Mapping quantitative trait loci underlying triploid endosperm traits

Endosperm, which is derived from two polar nuclei fusing with one sperm, is a triploid tissue in cereals. Endosperm tissue determines the grain quality of cereals. Improving grain quality is one of the important breeding objectives in cereals. However, current statistical methods for mapping quantitative trait loci (QTL) under diploid genetic control have not been effective for dealing with endosperm traits because of the complexity of their triploid inheritance. In this paper, we derive for the first time the conditional probabilities of F(3) endosperm QTL genotypes given different flanking marker genotypes in F(2) plants. Using these probabilities, we develop a multiple linear regression method implemented via the iteratively reweighted least-squares (IRWLS) algorithm and a maximum likelihood method (ML) implemented via the expectation-maximization (EM) algorithm to map QTL underlying endosperm traits. We use the mean value of endosperm traits of F(3) seeds as the dependent variable and the expectations of genotypic indicators for additive and dominance effect of a putative QTL flanked by a pair of markers as independent variables for IRWLS mapping. However, if an endosperm trait is measured quantitatively using a single endosperm sample, the ML mapping method can be used to separate the two dominance effects. Efficiency of the methods is verified through extensive Monte Carlo simulation studies. Results of simulation show that the proposed methods provide accurate estimates of both the QTL effects and locations with very high statistical power. With these methods, we are now ready to map endosperm traits, as we can for regular quantitative trait under diploid control.     

Informativeness of genetic markers for pairwise relationship and relatedness inference

Measuring the information content of markers in relationship/relatedness inferences is important in selecting highly informative markers to attain a given statistical power with the minimal genotyping effort. Using information-theoretic principles, I introduce the informativeness for relationship (I(R)) and the informativeness for relatedness (I(r)) to measure the amount of information provided by markers in inferring pairwise relationships (R) and relatedness (r), respectively. I also propose a fast and accurate algorithm to calculate the power (PW(R)) of a set of markers in differentiating two candidate relationships, and the reciprocal of the mean squared deviations of relatedness estimates (RMSD) to measure the amount of information of markers actually used by an estimator in estimating relatedness. All of the four measurements (I(R), I(r), PW(R), RMSD) apply to dominant and codominant markers, haploid and diploid individuals, and take into account of mutations and typing errors in data. The statistical properties of the four measurements and their relationships are investigated analytically and are examined by applying these methods to simulated and empirical data.     

Multilocus estimation of pairwise relatedness with dominant markers

Estimators for pairwise relatedness designed for dominant markers are derived, based on a genetic model that accounts for the full structure of pairwise relatedness between two individuals at a diploid locus with dominance. They jointly estimate 'relatedness' and 'fraternity', in which case the estimators are inherently multilocus, as at least two loci of differing gene frequency are required. Extensions to cases of zero fraternity and isolation by distance (inbreeding) are also examined. Properties of estimators are examined by simulation and compared to the estimator of Hardy. The most statistical power for pairwise relatedness occurs when roughly half of individuals are the recessive phenotype. Estimation procedures are implemented in the computer program mark.     

A Fisher scoring algorithm for the weighted regression method of QTL mapping

An improved weighted least square (LS) method for quantitative trait loci (QTL) mapping using the estimating equation (EE) algorithm was developed recently. The method is more efficient than both the LS and the weighted LS methods and slightly less efficient than the mixture model maximum likelihood (ML) method. The iteration process of the EE algorithm is implicit. We developed a Fisher-scoring algorithm for the weighted LS method. The iteration process is explicit and easy to program. In addition, the method automatically provides an approximate variance-covariance matrix for the estimated QTL parameters as a by-product of the iteration process. As a consequence, a W-test statistic can be used for testing the significance of QTL. To compare the Fisher scoring algorithm with the expectation maximization (EM)-based ML method, we also developed a slightly simplified method to compute the variance-covariance matrix of the estimated parameters under the EM algorithm.     

Mapping viability loci using molecular markers

In genetic mapping experiments, some molecular markers often show distorted segregation ratios. We hypothesize that these markers are linked to some viability loci that cause the observed segregation ratios to deviate from Mendelian expectations. Although statistical methods for mapping viability loci have been developed for line-crossing experiments, methods for viability mapping in outbred populations have not been developed yet. In this study, we develop a method for mapping viability loci in outbred populations using a full-sib family as an example. We develop a maximum likelihood (ML) method that uses the observed marker genotypes as data and the proportions of the genotypes of the viability locus as parameters. The ML solutions are obtained via the expectation-maximization algorithm. Application and efficiencies of the method are demonstrated and tested using a set of simulated data. We conclude that mapping viability loci can be accomplished using similar statistical techniques used in quantitative trait locus mapping for quantitative traits.     

genclone: a computer program to analyse genotypic data,test for clonality and describe spatial clonal organization

genclone 1.0 is designed for studying clonality and its spatial components using genotype data with molecular markers from haploid or diploid organisms. genclone 1.0 performs the following tasks. (i) discriminates distinct multilocus genotypes (MLGs), and uses permutation and resampling approaches to test for the reliability of sets of loci and sampling units for estimating genotypic and genetic diversity (a procedure also useful for nonclonal organisms); (ii) computes statistics to test for clonal propagation or clonal identity of replicates; (iii) computes various indices describing genotypic diversity; and (iv) summarizes the spatial organization of MLGs with adapted spatial autocorrelation methods and clonal subrange estimates.     

identix,a software to test for relatedness in a population using permutation methods

The computer program identix estimates relatedness in natural populations using multilocus genotypic data. Queller & Goodnight's (1989) and Lynch & Ritland's (1999) estimators of pairwise relatedness are implemented, as well as the identity index of Mathieu et al. (1990). Estimates of the confidence intervals around these pairwise values are also provided. The null hypothesis of no relatedness (multilocus genotypes are independent draws from a panmictic population) is tested using a permutation method that compares the observed distribution of the moments of pairwise relatedness coefficients to that expected in unstructured population.     

Definition and Properties of Disequilibrium Statistics for Associations between Nuclear and Cytoplasmic Genotypes

We define and establish the interrelationships of four components of statistical association between a diploid nuclear gene and a uniparentally transmitted, haploid cytoplasmic gene: an allelic (gametic) disequilibrium (D), which measures associations between alleles at the two loci; and three genotypic disequilibria (D1, D2, D3), which measure associations between two cytotypes and the three respective nuclear backgrounds. We also consider an alternative set of measures, including D and the residual disequilibrium (d). The dynamics of these disequilibria are then examined under three conventional models of the mating system: (1) random mating; (2a) assortative mating without dominance (the "mixed-mating model"); and (2b) assortative mating with dominance ("O'Donald's model"). The trajectories of gametic disequilibria are similar to those for pairs of unlinked nuclear loci. The dynamics of genotypic disequilibria exhibit a variety of behaviors depending on the model and the initial conditions. Procedures for statistical estimation of cytonuclear disequilibria are developed and applied to several real and hypothetical data sets. Special attention is paid to the biological interpretations of various categories of allelic and genotypic disequilibria in hybrid zones. Genetic systems for which these statistics might be appropriate include nuclear genotype frequencies in conjunction with those for mitochondrial DNA, chloroplast DNA, or cytoplasmically inherited microorganisms.     

Demerelate: calculating interindividual relatedness for kinship analysis based on codominant diploid genetic markers using R

The Demerelate package offers algorithms to calculate different interindividual relatedness measurements. Three different allele sharing indices, five pairwise weighted estimates of relatedness and four pairwise weighted estimates with sample size correction are implemented to analyse kinship structures within populations. Statistics are based on randomization tests; modelling relatedness coefficients by logistic regression, modelling relatedness with geographic distance by mantel correlation and comparing mean relatedness between populations using pairwise t‐tests. Demerelate provides an advance on previous software packages by including some estimators not available in R to date, along with F_IS, as well as combining analysis of relatedness and spatial structuring. An UPGMA tree visualizes genetic relatedness among individuals. Additionally, Demerelate summarizes information on data sets (allele vs. genotype frequencies; heterozygosity; F_IS values). Demerelate is – to our knowledge – the first R package implementing basic allele sharing indices such as Blouin's M_xy relatedness, the estimator of Wang corrected for sample size (wang_xy), estimators based on Morans I adapted to genetic relatedness as well as combining all estimators with geographic information. The R environment enables users to better understand relatedness within populations due to the flexibility of Demerelate of accepting different data sets as empirical data, reference data, geographical data and by providing intermediate results. Each statistic and tool can be used separately, which helps to understand the suitability of the data for relatedness analysis, and can be easily implemented in custom pipelines.     

Experimental support for multiple-locus complementary sex determination in the parasitoid Cotesia vestalis

Despite its fundamental role in development, sex determination is highly diverse among animals. Approximately 20% of all animals are haplodiploid, with haploid males and diploid females. Haplodiploid species exhibit diverse but poorly understood mechanisms of sex determination. Some hymenopteran insect species exhibit single-locus complementary sex determination (sl-CSD), where heterozygosity at a polymorphic sex locus initiates female development. Diploid males are homozygous at the sex locus and represent a genetic load because they are inviable or sterile. Inbreeding depression associated with CSD is therefore expected to select for other modes of sex determination resulting in fewer or no diploid males. Here, we investigate an alternative, heretofore hypothetical, mode of sex determination: multiple-locus CSD (ml-CSD). Under ml-CSD, diploid males are predicted to develop only from zygotes that are homozygous at all sex loci. We show that inbreeding for eight generations in the parasitoid wasp Cotesia vestalis leads to increasing proportions of diploid males, a pattern that is consistent with ml-CSD but not sl-CSD. The proportion of diploid males (0.27 ± 0.036) produced in the first generation of inbreeding (mother–son cross) suggests that two loci are likely involved. We also modeled diploid male production under CSD with three linked loci. Our data visually resemble CSD with linked loci because diploid male production in the second generation was lower than that in the first. To our knowledge, our data provide the first experimental support for ml-CSD.     

Estimating heritabilities and genetic correlations with marker-based methods: an experimental test in Mimulus guttatus

The calculation of heritabilities and genetic correlations, which are necessary for predicting evolutionary responses, requires knowledge about the relatedness between individuals. This information is often not directly available, especially not for natural populations, but can be inferred by using molecular markers such as allozymes. Several methods based on inferred relatedness from marker data have been developed to estimate heritabilities and genetic correlations in natural populations. Most methods use maximum-likelihood procedures to assign pairs or groups of individuals to predefined discrete relatedness classes (e.g., half sibs and unrelated individuals). The Ritland method, on the other hand, uses method of moments estimators to estimate pairwise relatedness among individuals as continuous values. We tested both the Ritland method and a maximum-likelihood method by applying them to a greenhouse population consisting of seed families of the herb Mimulus guttatus and comparing the results to the ones from a frequently used standard method based on half-sib families. Estimates of genetic correlations were far from accurate, especially when we used the Ritland method. However, this study shows that even with a few variable allozyme loci, it is possible to get qualitatively good indications about the presence of heritable genetic variation from marker-based methods, even though both methods underestimated it.     

Relative efficiencies of the maximum-likelihood, neighbor-joining, and maximum-parsimony methods when substitution rate varies with site

The relative efficiencies of the maximum-likelihood (ML), neighbor- joining (NJ), and maximum-parsimony (MP) methods in obtaining the correct topology and in estimating the branch lengths for the case of four DNA sequences were studied by computer simulation, under the assumption either that there is variation in substitution rate among different nucleotide sites or that there is no variation. For the NJ method, several different distance measures (Jukes-Cantor, Kimura two- parameter, and gamma distances) were used, whereas for the ML method three different transition/transversion ratios (R) were used. For the MP method, both the standard unweighted parsimony and the dynamically weighted parsimony methods were used. The results obtained are as follows: (1) When the R value is high, dynamically weighted parsimony is more efficient than unweighted parsimony in obtaining the correct topology. (2) However, both weighted and unweighted parsimony methods are generally less efficient than the NJ and ML methods even in the case where the MP method gives a consistent tree. (3) When all the assumptions of the ML method are satisfied, this method is slightly more efficient than the NJ method. However, when the assumptions are not satisfied, the NJ method with gamma distances is slightly better in obtaining the correct topology than is the ML method. In general, the two methods show more or less the same performance. The NJ method may give a correct topology even when the distance measures used are not unbiased estimators of nucleotide substitutions. (4) Branch length estimates of a tree with the correct topology are affected more easily than topology by violation of the assumptions of the mathematical model used, for both the ML and the NJ methods. Under certain conditions, branch lengths are seriously overestimated or underestimated. The MP method often gives serious underestimates for certain branches. (5) Distance measures that generate the correct topology, with high probability, do not necessarily give good estimates of branch lengths. (6) The likelihood-ratio test and the confidence-limit test, in Felsenstein's DNAML, for examining the statistical of branch length estimates are quite sensitive to violation of the assumptions and are generally too liberal to be used for actual data. Rzhetsky and Nei's branch length test is less sensitive to violation of the assumptions than is Felsenstein's test. (7) When the extent of sequence divergence is < or = 5% and when > or = 1,000 nucleotides are used, all three methods show essentially the same efficiency in obtaining the correct topology and in estimating branch lengths.(ABSTRACT TRUNCATED AT 400 WORDS)      

Mating patterns in a hybrid zone of fire-bellied toads (Bombina): inferences from adult and full-sib genotypes

We present two novel methods to infer mating patterns from genetic data. They differ from existing statistical methods of parentage inference in that they apply to populations that deviate from Hardy-Weinberg and linkage equilibrium, and so are suited for the study of assortative mating in hybrid zones. The core data set consists of genotypes at several loci for a number of full-sib clutches of unknown parentage. Our inference is based throughout on estimates of allelic associations within and across loci, such as heterozygote deficit and pairwise linkage disequilibrium. In the first method, the most likely parents of a given clutch are determined from the genotypic distribution of the associated adult population, given an explicit model of nonrandom mating. This leads to estimates of the strength of assortment. The second approach is based solely on the offspring genotypes and relies on the fact that a linear relation exists between associations among the offspring and those in the population of breeding pairs. We apply both methods to a sample from the hybrid zone between the fire-bellied toads Bombina bombina and B. variegata (Anura: Disco glossidae) in Croatia. Consistently, both approaches provide no evidence for a departure from random mating, despite adequate statistical power. Instead, B. variegata-like individuals among the adults contributed disproportionately to the offspring cohort, consistent with their preference for the type of breeding habitat in which this study was conducted.     

On the genealogy of a duplicated microsatellite

When a microsatellite locus is duplicated in a diploid organism, a single pair of PCR primers may amplify as many as four distinct alleles. To study the evolution of a duplicated microsatellite, we consider a coalescent model with symmetric stepwise mutation. Conditional on the time of duplication and a mutation rate, both in a model of completely unlinked loci and in a model of completely linked loci, we compute the probabilities for a sampled diploid individual to amplify one, two, three, or four distinct alleles with one pair of microsatellite PCR primers. These probabilities are then studied to examine the nature of their dependence on the duplication time and the mutation rate. The mutation rate is observed to have a stronger effect than the duplication time on the four probabilities, and the unlinked and linked cases are seen to behave similarly. Our results can be useful for helping to interpret genetic variation at microsatellite loci in species with a very recent history of gene and genome duplication.     

Epigenetic inheritance and genome regulation: is DNA methylation linked to ploidy in haplodiploid insects?

Organisms show great variation in ploidy level. For example, chromosome copy number varies among cells, individuals and species. One particularly widespread example of ploidy variation is found in haplodiploid taxa, wherein males are typically haploid and females are typically diploid. Despite the prevalence of haplodiploidy, the regulatory consequences of having separate haploid and diploid genomes are poorly understood. In particular, it remains unknown whether epigenetic mechanisms contribute to regulatory compensation for genome dosage. To gain greater insights into the importance of epigenetic information to ploidy compensation, we examined DNA methylation differences among diploid queen, diploid worker, haploid male and diploid male Solenopsis invicta fire ants. Surprisingly, we found that morphologically dissimilar diploid males, queens and workers were more similar to one another in terms of DNA methylation than were morphologically similar haploid and diploid males. Moreover, methylation level was positively associated with gene expression for genes that were differentially methylated in haploid and diploid castes. These data demonstrate that intragenic DNA methylation levels differ among individuals of distinct ploidy and are positively associated with levels of gene expression. Thus, these results suggest that epigenetic information may be linked to ploidy compensation in haplodiploid insects. Overall, this study suggests that epigenetic mechanisms may be important to maintaining appropriate patterns of gene regulation in biological systems that differ in genome copy number.     

A graphical approach to multi-locus match probability computation: revisiting the product rule

The genealogical relationships of individuals in a finite population can create statistical non-independence of alleles at unlinked loci. In this paper, we introduce a flexible graphical method for computing the probabilities that two individuals in a finite, randomly mating population have the same haplotype or genotype at several loci. This method allows us to generalize the analysis of Laurie and Weir [2003. Dependency effects in multi-locus match probabilities. Theor. Popul. Biol. 63, 207-219] to cases with more loci and other models of mating. We show that monogamy increases the probabilities of genotypic matches at unlinked loci and that the effect of monogamy increases with the number L of loci. We conjecture a sharp upper bound on the effect of monogamy for a given L.     

标题双胚苗水稻中单倍体和二倍体不同器官的cDNA- AFLP分析

SARII-628是四川农业大学水稻研究所的一个双胚苗自然群体, 每年都能定期分离出单倍体与二倍体(n:2n)。文章对单倍体和对应的二倍体进行了cDNA-AFLP分析。合成了3个单倍体和1个二倍体的根、茎、穗和叶的cDNA, 用EcoR I/ Msp I酶切组合, 通过cDNA-AFLP技术统计这16个样本的表达差异。共选用30对引物, 在633条扩增位点上筛选出49个有差异表达的序列。结果:(1)单倍化后cDNA-AFLP总体水平虽然在各单株间略有差异但变化不大, 表达变化的位点所占比例平均为5.14%, 高于二倍体的3.93%; (2)根据样本在根、茎、穗和叶中表达出带的有无, 在扩增出的14种带型中, 有4种只出现在单倍体中, 其对应位点的表达具有单倍体的特异性; (3)对这3个单倍体在不同器官的激活和沉默位点进行汇总, 发现在根和穗中, 发生沉默的位点多于激活的位点数, 而在茎和叶中的结果正好与之相反, 但是在单倍体的所有器官中发生激活变化的位点多于沉默变化的位点; (4)对不同器官中的发生表达变化(激活+沉默)位点分析, 发现根中的变化位点最多, 在穗中的变化最少, 说明位点的表达变化具有器官特异性。     

Analysis of population structure in autotetraploid species.

Population structure parameters commonly used for diploid species are reexamined for the particular case of tetrasomic inheritance (autotetraploid species). Recurrence equations that describe the evolution of identity probabilities for neutral genes in an "island model" of population structure are derived assuming tetrasomic inheritance. The expected equilibrium value of FST is computed. In contrast to diploids, the correlation of genes between individuals within populations with respect to genes between populations (FST) may vary among loci due to the particular segregation patterns expected under tetrasomic inheritance and is consequently inappropriate for estimating demographic parameters in such populations. We thus define a new parameter (rho) and derive its relationship with Nm. This relationship is shown to be independent from both the selfing rate and the proportion of double reduction. Finally, the statistical procedure required to evaluate these parameters using data on gene frequencies distribution among autotetraploid populations is developed.     

SPATIAL AND TEMPORAL VARIATION IN GROUP RELATEDNESS: EVIDENCE FROM THE IMPORTED WILLOW LEAF BEETLE

The distribution of genetic variance within and among socially interacting groups, often quantified as the average relatedness or r?, is an important determinant of the evolution of social behaviors. Models of social evolution often treat this average as a constant characteristic of a species. In this paper, we present data documenting the degree of temporal and spatial variation in the average relatedness of larval groups of imported willow leaf beetles, a species whose immatures display several primitive social behaviors. Collections of groups were made over three generations at three localities in Virginia and three localities in Illinois. Average relatedness was estimated from the distribution of electrophoretically determined genotypic frequencies within and among groups for each collection. Average relatedness ranged from 0.20 at one locality in Illinois to 0.65 at one locality in Virginia. Individual cases of pairwise differences between samples indicated that there were both temporal and locality effects. Further, statistical analysis showed the set of relatedness values to be heterogeneous with significant locality effects. Geographic genetic variance was also partitioned among trees sampled within localities in Illinois, among localities within each state, and between states. Notably, significant gene-frequency variation among groups of beetles occupying closely spaced trees was detected at several localities.     

Seasonal variation in the mode of reproduction of Ulva intestinalis in a brackish water environment

We explored the reproductive modes of Ulva intestinalis in the inner part of the Baltic Sea during three consecutive years by using five microsatellite loci to estimate the relative abundance of diploid sporophytes and haploid gametophytes. Our results suggest that both diploid sporophytes and haploid gametophytes occur regularly in the Baltic Sea. The ratio of haploid to diploid individuals changes with seasons. Sporophytes are more abundant than gametophytes throughout the year, but the proportion of haploids increases from 10% in early summer to 35% in September. The over-wintering takes primarily place as diploid spores released by sporophytes. The sporophytes appear to reproduce both sexually and asexually in the Baltic Sea, since clones were found for this life phase. The fraction of individuals which belonged to an apparent diploid clone was higher in spring (62%) than in autumn (33%). We also found evidence for asexual clones in haploid gametophytes. The presence of both diploid and haploid individuals and the pattern of genetic and genotypic diversity provide evidence of sexual reproduction in the Baltic Sea. Thus the sporophytes and gametophytes do not function as two reproductively separate units. Compared with many other algal species with a reduced reproductive cycle in low salinity, U. intestinalis differs by having a multitude of reproductive modes also in the brackish water Baltic Sea, which can in part explain the dynamic propagation and high adaptability of the species.