Genetic identity between populations when mutation rates vary within and across loci

A formula is derived for the probability that two genes taken at random from the same locus in two populations isolated at time t ago are of the same allelic type. The model assumed is a neutral one where there are possibly different mutation rates between different alleles. Inequalities are derived for this probability. A particular result is that for a fixed overall mutation rate, the probability is least for the infinite alleles model. Inequalities and approximations are found for Nei's genetic identity at one locus when mutation rates vary, and also for the identity across loci when the overall mutation rates per locus vary. Genetic identity at the molecular level is considered and a probability generating function found for the number of segregating sites between two randomly chosen gametes from two divergent populations, under various models.     

Selection in complex genetic systems IV. Multiple alleles and interactions between two loci

Summary A symmetric viability model for two loci with two alleles at one locus and m alleles at the other is suggested and analyzed. The analysis of the equilibria is complete if the two loci are absolutely linked, while if recombination is allowed the analysis is incomplete. The dynamics of the mode! resemble those of the two locus two allele model, namely that for loose linkage there will be no correlation between the loci and for tight linkage there may be strong correlation. The major caveats to this are: 1. The equilibria stable for tight linkage may belong to an array of different structures dependent on the selection and the number of alleles. 2. If both loci are overdominant in viability, the stable equilibria always contain all alleles segregating in the population; otherwise, the stable equilibria may only be two locus two allele high complementarity equilibria for tight linkage. 3. For intermediate linkage values and special selection values the boundary two locus two allele high complementarity equilibria may be stable simultaneously with the totally polymorphic central point at which there is no association between the loci.Dedicated to the memory of Ove Frydenberg.Research supported in part by a grant from the Danish Natural Science Research Council, a grant from National Science Foundation, U.S.A., and by USPHS grant NIH 10452-09-11.     

BoLA class I charge heterogeneity reflects the expression of more than two loci

Internationally recognized allo-antisera in lymphocyte microcytotoxicity assays are thought to detect allelic products of a single highly polymorphic class I locus. A recent report suggested that two bovine lymphocyte antigen (BoLA) class I loci are expressed at the protein level. However, 1D-IEF analysis of BoLA class I molecules reveals multi-band patterns which cannot be reconciled with the reported number of loci. The aim of this study was to investigate the origins of the charge diversity of BoLA class I molecules observed using 1D-IEF. BoLA class I molecules appear to be glycosy-lated at a single N-linked position with a complex type carbohydrate moiety which has up to three terminal sialic acid residues. Class I molecules immunoprecipitated from resting bovine PBL are not phosphorylated. Neither modification is responsible for the observed charge heterogeneity. Peptide mapping reveals that different BoLA charge variants have distinct digestion patterns. Furthermore, a number of different polypeptides are associated with each serological specificity. These polypeptides appear to be encoded by different loci which exist in linkage disequilibrium. The number of charge variants with different peptide maps indicates that the BoLA system has a minimum of three class I loci expressed at the protein level.     

Two-locus disease models with two marker loci: the power of affected-sib-pair tests.

Recently, Schork et al. found that two-trait-locus, two-marker-locus (parametric) linkage analysis can provide substantially more linkage information than can standard one-trait-locus, one-marker-locus methods. However, because of the increased burden of computation, Schork et al. do not expect that their approach will be applied in an initial genome scan. Further, the specification of a suitable two-locus segregation model can be crucial. Affected-sibpair tests are computationally simple and do not require an explicit specification of the disease model. In the past, however, these tests mainly have been applied to data with a single marker locus. Here, we consider sib-pair tests that make it possible to analyze simultaneously two marker loci. The power of these tests is investigated for different (epistatic and heterogeneous) two-trait-locus models, each trait locus being linked to one of the marker loci. We compare these tests both with the test that is optimal for a certain model and with the strategy that analyzes each marker locus separately. The results indicate that a straightforward extension of the well-known mean test for two marker loci can be much more powerful than single-marker-locus analysis and that is power is only slightly inferior to the power of the optimal test.     

Gamete frequencies at two sex-linked loci in random mating age-structured populations

A study is made of the change with time of frequencies of gametic types with one or two sex-linked loci in an infinite random mating age-structured population. Recurrence equations for these gamete frequencies are derived under the assumptions that all matings of adults are equally fertile and the number of matings at any time is proportional to the number of mature females at that time. These generalize others in the literature. It is shown that gamete frequencies approach their limiting values at geometric rates in the long run. This implies that the asymptotic behavior of the gamete frequencies is like what it is in populations with discrete generations if the unit of time is replaced by an appropriately chosen generation interval. With either one locus or two loci, the generation interval is bounded below by an analogous measure from standard demographic theory. This result also holds when there are two autosomal loci. In numerical examples from both this paper and a previous one by Pollak and Callanan, the lower bound is a good estimate of the generation interval.     

Genomic imprinting of two antagonistic loci

We present a model that considers the coevolution of genomic imprinting at a growth factor locus and an antagonistic growth suppressor locus. With respect to the two loci considered independently, our model makes the familiar predictions that an imprinted growth factor locus will only be expressed from the paternally derived allele and an imprinted growth suppressor locus only from the maternally derived allele. In addition, our coevolutionary model allows us to make predictions regarding the sequence of evolutionary events necessary for generating such a system. We conclude that imprinting at the growth factor locus preceded the evolution of growth suppressor function at the second locus, which in turn preceded imprinting at that locus. We then discuss the consistency of these predictions with currently available comparative data on the insulin-like growth factor 2 insulin-like growth factor 2 receptor system of mammals.     

An analysis of microsatellite loci in Arabidopsis thaliana: mutational dynamics and application

Microsatellite loci are among the most commonly used molecular markers. These loci typically exhibit variation for allele frequency distribution within a species. However, the factors contributing to this variation are not well understood. To expand on the current knowledge of microsatellite evolution, 20 microsatellite loci were examined for 126 accessions of the flowering plant, Arabidopsis thaliana. Substantial variability in mutation pattern among loci was found, most of which cannot be explained by the assumptions of the traditional stepwise mutation model or infinite alleles model. Here it is shown that the degree of locus diversity is strongly correlated with the number of contiguous repeats, more so than with the total number of repeats. These findings support a strong role for repeat disruptions in stabilizing microsatellite loci by reducing the substrate for polymerase slippage and recombination. Results of cluster analyses are also presented, demonstrating the potential of microsatellite loci for resolving relationships among accessions of A. thaliana.     

Analysis of two additional loci in Neurospora crassa related to Spore killer-2

Two new loci found in one strain of Neurospora crassa (P2604) collected in Malaya are related to the meiotic drive system Spore killer Sk-2. Sk-2 was found in Neurospora intermedia and introgressed into N. crassa. P2604 showed high resistance to killing when crossed to Sk-2. This resistance was found to be linked to, but not allelic to, resistance locus r(Sk-2) on LGIIIL. Analysis showed that the high resistance phenotype of P2604 requires resistance alleles at two different loci on LGIIIR. Strains carrying a resistance allele at only the proximal or the distal locus, respectively, were obtained and intercrossed. Highly resistant strains were obtained by rejoining the two genes. The proximal locus alone confers a low level of resistance. This locus was named pr(Sk-2) for partial resistance to Sk-2. The distal locus was named mod(pr) because its only known phenotype is to modify pr(Sk-2).     

Allelic variation at (TAA)n microsatellite loci in a world collection of chickpea (Cicer arietinum L.) germplasm

A set of 12 randomly selected (TAA)_n microsatellite loci of the cultivated chickpea (Cicer arietinum L.) were screened in a worldwide sample comprising 72 landraces, four improved cultivars and two wild species of the primary gene pool (C. reticulatum and C. echinosperum) to determine the level and pattern of polymorphism in these populations. A single fragment was amplified from all the accessions with each of 12 sequence-tagged microsatellite site markers, except for one locus where no fragment was obtained from either of the two wild species. There was a high degree of intraspecific polymorphism at these microsatellite loci, although isozymes, conventional RFLPs and RAPDs show very little or no polymorphism. Overall, the repeat number at a locus (excluding null alleles) ranged from 7 to 42. The average number of alleles per locus was 14.1 and the average genetic diversity was 0.86. Based on the estimates obtained, 11 out of the 12 frequency distributions of alleles at the loci tested can be considered to be non-normal. A significant positive correlation between the average number of repeats (size of the locus) and the amount of variation was observed, indicating that replication slippage may be the molecular mechanism involved in generation of variability at the loci. A comparison between the infinite allele and stepwise mutation models revealed that for 11 out of the 12 loci the number of alleles observed fell in between the values predicted by the two models. Phylogenetic analysis of microsatellite polymorphism in C. arietinum showed no relationship between accession and geographic origin, which is compatible with the recent expansion of this crop throughout the world. Received: 18 September 1998 / Accepted: 2 December 1998     

Nucleotide diversity at two phytochrome loci along a latitudinal cline in Pinus sylvestris

Forest tree species provide many examples of well-studied adaptive differentiation, where the search for the underlying genes might be possible. In earlier studies and in our common conditions in a greenhouse, northern populations set bud earlier than southern ones. A difference in latitude of origin of one degree corresponded to a change of 1.4 days in number of days to terminal bud set of seedlings. Earlier physiological and ecological genetics work in conifers and other plants have suggested that such variation could be governed by phytochromes. Nucleotide variation was examined at two phytochrome loci (PHYP and PHYO, homologues of the Arabidopsis thaliana PHYB and PHYA, respectively) in three populations: northern Finland, southern Finland and northern Spain. In our samples of 12-15 sequences (2980 and 1156 base pairs at the two loci) we found very low nonsynonymous variation; pi was 0.0003 and 0.0002 at PHYP and PHYO loci, respectively. There was no functional differentiation between populations at the photosensory domains of either locus. The overall silent variation was also low, only 0.0024 for the PHYP locus. The low estimates of silent variation are consistent with the estimated low synonymous substitution rates between Pinus sylvestris and Picea abies at the PHYO locus. Despite the low level of nucleotide variation, haplotypic diversity was relatively high (0.42 and 0.41 for fragments of 1156 nucleotides) at the two loci.     

Application of logistic regression to case-control association studies involving two causative loci

Models in which two susceptibility loci jointly influence the risk of developing disease can be explored using logistic regression analysis. Comparison of likelihoods of models incorporating different sets of disease model parameters allows inferences to be drawn regarding the nature of the joint effect of the loci. We have simulated case-control samples generated assuming different two-locus models and then analysed them using logistic regression. We show that this method is practicable and that, for the models we have used, it can be expected to allow useful inferences to be drawn from sample sizes consisting of hundreds of subjects. Interactions between loci can be explored, but interactive effects do not exactly correspond with classical definitions of epistasis. We have particularly examined the issue of the extent to which it is helpful to utilise information from a previously identified locus when investigating a second, unknown locus. We show that for some models conditional analysis can have substantially greater power while for others unconditional analysis can be more powerful. Hence we conclude that in general both conditional and unconditional analyses should be performed when searching for additional loci.     

Sojourn times and substitution rate at overdominant and linked neutral loci

The sojourn times until fixation of an overdominant allele were investigated based on the diffusion equation. Furthermore, the rate of accumulation of mutations, or the substitution rate, was predicted from the mean extinction time of a common overdominant allele. The substitution rate calculated theoretically agreed well with that determined by computer simulation. Overdominant selection enhances the polymorphism at linked loci, while its effect on the sojourn times and the substitution rate at linked loci has not been studied yet. To solve these problems, a model that assumed two linked loci, each with infinite alleles, was examined by computer simulation. A decrease in the recombination rate between two loci markedly changed the distribution of sojourn times of a neutral allele. Although overdominant selection obviously increased the sojourn times and the polymorphism at a linked locus, the rate of nucleotide substitution at the neutral locus was not influenced significantly even if complete linkage was assumed. These results suggest that, in regions containing overdominant genes, linked neutral loci will exhibit elevated levels of polymorphism, but their rate of molecular evolution remains that predicted by neutral theory.     

Isolation of microsatellite loci in the Capricorn silvereye,Zosterops lateralis chlorocephalus (Aves: Zosteropidae)

The Capricorn silvereye (Zosterops lateralis chlorocephalus) is ideally suited to investigating the genetic basis of body size evolution. We have isolated and characterized a set of microsatellite markers for this species. Seven out of 11 loci were polymorphic. The number of alleles detected ranged from two to five and observed heterozygosities between 0.12 and 0.67. One locus, ZL49, was found to be sex‐linked. This moderate level of diversity is consistent with that expected in an isolated, island population.     

Robust multipoint simultaneous identical-by-descent mapping for two linked loci

A challenging issue in genetic mapping of complex human diseases is localizing disease susceptibility genes when the genetic effects are small to moderate. There are greater complexities when multiple loci are linked to a chromosomal region. Liang et al. [Hum Hered 2001;51:64-78] proposed a robust multipoint method that can simultaneously estimate both the position of a trait locus and its effect on disease status by using affected sib pairs (ASPs). Based on the framework of generalized estimating equations (GEEs), the estimate and standard error of the position of a trait locus are robust to different genetic models. To utilize other relative pairs collected in pedigree data, Schaid et al. [Am J Hum Genet 2005;76:128-138] extended Liang's method to various types of affected relative pairs (ARPs) by two approaches: unconstrained and constrained methods. However, the above methods are limited to situations in which only one trait locus exists on the chromosome of interest. The mean functions are no longer correctly specified when there are multiple causative loci linked to a chromosomal region. To overcome this, Biernacka et al. [Genet Epidemiol 2005;28:33-47] considered the multipoint methods for ASPs to allow for two linked disease genes. We further generalize the approach to cover other types of ARPs. To reflect realistic situations for complex human diseases, we set modest sizes of genetic effects in our simulation. Our results suggest that several hundred independent pedigrees are needed, and markers with high information, to provide reliable estimates of trait locus positions and their confidence intervals. Bootstrap resampling can correct the downward bias of the robust variance for location estimates. These methods are applied to a prostate cancer linkage study on chromosome 20 and compared with the results for the one-locus model [Am J Hum Genet 2005;76:128-138]. We have implemented the multipoint IBD mapping for one and two linked loci in our software GEEARP, which allows analyses for five general types of ARPs.     

Linkage analysis of "necessary" disease loci versus "susceptibility" loci.

The association of some diseases with specific alleles of certain genetic markers has been difficult to explain. Several explanations have been proposed for the phenomenon of association, e.g. the existence of multiple, interacting genes (epistasis) or a disease locus in linkage disequilibrium with the marker locus. One might suppose that when marker data from families with associated diseases are analyzed for linkage, the existence of the association would assure that linkage will be found, and found at a tight recombination fraction. In fact, however, linkage analyses of some diseases associated with HLA, as well as diseases associated with alleles at other loci located throughout the genome, show significant evidence against linkage, and others show loose linkage, to the puzzlement of many researchers. In part, the puzzlement arises because linkage analysis is ideal for looking for loci that are necessary, even if not sufficient, for disease expression but may be much less useful for finding loci that are neither necessary nor sufficient for disease expression (so-called susceptibility loci). This work explores what happens when one looks for linkage to susceptibility loci. A susceptibility locus in this case means that the allele increases risk but is neither necessary nor sufficient for disease expression. It might be either an allele at the marker locus itself that is increasing susceptibility or an allele at a locus in linkage disequilibrium with the marker. This work uses computer simulation to examine how linkage analyses behave when confronted with data from such a model.(ABSTRACT TRUNCATED AT 250 WORDS)     

How to model a complex trait. 2. Analysis with two disease loci

Complex traits are often governed by more than one trait locus. The first step towards an adequate model for such diseases is a linkage analysis with two trait loci. Such an analysis can be expected to have higher power to detect linkage than a standard single-trait-locus linkage analysis. However, it is crucial to accurately specify the parameters of the two-locus model. Here, we recapitulate the general two-locus model with and without genomic imprinting. We relate heterogeneity, multiplicative, and additive two-locus models to biological or pathophysiological mechanisms, and give the corresponding averaged ("best-fitting") single-trait-locus models for each of the two loci. Furthermore, we derive the two-locus penetrances from the averaged single-locus models, under the assumption of one of the three model classes mentioned above. Using these formulae, if the best-fitting single-locus models are available, investigators may perform a two-trait-locus linkage analysis under a realistic model. This procedure will maximize the power to detect linkage for traits which are governed by two or more loci, and lead to more accurate estimates of the disease-locus positions.     

马尾松和黄山松两个核基因位点的群体遗传多样性和种间分化

利用两个核基因座位C3H和GI, 对重叠分布于中国东南部的两个松属(Pinus)物种马尾松(P. massoniana)和黄山松(P. hwangshanensis)的22个群体88个个体进行了遗传多样性和种间分化模式研究。在这两个核基因座位上, 两种植物都表现出较低的核苷酸多样性水平(马尾松π_sil = 0.001 71; 黄山松π_sil = 0.003 40), 但是马尾松要显著低于黄山松; 在种内分化水平上, 马尾松的种内遗传分化也明显低于黄山松(马尾松F_ST = 0.059; 黄山松F_ST = 0.339)。这可能是由于黄山松的海拔分布高于马尾松, 而高海拔分布使黄山松的分布区域更加片段化, 促使其形成较高的种内遗传多样性和遗传分化。分子变异分析(AMOVA)发现, 两物种基于两个核基因座位的种间差异为48.86%, 而GI基因座位上的种间差异明显高于C3H座位(GI: 77.24%, C3H: 20.48%), 同时, 基因谱系显示两物种的共享单倍型仅在C3H座位上存在。结合这两个基因的功能, 推测GI基因可能在物种形成过程中受到了一定的选择压力, 因为GI基因参与调控植物的开花时间, 而C3H与木质素表达水平的调控有关。不同的选择压力使得GI的进化速度相对较快, 从而加速了黄山松和马尾松的物种分化。     

The deviation from linkage equilibrium with multiple loci varying in a stepping-stone cline

The balance between the creation of associations between alleles at different loci by immigration and the convergence to linkage equilibrium due to the recombination process is studied in a theoretical model. The geographical structure of the model is a stepping-stone chain of populations linking two genetically constant source populations. The model assumes an arbitrary number of autosomal loci and considers genetic variation (two alleles at each locus) that is not subject to natural selection. The gene frequencies at each locus will then show a linear cline through the stepping-stone chain of populations. The deviation from linkage equilibrium through the stepping-stone cline is characterized by an equation for linear measures that provide the linkage disequilibrium measures for a given set of loci in terms of the gene frequencies and the linkage disequilibria in the source populations and in terms of the linkage disequilibrium measures through the cline for lower numbers of loci. Numerical examples of this iterative solution are given, and it is shown that the build-up of the higher order Bennett-disequilibria through the cline is considerably more pronounced than the build-up of two-locus disequilibria.     

On the prediction of simultaneous inbreeding coefficients at multiple loci

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.