Dynamics of correlated genetic systems. II. Simulation studies of chromosomal segments under selection

The dynamics of chromosomal segments under selection are investigated by comparing experimental data to simulations of simple models of selection. The simulations assume 93 loci distributed evenly along an entire chromosome. The two issues addressed in this paper concern rates of decay of linkage disequilibria for chromosomes under selection and rates of gene frequency change after perturbation of gametic frequencies to states near the edge of the gametic frequency simplex. The findings are: (1) If reasonable values of inbreeding depression are assumed, linkage disequilibria decays to zero but at a rate nearly twice that expected from neutral theory. Experimental results also show accelerated decay rates. The acceleration of decay seems to be a simple consequence of the increased heterozygosity produced by selection. It is, therefore, argued that massive linkage disequilibria, of the kind found by Franklin and Lewontin (1970) in their simulations, are unlikely to characterize the genetic structure of natural populations of random mating organisms. (2) It is possible to distinguish between two time-honored models of multilocus selection, known as the symmetric overdominant and classical models, on the basis of gene frequency change near the edge of the gametic frequency simplex assuming linkage disequilibria is intense. (3) Examination of experimental data from perturbation experiments shows that neither of these elementary models adequately account for observed rates of gene frequency change, although the symmetric overdominant model does provide the better fit. Instead the experimental data suggest a markedly nonuniform distribution of selective effects along the chromosome. The data also suggest that these selective effects combine in markedly nonadditive ways in determining joint fitness.     

Substrate length requirements for efficient mitotic recombination in Saccharomyces cerevisiae.

An ectopic recombination system using ura3 heteroalleles varying in size from 80 to 960 bp has been used to examine the effect of substrate length on spontaneous mitotic recombination. The ura3 heteroalleles were positioned either on nonhomologous chromosomes (heterochromosomal repeats) or as direct or inverted repeats on the same chromosome (intrachromosomal repeats). While the intrachromosomal events occur at rates at least 2 orders of magnitude greater than the corresponding heterochromosomal events, the recombination rate for each type of repeat considered separately exhibits a linear dependence on substrate length. The linear relationships allow estimation of the corresponding minimal efficient processing segments, which are approximately 250 bp regardless of the relative positions of the repeats in the yeast genome. An examination of the distribution of recombination events into simple gene conversion versus crossover events indicates that reciprocal exchange is more sensitive to substrate size than is gene conversion.     

A Study of Linkage Disequilibrium in British Populations of DROSOPHILA SUBOBSCURA

Data have been obtained concerning the genetic content of samples of O chromosomes from three British populations, and J chromosomes from one population, of Drosophila subobscura. Some improvements to the genetic map of the O and J chromosomes have been made. Allele frequencies at the loci studied do not show much geographical variation, except where associations with geographically varying gene arrangements distort the picture. Striking nonrandom associations between alleles at three enzyme loci and closely linked O chromosome gene arrangements are present. Some historical explanation for these associations cannot at present be ruled out, but it is clear that a very high degree of genetic differentiation must exist between different gene arrangements in this species. There is no convincing direct evidence for linkage disequilibrium between pairs of enzyme loci, although there is a significant association between close linkage and a high value of the linkage disequilibrium measure. This suggests that there may be disequilibria between closely linked enzyme loci that are too small to be individually detectable. These results are in broad agreement with those reported by workers on other Drosophila species. At present there appears to be no evidence to support the concept that selection is sufficiently strong at individual enzyme loci to produce a high degree of nonrandom associations. (Franklin and Lewontin 1970).     

The Genetics of DROSOPHILA SUBOBSCURA Populations. IX. Studies on Linkage Disequilibrium in Four Natural Populations

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.     

Meiotic Crossing over between Nonhomologous Chromosomes Affects Chromosome Segregation in Yeast

Meiotic recombination between artificial repeats positioned on nonhomologous chromosomes occurs efficiently in the yeast Saccharomyces cerevisiae. Both gene conversion and crossover events have been observed, with crossovers yielding reciprocal translocations. In the current study, 5.5-kb ura3 repeats positioned on chromosomes V and XV were used to examine the effect of ectopic recombination on meiotic chromosome segregation. Ura(+) random spores were selected and gene conversion vs. crossover events were distinguished by Southern blot analysis. Approximately 15% of the crossover events between chromosomes V and XV were associated with missegregation of one of these chromosomes. The missegregation was manifest as hyperploid spores containing either both translocations plus a normal chromosome, or both normal chromosomes plus one of the translocations. In those cases where it could be analyzed, missegregation occurred at the first meiotic division. These data are discussed in terms of a model in which ectopic crossovers compete efficiently with normal allelic crossovers in directing meiotic chromosome segregation.     

An Extension of a Model for the Evolution of Multigene Families by Unequal Crossing over

Evolution of a multigene family is studied from the standpoint of population genetics. It is assumed that the multigene family is undergoing continuous interchromosomal unequal crossing over, mutation and random frequency drift. The equilibrium properties of the probability of gene identity (clonality) are investigated, using two measures: identity probability within and between chromosomes. The measures represent homogeneity of genes within a family in one chromosome and similarity of gene families between two homologous chromosomes. The means, the variances and the covariance of these two measures of identity probability are obtained by using the diffusion equation method. It is shown that the means and the variances are generally smaller than those predicted in the previous model assuming intrachromosomal (sister chromatid) unequal crossing over (Ohta 1978a,b).     

Interchromosomal Biased Gene Conversion, Mutation and Selection in a Multigene Family

A mathematical model of the effects of interchromosomal biased gene conversion, mutation and natural selection on a multigene family is developed and analyzed. The model assumes two allelic states at each of n loci. The effects of genetic drift are ignored. The model is developed under the assumption of no recombination, but the analysis shows that, at equilibrium, there is no linkage disequilibrium, which implies that the conclusions are valid for arbitrary recombination among loci. At equilibrium, the balance between mutation, gene conversion and selection depends on the ratio of the mutation rates to the quantity [s + g(2α - 1)/ n], where s is the increment or decrement in relative fitness with each additional copy of one of the alleles, g is the conversion rate, and α is a measure of the bias in favor of one of the alleles. When this quantity is large relative to the mutation rates, the allele that has the net advantage, combining the effects of selection and conversion, will be nearly fixed in the multigene family. A comparison of these results with those from a comparable model of intrachromosomal biased conversion shows that biased interchromosomal conversion leads to approximately the same equilibrium copy number as does intrachromosomal conversion of the same strength. Interchromosomal conversion is much more effective in causing the substitution of one allele by another. The relative frequencies of interchromosomal and intrachromosomal conversion is indicated by the extent of the linkage disequilibrium among the loci in a multigene family.     

Generation of a Restriction Fragment Length Polymorphism Linkage Map for Toxoplasma Gondii

We have constructed a genetic linkage map for the parasitic protozoan, Toxoplasma gondii, using randomly selected low copy number DNA markers that define restriction fragment length polymorphisms (RFLPs). The inheritance patterns of 64 RFLP markers and two phenotypic markers were analyzed among 19 recombinant haploid progeny selected from two parallel genetic crosses between PLK and CEP strains. In these first successful interstrain crosses, these RFLP markers segregated into 11 distinct genetic linkage groups that showed close correlation with physical linkage groups previously defined by molecular karyotype. Separate linkage maps, constructed for each of the 11 chromosomes, indicated recombination frequencies range from approximately 100 to 300 kb per centimorgan. Preliminary linkage assignments were made for the loci regulating sinefungin resistance (snf-1) on chromosome IX and adenine arabinoside (ara-1) on chromosome V by linkage to RFLP markers. Despite random segregation of separate chromosomes, the majority of chromosomes failed to demonstrate internal recombination events and in 3/19 recombinant progeny no intramolecular recombination events were detected. The relatively low rate of intrachromosomal recombination predicts that tight linkage for unknown genes can be established with a relatively small set of markers. This genetic linkage map should prove useful in mapping genes that regulate drug resistance and other biological phenotypes in this important opportunistic pathogen.     

The IBD process along four chromosomes

In this note, we present the continuous-time Markov rate matrix that models identity by descent (ibd) patterns among four chromosomes in a population. The equilibrium distribution of this Markov process along a chromosome is the set of 4-gene state probabilities given by the Ewens sampling formula. This model will facilitate inference of identity by descent among the four chromosomes of a pair of individuals, using data at dense SNP loci among which there may be linkage disequilibrium.     

The probability that related individuals share some section of genome identical by descent

A formal mathematical framework is presented for the study of linkage in man and the concept of chromosome pedigree is defined for both autosomes and X chromosomes. It is shown that, assuming no interference, all the crossover processes in the pedigree may be viewed jointly as a continuous-time Markov random walk on the vertices of a hypercube, the time parameter being map distance along the chromosome. The event that two individuals have a segment of chromosome in common, thus proving them to be related, corresponds to the random walk hitting a particular set of vertices. The probability of this happening is calculated for various types of relationship, making use of the symmetry of the situation to partition the vertices into a very much smaller number of orbits and render the computation manageable. The probability that an individual with n children passes on all his or her genes to them is also calculated in this way.     

Linkage map of the peppered moth,Biston betularia (Lepidoptera,Geometridae): a model of industrial melanism

We have constructed a linkage map for the peppered moth (Biston betularia), the classical ecological genetics model of industrial melanism, aimed both at localizing the network of loci controlling melanism and making inferences about chromosome dynamics. The linkage map, which is based primarily on amplified fragment length polymorphisms (AFLPs) and genes, consists of 31 linkage groups (LGs; consistent with the karyotype). Comparison with the evolutionarily distant Bombyx mori suggests that the gene content of chromosomes is highly conserved. Gene order is conserved on the autosomes, but noticeably less so on the Z chromosome, as confirmed by physical mapping using bacterial artificial chromosome fluorescence in situ hybridization (BAC-FISH). Synteny mapping identified three pairs of B. betularia LGs (11/29, 23/30 and 24/31) as being orthologous to three B. mori chromosomes (11, 23 and 24, respectively). A similar finding in an outgroup moth (Plutella xylostella) indicates that the B. mori karyotype (n=28) is a phylogenetically derived state resulting from three chromosome fusions. As with other Lepidoptera, the B. betularia W chromosome consists largely of repetitive sequence, but exceptionally we found a W homolog of a Z-linked gene (laminin A), possibly resulting from ectopic recombination between the sex chromosomes. The B. betularia linkage map, featuring the network of known melanization genes, serves as a resource for melanism research in Lepidoptera. Moreover, its close resemblance to the ancestral lepidopteran karyotype (n=31) makes it a useful reference point for reconstructing chromosome dynamic events and ancestral genome architectures. Our study highlights the unusual evolutionary stability of lepidopteran autosomes; in contrast, higher rates of intrachromosomal rearrangements support a special role of the Z chromosome in adaptive evolution and speciation.     

Physical Mapping of Meiotic Crossover Events in a 200-Kb Region of Neurospora Crassa Linkage Group I

We propose a general restriction fragment length polymorphism-based strategy to analyze the distribution of meiotic crossover events throughout specific genetic intervals. We have isolated 64 recombinant chromosomes carrying independent meiotic crossover events in the genetic interval eth-1-un-2 on linkage group I of Neurospora crassa. Thirty-eight crossover events were physically mapped with reference to a 200-kb region cloned by chromosome walking, using N. crassa λ and cosmid libraries. Crossovers were homogeneously distributed at intervals of 5.0 +/- 2.3 kb along the entire cloned interval. The ratio of physical to genetic distance appears to be higher in the region than in the overall N. crassa genome, suggesting that recombinational activity is less in large chromosomes than in small ones. The present work provides a method for defining the centromeric-telomeric orientation of single cloned DNA fragments. Their physical distance can also be estimated with respect to linked loci, provided that crossover events are distributed homogeneously in the interval. This strategy overcomes typical difficulties in defining the position and direction of chromosome walking steps on conventional linkage maps.     

Migration, selection and histocompatibility

The extreme polymorphism of the HLA system allows a very precise definition of populations by gene frequencies. The existence of several linked loci (HLA-A, B, C, D, DR) induces the possibility of detection of preferential chromosomes in populations (particular associations of alleles or linkage disequilibria). These linkage disequilibria indicate that the conditions required for Hardy-Weinberg equilibrium are not met. The linkage disequilibria can be used as indicators for the evaluation of genetic dift, founder effect and inbreeding in small populations or for the detection of selection and migration in larger populations.     

Dynamics of linkage disequilibrium in bacterial genomes undergoing transformation and/or conjugation

Bacteria may undergo recombinational exchange either by conjugation followed by crossing over, or by transformation of small segments of DNA into the cell followed by incorporation into the chromosome by gene conversion. These two forms of recombination may have very different consequences on the patterns of linkage disequilibrium seen within bacterial genomes. In this paper deterministic recursions are obtained for three linked loci in populations having these two forms of recombination. Both neutral genetic variation and the case of one selected gene are considered. It is shown that the two forms of exchange have identical consequences on two-locus linkage disequilibria, but that three-locus disequilibria can have different behaviors. Hitchhiking also has different consequences on the pattern of disequilibrium seen between linked neutral genes in the region of the selected locus. Inference of the relative importance of these two modes of recombination from static samples of DNA sequences will hinge on the relationship between linkage map distance and disequilibria.     

Chromosome size-dependent control of meiotic reciprocal recombination in Saccharomyces cerevisiae: the role of crossover interference.

In the yeast Saccharomyces cerevisiae, small chromosomes undergo meiotic reciprocal recombination (crossing over) at rates (centimorgans per kilobases) greater than those of large chromosomes, and recombination rates respond directly to changes in the total size of a chromosomal DNA molecule. This phenomenon, termed chromosome size-dependent control of meiotic reciprocal recombination, has been suggested to be important for ensuring that homologous chromosomes cross over during meiosis. The mechanism of this regulation was investigated by analyzing recombination in identical genetic intervals present on different size chromosomes. The results indicate that chromosome size-dependent control is due to different amounts of crossover interference. Large chromosomes have high levels of interference while small chromosomes have much lower levels of interference. A model for how crossover interference directly responds to chromosome size is presented. In addition, chromosome size-dependent control was shown to lower the frequency of homologous chromosomes that failed to undergo crossovers, suggesting that this control is an integral part of the mechanism for ensuring meiotic crossing over between homologous chromosomes.     

Study of intrachromosomal duplications among the eukaryote genomes.

Complete eukaryote chromosomes were investigated for intrachromosomal duplications of nucleotide sequences. The analysis was performed by looking for nonexact repeats on two complete genomes, Saccharomyces cerevisiae and Caenorhabditis elegans, and four partial ones, Drosophila melanogaster, Plasmodium falciparum, Arabidopsis thaliana, and Homo sapiens. Through this analysis, we show that all eukaryote chromosomes exhibit similar characteristics for their intrachromosomal repeats, suggesting similar dynamics: many direct repeats have their two copies physically close together, and these close direct repeats are more similar and shorter than the other repeats. On the contrary, there are almost no close inverted repeats. These results support a model for the dynamics of duplication. This model is based on a continuous genesis of tandem repeats and implies that most of the distant and inverted repeats originate from these tandem repeats by further chromosomal rearrangements (insertions, inversions, and deletions). Remnants of these predicted rearrangements have been brought out through fine analysis of the chromosome sequence. Despite these dynamics, shared by all eukaryotes, each genome exhibits its own style of intrachromosomal duplication: the density of repeated elements is similar in all chromosomes issued from the same genome, but is different between species. This density was further related to the relative rates of duplication, deletion, and mutation proper to each species. One should notice that the density of repeats in the X chromosome of C. elegans is much lower than in the autosomes of that organism, suggesting that the exchange between homologous chromosomes is important in the duplication process.