Using lod scores to detect sex differences in male-female recombination fractions

Human recombination fraction (RF) can differ between males and females, but investigators do not always know which disease genes are located in genomic areas of large RF sex differences. Knowledge of RF sex differences contributes to our understanding of basic biology and can increase the power of a linkage study, improve gene localization, and provide clues to possible imprinting. One way to detect these differences is to use lod scores. In this study we focused on detecting RF sex differences and answered the following questions, in both phase-known and phase-unknown matings: (1) How large a sample size is needed to detect a RF sex difference? (2) What are "optimal" proportions of paternally vs. maternally informative matings? (3) Does ascertaining nonoptimal proportions of paternally or maternally informative matings lead to ascertainment bias? Our results were as follows: (1) We calculated expected lod scores (ELODs) under two different conditions: "unconstrained," allowing sex-specific RF parameters (theta(female), theta(male)); and "constrained," requiring theta(female) = theta(male). We then examined the DeltaELOD (identical with difference between maximized constrained and unconstrained ELODs) and calculated minimum sample sizes required to achieve statistically significant DeltaELODs. For large RF sex differences, samples as small as 10 to 20 fully informative matings can achieve statistical significance. We give general sample size guidelines for detecting RF differences in informative phase-known and phase-unknown matings. (2) We defined p as the proportion of paternally informative matings in the dataset; and the optimal proportion p(circ) as that value of p that maximizes DeltaELOD. We determined that, surprisingly, p(circ) does not necessarily equal (1/2), although it does fall between approximately 0.4 and 0.6 in most situations. (3) We showed that if p in a sample deviates from its optimal value, no bias is introduced (asymptotically) to the maximum likelihood estimates of theta(female) and theta(male), even though ELOD is reduced (see point 2). This fact is important because often investigators cannot control the proportions of paternally and maternally informative families. In conclusion, it is possible to reliably detect sex differences in recombination fraction.     

Maximum likelihood vs. minimum chi-square--a general comparison with applications to the estimation of recombination fractions in two-point linkage analysis.

Some relationships between the estimates of recombination fraction in two-point linkage analysis obtained by maximum likelihood, minimum chi-square, and general least squares are derived. These theoretical results are based on an approximation for the multinomial distribution. Applications (theoretical and experimental) with RFLP (restriction fragment length polymorphism) markers for a segregating F2 population are given. The minimum chi-square estimate is slightly larger than the maximum likelihood estimate. For applications, however, both estimates must be considered to be approximately equal. The least squares estimates are slightly different (larger or smaller) from these estimates.     

Linkage analysis in the presence of errors I: complex-valued recombination fractions and complex phenotypes

Linkage is a phenomenon that correlates the genotypes of loci, rather than the phenotypes of one locus to the genotypes of another. It is therefore necessary to convert the observed trait phenotypes into trait-locus genotypes, which can then be analyzed for coinheritance with marker-locus genotypes. However, if the mode of inheritance of the trait is not known accurately, this conversion can often result in errors in the inferred trait-locus genotypes, which, in turn, can lead to the misclassification of the recombination status of meioses. As a result, the recombination fraction can be overestimated in two-point analysis, and false exclusions of the true trait locus can occur in multipoint analysis. We propose a method that increases the robustness of multipoint analysis to errors in the mode of inheritance assumptions of the trait, by explicitly allowing for misclassification of trait-locus genotypes. To this end, the definition of the recombination fraction is extended to the complex plane, as Theta=straight theta+straightepsiloni; theta is the recombination fraction between actual ("real") genotypes of marker and trait loci, and straightepsilon is the probability of apparent but false ("imaginary") recombinations between the actual and inferred trait-locus genotypes. "Complex" multipoint LOD scores are proven to be stochastically equivalent to conventional two-point LOD scores. The greater robustness to modeling errors normally associated with two-point analysis can thus be extended to multiple two-point analysis and multipoint analysis. The use of complex-valued recombination fractions also allows the stochastic equivalence of "model-based" and "model-free" methods to be extended to multipoint analysis.     

Estimating recombination rates from population genetic data.

We introduce a new method for estimating recombination rates from population genetic data. The method uses a computationally intensive statistical procedure (importance sampling) to calculate the likelihood under a coalescent-based model. Detailed comparisons of the new algorithm with two existing methods (the importance sampling method of Griffiths and Marjoram and the MCMC method of Kuhner and colleagues) show it to be substantially more efficient. (The improvement over the existing importance sampling scheme is typically by four orders of magnitude.) The existing approaches not infrequently led to misleading results on the problems we investigated. We also performed a simulation study to look at the properties of the maximum-likelihood estimator of the recombination rate and its robustness to misspecification of the demographic model.     

The evolution of sex and recombination in response to abiotic or coevolutionary fluctuations in epistasis

Evolutionary biologists have identified several factors that could explain the widespread phenomena of sex and recombination. One hypothesis is that host-parasite interactions favor sex and recombination because they favor the production of rare genotypes. A problem with many of the early models of this so-called Red Queen hypothesis is that several factors are acting together: directional selection, fluctuating epistasis, and drift. It is thus difficult to identify what exactly is selecting for sex in these models. Is one factor more important than the others or is it the synergistic action of these different factors that really matters? Here we focus on the analysis of a simple model with a single mechanism that might select for sex: fluctuating epistasis. We first analyze the evolution of sex and recombination when the temporal fluctuations are driven by the abiotic environment. We then analyze the evolution of sex and recombination in a two-species coevolutionary model, where directional selection is absent (allele frequencies remain fixed) and temporal variation in epistasis is induced by coevolution with the antagonist species. In both cases we contrast situations with weak and strong selection and derive the evolutionarily stable (ES) recombination rate. The ES recombination rate is most sensitive to the period of the cycles, which in turn depends on the strength of epistasis. In particular, more virulent parasites cause more rapid cycles and consequently increase the ES recombination rate of the host. Although the ES strategy is maximized at an intermediate period, some recombination is favored even when fluctuations are very slow. By contrast, the amplitude of the cycles has no effect on the ES level of sex and recombination, unless sex and recombination are costly, in which case higher-amplitude cycles allow the evolution of higher rates of sex and recombination. In the coevolutionary model, the amount of recombination in the interacting species also has a large effect on the ES, with evolution favoring higher rates of sex and recombination than in the interacting species. In general, the ES recombination rate is less than or equal to the recombination rate that would maximize mean fitness. We also discuss the effect of migration when sex and recombination evolve in a metapopulation. We find that intermediate parasite migration rates maximize the degree of local adaptation of the parasite and lead to a higher ES recombination rate in the host.     

Absence of age effect on meiotic recombination between human X and Y chromosomes

Recombination between the X and Y chromosomes is limited to the pseudoautosomal region and is necessary for proper segregation of the sex chromosomes during spermatogenesis. Failure of the sex chromosomes to disjoin properly during meiosis can result in individuals with a 47,XXY constitution, and approximately one-half of these result from paternal nondisjunction at meiosis I. Analysis of individuals with paternally derived 47,XXY has shown that the majority are the result of meiosis in which the X and Y chromosomes have failed to recombine. Our studies of sperm have demonstrated that aneuploid 24,XY sperm have a decreased recombination frequency, compared with that of normal sperm. Some studies have indicated a relationship of increased paternal age with 47,XXY offspring and with the production of XY disomic sperm, whereas others have failed to find such relationships. To determine whether there is a relationship between paternal age and recombination in the pseudoautosomal region, single-sperm genotyping was performed to measure the frequency of recombination between a sex-specific locus, STS/STS pseudogene, and a pseudoautosomal locus, DXYS15, in younger men (age < or =30 years) compared with older men (age > or =50 years). A total of 2,329 sperm cells were typed by single-sperm PCR in 20 men who were heterozygous for the DXYS15 locus (1,014 sperm from 10 younger men and 1,315 sperm from 10 older men). The mean recombination frequency was 39.2% in the younger men and 37.8% in the older men. There was no heterogeneity in the frequency of recombination rates. There was no significant difference between the recombination frequencies among the younger men and those among the older men, when analyzed by the clustered binomial Z test (Z=.69, P=.49). This result suggests that paternal age has no effect on the recombination frequency in the pseudoautosomal region.     

Selection for recombination in structured populations

In finite populations, linkage disequilibria generated by the interaction of drift and directional selection (Hill-Robertson effect) can select for sex and recombination, even in the absence of epistasis. Previous models of this process predict very little advantage to recombination in large panmictic populations. In this article we demonstrate that substantial levels of linkage disequilibria can accumulate by drift in the presence of selection in populations of any size, provided that the population is subdivided. We quantify (i) the linkage disequilibrium produced by the interaction of drift and selection during the selective sweep of beneficial alleles at two loci in a subdivided population and (ii) the selection for recombination generated by these disequilibria. We show that, in a population subdivided into n demes of large size N, both the disequilibrium and the selection for recombination are equivalent to that expected in a single population of a size intermediate between the size of each deme (N) and the total size (nN), depending on the rate of migration among demes, m. We also show by simulations that, with small demes, the selection for recombination is stronger than both that expected in an unstructured population (m = 1 - 1/n) and that expected in a set of isolated demes (m = 0). Indeed, migration maintains polymorphisms that would otherwise be lost rapidly from small demes, while population structure maintains enough local stochasticity to generate linkage disequilibria. These effects are also strong enough to overcome the twofold cost of sex under strong selection when sex is initially rare. Overall, our results show that the stochastic theories of the evolution of sex apply to a much broader range of conditions than previously expected.     

Sex‐antagonistic genes,XY recombination and feminized Y chromosomes

The canonical model of sex‐chromosome evolution predicts that sex‐antagonistic (SA) genes play an instrumental role in the arrest of XY recombination and ensuing Y chromosome degeneration. Although this model might account for the highly differentiated sex chromosomes of birds and mammals, it does not fit the situation of many lineages of fish, amphibians or nonavian reptiles, where sex chromosomes are maintained homomorphic through occasional XY recombination and/or high turnover rates. Such situations call for alternative explanatory frameworks. A crucial issue at stake is the effect of XY recombination on the dynamics of SA genes and deleterious mutations. Using individual‐based simulations, we show that a complete arrest of XY recombination actually benefits females, not males. Male fitness is maximized at different XY recombination rates depending on SA selection, but never at zero XY recombination. This should consistently favour some level of XY recombination, which in turn generates a recombination load at sex‐linked SA genes. Hill–Robertson interferences with deleterious mutations also impede the differentiation of sex‐linked SA genes, to the point that males may actually fix feminized phenotypes when SA selection and XY recombination are low. We argue that sex chromosomes might not be a good localization for SA genes, and sex conflicts seem better solved through the differential expression of autosomal genes.     

A new strategy for estimating recombination fractions between dominant markers from an F2 population

Although most high-density linkage maps have been constructed from codominant markers such as single-nucleotide polymorphisms (SNPs) and microsatellites due to their high linkage information, dominant markers can be expected to be even more significant as proteomic technique becomes widely applicable to generate protein polymorphism data from large samples. However, for dominant markers, two possible linkage phases between a pair of markers complicate the estimation of recombination fractions between markers and consequently the construction of linkage maps. The low linkage information of the repulsion phase and high linkage information of coupling phase have led geneticists to construct two separate but related linkage maps. To circumvent this problem, we proposed a new method for estimating the recombination fraction between markers, which greatly improves the accuracy of estimation through distinction between the coupling phase and the repulsion phase of the linked loci. The results obtained from both real and simulated F2 dominant marker data indicate that the recombination fractions estimated by the new method contain a large amount of linkage information for constructing a complete linkage map. In addition, the new method is also applicable to data with mixed types of markers (dominant and codominant) with unknown linkage phase.     

Individual variation in recombination among human males.

Studies of recombination between the markers D6S291 and D6S109 in individuals by sperm typing provide direct evidence for significant variation in recombination among humans. A statistically significant difference in the recombination fraction (range 5.1%-11.2%) was detected among five donors. This variation could reflect polymorphisms in genes affecting recombination or in chromosome structure. Ignoring this variability in studies designed to examine the relationship between physical and genetic distances could lead to incorrect inferences. Individual variation in recombination makes it difficult to predict the recombination fraction for an interval in any particular individual. This could be important in certain genetic counseling situations.     

The appropriate threshold for declaring linkage when allowing sex-specific recombination rates.

In human genetics, two loci are declared to be linked when the lod score at the maximum likelihood recombination fraction theta exceeds the threshold of 3.0. Since recombination rates differ between the sexes, one can alternatively detect linkage by estimating separate recombination rates, theta m and theta f, for male and female meiosis and examining the corresponding sex-specific lod scores. The question arises: In order to maintain the same chance of falsely declaring linkage, what is the correct threshold for declaring linkage when sex-specific lod scores are used? We show here that the appropriate threshold is about 3.5. If the restriction that theta f greater than theta m is added, the appropriate threshold falls to about 3.25. We also discuss the relative efficiency of detecting linkage by using sex-specific and sex-averaged lod scores.     

The role of recombination and selection in the modifier theory of sex-ratio distortion

The equilibrium configurations for a two-locus multialle model of sex-linked meiotic drive are studied with regard to the recombination fraction:limit cycles can occur in the case of small recombination while stable equilibrium points associated with linkage equilibrium can exist for an intermediate range of recombination values depending on the equilibrium sex ratio, linkage disequilibrium at nearby equilibrium points taking turn with loser linkage. The evolutionary dynamics in two-locus sex-ratio distortion systems is enlightened: while equilibria with a sex ratio closer to 1/2 are more likely to be stable with respect to perturbations on the frequencies of sex-ratio distorters that are represented at equilibrium, such equilibria are also more vulnerable to the invasion of mutant distorters when there is some degree of linkage with the sex-determining locus. For X-linked multimodifier systems of sex-ratio distortion, differential fertilities and viabilities are incorporated and a maximum principle is suggested.     

Biased estimation of the recombination fraction using half-sib families and informative offspring

A maximum-likelihood method to estimate the recombination fraction and its sampling variance using informative and noninformative half-sib offspring is derived. Estimates of the recombination fraction are biased up to 20 cM when noninformative offspring are discarded. In certain scenarios, the sampling variance can be increased or reduced up to fivefold due to the bias in estimating the recombination fraction and the LOD score can be reduced up to 5 units when discarding noninformative offspring. Comparison of the estimates of recombination fraction, map distance, and LOD score when constructing a genetic map with 251 two-point linkage analyses and six families of Norwegian cattle was carried out to evaluate the implications of discarding noninformative offspring in practical situations. The average discrepancies in absolute value (average difference when using and neglecting noninformative offspring) were 0.0146, 1.64 cM, and 2.61 for the recombination fraction, map distance, and the LOD score, respectively. A method for simultaneous estimation of allele frequencies in the dam population and a transmission disequilibrium parameter is proposed. This method might account for the bias in estimating allele frequencies in the dam population when the half-sib offspring is selected for production traits.     

Sex differences in recombination

One of the stronger empirical generalizations to emerge from the study of genetic systems is that achiasmate meiosis, which has evolved 25–30 times, is always restricted to the heterogametic sex in dioecious species, usually the male. Here we collate data on quantitative sex differences in chiasma frequency from 54 species (4 hermaphroditic flatworms, 18 dioecious insects and vertebrates and 32 hermaphroditic plants) to test whether similar trends hold. Though significant sex differences have been observed within many species, only the Liliaceae show a significant sexual dimorphism in chiasma frequency across species, with more crossing over in embryo mother cells than in pollen mother cells; chiasma frequencies are unrelated to sex and gamety in all other higher taxa studied. Further, the magnitude of sexual dimorphism, independent of sign, does not differ among the three main ecological groups (dioecious animals, plants, and hermaphroditic animals), contrary to what would be expected if it reflected sex-specific selection on recombination. These results indicate that the strong trends for achiasmate meiosis do not apply to quantitative sex differences in recombination, and contradict theories of sex-specific costs and benefits. An alternative hypothesis suggests that sex differences may be more-or-less neutral, selection determining only the mean rate of recombination. While male and female chiasma frequencies are more similar than would be expected under complete neutrality, a less absolute form of the hypothesis is more difficult to falsify. In female mice the sex bivalent has more chiasmata for its length than the autosomes, perhaps compensating for the absence of recombination in males. Finally, we observe that chiasma frequencies in males and females are positively correlated across species, validating the use of only one sex in comparative studies of recombination.     

Sex-specific recombination rates in Parus major and P. caeruleus, an exception to Huxley's rule

Huxley's rule predicts lower recombination rates in the heterogametic sex than in the homogametic one. The genotyping of Parus major and P. caeruleus families at 8 microsatellite and 4 enzyme loci yielded contradicting data. Significant genotypic disequilibrium was observed between esterase-1, esterase-2 and esterase-3 in adults of P. major and between esterase-2/esterase-3 and esterase-2/microsatellite PK-12 in P. caeruleus. Support comes from linkage analyses of nuclear families. In P. major, the recombination rate of esterase-2/esterase -3 in males is significantly lower than in females (theta(male) = 0.076, theta(female) = 0.145). The opposite is found for the recombination rates of esterase-1/esterase-2 and esterase-2/esterase-3 in P. caeruleus (EST-1/EST-2: theta(female) = 0.218, theta(male) = 0.5, EST-2/EST-3: theta(female) = 0.109, theta(male) = 0.194). We conclude that the basis of differences in recombination rates cannot be heterogamety, per se, but must have multiple genetic causes including chromosomal rearrangments that have evolved after the cladogenesis of the two species.     

Mating-induced recombination in fruit flies

In traditional deterministic models the conditions for the evolution of sex and sexual behavior are limited because their benefits are context dependent. In novel and adverse environments both multiple mating and recombination can help generate gene combinations that allow for rapid adaptation. Mating frequency often increases in conditions in which recombination might be beneficial; therefore, increased sexual behavior might evolve to act as a cue that stimulates recombination. We conducted two experiments in the fruit fly, Drosophila melanogaster, using linked phenotypic markers to determine how recent bouts of additional mating affect female recombination rate. The first experiment examined the effect of additional mating, mating history, and age on female recombination rate. The second experiment assessed the effect of recent mating events on recombination rate. Together, the experiments suggest that each additional bout of mating temporarily increases female recombination rate. These findings imply that the conditions favoring the evolution of sexual reproduction and multiple mating behaviors are broader than currently appreciated.     

Phylogenetic evidence for recombination in dengue virus.

A split decomposition analysis of dengue (DEN) virus gene sequences revealed extensive networked evolution, indicative of recombination, among DEN-1 strains but not within serotypes DEN-2, DEN-3, or DEN-4. Within DEN-1, two viruses sampled from South America in the last 10 years were identified as recombinants. To map the breakpoints and test their statistical support, we developed a novel maximum likelihood method. In both recombinants, the breakpoints were found to be in similar positions, within the fusion peptide of the envelope protein, demonstrating that a single recombination event occurred prior to the divergence of these two strains. This is the first report of recombination in natural populations of dengue virus.     

The incorporation of prior genomic information does not necessarily improve the performance of Bayesian linkage methods: an example involving sex-specific recombination and the two-point PPL

OBJECTIVE: We continue statistical development of the posterior probability of linkage (PPL). We present a two-point PPL allowing for unequal male and female recombination fractions, thetaM and thetaF, and consider alternative priors on thetaM, thetaF. METHODS: We compare the sex-averaged PPL (PPLSA), assuming thetaM = thetaF, to the sex-specific PPL (PPLSS) in (thetaM, thetaF), in a series of simulations; we also compute the PPLSS using alternative priors on (thetaM, thetaF). RESULTS: The PPLSS based on a prior that ignores prior genomic information on sex specific recombination rates performs essentially identically to the PPLSA, even in the presence of large thetaM, thetaF differences. Moreover, adaptively skewing the prior, to incorporate (correct) genomic information on thetaM, thetaF differences, actually worsens performance of the PPLSS. We demonstrate that this has little to do with the PPLSS per se, but is rather due to extremely high levels of variability in the location of the maximum likelihood estimates of (thetaM, thetaF) in realistic data sets. CONCLUSIONS: Incorporating (correct) prior genomic information is not always helpful. We recommend that the PPLSA be used as the standard form of the PPL regardless of the sex-specific recombination rates in the region of the marker in question.     

Deleterious effects of recombination and possible nonrecombinatorial advantages of sex in a fungal model

Why sexual reproduction is so prevalent in nature remains a major question in evolutionary biology. Most of the proposed advantages of sex rely on the benefits obtained from recombination. However, it is still unclear whether the conditions under which these recombinatorial benefits would be sufficient to maintain sex in the short term are met in nature. Our study addresses a largely overlooked hypothesis, proposing that sex could be maintained in the short term by advantages due to functions linked with sex, but not related to recombination. These advantages would be so essential that sex could not be lost in the short term. Here, we used the fungus Aspergillus nidulans to experimentally test predictions of this hypothesis. Specifically, we were interested in (i) the short‐term deleterious effects of recombination, (ii) possible nonrecombinatorial advantages of sex particularly through the elimination of mutations and (iii) the outcrossing rate under choice conditions in a haploid fungus able to reproduce by both outcrossing and haploid selfing. Our results were consistent with our hypotheses: we found that (i) recombination can be strongly deleterious in the short term, (ii) sexual reproduction between individuals derived from the same clonal lineage provided nonrecombinatorial advantages, likely through a selection arena mechanism, and (iii) under choice conditions, outcrossing occurs in a homothallic species, although at low rates.     

iRSpot-PseDNC: identify recombination spots with pseudo dinucleotide composition

Meiotic recombination is an important biological process. As a main driving force of evolution, recombination provides natural new combinations of genetic variations. Rather than randomly occurring across a genome, meiotic recombination takes place in some genomic regions (the so-called ‘hotspots’) with higher frequencies, and in the other regions (the so-called ‘coldspots’) with lower frequencies. Therefore, the information of the hotspots and coldspots would provide useful insights for in-depth studying of the mechanism of recombination and the genome evolution process as well. So far, the recombination regions have been mainly determined by experiments, which are both expensive and time-consuming. With the avalanche of genome sequences generated in the postgenomic age, it is highly desired to develop automated methods for rapidly and effectively identifying the recombination regions. In this study, a predictor, called ‘iRSpot-PseDNC’, was developed for identifying the recombination hotspots and coldspots. In the new predictor, the samples of DNA sequences are formulated by a novel feature vector, the so-called ‘pseudo dinucleotide composition’ (PseDNC), into which six local DNA structural properties, i.e. three angular parameters (twist, tilt and roll) and three translational parameters (shift, slide and rise), are incorporated. It was observed by the rigorous jackknife test that the overall success rate achieved by iRSpot-PseDNC was >82% in identifying recombination spots in Saccharomyces cerevisiae, indicating the new predictor is promising or at least may become a complementary tool to the existing methods in this area. Although the benchmark data set used to train and test the current method was from S. cerevisiae, the basic approaches can also be extended to deal with all the other genomes. Particularly, it has not escaped our notice that the PseDNC approach can be also used to study many other DNA-related problems. As a user-friendly web-server, iRSpot-PseDNC is freely accessible at http://lin.uestc.edu.cn/server/iRSpot-PseDNC.