An efficient method of computing the numerator relationship matrix and its inverse matrix with inbreeding for large sets of animals

Summary The numerator relationship matrix describes the genetic relationships between individuals of a population. Its inverse is used for the prediction of breeding values, as outlined by Henderson (1975a).For large populations, the recursive method commonly used is difficult to apply because of the size of the relationship matrix. Recently Henderson (1975b) derived a method which allows computing the inverse of the numerator relationship matrix itself for a large number of animals, provided the population is non-inbred. The method presented here is an extension of Henderson's method to allow for inbreeding with large number of animals. It takes inbreeding into account and computes the numerator relationship matrix as well as its inverse. The method is particularly efficient in computer storage in that it allows handling of sets of animals larger than 5000 animals, and is almost as fast as the recursive method.     

Two unisexual artificial polyploid clones constructed by genome addition of common carp (<Emphasis Type="Italic">Cyprinus carp</Emphasis>) and crucian carp (<Emphasis Type="Italic">Carassius auratus</Emphasis>)

A polyploid hybrid fish with natural gynogenesis can prevent segregation and maintain their hybrid vigor in their progenies. Supposing the reproduction mode of induced polyploid fish being natural gynogenesis, allopolyploid hybrid between common carp and crucian carp into allopolyploid was performed. The purpose of this paper is to describe a lineage from sexual diploid carp transforming into allotriploid and allotetraploid unisexual clones by genome addition. The diploid hybrid between common carp and crucian carp reproduces an unreduced nucleus consisting of two parental genomes. This unreduced female pronucleus will fuse with male pronucleus and form allotriploid zygote after penetration of related species sperms. Allotriploid embryos grow normally, and part of female allotriploid can produce unreduced mature ova with three genomes. Mature ova of most allotriploid females are provided with natural gynogenetic trait and their nuclei do not fuse with any entrance sperm. All female offspring are produced by gynogenesis of allotriploid egg under activation of penetrating sperms. These offspring maintain morphological traits of their allotriploid maternal and form an allotetraploid unisexual clone by gynogenetic reproduction mode. However, female nuclei of rare allotriploid female can fuse with penetrating male pronuclei and result in the appearance of allotetraploid individuals by means of genome addition. All allotetraploid females can reproduce unreduced mature eggs containing four genomes. Therefore, mature eggs of allotetraploid maintain gynogenetic trait and allotetraploid unisexual clone is produced under activation of related species sperms.     

Genetic Evidence for Gonochoristic Reproduction in Gynogenetic Silver Crucian Carp (Carassius auratus gibelio Bloch) as Revealed by RAPD Assays

Sex evolution has been a debating focus in evolutionary genetics. In lower vertebrates of reptiles, amphibians, and fish, a species or a bioform reproduces either sexually or asexually but never both. A few species were found to consist of all females in fish. These all-female species can propagate by asexual reproduction modes, such as gynogenesis and hybridogenesis. However, the coexistence of sexuality and asexuality in a single species was recently noted only in a cyprinid fish silver crucian carp, Carassius auratus gibelio. This fish had been demonstrated to be capable of gynogenesis stimulated by sperm from other related species. Surprisingly, natural populations of this fish consist of a minor but significant portion (approx. 20%) of males. As different clones with specific phenotypic and genetic characteristics have been found, and RAPD markers specific to each clone have recently been identified, this fish offers many advantages for analyzing whether or not genetic recombination occurs between different clones. In this study, artificial propagation was performed in clone F and clone D. Ovulated eggs from clone F were divided into two parts and respectively inseminated with sperm from a clone D male and from a red common carp (Cyprinus carpio) male. The control clone D individuals were selected from gynogenetic offspring of clone D activated by sperm of red common carp. The phenotype and sex ratio in the experimental groups were also observed. Using RAPD molecular markers, which allow for reliable discrimination and genetic analysis of different clones, we have revealed direct molecular evidence for gonochoristic reproduction in the gynogenetic silver crucian carp and confirmed a previous hypothesis that the silver crucian carp might reproduce both gynogenetically and gonochoristically. Therefore, we conclude that the silver crucian carp possesses two reproductive modes, i.e., gynogenetic and gonochoristic reproduction. The response mechanism of two reproductive development modes may be the first discovery in vertebrates. Additionally, we discuss the evolutionary implication between gynogenetic and gonochoristic reproduction modes and the contribution of the minor proportion of males to genetic flexibility in the gynogenetic silver crucian carp. Received: 5 January 2000 / Accepted: 3 August 2000     

Gynogenesis Assessment Using Microsatellite Genetic Markers in Turbot (<Emphasis Type="Italic">Scophthalmus maximus</Emphasis>)

Gynogenesis was assessed by different methods in 2 families of gynogenetic offspring in turbot (Scophthalmus maximus). Karyotype analysis in embryos and larvae demonstrated high accuracy in estimation of ploidy level, but performance was uneven given the low quality and number of plates obtained. The use of silver staining to estimate the number of nucleoli per nucleus resulted in a straightforward and easy method to evaluate the ploidy of the samples studied. However, the existence of a nucleolus organizer region polymorphism in turbot determined a small error in ploidy estimation, important when checking ploidy in specific individuals. The use of a set of 11 highly variable microsatellite loci proved to be a powerful method to confirm the exclusive maternal inheritance to gynogenetic offspring in turbot, with probabilities of detection of putative paternal genetic contribution above 99.99%.     

Two unisexual artificial polyploid clones constructed by genome addition of common carp (Cyprinus carp) and crucian carp (Carassius auratus)

The application of hybrid vigor and crossbreeding is conventional and proved effective. Nevertheless, the phenotype of the progeny of hybrids, which carry hybrid vigor and produce their offspring through bisexual reproduction, will segregate inevitably and their hybrid vigor will de-crease in subsequent generations. The more serious consequence might result in destroying com-pletely those endemic populations when hybrids are released into open water bodies, because hy-brids will cross with the…     

INBREEDING DEPRESSION VARIES WITH INVESTMENT IN SEX IN A FACULTATIVE PARTHENOGEN

The reproductive mode of facultative parthenogens allows recessive mutations that accumulate during the asexual phase to be unmasked following sexual reproduction. Longer periods of asexual reproduction should increase the accumulation of deleterious mutations within individuals, reduce population-level genetic diversity via competition and increase the probability of mating among close relatives. Having documented that the investment in sexual reproduction differs among populations and clones of Daphnia pulicaria , we ask if this variation is predictive of the level of inbreeding depression across populations. In four lake populations that vary in sex investment, we raised multiple families (mother, field-produced daughter, laboratory-produced daughter) on high food and estimated the fitness reduction in both sexually produced offspring relative to the maternal genotype. Inbred individuals had lower fitness than their field-produced siblings. The magnitude of fitness reduction in inbred offspring increased as population-level investment in sex decreased. However, there was less of a fitness reduction following sex in the field-produced daughters, suggesting that many field-collected mothers were involved in outcross mating.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

SNP-based heritability estimation using a Bayesian approach

Heritability is a central element in quantitative genetics. New molecular markers to assess genetic variance and heritability are continually under development. The availability of molecular single nucleotide polymorphism (SNP) markers can be applied for estimation of variance components and heritability on population, where relationship information is unknown. In this study, we evaluated the capabilities of two Bayesian genomic models to estimate heritability in simulated populations. The populations comprised different family structures of either no or a limited number of relatives, a single quantitative trait, and with one of two densities of SNP markers. All individuals were both genotyped and phenotyped. Results illustrated that the two models were capable of estimating heritability, when true heritability was 0.15 or higher and populations had a sample size of 400 or higher. For heritabilities of 0.05, all models had difficulties in estimating the true heritability. The two Bayesian models were compared with a restricted maximum likelihood (REML) approach using a genomic relationship matrix. The comparison showed that the Bayesian approaches performed equally well as the REML approach. Differences in family structure were in general not found to influence the estimation of the heritability. For the sample sizes used in this study, a 10-fold increase of SNP density did not improve precision estimates compared with set-ups with a less dense distribution of SNPs. The methods used in this study showed that it was possible to estimate heritabilities on the basis of SNPs in animals with direct measurements. This conclusion is valuable in cases when quantitative traits are either difficult or expensive to measure.     

Life history variation among low-arctic clones of obligately parthenogenetic Daphnia pulex: a diploid-polyploid complex

Summary Laboratory life table experiments were conducted using nine clones of obligately parthenogenetic Daphnia pulex that were collected from a site in the Canadian low-arctic. Two of the nine clones were diploids, while the other seven clones were polyploids. Significant clonal differences in age at first reproduction, size at first reproduction, number of offspring in each of the first three broods, offsrring sizes for the first two broods, and intrinsic rates of natural increase were detected. Differences in life histories were evident between polyploids and diploids. Generally, polyploid clones reached maturity at later ages, matured at larger sizes, produced smaller broods, and larger offspring than the diploid clones. The data are discussed in reference to potential biotic (i.e. invertebrate predation) and abiotic factors (i.e. physicochemical gradients) that may influence life history variation in this clonal assemblage.     

Implications of non-linear economic weights for breeding

Summary Relationships were studied theoretically between phenotypic values of selection candidates (parents) and economic worth of the offspring that would belong to production populations. The candidates could include individuals, crosses or clones, and the offspring could be produced either sexually or vegetatively. Cases considered included: three systems for generating production populations [clonal propagation, pair(full-sib)crosses and half-sib crosses]; three economic-worth (profit) functions for individual offspring (linear, intermediate optimum, acceptable versus cull); and independently varying heritabilities for both parents and offspring. The heritabilities were varied in the model against a background of fixed genetic variance. Parental values were considered in terms of phenotypic standard deviations from the population mean, assuming normality. Lower heritabilities and, to a lesser extent, genetic segregation severely damped down the non-linearities of economic worth in relation to measured parental values, such that the linear weightings for traits in a selection index should usually be a good approximation, provided the profit function for individual offspring is monotonic. The economic advantages of corrective mating within a select population may be minimal if both heritabilities are low and the profit functions apply to individual offspring. The economic advantages accruing from genetic uniformity of clones (or crosses between inbreds) in conjunction with non-linear profit functions are strongly dependent on achieving high broad-sense heritabilites, particularly in the offspring (production population).     

Genetically identical copies of the mulberry silkworm

Summary Genetically identical copies of the silkworm female obtained via ameiotic parthenogenesis are insignificantly depressed by artificial reproduction, and notwithstanding their isogenous pattern, they show the same variability in quantitative characters as in the heterogenous forms.By means of androgenesis, genetically identical copies of strictly homozygous males were obtained; the latter were produced via meiotic parthenogenesis. The androgenetic clones of these males were transformed by backcrosses into homozygous bisexual lines. Viability and cocoon weight in these lines were higher than those in androgenetic clones of similar genotype, but they were far from the norm due to the depressing effect of semilethals left in them in a homozygous state. An extremely low phenotypical variability of quantitative characters is observed in the isogenous hybrids F₁ obtained from crossing two genetically dissimilar strictly homozygous individuals. These hybrids make excellent material for phenogenetical studies. The female and male isogenous clones have an increased combining ability which is acquired in the course of their selection for high disposition towards complete parthenogenesis. For practical purposes it is proposed to take a female and a male which when mated produce a high-quality family and clone them separately, the first via parthenogenesis, the latter via androgenesis. After mating these reproduced bisexual clones, it will be possible to obtain in successive generations a vast number of families repeating the prominent productivity of the initial family.     

Methods to estimate breeding values in honey bees

Background

Efficient methodologies based on animal models are widely used to estimate breeding values in farm animals. These methods are not applicable in honey bees because of their mode of reproduction. Observations are recorded on colonies, which consist of a single queen and thousands of workers that descended from the queen mated to 10 to 20 drones. Drones are haploid and sperms are copies of a drone’s genotype. As a consequence, Mendelian sampling terms of full-sibs are correlated, such that the covariance matrix of Mendelian sampling terms is not diagonal.

Results

In this paper, we show how the numerator relationship matrix and its inverse can be obtained for honey bee populations. We present algorithms to derive the covariance matrix of Mendelian sampling terms that accounts for correlated terms. The resulting matrix is a block-diagonal matrix, with a small block for each full-sib family, and is easy to invert numerically. The method allows incorporating the within-colony distribution of progeny from drone-producing queens and drones, such that estimates of breeding values weigh information from relatives appropriately. Simulation shows that the resulting estimated breeding values are unbiased predictors of true breeding values. Benefits for response to selection, compared to an existing approximate method, appear to be limited (~5%). Benefits may however be greater when estimating genetic parameters.

Conclusions

This work shows how the relationship matrix and its inverse can be developed for honey bee populations, and used to estimate breeding values and variance components.     

Heritability of dispersal rate and other life history traits in the Glanville fritillary butterfly

Knowing the variances and heritabilities (h(2)) of life history traits in populations living under natural conditions is necessary for a mechanistic understanding of respective evolutionary processes. I estimated heritabilities of several life history traits, including dispersal rate, body mass, age at first reproduction, egg mass, clutch size and lifetime reproductive success, in the Glanville fritillary butterfly (Melitaea cinxia) using parent-offspring regression. Experiments were conducted under field conditions in a large population cage (32 x 26 m). Heritability estimates ranged from zero to almost one and several were significantly different from zero. Body size for both sexes, female age at first reproduction and egg weight were all moderately to highly heritable, whereas heritabilities were low or non-existent in clutch size and lifetime egg production. Heritability estimates for dispersal rate varied between the sexes, so that dispersal was heritable from mother to her female offspring only. This finding is consistent with previous results showing that the F1 female but not male offspring of females that naturally established new populations in the field are significantly more dispersive than butterflies in old populations.     

人工诱导荷包红鲤雌核发育子代与亲本的染色体组型及几种酶的组织化学比较

作者使用元江鲤失活的精子,诱导荷包红鲤卵子进行雌核发育所获得的子代,同亲本作了染色体组型和几种酶的组织化学比较。雌核发育子代的染色体组型与母本荷包红鲤完全相同,与父本元江鲤有不同。元江鲤的体色黑灰色,是由于肌肉中有酪氨酸酶存在,能将酪氨酸氧化成黑色素的缘故;荷包红鲤肌肉中无此酶,不能形成黑色素,所以体色呈桔红色;雌核发育子代肌肉中,也无酪氨酸酶,其体色同母本一样为桔红色;乳酸脱氢酶、非特异性酯酶的分布和含量也都与母本一致,与父本有差异。     

锦鲤4个人工雌核发育家系的微卫星标记研究

利用Crooijmans et al.(1997)分离的包含CA重复单元的普通鲤鱼（Cyprinus carpio L.)的8个微卫星DNA标记,对从锦鲤（Cyprinus carpio L.)的红白,大正和昭和3个不同品系中所获得的4个不同人工雌核发育家系的20尾个体进行PCR扩增。电泳结果表明,8对引物在20尾个体中均能重复稳定地扩增出相应的同源序列。随引物不同,各等位基因数为1－11个,大小在68－264bp。在MFW4,MFW7,MFW19,MFW20,MFW23和MFW24 6个微卫星的扩增结果中,20尾个体的扩增图谱呈现了高度的遗传多态性,不同雌核发育家系内个体的遗传异质性也较大。其中大正（TaS)和红白1（RW1）的个体不仅花色分化显著,而且个体间的平均遗传距离分别高达0．28。通过对微卫星等位基因和基因型分析发现,由于锦鲤品系中的每一个体是通过不断地杂交选育而获得,基因组来源复杂,基因高度杂合。因此,只进行1代的人工雌核发育,其家系内仅部分个体的部分座位出现纯合。所获得的人工雌核发育锦鲤为后续的色素遗传调控机制研究提供了必要的实验材料;同时,所鉴定的微卫星分子标记为进行锦鲤的分子标记育种的基因组作图提供了理想的工具。     

Rainbow trout offspring with different resistance to viral haemorrhagic septicaemia

To study immunological and immunogenetical parameters related to resistance against viral haemorrhagic septicaemia (VHS), attempts to make gynogenetic strains of rainbow trout selected for high and low resistance to VHS were initiated in 1988. The first gynogenetic generation of inbreeding resulted in the more resistant offspring E8 and the low resistance offspring K3; the K3 offspring having the same high mortality as the susceptible reference strain of outbred trout in infection trials. A second gynogenetic generation derived from the E8 strain resulted in some low resistance offspring, and two gynogenetic families in which all, or nearly all, fish survived challenge with VHS virus. In this study, an attempt to associate the distribution of different MHC class II genotypes with low and high resistance gynogenetic offspring was performed. Two different MHC haplotypes could be distinguished, and in both low and high resistance families all three genotypes were found, which could be explained by the fact that the mother fish carried the heterozygous genotype. Although no significant differences in MHC II genotypes were found between the high and low resistance offspring, a significantly different distribution of haplotypes in the low resistance offspring was observed, that could not be explained by a one- or two-locus model.     

Use of Multiple Genetic Markers in Prediction of Breeding Values

Genotypes at a marker locus give information on transmission of genes from parents to offspring and that information can be used in predicting the individuals' additive genetic value at a linked quantitative trait locus (MQTL). In this paper a recursive method is presented to build the gametic relationship matrix for an autosomal MQTL which requires knowledge on recombination rate between the marker locus and the MQTL linked to it. A method is also presented to obtain the inverse of the gametic relationship matrix. This information can be used in a mixed linear model for simultaneous evaluation of fixed effects, gametic effects at the MQTL and additive genetic effects due to quantitative trait loci unlinked to the marker locus (polygenes). An equivalent model can be written at the animal level using the numerator relationship matrix for the MQTL and a method for obtaining the inverse of this matrix is presented. Information on several unlinked marker loci, each of them linked to a different locus affecting the trait of interest, can be used by including an effect for each MQTL. The number of equations per animal in this case is 2m + 1 where m is the number of MQTL. A method is presented to reduce the number of equations per animal to one by combining information on all MQTL and polygenes into one numerator relationship matrix. It is illustrated how the method can accommodate individuals with partial or no marker information. Numerical examples are given to illustrate the methods presented. Opportunities to use the presented model in constructing genetic maps are discussed.     

A somatic mosaic of the gynogenetic Amazon molly

Breeding experiments with the gynogenetic Amazon molly, Poecilia formosa , proved that mosaicism, detected by flow cytometry with the fluorescent dye DAPI was restricted to the soma, and that gynogenetic reproduction was maintained by the offspring. Potential pathways for how mosaicism might have arisen in P. formosa are discussed.     

Comparison of genetic parameters from marker-based relationship, sibship, and combined models in Scots pine multi-site open-pollinated tests

Nine microsatellite DNA markers (simple sequence repeats, SSRs) were used to estimate pairwise relationships among 597 Scots pine (Pinus sylvestris) trees as well as to generate a sibship structure for quantitative genetic parameters’ estimation comparison. The studied trees were part of an open-pollinated progeny test of 102 first-generation parents. Three methods were used to estimate variance components and heritabilities, namely, structured pedigree (half- and full-sib), marker-based pairwise relationships (four pairwise estimators), and a combined pedigree and marker-based relationship. In each of the three methods, the same animal model was used to compute variances except when marker-based relationship was used wherein we substituted the average numerator relationship matrix (i.e., pedigree-based matrix) with that computed based on markers’ pairwise relationships. Our results showed a high correlation in estimated breeding values between the pedigree (full-sib) and the combined marker-pedigree estimates. The marker-based relationship method produced high correlations when individual site data were analyzed. In contrast, the marker-based relationship method resulted in a significant decrease in both variance estimation and their standard errors which were in concordance with earlier published results; however, no estimates were produced when across-site analyses were attempted. We concluded that the combined pedigree method is the best approach as it represents the historical (pairwise) and contemporary (pedigree) relationships among the tested individuals, a situation that cannot be attained by any of the used methods individually. This method is dependent on the number and informativeness of the markers used.     

An indirect approach to the extensive calculation of relationship coefficients

A method was described for calculating population statistics on relationship coefficients without using corresponding individual data. It relied on the structure of the inverse of the numerator relationship matrix between individuals under investigation and ancestors. Computation times were observed on simulated populations and were compared to those incurred with a conventional direct approach. The indirect approach turned out to be very efficient for multiplying the relationship matrix corresponding to planned matings (full design) by any vector. Efficiency was generally still good or very good for calculating statistics on these simulated populations. An extreme implementation of the method is the calculation of inbreeding coefficients themselves. Relative performances of the indirect method were good except when many full-sibs during many generations existed in the population.