A simulation module in the computer program colony for sibship and parentage analysis

A simulation module is built into the software package colony to simulate marker genotype data of individuals with a predefined parentage and sibship structure. The simulated data can then be used to compare the accuracy, robustness and computational efficiency of different methods for sibship and parentage reconstruction, to examine the impact of different parameter options in a software on its accuracy and computational efficiency and to assess the information sufficiency of a given set of markers for a sibship and parentage analysis. This computer note describes the method used for simulating genotype data with a pedigree and its possible applications. The method can quickly generate genotype data for a one‐ or two‐generation pedigree of virtually any complexity with up to 30k offspring, at up to 30k codominant or dominant loci with an arbitrary degree of linkage and a user‐defined mistyping rate. The data can be fed directly into the colony program for analysis by three sibship and parentage reconstruction methods and can also be imported into other programs such as Excel and R. With slight modification, the data can be analysed by other relationship analysis software.     

Estimation of allele frequencies in polyploids under certain patterns of inheritance

Allele frequencies have long been studied by biologists interested in evolution and speciation. More recently, with the application of molecular markers in human DNA profiling we have also seen the need for reliable population allele frequency estimates for making probabilistic inferences. There is now interest in applying the same DNA profiling technology to identification of plant varieties. HortResearch maintains a large germplasm of horticultural plant species. It is becoming evident that accurate identification of these accessions through DNA fingerprinting is essential for effective utilisation and maintenance of this germplasm. Microsatellites are the markers of choice for this fingerprinting. However, such markers do not reveal the dosage of alleles in a polyploid. Polyploidy is common amongst horticultural plants. Estimating allele frequencies in a polyploid population is, therefore, complicated because of some marker genotypes being phenotypically indistinguishable. For example, in a tetraploid, with four alleles at a locus showing polysomic inheritance, although 35 genotypes are possible, these will fall into only 15 marker phenotypic classes. Furthermore 'null' individuals are rarely detected in polyploids. Furthermore, some polyploids can be cryptic exhibiting disomy, instead of the polysomic inheritance. We will discuss the implications of these factors and present an EM-type algorithm for estimating allele frequencies of a polyploid population under certain patterns of inheritance. The method will be demonstrated on simulated data. We also discuss the nature of some of the additional problems that may be encountered with estimating allele frequencies in polyploids for which other solutions still need to be developed.     

Parentage and Sibship Inference From Multilocus Genotype Data Under Polygamy

Likelihood methods have been developed to partition individuals in a sample into sibling clusters using genetic marker data without parental information. Most of these methods assume either both sexes are monogamous to infer full sibships only or only one sex is polygamous to infer full sibships and paternal or maternal (but not both) half sibships. We extend our previous method to the more general case of both sexes being polygamous to infer full sibships, paternal half sibships, and maternal half sibships and to the case of a two-generation sample of individuals to infer parentage jointly with sibships. The extension not only expands enormously the scope of application of the method, but also increases its statistical power. The method is implemented for both diploid and haplodiploid species and for codominant and dominant markers, with mutations and genotyping errors accommodated. The performance and robustness of the method are evaluated by analyzing both simulated and empirical data sets. Our method is shown to be much more powerful than pairwise methods in both parentage and sibship assignments because of the more efficient use of marker information. It is little affected by inbreeding in parents and is moderately robust to nonrandom mating and linkage of markers. We also show that individually much less informative markers, such as SNPs or AFLPs, can reach the same power for parentage and sibship inferences as the highly informative marker simple sequence repeats (SSRs), as long as a sufficient number of loci are employed in the analysis.     

Computationally efficient sibship and parentage assignment from multilocus marker data

Quite a few methods have been proposed to infer sibship and parentage among individuals from their multilocus marker genotypes. They are all based on Mendelian laws either qualitatively (exclusion methods) or quantitatively (likelihood methods), have different optimization criteria, and use different algorithms in searching for the optimal solution. The full-likelihood method assigns sibship and parentage relationships among all sampled individuals jointly. It is by far the most accurate method, but is computationally prohibitive for large data sets with many individuals and many loci. In this article I propose a new likelihood-based method that is computationally efficient enough to handle large data sets. The method uses the sum of the log likelihoods of pairwise relationships in a configuration as the score to measure its plausibility, where log likelihoods of pairwise relationships are calculated only once and stored for repeated use. By analyzing several empirical and many simulated data sets, I show that the new method is more accurate than pairwise likelihood and exclusion-based methods, but is slightly less accurate than the full-likelihood method. However, the new method is computationally much more efficient than the full-likelihood method, and for the cases of both sexes polygamous and markers with genotyping errors, it can be several orders faster. The new method can handle a large sample with thousands of individuals and the number of markers limited only by the computer memory.     

Parentage and sibship exclusions: higher statistical power with more family members

Parentage exclusion probabilities are now routinely calculated in genetic marker-assisted parentage analyses to indicate the statistical power of the analyses achievable for a given set of markers, and to measure the informativeness of a set of markers for parentage inference. Previous formulas invariably assume that parentage is to be sought for a single offspring, while in practice multiple full siblings might be sampled (for example, seeds, eggs or young from a pair of monogamous parents) and their father, mother or both are to be assigned among a number of candidates. In this study, I derive formulas for parentage exclusion probabilities for an arbitrary number (n) of fullsibs, which reduce to previous equations for the special case of n=1. I also derive sibship exclusion probabilities, and investigate the power of differentiating half-sib, avuncular and grandparent-grandoffspring relationships using unlinked autosomal markers among different numbers of tested individuals. Applications of the formulas are demonstrated using both theoretical and empirical data sets of allele frequencies. The results from the study highlight the conclusion that the power of genealogical relationship inferences can be enhanced enormously by analysing multiple individuals for a given set of markers. The equations derived in this study allow more accurate determination of marker information and of the power of a parentage/sibship analysis. In addition, they can be used to guide experimental designs of parentage analyses in selecting markers and determining the number of offspring to be sampled and genotyped.     

p-loci: a computer program for choosing the most efficient set of loci for parentage assignment

Determining how many and which codominant marker loci are required for accurate parentage assignment is not straightforward because levels of marker polymorphism, linkage, allelic distributions among potential parents and other factors produce differences in the discriminatory power of individual markers and sets of markers. p-loci software identifies the most efficient set of codominant markers for assigning parentage at a user-defined level of success, using either simulated or actual offspring genotypes of known parentage. Simulations can incorporate linkage among markers, mating design and frequencies of null alleles and/or genotyping errors. p-loci is available for windows systems at http://marineresearch.oregonstate.edu/genetics/ploci.htm.     

COLONY: a program for parentage and sibship inference from multilocus genotype data

Pedigrees, depicting genealogical relationships between individuals, are important in several research areas. Molecular markers allow inference of pedigrees in wild species where relationship information is impossible to collect by observation. Marker data are analysed statistically using methods based on Mendelian inheritance rules. There are numerous computer programs available to conduct pedigree analysis, but most software is inflexible, both in terms of assumptions and data requirements. Most methods only accommodate monogamous diploid species using codominant markers without genotyping error. In addition, most commonly used methods use pairwise comparisons rather than a full-pedigree likelihood approach, which considers the likelihood of the entire pedigree structure and allows the simultaneous inference of parentage and sibship. Here, we describe colony, a computer program implementing full-pedigree likelihood methods to simultaneously infer sibship and parentage among individuals using multilocus genotype data. colony can be used for both diploid and haplodiploid species; it can use dominant and codominant markers, and can accommodate, and estimate, genotyping error at each locus. In addition, colony can carry out these inferences for both monoecious and dioecious species. The program is available as a Microsoft Windows version, which includes a graphical user interface, and a Macintosh version, which uses an R-based interface.     

Microsatellite-AFLP for genetic mapping of complex polyploids.

In spite of the economical relevance of polyploid crops, genetic mapping of these species has been relatively overlooked. This is because of intrinsic difficulties such as the uncertainty of the chromosome behavior at meiosis I and the need for very large segregating populations. An important, yet underestimated issue, in mapping polyploids is the choice of the molecular marker system. An ideal molecular marker system for polyploid mapping should maximize the percentage of single dose markers (SDMs) detected and the possibility of recognizing allelic markers. In the present work, the marker index for genetic mapping (MIgm) of M-AFLP is compared with that of AFLP and SAMPL. M-AFLPs have the highest MIgm values (22 vs. 18.5 of SAMPL and 9.83 of AFLP) mostly because of their high power to detect polymorphism. Owing to their prevalent codominant inheritance, it is proposed that M-AFLP can be used for the preliminary identification of hom(e)ologous groups.     

Estimation of copy number in polyploid plants: the good,the bad,and the ugly

Genetic studies in polyploid plants rely heavily on the collection of data from dominant marker loci. A dominant marker locus is a locus for which only the presence or absence of an observable (dominant) allele is recorded. Before these marker loci can be used for genetic exploration, the number of copies of a dominant allele carried by a parent (copy number) must be determined for each marker locus. Copy number in polyploids is estimated using a hypothesis testing procedure. The performance of this estimation procedure has never been evaluated. In this paper, I quantify whether the highly sought after single-copy markers can be accurately identified, if the performance of the estimation procedure improves with increasing sample size, and whether the estimation procedure is capable of accurately estimating the copy number of high copy markers. I found that the probability of incorrectly estimating copy number is quite low and that more data can actually reduce the accuracy of the estimation procedure when the testing assumptions are violated. Fortunately, when a significant result is obtained, it is almost always correct. The challenge often is in obtaining a significant result.     

Amplified fragment length polymorphisms and sequence data in the phylogenetic analysis of polyploids: multiple origins of Veronica cymbalaria (Plantaginaceae)

The origin of polyploid Veronica cymbalaria (Plantaginaceae) was investigated using DNA sequence data and amplified fragment length polymorphism (AFLP) fingerprints to reveal the parentage of this taxon. The use of AFLP fingerprints in phylogenetic analysis is problematic and various methods have therefore been compared. DNA sequence data (for the internal transcribed spacer (ITS) region and the plastid trnL-F region (trnL intron, 3'exon, and trnL-F spacer)) and polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) analysis of the ITS region suggested a reliable hypothesis for the evolution of the V. cymbalaria complex. This hypothesis allowed evaluation of the effect of different distance measures (Jaccard and Nei-Li) in phenetic, character-state weighted parsimony, and Bayesian analyses of AFLP markers. The study establishes that tetraploid V. cymbalaria originated at least twice in the eastern Mediterranean, with one parent differing in the two separate origins. Hexaploid V. cymbalaria originated even more often. The results illustrate that even subtle differences in the analyses of AFLP markers can lead to drastically different conclusions. The study reveals multiple origins of a Mediterranean polyploid species. Furthermore, it demonstrates that the analysis of a complex marker system such as AFLP fingerprints using only one type of analysis can easily be misleading.     

DYNAMICS OF POLYPLOID FORMATION IN TRAGOPOGON (ASTERACEAE): RECURRENT FORMATION,GENE FLOW,AND POPULATION STRUCTURE

Polyploidy is a major feature of angiosperm evolution and diversification. Most polyploid species have formed multiple times, yet we know little about the genetic consequences of recurrent formations. Among the clearest examples of recurrent polyploidy are Tragopogon mirus and T. miscellus (Asteraceae), each of which has formed repeatedly in the last ～80 years from known diploid progenitors in western North America. Here, we apply progenitor‐specific microsatellite markers to examine the genetic contributions to each tetraploid species and to assess gene flow among populations of independent formation. These data provide fine‐scale resolution of independent origins for both polyploid species. Importantly, multiple origins have resulted in considerable genetic variation within both polyploid species; however, the patterns of variation detected in the polyploids contrast with those observed in extant populations of the diploid progenitors. The genotypes detected in the two polyploid species appear to represent a snapshot of historical population structure in the diploid progenitors, rather than modern diploid genotypes. Our data also indicate a lack of gene flow among polyploid plants of independent origin, even when they co‐occur, suggesting potential reproductive barriers among separate lineages in both polyploid species.     

Molecular phylogeny and reticulate origins of the polyploid Bromus species from section Genea (Poaceae)

The origin of polyploid Bromus species of section Genea was investigated using molecular data. This group of annual species native from the Old-World is composed of three diploids, two tetraploids, one hexaploid, and one octoploid. Molecular cloning, sequencing, and phylogenetic analyses were performed on several accessions per species. We used the low copy nuclear gene Waxy, repeated rDNA spacers ITS1 and ITS2 and chloroplast spacers trnT-trnL and trnL-trnF. Our analyses revealed four different lineages involved in the parentage of the polyploids and confirmed their reticulate origin. Three of these lineages are closely related to the diploid species B. sterilis, B. tectorum, and B. fasciculatus. The fourth lineage could not be related to any diploid according to the available data. Our data gave insights on the origin of all the polyploids of section Genea, and chloroplast data allowed us to identify the maternal lineages. The Waxy gene was the most informative regarding origin of the polyploids. The Waxy copies duplicated by polyploidy appear selectively maintained in the polyploid species. No sequence heterogeneity was encountered in the ITS region, where concerted evolution seems to have occurred toward either maternal or paternal repeats. These results provide new information about the origin and molecular evolution of these polyploids and will allow a more accurate taxonomic treatment of the concerned species, based on their evolutionary history.     

Using molecular markers for pedigree reconstruction of the greater amberjack (Seriola dumerili) in the absence of parental information

Ensuring appropriate levels of genetic diversity in captive populations is essential to avoid inbreeding and loss of rare alleles by genetic drift. Pedigree reconstruction and parentage analysis in the absence of parental genotypes can be a challenging task that relies in the assignment of sibship relationships among the offspring. Here, we used eight highly variable microsatellite markers and three different assignment methods to reconstruct the most likely genotypes of a parental group of wild Seriola dumerili fish based on the genotypes of six cohorts of their offspring, to assess their relative contributions to the offspring. We found that a combination of the four most variable microsatellites was enough to identify the number of parents and their contribution to the offspring, suggesting that the variability of the markers can be more critical than the number of markers. Estimated effective population sizes were lower than the number of breeders and variable among years. The results suggest unequal parental contribution that should be accounted for breeding programs in the future.     

Detecting and mapping repulsion-phase linkage in polyploids with polysomic inheritance

It has been suggested that ratios of coupling- to repulsion-phase linked markers can be used to distinguish between allopolyploids and autopolyploids, because repulsion-phase linkages are much more difficult to detect in autopolyploids with polysomic inheritance than allopolyploids with disomic inheritance. In this report, we analyze the segregation pattern of repulsion-phase linked markers in polyploids without complete preferential pairing. The observed repulsion-phase recombination fraction (R) in such polyploids is composed of a fraction due to crossing-over (R_c) and another fraction due to independent assortment (R_i). R_i is the minimum distance that can be detected between repulsion-phase linked markers. Because R_i is high in autopolyploids (0.3373, 0.4000, 0.4286 and 0.4444) for autopolyploids of 2n=4x, 6x, 8x and 10x), large population sizes are required to reliably detect repulsion linkages. In addition, the default linkage used in mapping-programs must be greater than the corresponding R_i to determine whether a polyploid is a true autopolyploid. Unfortunately, much lower default linkages than the R_is have been used in recent polyploid studies to determine polyploid type, and markers have been incorporated into polyploid maps based on the R values. Herein, we describe how mapping repulsion linkages can result in spurious results, and present methods to accurately detect the degree of preferential pairing in polyploids using repulsion linkage analysis. Received: 29 February 2000 / Accepted: 17 July 2000     

High-throughput single nucleotide polymorphism genotyping in wheat (Triticum spp.)

Over the past few years, considerable progress has been made in high-throughput single nucleotide polymorphism (SNP) genotyping technologies, largely through the investment of the human genetics community. These technologies are well adapted to diploid species. For plant breeding purposes, it is important to determine whether these genotyping methods are adapted to polyploidy, as most major crops are former or recent polyploids. To address this problem, we tested the capacity of the multiplex technology SNPlex™ with a set of 47 wheat SNPs to genotype DNAs of 1314 lines that were organized in four 384-well plates. These lines represented different taxa of tetra- and hexaploid Triticum species and their wild diploid relatives. We observed 40 markers which gave less than 20% missing data. Different methods, based on either Sanger sequencing or the MassARRAY^® genotyping technology, were then used to validate the genotypes obtained by SNPlex™ for 11 markers. The concordance of the genotypes obtained by SNPlex™ with the results obtained by the different validation methods was 96%, except for one discarded marker. Furthermore, a mapping study on six markers showed the expected genetic positions previously described. To conclude, this study showed that high-throughput genotyping technologies developed for diploid species can be used successfully in polyploids, although there is a need for manual reading. For the first time in wheat species, a core of 39 SNPs is available that can serve as the basis for the development of a complete SNPlex™ set of 48 markers.     

Kinship analyses identify fish dispersal events on a temperate coastline

Connectivity is crucial for the persistence and resilience of marine species, the establishment of networks of marine protected areas and the delineation of fishery management units. In the marine environment, understanding connectivity is still a major challenge, due to the technical difficulties of tracking larvae. Recently, parentage analysis has provided a means to address this question effectively. To be effective, this method requires limited adult movement and extensive sampling of parents, which is often not possible for marine species. An alternative approach that is less sensitive to constraints in parental movement and sampling could be the reconstruction of sibships. Here, we directly measure connectivity and larval dispersal in a temperate marine ecosystem through both analytical approaches. We use data from 178 single nucleotide polymorphism markers to perform parentage and sibship reconstruction of the black-faced blenny (Tripterygion delaisi) from an open coastline in the Mediterranean Sea. Parentage analysis revealed a decrease in dispersal success in the focal area over 1 km distance and approximately 6.5% of the juveniles were identified as self-recruits. Sibship reconstruction analysis found that, in general, full siblings did not recruit together to the same location, and that the largest distance between recruitment locations was much higher (11.5 km) than found for parent–offspring pairs (1.2 km). Direct measurements of dispersal are essential to understanding connectivity patterns in different marine habitats, and show the degree of self-replenishment and sustainability of populations of marine organisms. We demonstrate that sibship reconstruction allows direct measurements of dispersal and family structure in marine species while being more easily applied in those species for which the collection of the parental population is difficult or unfeasible.     

A bivalent polyploid model for linkage analysis in outcrossing tetraploids

Polyploids can be classified as either allopolyploids or autopolyploids based on their presumed origins. From a perspective of linkage analysis, however, the nature of polyploids can be better described as bivalent polyploids, in which two chromosomes pair at meiosis, multivalent polyploids, in which more than two chromosomes pair, and general polyploids, in which bivalent and multivalent formations occur simultaneously. In this paper, we develop a statistical method for linkage analysis of polymorphic markers in bivalent polyploids. This method takes into account a unique cytological pairing mechanism for the formation of diploid gametes in tetraploids-preferential bivalent pairings at meiosis during which two homologous chromosomes pair with a higher probability than two homoeologous chromosomes. The higher frequency of homologous over homoeologous pairing, defined as the preferential pairing factor, affects the segregation patterns and linkage analysis of different genes on the same chromosome. A maximum likelihood method implemented with the EM algorithm is proposed to simultaneously estimate linkage and parental linkage phases over a pair of markers from any possible marker cross type between two outbred bivalent tetraploid parents demonstrating preferential bivalent pairings. Simulation studies display that the method can be well used to estimate the recombination fraction between different marker types and the preferential pairing factor typical of bivalent tetraploids. The implications of this method for current genome projects in polyploid species are discussed.     

A mixed polyploid model for linkage analysis in outcrossing tetraploids using a pseudo-test backcross design.

Based on how chromosomes pair at meiosis, the nature of polyploids can be described by bivalent polyploids, multivalent polyploids, and mixed polyploids. In bivalent polyploids, only two chromosomes pair, during which two more similar chromosomes have a higher pairing probability (preferential pairing) than two less similar chromosomes, whereas in multivalent polyploids more than two chromosomes pair at a time, which results in double reduction. Preferential chromosome pairings and double reduction affect the frequencies of gamete formation and, therefore, linkage analysis of polymorphic markers in bivalent and multivalent polyploids, respectively. For mixed polyploids, in which both bivalent and multivalent formations occur simultaneously, linkage analysis is affected by both preferential pairings and double reduction. In this study, we develop a hierarchical maximum likelihood model for discerning gamete genotypes derived from different pairing mechanisms and different formation modes. The first-stage model in the hierarchy is formulated to characterize the relative frequencies of bivalent and multivalent pairing configurations in terms of the preferential pairing factor. The second-stage model is derived to rule out identical gamete genotypes into their different formation modes with relative probabilities determined by the recombination fraction. The first-stage pairing mechanism and second-stage formation mode are integrated to provide the simultaneous maximum likelihood estimates of the preferential pairing factor, the frequency of double reduction, and the recombination fraction, by implementing the EM algorithm. We performed extensive simulation studies to demonstrate the statistical properties of our hierarchical model for linkage analysis in tetraploids. The implications of our model for polyploid linkage mapping are discussed.     

Using genetic markers to directly estimate gene flow and reproductive success parameters in plants on the basis of naturally regenerated seedlings

Estimating seed and pollen gene flow in plants on the basis of samples of naturally regenerated seedlings can provide much needed information about "realized gene flow," but seems to be one of the greatest challenges in plant population biology. Traditional parentage methods, because of their inability to discriminate between male and female parentage of seedlings, unless supported by uniparentally inherited markers, are not capable of precisely describing seed and pollen aspects of gene flow realized in seedlings. Here, we describe a maximum-likelihood method for modeling female and male parentage in a local plant population on the basis of genotypic data from naturally established seedlings and when the location and genotypes of all potential parents within the population are known. The method models female and male reproductive success of individuals as a function of factors likely to influence reproductive success (e.g., distance of seed dispersal, distance between mates, and relative fecundity--i.e., female and male selection gradients). The method is designed to account for levels of seed and pollen gene flow into the local population from unsampled adults; therefore, it is well suited to isolated, but also wide-spread natural populations, where extensive seed and pollen dispersal complicates traditional parentage analyses. Computer simulations were performed to evaluate the utility and robustness of the model and estimation procedure and to assess how the exclusion power of genetic markers (isozymes or microsatellites) affects the accuracy of the parameter estimation. In addition, the method was applied to genotypic data collected in Scots pine (isozymes) and oak (microsatellites) populations to obtain preliminary estimates of long-distance seed and pollen gene flow and the patterns of local seed and pollen dispersal in these species.     

Multiple origins of polyploidy and the geographic structure of Heuchera grossulariifolia

Multiple origins of polyploidy from an ancestral diploid plant species were investigated using restriction site polymorphism and sequence variation in the chloroplast DNA (cpDNA) of Heuchera grossulariifolia (Saxifragaceae). Phylogenetic analysis indicated that autopolyploidy has arisen at least twice in the evolutionary history of this species and potentially up to as many as seven times. These results suggest a greater range of independent polyploid origins as compared to a previous study of H. grossulariifolia using cpDNA restriction sites that indicated a minimum of three independent origins. Moreover, most polyploid populations did not contain cpDNA haplotypes from a single origin, but rather combined haplotypes from at least two polyploid origins. Past migration among polyploid populations of independent origin or localized polyploid formation may explain the distribution of polyploid haplotypes within and among populations. The analysis also revealed a discrepancy between relatedness and geographical location. In nearly all sympatric populations of diploids and polyploids, polyploids had the same cpDNA haplotypes as diploids from a geographically remote population. This geographical discordance has several possible explanations, including small sample sizes, extinction of parental diploid haplotypes, chloroplast introgression, and homoplasy in the cpDNA sequence data. We conclude that the recurrent formation of polyploids is an important evolutionary mechanism in the diversification of H. grossulariifolia .