The multiple-locus symmetric fertility model

Selection due to variation in the fecundity among matings of genotypes with respect to many loci each with two alleles is studied. The fitness of a mating depends only on the genotypic distinction between homozygote and heterozygote at each locus in the two individuals, and differences among loci are allowed. This symmetric fertility model is therefore a generalization of the multiple-locus symmetric viability model. The phenomena seen in the two-locus symmetric fertility model generalize—e.g., the possibility of joint stability of equilibria with linkage equilibrium and with linkage disequilibrium, and the existence of different types of totally polymorphic equilibria with the gametic proportions in linkage equilibrium. The central equilibrium with genotypic frequencies in Hardy-Weinberg proportions and gametic frequencies in Robbins proportions exists for all symmetric fertility models. For some symmetric fertility regimes additional equilibria exist with gametic frequencies in linkage equilibrium and with genotypic frequencies in Hardy-Weinberg proportions at all except one locus. These equilibria may exist in the dioecious symmetric viability model, and then they will be locally stable. For free recombination the stable equilibria show linkage equilibrium, but several of these with different numbers of polymorphic loci may be stable simultaneously.     

Chromosome Fusion Affects Genetic Diversity and Evolutionary Turnover of Functional Loci but Consistently Depends on Chromosome Size

Major changes in chromosome number and structure are linked to a series of evolutionary phenomena, including intrinsic barriers to gene flow or suppression of recombination due to chromosomal rearrangements. However, chromosome rearrangements can also affect the fundamental dynamics of molecular evolution within populations by changing relationships between linked loci and altering rates of recombination. Here, we build chromosome-level assembly Eueides isabella and, together with a recent chromosome-level assembly of Dryas iulia, examine the evolutionary consequences of multiple chromosome fusions in Heliconius butterflies. These assemblies pinpoint fusion points on 10 of the 20 autosomal chromosomes and reveal striking differences in the characteristics of fused and unfused chromosomes. The ten smallest autosomes in D. iulia and E. isabella, which have each fused to a longer chromosome in Heliconius, have higher repeat and GC content, and longer introns than predicted by their chromosome length. When fused, these characteristics change to become more in line with chromosome length. The fusions also led to reduced diversity, which likely reflects increased background selection and selection against introgression between diverging populations, following a reduction in per-base recombination rate. We further show that chromosome size and fusion impact turnover rates of functional loci at a macroevolutionary scale. Together these results provide further evidence that chromosome fusion in Heliconius likely had dramatic effects on population level processes shaping rates of neutral and adaptive divergence. These effects may have impacted patterns of diversification in Heliconius, a classic example of an adaptive radiation.     

Female choice via indicator traits easily evolves in the face of recombination and migration

Species that exist in heterogeneous environments experience selection for specialization that is opposed by the homogenizing forces of migration and recombination. Migration tends to reduce associations between alleles and habitats, whereas recombination tends to break down associations among loci. The idea that heterogeneity should favor the evolution of isolating mechanisms has motivated evolutionary studies of reduced migration, habitat preference, and assortative mating. However, costly female choice of high-quality males can also evolve in heterogeneous populations and is not hindered by either recombination or migration. When information on male fitness is available through indicator traits, female choice based on these traits increases associations between female choice alleles and locally adapted alleles. Not only does female choice evolve in a heterogeneous environment, it acts to enhance the level of genetic variation and is thus self-reinforcing. The amount of female choice at equilibrium depends on how well mixed the habitats are, how much information on male genotype is available, and how different the habitats are. Female choice reaches the highest levels for intermediate levels of heterogeneity, because at such levels of heterogeneity there is both a high risk and high cost of mismating.     

The effects of linkage and gene flow on local adaptation: a two-locus continent-island model

Population subdivision and migration are generally considered to be important causes of linkage disequilibrium (LD). We explore the combined effects of recombination and gene flow on the amount of LD, the maintenance of polymorphism, and the degree of local adaptation in a subdivided population by analyzing a diploid, deterministic continent–island model with genic selection on two linked loci (i.e., no dominance or epistasis). For this simple model, we characterize explicitly all possible equilibrium configurations. Simple and intuitive approximations for many quantities of interest are obtained in limiting cases, such as weak migration, weak selection, weak or strong recombination. For instance, we derive explicit expressions for the measures and r² (the squared correlation in allelic state) of LD. They depend in qualitatively different ways on the migration rate. Remarkably high values of r² are maintained between weakly linked loci, especially if gene flow is low. We determine how the maximum amount of gene flow that admits preservation of the locally adapted haplotype, hence of polymorphism at both loci, depends on recombination rate and selection coefficients. We also investigate the evolution of differentiation by examining the invasion of beneficial mutants of small effect that are linked to an already present, locally adapted allele. Mutants of much smaller effect can invade successfully than predicted by naive single-locus theory provided they are at least weakly linked. Finally, the influence of linkage on the degree of local adaptation, the migration load, and the effective migration rate at a neutral locus is explored. We discuss possible consequences for the evolution of genetic architecture, in particular, for the emergence of clusters of tightly linked, slightly beneficial mutations and the evolution of recombination and chromosome inversions.     

Nonrecombining genes in a recombination environment: the Drosophila "dot" chromosome

Rate of recombination is a powerful variable affecting several aspects of molecular variation and evolution. A nonrecombining portion of the genome of most Drosophila species, the "dot" chromosome or F element, exhibits very low levels of variation and unusual codon usage. One lineage of Drosophila, the willistoni/saltans groups, has the F element fused to a normally recombining E element. Here, we present polymorphism data for genes on the F element in two Drosophila willistoni and one D. insularis populations, genes previously studied in D. melanogaster. The D. willistoni populations were known to be very low in inversion polymorphism, thus minimizing the recombination suppression effect of inversions. We first confirmed, by in situ hybridization, that D. insularis has the same E + F fusion as D. willistoni, implying this was a monophyletic event. A clear gradient in codon usage exists along the willistoni F element, from the centromere distally to the fusion with E; estimates of recombination rates parallel this gradient and also indicate D. insularis has greater recombination than D. willistoni. In contrast to D. melanogaster, genes on the F element exhibit moderate levels of nucleotide polymorphism not distinguishable from two genes elsewhere in the genome. Although some linkage disequilibrium (LD) was detected between polymorphic sites within genes (generally <500 bp apart), no long-range LD between F element loci exists in the two willistoni group species. In general, the distribution of allele frequencies of F element genes display the typical pattern of expectations of neutral variation at equilibrium. These results are consistent with the hypothesis that recombination allows the accumulation of nucleotide variation as well as allows selection to act on synonymous codon usage. It is estimated that the fusion occurred ～20 Mya and while the F element in the willistoni lineage has evolved "normal" levels and patterns of nucleotide variation, equilibrium may not have been reached for codon usage.     

The consequences of gene flow for local adaptation and differentiation: a two-locus two-deme model

We consider a population subdivided into two demes connected by migration in which selection acts in opposite direction. We explore the effects of recombination and migration on the maintenance of multilocus polymorphism, on local adaptation, and on differentiation by employing a deterministic model with genic selection on two linked diallelic loci (i.e., no dominance or epistasis). For the following cases, we characterize explicitly the possible equilibrium configurations: weak, strong, highly asymmetric, and super-symmetric migration, no or weak recombination, and independent or strongly recombining loci. For independent loci (linkage equilibrium) and for completely linked loci, we derive the possible bifurcation patterns as functions of the total migration rate, assuming all other parameters are fixed but arbitrary. For these and other cases, we determine analytically the maximum migration rate below which a stable fully polymorphic equilibrium exists. In this case, differentiation and local adaptation are maintained. Their degree is quantified by a new multilocus version of $F_\mathrm{ST}$ and by the migration load, respectively. In addition, we investigate the invasion conditions of locally beneficial mutants and show that linkage to a locus that is already in migration-selection balance facilitates invasion. Hence, loci of much smaller effect can invade than predicted by one-locus theory if linkage is sufficiently tight. We study how this minimum amount of linkage admitting invasion depends on the migration pattern. This suggests the emergence of clusters of locally beneficial mutations, which may form ‘genomic islands of divergence’. Finally, the influence of linkage and two-way migration on the effective migration rate at a linked neutral locus is explored. Numerical work complements our analytical results.     

Central equilibria in multilocus systems. I. Generalized nonepistatic selection regimes

The generalized nonepistatic selection regime encompasses combinations of multiplicative and neutral viability effects distributed across a set of loci. These subsume, in particular, mixtures of the classical modes of multiplicative and additive fitness evaluations for multilocus traits. Exact analytic conditions for existence and stability of a multilocus Hardy-Weinberg (H-W) polymorphic equilibrium configuration are ascertained. It is established that the central H-W polymorphism is stable only if the component loci are "over-dominant" and sufficient recombination is in force. The H-W central equilibrium is never stable for tight linkage whenever some multiplicative selection effects are contributed by at least two of the loci involved. In the case of additive selection expression and individual overdominant loci, the H-W polymorphism is stable independently of the level of recombination. In the context of "natural" recombination schemes, "more recombination" enhances the stability of the H-W polymorphic equilibrium.     

Partial isodisomy for maternal chromosome 7 and short stature in an individual with a mutation at the COL1A2 locus.

Uniparental disomy for chromosome 7 has been described previously in two individuals with cystic fibrosis. Here, we describe a third case that was discovered because the proband was homozygous for a mutation in the COL1A2 gene for type I procollagen, although his mother was heterozygous and his father did not have the mutation. Phenotypically, the proband was similar to the two previously reported cases with uniparental disomy for chromosome 7, in that he was short in stature and growth retarded. Paternity was assessed with five polymorphic markers. Chromosome 7 inheritance in the proband was analyzed using 12 polymorphic markers distributed along the entire chromosome. Similar analysis of the proband's two brothers established the phase of the alleles at the various loci, assuming minimal recombination. The proband inherited only maternal alleles at five loci and was homozygous at all loci examined, except one. He was heterozygous for an RFLP at the IGBP-1 locus at 7p13-p12. The results suggest that the isodisomy was not complete because of a recombination event involving the proximal short arms of two maternal chromosomes. In addition, the phenotype of proportional dwarfism in the proband suggests imprinting of one or more growth-related genes on chromosome 7.     

Nonuniform linkage disequilibrium within a 1,500-kb region of the human immunoglobulin heavy-chain complex.

We have characterized 10 VH polymorphic loci of the VH2, VH3, VH4, and VH5 families. Eight of 10 VH polymorphisms were found to be insertion/deletion polymorphisms, probably the result of nonhomologous recombination over the course of evolution of the current human VH repertoire. The 10 VH polymorphic loci were analyzed in 10 three-generation and 10 two-generation Canadian caucasoid families. Linkage disequilibrium (allelic association) was measured between pairs of VH polymorphic loci, and 12 significant associations were found. The degree of linkage disequilibrium measured between IGH polymorphic loci was then compared with the physical distance separating the loci. The physical distance between IGH polymorphic loci does not entirely determine the degree of linkage disequilibrium between polymorphic loci. Two regions, one in the VH region (between VH3f-2 and VH5-2 and one in the CH region (between C delta and C gamma 3), were found to have linkage disequilibrium values approximately 1/3,000 of that observed in other portions of the IGH region. The previous identification of recombinants in the C delta-to C gamma 3 region indicates that these areas of low linkage disequilibrium are consistent with the presence of recombination hot spots. The observed high amount of recombination in the subtelomeric portion of chromosome 14 therefore appears to be the result of specific hot spots for recombination, rather than a general increase in recombination in this region.     

Telomere stability and development of ctc1 mutants are rescued by inhibition of EJ recombination pathways in a telomerase-dependent manner

The telomeres of linear eukaryotic chromosomes are protected by caps consisting of evolutionarily conserved nucleoprotein complexes. Telomere dysfunction leads to recombination of chromosome ends and this can result in fusions which initiate chromosomal breakage–fusion–bridge cycles, causing genomic instability and potentially cell death or cancer. We hypothesize that in the absence of the recombination pathways implicated in these fusions, deprotected chromosome ends will instead be eroded by nucleases, also leading to the loss of genes and cell death. In this work, we set out to specifically test this hypothesis in the plant, Arabidopsis. Telomere protection in Arabidopsis implicates KU and CST and their absence leads to chromosome fusions, severe genomic instability and dramatic developmental defects. We have analysed the involvement of end-joining recombination pathways in telomere fusions and the consequences of this on genomic instability and growth. Strikingly, the absence of the multiple end-joining pathways eliminates chromosome fusion and restores normal growth and development to cst ku80 mutant plants. It is thus the chromosomal fusions, per se, which are the underlying cause of the severe developmental defects. This rescue is mediated by telomerase-dependent telomere extension, revealing a competition between telomerase and end-joining recombination proteins for access to deprotected telomeres.     

Selection for Linkage Modification II. a Recombination Balance for Neutral Modifiers

A stable polymorphic equilibrium may be established at a selectively-neutral gene locus which controls the extent of recombination between two other selected loci. The condition for the existence of the stable polymorphism is analogous to heterozygous advantage. The heterozygote at the modifying locus should produce a recombination fraction allowing the greatest linkage disequilibrium. In the models treated this has the effect of producing the highest mean fitness. The relationship of these findings to general problems of coadaptation is discussed.     

Isocitrate dehydrogenase in Aedes aegypti: formal genetics, preliminary linkage data and study of natural populations

Two loci for isocitrate dehydrogenase (Idh-1 ad Idh-2) are described in Ae. aegypti, both polymorphic with two codominant alleles. Crosses made to test linkage relationships of Idh-1 indicate that this locus is independent from sex (chromosome 1) and from Sod-1 and Hk-1 loci (chromosome 3), while it is linked to Pgm on the second chromosome. Average percent of recombination is 11.37, but significant differences have been found among strains. Data on genetic variability of Idh-1 and Idh-2 in three domestic african field populations are presented.     

RFLP Analysis of Chromosomal Segregation in Progeny from an Interspecific Hexaploid Somatic Hybrid between Solanum Brevidens and Solanum Tuberosum

Segregation of restriction fragment length polymorphism (RFLP) loci was monitored to determine the degree of homeologous pairing and recombination in a hexaploid somatic hybrid, A206, the result of protoplast fusion between Solanum tuberosum (PI 203900, a tetraploid cultivated potato) and Solanum brevidens (PI 218228), a diploid, sexually incompatible, distant relative harboring several traits for disease resistance. Somatic hybrid A206 was crossed to Katahdin, a tetraploid potato cultivar, to generate a segregating population of pentaploid progeny. Although the clones of the tetraploid S. tuberosum lines PI 203900 and Katahdin were highly polymorphic, the diploid S. brevidens clone was homozygous at all but two of the tested RFLP loci. Thus, homeologous recombination could be detected only when S. tuberosum and S. brevidens chromosomes paired and the S. brevidens homologs then segregated into separate gametes. A bias toward homologous pairing was observed for all 12 chromosomes. At least four and perhaps six chromosomes participated in homologous pairing only; each of 24 progeny contained all S. brevidens-derived RFLP markers for chromosomes 4, 8, 9 and 10. The remaining six chromosomes paired with their homolog(s) about twice as often as expected if hexaploid pairings were completely random. Where detectable with RFLPs, homeologous recombinations (both single and double) occurred at a frequency of 1.31 per chromosome. Cytological observations of meiosis I in the somatic hybrid indicated that homeologous pairing had occurred. Enhanced recombinational activity was observed for chromosome 2. A specific small deletion from chromosome 4 was detected in A206 and 11 other somatic hybrids out of 14 screened. These hybrids represent 13 independent fusion events between the same clones of S. brevidens and S. tuberosum. In one instance, this deletion occurred in one of two plants resulting from the same callus, indicating that the loss occurred in culture after fusion had taken place. It is possible that this deletion contributes to somaclonal variation.     

Genetic structure of five susceptibility gene regions for coronary artery disease: disequilibria within and among regions

We analyzed two-locus disequilibria for 16 polymorphic loci of seven susceptibility genes for coronary artery disease located in five chromosomal regions distributed across four chromosomes. Included were the genes coding for apolipoprotein B (ApoB, chromosome 2, four marker loci), lipoprotein lipase (LPL, chromosome 8, three marker loci), apolipoproteins AI, CIII, AIV (ApoAI–CIII–AIV, chromosome 11, three marker loci), apolipoprotein E (ApoE, chromosome 19, two marker loci), and the low density lipoprotein receptor (LDLR, chromosome 19, four marker loci). Our sample included 540 unrelated individuals from the Rochester, Minn. population. There were no statistically significant deviations of single-locus genotypes from Hardy-Weinberg equilibrium. The strongest associations within genes were for composite diallelic disequilibria; 17/19 were significant (13 at Pr <0.001, 1 at Pr <0.01, 3 at Pr <0.05). These observations suggest marker alleles within genes have a shared evolutionary history reflected by disequilibria that have not been dissipated by recombination. Disequilibrium was not generally concordant with the physical orderings of markers. Only two significant higher-order disequilibria were observed although 12 triallelic disequilibria were at maximum possible values. We observed 19 statistically significant disequilibria (Pr <0.05; 4 composite diallelic, 13 triallelic, and 2 quadriallelic) between 101 pairs of marker loci, where each locus in a pair was from a different unlinked region. These unexpected results are most likely explained by recent historical factors, including worldwide population expansion and amalgamation with continuous admixture, that influence the genetic structure (organization of alleles and non-alleles into genotypes) of a population. We conclude that disequilibria between loci from unlinked regions may be more extensive than is commonly assumed. Our findings also suggest that it is, on average, at least 15 times more likely to not detect significant disequilibrium among unlinked loci when it is really present than to make a false positive inference. Disequilibria between functional loci within or between regions will impact estimates of genetic variance associated with particular functional mutations within a susceptibility gene region. Received: 15 January 1998 / Accepted: 24 June 1998     

Lack of detectable genetic recombination on the X chromosome during the parthenogenetic production of female and male aphids

We used polymorphic microsatellite markers to look for recombination during parthenogenetic oogenesis between the X chromosomes of aphids of the tribe Macrosiphini. We examined the X chromosome because it comprises approximately 25 % of the genome and previous cytological observations of chromosome pairing and nucleolar organizer (NOR) heteromorphism suggest recombination, although the same is not true for autosomes. A total of 564 parthenogenetic females of Myzus clones with three distinct reproductive modes (cyclical parthenogenesis, obligate parthenogenesis and obligate parthenogenesis with male production) were genotyped at three informative X-linked loci. Also, parthenogenetically produced males from clones encompassing the full range of male-producing reproductive strategies were genotyped. These included 391 Myzus persicae males that were genotyped at three X-linked loci and 538 males from Sitobion clones that were genotyped at five informative X-linked loci. Our results show no departure from clonality in parthenogenetic generations of aphids of the tribe Macrosiphini: no recombinant genotypes were observed in parthenogenetically produced males or females.     

Selection on recombination in clines

Computer runs have been done to examine Slatkin's (1975) model for selection on recombination rates in linear sets of populations with environmental changes affecting two loci. In order to determine whether the suggested selection pressures on recombination do, in fact, exist, we follow the changes in frequency at a third locus that is polymorphic for alleles affecting the recombination rate between the two selected loci. With haploid or diploid selection models, there can be selection for increased recombination if the parameter values are chosen suitably, but changes in parameter values often lead to changes in the direction of selection, so that decreased recombination is favored. The selection for increased recombination is usually weak, while that for decreased recombination is frequently much stronger. Weaker selection on the selected loci often leads to increasing selection for decreased recombination.     

REDUCED GENE FLOW AT PERICENTROMERIC LOCI IN A HYBRID ZONE INVOLVING CHROMOSOMAL RACES OF THE HOUSE MOUSE MUS MUSCULUS DOMESTICUS

The West European house mouse, Mus musculus domesticus, is a particularly suitable model to investigate the role of chromosomal rearrangements in reproductive isolation. In fact, it exhibits a broad range of chromosomal polymorphism due to Robertsonian (Rb) fusions leading to various types of contact zones between different chromosomal races. In the present study, we analyzed a parapatric contact in central Italy between the Cittaducale chromosomal race (CD: 2n= 22) and the surrounding populations with standard karyotype (2n= 40) to understand if Rb fusions play a causative role in speciation. One hundred forty‐seven mice from 17 localities were genotyped by means of 12 microsatellite loci. A telomeric and a pericentromeric locus situated on six chromosome arms (four Rbs and one telocentric) were selected to detect differences in the amount of gene flow for each locus in different chromosomal positions. The analyses performed on the two subsets of loci show differences in the level of gene flow, which is more restricted near the centromeres of Rb chromosomes. This effect is less pronounced in the homozygotes populations settled at the border of the hybrid zone. We discuss the possible cause of the differential porosity of gene flow in Rbs considering “hybrid dysfunctions” and “suppressed recombination” models.     

The probability of fusions joining sex chromosomes and autosomes

Chromosome fusion and fission are primary mechanisms of karyotype evolution. In particular, the fusion of a sex chromosome and an autosome has been proposed as a mechanism to resolve intralocus sexual antagonism. If sexual antagonism is common throughout the genome, we should expect to see an excess of fusions that join sex chromosomes and autosomes. Here, we present a null model that provides the probability of a sex chromosome autosome fusion, assuming all chromosomes have an equal probability of being involved in a fusion. This closed-form expression is applicable to both male and female heterogametic sex chromosome systems and can accommodate unequal proportions of fusions originating in males and females. We find that over 25% of all chromosomal fusions are expected to join a sex chromosome and an autosome whenever the diploid autosome count is fewer than 16, regardless of the sex chromosome system. We also demonstrate the utility of our model by analysing two contrasting empirical datasets: one from Drosophila and one from the jumping spider genus Habronattus. We find that in the case of Habronattus, there is a significant excess of sex chromosome autosome fusions but that in Drosophila there are far fewer sex chromosome autosome fusions than would be expected under our null model.     

Genetic control of lymphocyte antigens in sheep: TheOLA complex and two minor loci

Lymphocytotoxic reagents allowed us to define 11 lymphocyte factors in sheep. After a genetic control of monospecificity had been made, a genetic study based on 400 crossings indicated that nine factors are transmitted in two haplotypes containing 0.1 or 2 factors. The linked factors of the bifactorial haplotypes are the products of two genes at two closely linked loci,OLA- A andOLA- B, having a recombination rate of about 0.6%. The nine factors are the products of fiveOLA- A and fourOLA- B alleles. Allelic frequencies at the two loci, ranging from 0.05 to 0.23 were obtained by two methods. A linkage disequilibrium between the loci is described. Among the possible causes of this, inbreeding is excluded, whereas selective pressure or more probably old fusions between sheep populations must be retained. A tenth factor (frequency 0.33 to 0.35) has a 26% recombination with OLA factors; its locus (OL-X) would be on the same chromosome but very far from theOLA complex. An 11th factor (frequency 0.30) is probably independent ofOLA; its locus (OL-Z) may be on another chromosome. The two linkedOLA loci give evidence of a major histocompatibility complex in sheep; the observed linkage disequilibrium allows one to foretell certain applications in phylogeny and perhaps in selection.     

The Evolution of the Y Chromosome with X-Y Recombination

A theoretical population genetic model is developed to explore the consequences of X-Y recombination in the evolution of sex chromosome polymorphism. The model incorporates one sex-determining locus and one locus subject to natural selection. Both loci have two alleles, and the rate of classical meiotic recombination between the loci is r. The alleles at the sex-determining locus specify whether the chromosome is X or Y, and the alleles at the selected locus are arbitrarily labeled A and a. Natural selection is modeled as a process of differential viabilities. The system can be expressed in terms of three recurrence equations, one for the frequency of A on the X-bearing gametes produced by females, one for each of the frequency of A on the X- and Y-bearing gametes produced by males. Several special cases are examined, including X chromosome dominance and symmetric selection. Unusual equilibria are found with the two sexes having very different allele frequencies at the selected locus. A significant finding is that the allowance of recombination results in a much greater opportunity for polymorphism of the Y chromosome. Tighter linkage results in a greater likelihood for equilibria with a large difference between the sex chromosomes in allele frequency.