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.     

Estimates of genetic parameters and breeding values from western larch open-pollinated families using marker-based relationship

The availability and affordability of genetic markers made it possible to estimate quantitative genetic parameters without mating designs' structured pedigree. Here, we compared 4-year height's heritability and individuals' breeding values for a western larch common-garden population of 1,418 offspring representing 15 open-pollinated families from a 41-clone seed orchard using (a) classical pedigree models such as half- and full-sib families and (b) a molecular marker-based pedigree-free model using four pair-wise relationship estimation methods using eight informative SSR markers. The results highlighted the commonly observed inflated estimates of genetic parameters often obtained from half-sib analyses, as well as demonstrating some of the full-sib analyses' caveats. The pedigree reconstruction permitted the identification of selfed individuals, thus allowing evaluating the impact of selfing on marker-based genetic parameter estimation. The results demonstrated the utility of marker-based methods as an alternative to the classical pedigree-based approaches. Unlike the pedigree-based methods, the marker-based approach allowed better partitioning the variance components as well as separating the non-additive and additive genetic variance. The theoretical underpinning of the marker-based approach was discussed.     

Development and testing of a genetic marker‐based pedigree reconstruction system ‘PR‐genie’ incorporating size‐class data

For wildlife populations, it is often difficult to determine biological parameters that indicate breeding patterns and population mixing, but knowledge of these parameters is essential for effective management. A pedigree encodes the relationship between individuals and can provide insight into the dynamics of a population over its recent history. Here, we present a method for the reconstruction of pedigrees for wild populations of animals that live long enough to breed multiple times over their lifetime and that have complex or unknown generational structures. Reconstruction was based on microsatellite genotype data along with ancillary biological information: sex and observed body size class as an indicator of relative age of individuals within the population. Using body size‐class data to infer relative age has not been considered previously in wildlife genealogy and provides a marked improvement in accuracy of pedigree reconstruction. Body size‐class data are particularly useful for wild populations because it is much easier to collect noninvasively than absolute age data. This new pedigree reconstruction system, PR‐genie, performs reconstruction using maximum likelihood with optimization driven by the cross‐entropy method. We demonstrated pedigree reconstruction performance on simulated populations (comparing reconstructed pedigrees to known true pedigrees) over a wide range of population parameters and under assortative and intergenerational mating schema. Reconstruction accuracy increased with the presence of size‐class data and as the amount and quality of genetic data increased. We provide recommendations as to the amount and quality of data necessary to provide insight into detailed familial relationships in a wildlife population using this pedigree reconstruction technique.     

The estimation of genetic relationships using molecular markers and their efficiency in estimating heritability in natural populations

Molecular marker data collected from natural populations allows information on genetic relationships to be established without referencing an exact pedigree. Numerous methods have been developed to exploit the marker data. These fall into two main categories: method of moment estimators and likelihood estimators. Method of moment estimators are essentially unbiased, but utilise weighting schemes that are only optimal if the analysed pair is unrelated. Thus, they differ in their efficiency at estimating parameters for different relationship categories. Likelihood estimators show smaller mean squared errors but are much more biased. Both types of estimator have been used in variance component analysis to estimate heritability. All marker-based heritability estimators require that adequate levels of the true relationship be present in the population of interest and that adequate amounts of informative marker data are available. I review the different approaches to relationship estimation, with particular attention to optimizing the use of this relationship information in subsequent variance component estimation.     

The use of marker‐based relationship information to estimate the heritability of body weight in a natural population: a cautionary tale

A number of procedures have been developed that allow the genetic parameters of natural populations to be estimated using relationship information inferred from marker data rather than known pedigrees. Three published approaches are available; the regression, pair‐wise likelihood and Markov Chain Monte Carlo (MCMC) sib‐ship reconstruction methods. These were applied to body weight and molecular data collected from the Soay sheep population of St. Kilda, which has a previously determined pedigree. The regression and pair‐wise likelihood approaches do not specify an exact pedigree and yielded unreliable heritability estimates, that were sensitive to alteration of the fixed effects. The MCMC method, which specifies a pedigree prior to heritability estimation, yielded results closer to those determined using the known pedigree. In populations of low average relationship, such as the Soay sheep population, determination of a reliable pedigree is more useful than indirect approaches that do not specify a pedigree.     

Estimation of pairwise relatedness between individuals and characterization of isolation-by-distance processes using dominant genetic markers

A new estimator of the pairwise relatedness coefficient between individuals adapted to dominant genetic markers is developed. This estimator does not assume genotypes to be in Hardy-Weinberg proportions but requires a knowledge of the departure from these proportions (i.e. the inbreeding coefficient). Simulations show that the estimator provides accurate estimates, except for some particular types of individual pairs such as full-sibs, and performs better than a previously developed estimator. When comparing marker-based relatedness estimates with pedigree expectations, a new approach to account for the change of the reference population is developed and shown to perform satisfactorily. Simulations also illustrate that this new relatedness estimator can be used to characterize isolation by distance within populations, leading to essentially unbiased estimates of the neighbourhood size. In this context, the estimator appears fairly robust to moderate errors made on the assumed inbreeding coefficient. The analysis of real data sets suggests that dominant markers (random amplified polymorphic DNA, amplified fragment length polymorphism) may be as valuable as co-dominant markers (microsatellites) in studying microgeographic isolation-by-distance processes. It is argued that the estimators developed should find major applications, notably for conservation biology.     

A General Unified Framework to Assess the Sampling Variance of Heritability Estimates Using Pedigree or Marker-Based Relationships

Heritability is a population parameter of importance in evolution, plant and animal breeding, and human medical genetics. It can be estimated using pedigree designs and, more recently, using relationships estimated from markers. We derive the sampling variance of the estimate of heritability for a wide range of experimental designs, assuming that estimation is by maximum likelihood and that the resemblance between relatives is solely due to additive genetic variation. We show that well-known results for balanced designs are special cases of a more general unified framework. For pedigree designs, the sampling variance is inversely proportional to the variance of relationship in the pedigree and it is proportional to 1/N, whereas for population samples it is approximately proportional to 1/N², where N is the sample size. Variation in relatedness is a key parameter in the quantification of the sampling variance of heritability. Consequently, the sampling variance is high for populations with large recent effective population size (e.g., humans) because this causes low variation in relationship. However, even using human population samples, low sampling variance is possible with high N.     

Testing marker-based estimates of heritability in the wild

Marker-based estimates of heritability are an attractive alternative to pedigree-based methods for estimating quantitative genetic parameters in field studies where it is difficult or impossible to determine relationships and pedigrees. Here I test the ability of the marker-based method to estimate heritability of a suite of traits in a wild population of bighorn sheep (Ovis canadensis) using marker data from 32 microsatellite loci. I compared marker-based estimates with estimates obtained using a pedigree and the animal model. Marker-based estimates of heritability were imprecise and downwardly biased. The high degree of uncertainty in marker-based estimates suggests that the method may be sufficient to detect the presence of genetic variance for highly heritable traits, but not sufficiently reliable to estimate genetic parameters.     

Craniometric variation,genetic theory,and modern human origins

Recent controversies surrounding models of modern human origins have focused on among-group variation, particularly the reconstruction of phylogenetic trees from mitochondrial DNA (mtDNA) and, the dating of population divergence. Problems in tree estimation have been seen as weakening the case for a replacement model and favoring a multiregional evolution model. There has been less discussion of patterns of within-group variation, although the mtDNA evidence has consistently shown the greatest diversity within African populations. Problems of interpretation abound given the numerous factors that can influence within-group variation, including the possibility of earlier divergence, differences in population size, patterns of population expansion, and variation in migration rates. We present a model of within-group phenotypic variation and apply it to a large set of craniometric data representing major Old World geographic regions (57 measurements for 1,159 cases in four regions: Europe, Sub-Saharan Africa, Australasia, and the Far East). The model predicts a linear relationship between variation within populations (the average within-group variance) and variation between populations (the genetic distance of populations to pooled phenotypic means). On a global level this relationship should hold if the long-term effective population sizes of each region are correctly specified. Other potential effects on withingroup variation are accounted for by the model. Comparison of observed and expected variances under the assumption of equal effective sizes for four regions indicates significantly greater within-group variation in Africa and significantly less within-group variation in Europe. These results suggest that the long-term effective population size was greatest in Africa. Closer examination of the model suggests that the long-term African effective size was roughly three times that of any other geographic region. Using these estimates of relative population size, we present a method for analyzing ancient population structure, which provides estimates of ancient migration. This method allows us to reconstruct migration history between geographic regions after adjustment for the effect of genetic drift on interpopulational distances. Our results show a clear isolation of Africa from other regions. We then present a method that allows direct estimation of the ancient migration matrix, thus providing us with information on the actual extent of interregional migration. These methods also provide estimates of time frames necessary to reach genetic equilibrium. The ultimate goal is extracting as much information from present-day patterns of human variation relevannt to issues of human origins. Our results are in agreement with mismatch distribution analysis of mtDNA, and they support a “weak Garden o Eden” model. In this model, modern-day variation can be explained by divergence from an initial source (perhaps Africa) into a number o small isolated populations, followed by later population expansion throughout our species. The major populationn expansions of Homo sapiens during and after the late Pleistocene have had the effect of “freezing” ancient patterns of population structure. While this is not the only possible scenario, we do note the close agreement with ecent analyses of mtDNA mismatch distibutions. © 1994 Wiley-Liss, Inc.     

Integrating microsatellite and pedigree analyses to facilitate the captive management of the endangered Mississippi sandhill crane (Grus canadensis pulla)

The minimization of kinship in captive populations is usually achieved through the use of pedigree information. However, pedigree knowledge alone is not sufficient if pedigree information is missing, questionable, or when the founders of the captive population are related to one another. If this is the case, higher levels of inbreeding and lower levels of genetic diversity may be present in a captive population than those calculated by pedigree analyses alone. In this study, the genetic status of the critically endangered Mississippi sandhill crane (MSC) (Grus canadensis pulla) was analyzed using studbook data from the U.S. Fish and Wildlife Service managed captive breeding program as well as microsatellite DNA data. These analyses provided information on shared founder genotypes, allowing for refined analysis of genetic variation in the population, and the development of a new DNA-based studbook pedigree that will assist in the genetic management of the MSC population.     

Assessment of relationships between pigs based on pedigree and genomic information

Relationships play a very important role in studies on quantitative genetics. In traditional breeding, pedigree records are used to establish relationships between animals; while this kind of relationship actually represents one kind of relatedness, it cannot distinguish individual specificity, capture the variation between individuals or determine the actual genetic superiority of an animal. However, with the popularization of high-throughput genotypes, assessments of relationships among animals based on genomic information could be a better option. In this study, we compared the relationships between animals based on pedigree and genomic information from two pig breeding herds with different genetic backgrounds and a simulated dataset. Two different methods were implemented to calculate genomic relationship coefficients and genomic kinship coefficients, respectively. Our results show that, for the same kind of relative, the average genomic relationship coefficients (G matrix) were very close to the pedigree relationship coefficients (A matrix), and on average, the corresponding values were halved in genomic kinship coefficients (K matrix). However, the genomic relationship yielded a larger variation than the pedigree relationship, and the latter was similar to that expected for one relative with no or little variation. Two genomic relationship coefficients were highly correlated, for farm1, farm2 and simulated data, and the correlations for the parent-offspring, full-sib and half-sib were 0.95, 0.90 and 0.85; 0.93, 0.96 and 0.89; and 0.52, 0.85 and 0.77, respectively. When the inbreeding coefficient was measured, the genomic information also yielded a higher inbreeding coefficient and a larger variation than that yielded by the pedigree information. For the two genetically divergent Large White populations, the pedigree relationship coefficients between the individuals were 0, and 62 310 and 175 271 animal pairs in the G matrix and K matrix were greater than 0. Our results demonstrated that genomic information outperformed the pedigree information; it can more accurately reflect the relationships and capture the variation that is not detected by pedigree. This information is very helpful in the estimation of genomic breeding values or gene mapping. In addition, genomic information is useful for pedigree correction. Further, our findings also indicate that genomic information can establish the genetic connection between different groups with different genetic background. In addition, it can be used to provide a more accurate measurement of the inbreeding of an animal, which is very important for the assessment of a population structure and breeding plan. However, the approaches for measuring genomic relationships need further investigation.     

Heterozygosity, inbreeding and neonatal traits in Soay sheep on St Kilda

We investigated whether birth weight and neonatal survival, a period within which 24% of all mortalities occur, were correlated with levels of inbreeding in St Kilda Soay sheep, using pedigree inbreeding coefficients and four marker-based estimators of inbreeding. None of the inbreeding estimators, either of the offspring, or of their mothers, explained significant variation in a lamb's birth weight or probability of surviving the neonatal period, suggesting low inbreeding depression for these traits. We evaluated the correlation between the marker-based measures of inbreeding and inbreeding coefficients obtained from the Soay pedigree, where paternal links were inferred using the same panel of microsatellite markers. Even when using a relatively complete portion of the pedigree, in which all individuals had known maternal and paternal grandparents, the correlation was found to be weak (r = -0.207, where mean f = 0.0168). These results add support to the recent prediction that when the mean and variance in inbreeding are low in a population, heterozygosity-fitness correlations can be very weak or even undetectable. The pursuit of more detailed pedigrees offers the best prospect for identifying inbreeding depression within this study population.     

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.     

MIGRATION AND GENETIC DRIFT IN HUMAN POPULATIONS

In humans and many other species, mortality is concentrated early in the life cycle, and is low during the ages of dispersal and reproduction. Yet precisely the opposite is assumed by classical population-genetics models of migration and genetic drift. We introduce a model in which population regulation occurs before migration. In contrast to the conventional model, our model implies that geographic variation in the allele frequencies of newborns should exceed that of adults. Thus, it is important to distinguish genetic variation of adults from that of newborns in species with human-like life cycles. Classical models deal with the variance of group allele frequencies about the allele frequency of a hypothetical “continent” or “foundation stock.” Empirical studies, however, can only measure “reduced” variance, i.e., variance about the current population mean. Our model deals with reduced variance, and should therefore be more relevant to field studies. We show that reduced variance converges faster, which implies that populations are more likely to be at equilibrium with respect to reduced than unreduced variance. To summarize the effect of migration on genetic population structure, we introduce a new parameter, the effective migration rate. Unlike most population structure statistics, it does not confound the effects of mobility and population size, and it should therefore be useful for comparisons between populations. Finally, we show that the difference between geographic variation of newborn and adult allele frequencies contains information about both effective population size and effective migration rate.     

Genome-Wide Estimates of Coancestry and Inbreeding in a Closed Herd of Ancient Iberian Pigs

Maintaining genetic variation and controlling the increase in inbreeding are crucial requirements in animal conservation programs. The most widely accepted strategy for achieving these objectives is to maximize the effective population size by minimizing the global coancestry obtained from a particular pedigree. However, for most natural or captive populations genealogical information is absent. In this situation, microsatellites have been traditionally the markers of choice to characterize genetic variation, and several estimators of genealogical coefficients have been developed using marker data, with unsatisfactory results. The development of high-throughput genotyping techniques states the necessity of reviewing the paradigm that genealogical coancestry is the best parameter for measuring genetic diversity. In this study, the Illumina PorcineSNP60 BeadChip was used to obtain genome-wide estimates of rates of coancestry and inbreeding and effective population size for an ancient strain of Iberian pigs that is now in serious danger of extinction and for which very accurate genealogical information is available (the Guadyerbas strain). Genome-wide estimates were compared with those obtained from microsatellite and from pedigree data. Estimates of coancestry and inbreeding computed from the SNP chip were strongly correlated with genealogical estimates and these correlations were substantially higher than those between microsatellite and genealogical coefficients. Also, molecular coancestry computed from SNP information was a better predictor of genealogical coancestry than coancestry computed from microsatellites. Rates of change in coancestry and inbreeding and effective population size estimated from molecular data were very similar to those estimated from genealogical data. However, estimates of effective population size obtained from changes in coancestry or inbreeding differed. Our results indicate that genome-wide information represents a useful alternative to genealogical information for measuring and maintaining genetic diversity.     

Prediction of identity by descent probabilities from marker-haplotypes

The prediction of identity by descent (IBD) probabilities is essential for all methods that map quantitative trait loci (QTL). The IBD probabilities may be predicted from marker genotypes and/or pedigree information. Here, a method is presented that predicts IBD probabilities at a given chromosomal location given data on a haplotype of markers spanning that position. The method is based on a simplification of the coalescence process, and assumes that the number of generations since the base population and effective population size is known, although effective size may be estimated from the data. The probability that two gametes are IBD at a particular locus increases as the number of markers surrounding the locus with identical alleles increases. This effect is more pronounced when effective population size is high. Hence as effective population size increases, the IBD probabilities become more sensitive to the marker data which should favour finer scale mapping of the QTL. The IBD probability prediction method was developed for the situation where the pedigree of the animals was unknown (i.e. all information came from the marker genotypes), and the situation where, say T, generations of unknown pedigree are followed by some generations where pedigree and marker genotypes are known.     

Unraveling Additive from Nonadditive Effects Using Genomic Relationship Matrices

The application of quantitative genetics in plant and animal breeding has largely focused on additive models, which may also capture dominance and epistatic effects. Partitioning genetic variance into its additive and nonadditive components using pedigree-based models (P-genomic best linear unbiased predictor) (P-BLUP) is difficult with most commonly available family structures. However, the availability of dense panels of molecular markers makes possible the use of additive- and dominance-realized genomic relationships for the estimation of variance components and the prediction of genetic values (G-BLUP). We evaluated height data from a multifamily population of the tree species Pinus taeda with a systematic series of models accounting for additive, dominance, and first-order epistatic interactions (additive by additive, dominance by dominance, and additive by dominance), using either pedigree- or marker-based information. We show that, compared with the pedigree, use of realized genomic relationships in marker-based models yields a substantially more precise separation of additive and nonadditive components of genetic variance. We conclude that the marker-based relationship matrices in a model including additive and nonadditive effects performed better, improving breeding value prediction. Moreover, our results suggest that, for tree height in this population, the additive and nonadditive components of genetic variance are similar in magnitude. This novel result improves our current understanding of the genetic control and architecture of a quantitative trait and should be considered when developing breeding strategies.     

Pedigree analysis of the closed nucleus of Iranian Baluchi sheep

A study was conducted to characterise genetic diversity in the closed nucleus of Baluchi sheep using pedigree analysis. Herdbook information collected between 1979 and 2008, including pedigree records on 21,721 animals, was used to compute inbreeding and average generation intervals. Effective population size and parameters derived from probability of gene origin were computed for ewes born between 2005 and 2008 with both parents known (female reference population). The average complete generation equivalent of the female reference population was 5.47. The mean generation interval was 3.33 years in the studied period. From 1983 to 1994, the rate of increase in inbreeding was approximately 0.2% per year, but, after 1994, inbreeding did not increase as in the preceding years and had an approximately flat trend over time. The mean relationship coefficients among rams, among ewes and between rams and ewes in active animals were calculated to predict the future level of inbreeding. The effective number of founders, effective number of ancestors and founder genome equivalent of the reference population were 80, 47 and 19.5, respectively. The realised effective population size was 134 animals. The results of this study indicated that the population under study has fairly good genetic variability.     

Modelling problems in conservation genetics using Drosophila: consequences of fluctuating population sizes

Many natural populations fluctuate widely in population size. This is predicted to reduce effective population size, genetic variation, and reproductive fitness, and to increase inbreeding. The effects of fluctuating population size were examined in small populations of Drosophila melanogaster of the same average size, but maintained using either fluctuating ( FPS ) or equal ( EPS ) population sizes.FPS lines were maintained using seven pairs and one pair in alternate generations, and EPS lines with four pairs per generation. Ten replicates of each treatment were maintained. After eight generations, FPS had a higher inbreeding coefficient than EPS (0.60 vs. 0.38), a lower average allozyme heterozygosity (0.068 vs. 0.131), and a much lower relative fitness (0.03 vs. 0.25). Estimates of effective population sizes for FPS and EPS were 3.8 and 7.9 from pedigree inbreeding, and 4.9 vs. 7.1 from changes in average heterozygosities, as compared to theoretical expectations of 3.3 vs. 8.0. Results were generally in accordance with theoretical predictions. Management strategies for populations of rare and endangered species should aim to minimize population fluctuations over generations.     

A comparison of microsatellite-based pairwise relatedness estimators

Studies of inbreeding depression or kin selection require knowledge of relatedness between individuals. If pedigree information is lacking, one has to rely on genotypic information to infer relatedness. In this study we investigated the performance (absolute and relative) of 10 marker-based relatedness estimators using allele frequencies at microsatellite loci obtained from natural populations of two bird species and one mammal species. Using Monte Carlo simulations we show that many factors affect the performance of estimators and that different sets of loci promote the use of different estimators: in general, there is no single best-performing estimator. The use of locus-specific weights turns out to greatly improve the performance of estimators when marker loci are used that differ strongly in allele frequency distribution. Microsatellite-based estimates are expected to explain between 25 and 79% of variation in true relatedness depending on the microsatellite dataset and on the population composition (i.e. the frequency distribution of relationship in the population). We recommend performing Monte Carlo simulations to decide which estimator to use in studies of pairwise relatedness.