Inclusion of genetically identical animals to a numerator relationship matrix and modification of its inverse

In the field of animal breeding, estimation of genetic parameters and prediction of breeding values are routinely conducted by analyzing quantitative traits. Using an animal model and including the direct inverse of a numerator relationship matrix (NRM) into a mixed model has made these analyses possible. However, a method including a genetically identical animal (GIA) in NRM if genetic relationships between pairs of GIAs are not perfect, is still lacking. Here, we describe a method to incorporate GIAs into NRM using a K matrix in which diagonal elements are set to 1.0, off-diagonal elements between pairs of GIAs to (1-x) and the other elements to 0, where x is a constant less than 0.05. The inverse of the K matrix is then calculated directly by a simple formula. Thus, the inverse of the NRM is calculated by the products of the lower triangular matrix that identifies the parents of each individual, its transpose matrix, the inverse of the K matrix and the inverse of diagonal matrix D, in which the diagonal elements comprise a number of known parents and their inbreeding coefficients. The computing method is adaptable to the analysis of a data set including pairs of GIAs with imperfect relationships.     

StAMPP: an R package for calculation of genetic differentiation and structure of mixed‐ploidy level populations

Statistical Analysis of Mixed‐Ploidy Populations (StAMPP) is a freely available R package for calculation of population structure and differentiation based on single nucleotide polymorphism (SNP) genotype data from populations of any ploidy level, and/or mixed‐ploidy levels. StAMPP provides an advance on previous similar software packages, due to an ability to calculate pairwise F_ST values along with confidence intervals, Nei's genetic distance and genomic relationship matrixes from data sets of mixed‐ploidy level. The software code is designed to efficiently handle analysis of large genotypic data sets that are typically generated by high‐throughput genotyping platforms. Population differentiation studies using StAMPP are broadly applicable to studies of molecular ecology and conservation genetics, as well as animal and plant breeding.     

Computation of the inverse additive relationship matrix for autopolyploid and multiple-ploidy populations

Key message

Rules to generate the inverse additive relationship matrix (A ^?1 ) are defined to enable the adoption restricted maximum likelihood (REML) and best linear unbiased prediction (BLUP) in autopolyploid populations with multiple ploidy levels.

Abstract

Many important agronomic, horticultural, ornamental, forestry, and aquaculture species are autopolyploids. However, the adoption of restricted maximum likelihood (REML), for estimating co/variance components, and best linear unbiased prediction (BLUP), for predicting breeding values, has been hampered in autopolyploid breeding by the absence of an appropriate means of generating the inverse additive relationship matrix (A ^?1 ). This paper defines rules to generate the A ^?1 of autopolyploid populations comprised of individuals of the same or different ploidy-levels, including populations exhibiting (1) odd-numbered ploidy levels (e.g. triploids), (2) sex-based differences in the probability that gametic genes are identical by descent and (3) somatic chromosome doubling. Inbreeding, due to double reduction, in autopolyploid founders in the absence of mating among relatives is also accounted for. A previously defined approach is modified, whereby rules are initially defined to build an inverse matrix of kinship coefficients (K ^?1 ), which is then used to generate A ^?1 . An R package (polyAinv; https://github.com/mghamilton/polyAinv) to implement these rules has been developed and examples of analyses provided. The adoption of REML and BLUP methods made possible by these new rules has the potential to provide further insights into the quantitative genetic architecture of autopolyploid and multiple-ploidy populations, improve estimates of breeding values, and increase genetic gains made through recurrent selection.

     

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.     

Microsatellite segregation analysis and cytogenetic evidence for tetrasomic inheritance in the American yam Dioscorea trifida and a new basic chromosome number in the Dioscoreae

Despite the economic and cultural importance of the indigenous “Amerindian” yam Dioscorea trifida, very little is known about their origin, phylogeny, diversity and genetics. Consequently, conventional breeding efforts for the selection of D. trifida genotypes resistant to potyviruses which are directly involved in the regression of this species have been seriously limited. Our objective of this paper is to contribute to the clarification of the cytogenetic status, i.e., inheritance and chromosome number. Our results provide genetic evidence supporting tetrasomic behaviour of the genome of D. trifida based on chromosomal segregation pattern analysis using eight SSRs markers in three different crosses. This is the first reliable evidence of an autopolyploid species in the genus Dioscorea. The second major result in this study is the revealing of a new base chromosome number in the botanical section Macrogynodium to which D. trifida belongs. To date, our assumptions about the ploidy level of yams are based on the observations that the basic chromosome number is 10 or 9, and D. trifida was described as octoploid. The chromosome number of D. trifida accessions was also assessed using somatic chromosomic count techniques. Flow cytometry did not show significant variation of 2C DNA content among 80 accessions indicating homogeneity of the ploidy level of the cultivated D. trifida. This suggests that autotetraploidy is well established as well as the rule for the cultivated pool of D. trifida, even if the direct diploid ancestor remains to be identified. The data presented in this paper are significant and important for the effective breeding and conservation of the species and for elucidating the phylogeny and the origins of the yam and the evolution of the genus Dioscorea.     

Population genetics of autopolyploids under a mixed mating model and the estimation of selfing rate

Nowadays, the population genetics analysis of autopolyploid species faces many difficulties due to (i) limited development of population genetics tools under polysomic inheritance, (ii) difficulties to assess allelic dosage when genotyping individuals and (iii) a form of inbreeding resulting from the mechanism of ‘double reduction’. Consequently, few data analysis computer programs are applicable to autopolyploids. To contribute bridging this gap, this article first derives theoretical expectations for the inbreeding and identity disequilibrium coefficients under polysomic inheritance in a mixed mating model. Moment estimators of these coefficients are proposed when exact genotypes or just markers phenotypes (i.e. allelic dosage unknown) are available. This led to the development of estimators of the selfing rate based on adult genotypes or phenotypes and applicable to any even‐ploidy level. Their statistical performances and robustness were assessed by numerical simulations. Contrary to inbreeding‐based estimators, the identity disequilibrium‐based estimator using phenotypes is robust (absolute bias generally < 0.05), even in the presence of double reduction, null alleles or biparental inbreeding due to isolation by distance. A fairly good precision of the selfing rate estimates (root mean squared error < 0.1) is already achievable using a sample of 30–50 individuals phenotyped at 10 loci bearing 5–10 alleles each, conditions reachable using microsatellite markers. Diallelic markers (e.g. SNP) can also perform satisfactorily in diploids and tetraploids but more polymorphic markers are necessary for higher ploidy levels. The method is implemented in the software SPAGeDi and should contribute to reduce the lack of population genetics tools applicable to autopolyploids.     

Ploidy level manipulations in potato through sexual hybridisation

There is no better use of sexual reproduction in regard to breeding and genetic research than the ploidy level manipulations possible in the potato and its relatives. Unique reproductive characteristics of tuber‐bearing Solanum species make possible: the production of gametes with unreduced chromosome number; the presence of an endosperm dosage system that regulates success of interploidy/interspecific crosses; the possibility to easily extract maternal haploids following crosses with S. phureja. This paper reviews results obtained in scaling genomic multiples up and down in potato, and relates these manipulations to breeding strategies for the genetic improvement of the cultivated potato. Several ploidy series have been developed, ranging from the monoploid to the hexaploid level. Cultivated tetraploids were scaled down to the diploid and monoploid level by haploidy. Scaling upward was achieved by sexual polyploidisation via 2n gametes that resulted in triploid, tetraploid, pentaploid, and hexaploid genotypes with a broad genetic base. Altogether, the success of ploidy level manipulations constitutes further proof that sexual polyploidisation played an important role in the polyploid evolution of Solanum species, and supports the idea that gene flow can be relatively easily accomplished through interploid and bridge crosses.     

动物模型及多性状BLUP在家禽遗传鉴定中的应用

利用最佳线性无偏预测法(BLUP)估计家畜的育种值,目前除家禽外已在其它各家畜中得到了广泛的应用。本文利用动物模型和多性状BLUP对“京白Ⅰ系”蛋鸡在1986—1987年24个家系的777个个体的系统分组资料进行了分析,估计出了所有个体的复合育种值。其中考虑了两个性状(40周产蛋数和36周蛋重)和两个固定效应(鸡舍-鸡笼效应和孵化批次效应)。同时还对混合模型方程组维数较大时如何在微机上实现进行了研究,即(1)利用磁盘存取系数矩阵的非零元素和中间计算结果;(2)简化了多性状BLUP的计算,利用乔列斯基(Cholesky)分解变换后,此法建立的方程数是常规算法方程数的1/q(q为性状数);(3)简化了方程组迭代求解的方法,即利用块迭代法,这样大大缩短了计算的机吋,节省了费用,使BLUP在家禽中的推广应用成为可能。     

Polyploidy creates higher diversity among Cynodon accessions as assessed by molecular markers

Developing a better understanding of associations among ploidy level, geographic distribution, and genetic diversity of Cynodon accessions could be beneficial to bermudagrass breeding programs, and would enhance our understanding of the evolutionary biology of this warm season grass species. This study was initiated to: (1) determine ploidy analysis of Cynodon accessions collected from Turkey, (2) investigate associations between ploidy level and diversity, (3) determine whether geographic and ploidy distribution are related to nuclear genome variation, and (4) correlate among four nuclear molecular marker systems for Cynodon accessions’ genetic analyses. One hundred and eighty-two Cynodon accessions collected in Turkey from an area south of the Taurus Mountains along the Mediterranean cost and ten known genotypes were genotyped using sequence related amplified polymorphism (SRAP), peroxidase gene polymorphism (POGP), inter-simple sequence repeat (ISSR), and random amplified polymorphic DNA (RAPD). The diploids, triploids, tetraploids, pentaploids, and hexaploids revealed by flow cytometry had a linear present band frequency of 0.36, 0.47, 0.49, 0.52, and 0.54, respectively. Regression analysis explained that quadratic relationship between ploidy level and band frequency was the most explanatory (r = 0.62, P < 0.001). The AMOVA results indicated that 91 and 94% of the total variation resided within ploidy level and provinces, respectively. The UPGMA analysis suggested that commercial bermudagrass cultivars only one-third of the available genetic variation. SRAP, POGP, ISSR, and RAPD markers differed in detecting relationships among the bermudagrass genotypes and rare alleles, suggesting more efficiency of combinatory analysis of molecular marker systems. Elucidating Cynodon accessions’ genetic structure can aid to enhance breeding programs and broaden genetic base of commercial cultivars. O. Gulsen and S. Sever-Mutlu contributed equally to this work.     

POLYSAT: an R package for polyploid microsatellite analysis

We present an R package to help remedy the lack of software for manipulating and analysing autopolyploid and allopolyploid microsatellite data. POLYSAT can handle genotype data of any ploidy, including populations of mixed ploidy, and assumes that allele copy number is always ambiguous in partial heterozygotes. It can import and export genotype data in eight different formats, calculate pairwise distances between individuals using a stepwise mutation and infinite alleles model, estimate ploidy based on allele counts and estimate allele frequencies and pairwise F(ST) values. This software is freely available through the Comprehensive R Archive Network (http://cran.r-project.org/) and includes a thorough tutorial.     

Androgenesis,gynogenesis, and parthenogenesis haploids in cucurbit species

Haploids and doubled haploids are critical components of plant breeding. This review is focused on studies on haploids and double haploids inducted in cucurbits through in vitro pollination with irradiated pollen, unfertilized ovule/ovary culture, and anther/microspore culture during the last 30 years, as well as comprehensive analysis of the main factors of each process and comparison between chromosome doubling and ploidy identification methods, with special focus on the application of double haploids in plant breeding and genetics. This review identifies existing problems affecting the efficiency of androgenesis, gynogenesis, and parthenogenesis in cucurbit species. Donor plant genotypes and surrounding environments, developmental stages of explants, culture media, stress factors, and chromosome doubling and ploidy identification are compared at length and discussed as methodologies and protocols for androgenesis, gynogenesis, and parthenogenesis in haploid and double haploid production technologies.     

A comparative study of distant hybridization in plants and animals

Distant hybridization refers to crosses between two different species, genera, or higher-ranking taxa, which can break species limits, increase genetic variation, and combine the biological characteristics of existing species. It is an important way of creating genetic variation, fertile strains, and excellent characteristics in new strains and populations. Combining analyses and summaries from many inter-related documents in plants and animals, both domestic and international, including examples and long-standing research on distant hybridization in fish from our laboratory, we summarize and compare the similarities and differences in plant and animal distant hybridization. In addition, we analyze and review the biological characteristics of their different ploidy progenies and the possible causes of disparity in survival rates. Mechanisms of sterility in animal and plant distant hybrids are also discussed, and research methods for the study of biological characteristics of hybrids, including morphology, cytology,and molecular cytogenetics are presented. This paper aims to provide comprehensive research materials and to systematically compare the general and specific characteristics of plant and animal hybrids with regards to reproduction, genetics, growth traits,and other biological characteristics. It is hoped that this paper will have great theoretical and practical significance for the study of genetic breeding and biological evolution of plant and animal distant hybridization.     

Transference of natural diversity from the apomictic germplasm of Paspalum notatum to a sexual synthetic population

Genetic improvement in apomictic forage species has been restricted because of the absence of genetic variability in sexual germplasm with the same ploidy level. Following a new breeding scheme, a sexual synthetic tetraploid population (SSTP) of Paspalum notatum has been generated. The objectives of this work were: (a) to evaluate the genetic variability in SSTP by means of molecular markers, morphologic and agronomic traits, and seed fertility and quality traits and (b) to assess the transference of genetic variability from the apomictic germplasm to the sexual one. Molecular markers revealed a twofold higher level of variability in the SSTP in comparison with the sexual germplasm utilised for its generation, and similar levels with the apomictic ones; moreover, markers showed that most of the variability was inherited from the apomictic germplasm. Morphologic and agronomic traits and seed fertility and quality traits showed high levels of variation in the three groups of genotypes indicating that the new breeding scheme was effective in transferring variability from the apomictic germplasm to the SSTP. This new population will be useful in breeding of P. notatum, and the breeding scheme used for its generation may be used in other apomictic species.     

Optimizing whole-genomic prediction for autotetraploid blueberry breeding

Blueberry (Vaccinium spp.) is an important autopolyploid crop with significant benefits for human health. Apart from its genetic complexity, the feasibility of genomic prediction has been proven for blueberry, enabling a reduction in the breeding cycle time and increasing genetic gain. However, as for other polyploid crops, sequencing costs still hinder the implementation of genome-based breeding methods for blueberry. This motivated us to evaluate the effect of training population sizes and composition, as well as the impact of marker density and sequencing depth on phenotype prediction for the species. For this, data from a large real breeding population of 1804 individuals were used. Genotypic data from 86,930 markers and three traits with different genetic architecture (fruit firmness, fruit weight, and total yield) were evaluated. Herein, we suggested that marker density, sequencing depth, and training population size can be substantially reduced with no significant impact on model accuracy. Our results can help guide decisions toward resource allocation (e.g., genotyping and phenotyping) in order to maximize prediction accuracy. These findings have the potential to allow for a faster and more accurate release of varieties with a substantial reduction of resources for the application of genomic prediction in blueberry. We anticipate that the benefits and pipeline described in our study can be applied to optimize genomic prediction for other diploid and polyploid species.     

Application of TILLING and EcoTILLING as Reverse Genetic Approaches to Elucidate the Function of Genes in Plants and Animals

With the fairly recent advent of inexpensive, rapid sequencing technologies that continue to improve sequencing efficiency and accuracy, many species of animals, plants, and microbes have annotated genomic information publicly available. The focus on genomics has thus been shifting from the collection of whole sequenced genomes to the study of functional genomics. Reverse genetic approaches have been used for many years to advance from sequence data to the resulting phenotype in an effort to deduce the function of a gene in the species of interest. Many of the currently used approaches (RNAi, gene knockout, site-directed mutagenesis, transposon tagging) rely on the creation of transgenic material, the development of which is not always feasible for many plant or animal species. TILLING is a non-transgenic reverse genetics approach that is applicable to all animal and plant species which can be mutagenized, regardless of its mating / pollinating system, ploidy level, or genome size. This approach requires prior DNA sequence information and takes advantage of a mismatch endonuclease to locate and detect induced mutations. Ultimately, it can provide an allelic series of silent, missense, nonsense, and splice site mutations to examine the effect of various mutations in a gene. TILLING has proven to be a practical, efficient, and an effective approach for functional genomic studies in numerous plant and animal species. EcoTILLING, which is a variant of TILLING, examines natural genetic variation in populations and has been successfully utilized in animals and plants to discover SNPs including rare ones. In this review, TILLING and EcoTILLING techniques, beneficial applications and limitations from plant and animal studies are discussed.Key Words: Reverse genetics, functional genomics, TILLING (target induced local lesions in genomes), EcoTILLING (Ecotype TILLING), sequencing, SNP (single nucleotide polymorphism), genetic stocks.     

Current status in production and utilization of dihaploids from somatic hybrids between eggplant (Solanum melongena L.) and its wild relatives

The major constrains for practical exploitation of the somatic hybrids between eggplant and its wild relatives have been their sterility and tetraploidy which prevented their incorporation into breeding programs. Here we demonstrate that anther culture was successfully utilized to bring back the ploidy level to the diploid status in tetraploid interspecific hybrids between eggplant and the allied species S. integrifolium and S. aethiopicum gr. gilo. Both the relative species are resistant to Fusarium oxysporum f. sp. melongenae and to some strains of bacterial wilt (Ralstonia solanacearum) which are very destructive diseases of eggplant. Dihaploid androgenetic plants were obtained from the somatic hybrids, from the “double somatic hybrid” obtained by sexual cross of the two somatic hybrids [(eggplant + S. aethiopicum) × (eggplant + S. integrifolium)], and from tetraploid backcrossed plants between the somatic hybrid with S. aethiopicum and eggplant. Phenotypical, molecular, biological and biochemical characterization, and also artificial inoculation with Fusarium oxysporum are consistent with a recombination between the genomes of the species involved in the hybridizations. Dihaploids resistant to Fusarium were successfully backcrossed with eggplant. Besides their utility as potential valuable breeding materials, the introgressed lines obtained may be utilized in genetic and molecular studies about the resistance to Fusarium from S. integrifolium and S. aethiopicum gr. gilo.     

Synthetic polyploid production of Miscanthus sacchariflorus,Miscanthus sinensis,and Miscanthus x giganteus

Plants from the genus Miscanthus are potential renewable sources of lignocellulosic biomass for energy production. A potential strategy for Miscanthus crop improvement involves interspecific manipulation of ploidy levels to generate superior germplasm and to circumvent reproductive barriers for the introduction of new genetic variation into core germplasm. Synthetic autotetraploid lines of Miscanthus sacchariflorus and Miscanthus sinensis, and autoallohexaploid Miscanthus x giganteus were produced in tissue culture from oryzalin treatments to seed‐ and immature inflorescence‐derived callus lines. This is the first report of the genome doubling of diploid M. sacchariflorus. Genome doubling of diploid M. sinensis, M. sacchariflorus, and triploid M. x giganteus to generate tetraploid and hexaploid lines was confirmed by stomata size, nuclear DNA content, and chromosome counts. A putative pentaploid line was also identified among the M. x giganteus synthetic polyploid lines by nuclear DNA content and chromosome counts. Comparisons of phenotypic performance of synthetic polyploid lines with their diploid and triploid progenitors in the greenhouse found species‐specific differences in plant tiller number, height, and flowering time among the doubled lines. Stem diameter tended to increase after polyploidization but there were no significant improvements in biomass traits. Under field conditions, M. x giganteus synthetic hexaploid lines showed greater phenotypic variation, in terms of plant height, stem diameter, and tiller number, than their progenitor lines. Production of synthetic autopolyploid lines displaying significant phenotypic variation suggests that ploidy manipulation can introduce useful genetic diversity in the limited Miscanthus germplasm currently available in the United States. The role of polyploidization in the evolution and breeding of the genus Miscanthus is discussed.     

Uses and usefulness of endosperm balance number

 The Endosperm Balance Number (EBN) hypothesis was developed in the early ’80s to explain the basis for normal seed development after intra- and inter-specific crosses, first in the potato and then in several other crop species. According to this hypothesis, each species has a genome-specific effective ploidy, the EBN, which must be in a 2 : 1 maternal to paternal ratio in the hybrid endosperm for normal development of the endosperm itself. This paper reviews how the EBN may act as a powerful isolating mechanism in sexual reproduction, maintaining the genome integrity of the species and playing an important role in the speciation of polyploids from diploids. We also provide further evidence that EBN is more important than chromosome ploidy in determining the success or failure of interspecific crosses. In fact, results from inter-ploidy and inter-EBN crosses to infuse 1EBN Solanum commersonii into 4EBN S. tuberosum demonstrated that the knowledge and manipulation of EBN is a useful tool in designing breeding schemes and in predicting the offspring ploidy and EBN. In this paper we also discuss the exceptions to the 2 : 1 EBN ratio, and report the evidence for endomitosis in the polar nuclei to explain exceptions to the EBN model in the potato. Received: 22 December 1997 / Accepted: 19 May 1998