Pedigree-free animal models: the relatedness matrix reloaded

Animal models typically require a known genetic pedigree to estimate quantitative genetic parameters. Here we test whether animal models can alternatively be based on estimates of relatedness derived entirely from molecular marker data. Our case study is the morphology of a wild bird population, for which we report estimates of the genetic variance-covariance matrices (G) of six morphological traits using three methods: the traditional animal model; a molecular marker-based approach to estimate heritability based on Ritland's pairwise regression method; and a new approach using a molecular genealogy arranged in a relatedness matrix (R) to replace the pedigree in an animal model. Using the traditional animal model, we found significant genetic variance for all six traits and positive genetic covariance among traits. The pairwise regression method did not return reliable estimates of quantitative genetic parameters in this population, with estimates of genetic variance and covariance typically being very small or negative. In contrast, we found mixed evidence for the use of the pedigree-free animal model. Similar to the pairwise regression method, the pedigree-free approach performed poorly when the full-rank R matrix based on the molecular genealogy was employed. However, performance improved substantially when we reduced the dimensionality of the R matrix in order to maximize the signal to noise ratio. Using reduced-rank R matrices generated estimates of genetic variance that were much closer to those from the traditional model. Nevertheless, this method was less reliable at estimating covariances, which were often estimated to be negative. Taken together, these results suggest that pedigree-free animal models can recover quantitative genetic information, although the signal remains relatively weak. It remains to be determined whether this problem can be overcome by the use of a more powerful battery of molecular markers and improved methods for reconstructing genealogies.     

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.     

On the use of large marker panels to estimate inbreeding and relatedness: empirical and simulation studies of a pedigreed zebra finch population typed at 771 SNPs

In recent years there has been a dramatic increase in the availability of high density genetic marker data for both model and non‐model organisms. A potential application of these data is to infer relatedness in the absence of a complete pedigree. Using a marker panel of 771 SNPs genotyped in three generations of an extensive zebra finch pedigree, correlations between pedigree relatedness and seven marker‐based estimates of relatedness were examined, as was the relationship between heterozygosity and inbreeding. Although marker‐based and pedigree relatedness were highly correlated, the variance in estimated relatedness was high. Further, the correlation between heterozygosity and inbreeding was weak, even though mean inbreeding coefficient is typical of that seen in wild vertebrate pedigrees; the weak relationship was in part due to the small variance in inbreeding in the pedigree. Our data suggest that using marker information to reconstruct the pedigree, and then calculating relatedness from the pedigree, is likely to give more accurate relatedness estimates than using marker‐based estimators directly.     

Performance of marker-based relatedness estimators in natural populations of outbred vertebrates

Knowledge of relatedness between pairs of individuals plays an important role in many research areas including evolutionary biology, quantitative genetics, and conservation. Pairwise relatedness estimation methods based on genetic data from highly variable molecular markers are now used extensively as a substitute for pedigrees. Although the sampling variance of the estimators has been intensively studied for the most common simple genetic relationships, such as unrelated, half- and full-sib, or parent-offspring, little attention has been paid to the average performance of the estimators, by which we mean the performance across all pairs of individuals in a sample. Here we apply two measures to quantify the average performance: first, misclassification rates between pairs of genetic relationships and, second, the proportion of variance explained in the pairwise relatedness estimates by the true population relatedness composition (i.e., the frequencies of different relationships in the population). Using simulated data derived from exceptionally good quality marker and pedigree data from five long-term projects of natural populations, we demonstrate that the average performance depends mainly on the population relatedness composition and may be improved by the marker data quality only within the limits of the population relatedness composition. Our five examples of vertebrate breeding systems suggest that due to the remarkably low variance in relatedness across the population, marker-based estimates may often have low power to address research questions of interest.     

spip 1.0: a program for simulating pedigrees and genetic data in age‐structured populations

We present the program spip for simulating multilocus genetic data on individuals in age‐structured populations. In addition to genetic data on sampled individuals, the pedigree connecting all individuals in the population is recorded. This allows investigation of the relationship between family structure and population parameters. We foresee that spip will be useful for evaluating multilocus estimators of pairwise relatedness and population structure, and for simulating the distribution of relatedness in populations with varying demographies. It also provides a method for simulating genetic drift in complex populations.     

Sibship reconstruction in hierarchical population structures using Markov chain Monte Carlo techniques

Markov chain Monte Carlo procedures allow the reconstruction of full-sibships using data from genetic marker loci only. In this study, these techniques are extended to allow the reconstruction of nested full- within half-sib families, and to present an efficient method for calculating the likelihood of the observed marker data in a nested family. Simulation is used to examine the properties of the reconstructed sibships, and of estimates of heritability and common environmental variance of quantitative traits obtained from those populations. Accuracy of reconstruction increases with increasing marker information and with increasing size of the nested full-sibships, but decreases with increasing population size. Estimates of variance component are biased, with the direction and magnitude of bias being dependent upon the underlying errors made during pedigree reconstruction.     

Ex situ population management in the absence of pedigree information

For captive breeding to play a significant role in conservation, ex situ populations must be scientifically managed to meet objective goals for retaining representative genetic variation. Imperfect genealogical information requires fundamental assumptions to be made that may bias downstream measures of genetic importance, upon which management decisions are based. The impacts of such assumptions are most pronounced within breeding programmes characterized by a high proportion of individuals of unknown ancestry, as exemplified by the large captive population of the St Vincent parrot (Amazona guildingii). The degree to which microsatellite-based estimates of relatedness may improve upon the assumptions of conventional pedigree-based management was investigated using genotypic data collected at eight microsatellite loci and two marker-based relatedness estimators. The measure, rxyLR, was found to explain the highest amount of variation in true relatedness. Integration of pairwise estimates of founder relatedness with studbook data transformed current understanding of the relatedness structure of the A. guildingii population from two subgroups characterized by a high and low degree of relatedness, respectively, to a situation where all 72 individuals are prioritized for breeding according to their estimated mean kinships. Furthermore, the discovery of opposing, directional bias exhibited by rxyLR and rxyQG in assigning dyads to a given relationship category suggests that an approach that utilizes a combination of pairwise relatedness estimators may provide the most genetic information for balancing the dual considerations of maximizing gene diversity and minimizing inbreeding in developing breeding recommendations.     

Estimating quantitative genetic parameters in wild populations: a comparison of pedigree and genomic approaches

The estimation of quantitative genetic parameters in wild populations is generally limited by the accuracy and completeness of the available pedigree information. Using relatedness at genomewide markers can potentially remove this limitation and lead to less biased and more precise estimates. We estimated heritability, maternal genetic effects and genetic correlations for body size traits in an unmanaged long‐term study population of Soay sheep on St Kilda using three increasingly complete and accurate estimates of relatedness: (i) Pedigree 1, using observation‐derived maternal links and microsatellite‐derived paternal links; (ii) Pedigree 2, using SNP‐derived assignment of both maternity and paternity; and (iii) whole‐genome relatedness at 37 037 autosomal SNPs. In initial analyses, heritability estimates were strikingly similar for all three methods, while standard errors were systematically lower in analyses based on Pedigree 2 and genomic relatedness. Genetic correlations were generally strong, differed little between the three estimates of relatedness and the standard errors declined only very slightly with improved relatedness information. When partitioning maternal effects into separate genetic and environmental components, maternal genetic effects found in juvenile traits increased substantially across the three relatedness estimates. Heritability declined compared to parallel models where only a maternal environment effect was fitted, suggesting that maternal genetic effects are confounded with direct genetic effects and that more accurate estimates of relatedness were better able to separate maternal genetic effects from direct genetic effects. We found that the heritability captured by SNP markers asymptoted at about half the SNPs available, suggesting that denser marker panels are not necessarily required for precise and unbiased heritability estimates. Finally, we present guidelines for the use of genomic relatedness in future quantitative genetics studies in natural populations.     

Population Genetics,Dispersal, and Kinship Among Wild Squirrel Monkeys (Saimiri sciureus macrodon): Preferential Association Between Closely Related Females and Its Implications for Insect Prey Capture Success

Little genetic information is available to evaluate hypotheses concerning the parameters that affect population genetic structure in primate taxa that exhibit interspecific variation in social systems, such as squirrel monkeys (Saimiri). Here, we used genetic data to assess dispersal patterns, kin structure, and preferential association with same-sex kin in a wild population of Saimiri sciureus macrodon. We also analyzed behavioral data to assess whether individuals that maintain shorter interindividual distances show increased insect foraging success. If there was greater male than female dispersal, then we expected mean pairwise relatedness, F _ST values, and intragroup mean corrected assignment indices to be greater among adult females than among adult males. We also expected matrices of pairwise affinity indices (PAIs) for “association” (time spent ≤5 m) and “proximity” (time spent ≤10 m) among female dyads to positively correlate with a matrix of female pairwise relatedness. Not only did we find support for female philopatry, but we also found significant positive relationships between the relatedness matrix and each of the PAI matrices: females were more likely to be associated with (and proximal to) close female relatives than more distant relatives or unrelated individuals. Foraging analyses revealed that females had higher insect capture rates than males, and this sex difference may be related to a smaller mean interindividual distance among closely related female group members. Our result shows how estimates of genetic relatedness are useful for testing predictions regarding the evolution of sex-biased dispersal patterns, as well as potential relationships between kin-biased social behaviors and foraging success.     

Marker-inferred relatedness as a tool for detecting heritability in nature

This paper presents a perspective of how inferred relatedness, based on genetic marker data such as microsatellites or amplified fragment length polymorphisms (AFLPs), can be used to demonstrate quantitative genetic variation in natural populations. Variation at two levels is considered: among pairs of individuals within populations, and among pairs of subpopulations within a population. In the former, inferred pairwise relatedness, combined with trait measures, allow estimates of heritability 'in the wild'. In the latter, estimates of QST are obtained, in the absence of known heritabilities, via estimates of pairwise FST. Estimators of relatedness based on the 'Kronecker operator' are given. Both methods require actual variation of relationship, a rarely studied aspect of population structure, and not necessarily present. Some conditions for appropriate population structures in the wild are identified, in part through a review of recent studies.     

Consistency between marker- and genealogy-based heritability estimates in an experimental stand of Prosopis alba (Leguminosae)

Prosopis represents a valuable forest resource in arid and semiarid regions. Management of promising species requires information about genetic parameters, mainly the heritability (h(2)) of quantitative profitable traits. This parameter is traditionally estimated from progeny tests or half-sib analysis conducted in experimental stands. Such an approach estimates h(2) from the ratio of between-family/total phenotypic variance. These analyses are difficult to apply to natural populations of species with a long life cycle, overlapping generations, and a mixed mating system, without genealogical information. A promising alternative is the use of molecular marker information to infer relatedness between individuals and to estimate h(2) from the regression of phenotypic similarity on inferred relatedness. In the current study we compared h(2) of 13 quantitative traits estimated by these two methods in an experimental stand of P. alba, where genealogical information was available. We inferred pairwise relatedness by Ritland's method using six microsatellite loci. Relatedness and heritability estimates from molecular information were highly correlated to the values obtained from genealogical data. Although Ritland's method yields lower h(2) estimates and tends to overestimate genetic correlations between traits, this approach is useful to predict the expected relative gain of different quantitative traits under selection without genealogical information.     

Estimating heritabilities and genetic correlations: comparing the 'animal model' with parent-offspring regression using data from a natural population

Quantitative genetic parameters are nowadays more frequently estimated with restricted maximum likelihood using the 'animal model' than with traditional methods such as parent-offspring regressions. These methods have however rarely been evaluated using equivalent data sets. We compare heritabilities and genetic correlations from animal model and parent-offspring analyses, respectively, using data on eight morphological traits in the great reed warbler (Acrocephalus arundinaceus). Animal models were run using either mean trait values or individual repeated measurements to be able to separate between effects of including more extended pedigree information and effects of replicated sampling from the same individuals. We show that the inclusion of more pedigree information by the use of mean traits animal models had limited effect on the standard error and magnitude of heritabilities. In contrast, the use of repeated measures animal model generally had a positive effect on the sampling accuracy and resulted in lower heritabilities; the latter due to lower additive variance and higher phenotypic variance. For most trait combinations, both animal model methods gave genetic correlations that were lower than the parent-offspring estimates, whereas the standard errors were lower only for the mean traits animal model. We conclude that differences in heritabilities between the animal model and parent-offspring regressions were mostly due to the inclusion of individual replicates to the animal model rather than the inclusion of more extended pedigree information. Genetic correlations were, on the other hand, primarily affected by the inclusion of more pedigree information. This study is to our knowledge the most comprehensive empirical evaluation of the performance of the animal model in relation to parent-offspring regressions in a wild population. Our conclusions should be valuable for reconciliation of data obtained in earlier studies as well as for future meta-analyses utilizing estimates from both traditional methods and the animal model.     

Identification of kin structure among Guam rail founders: a comparison of pedigrees and DNA profiles

Kin structure among founders can have a significant effect on subsequent population structure. Here we use the correlation between DNA profile similarity and relatedness calculated from pedigrees to test hypotheses regarding kin structure among founders to the captive Guam rail (Rallus owstoni) population. Five different pedigrees were generated under the following hypotheses: (i) founders are unrelated; (ii) founders are unrelated except for same-nest chicks; (iii) founders from the same major site are siblings; (iv) founders from the same local site are siblings; and (v) founders are related as defined by a UPGMA cluster analysis of DNA similarity data. Relatedness values from pedigrees 1, 2 and 5 had the highest correlation with DNA similarity but the correlation between relatedness and similarity were not significantly different among pedigrees. Pedigree 5 resulted in the highest correlation overall when using only relatedness values that changed as a result of different founder hypotheses. Thus, founders were assigned relatedness based on pedigree 5 because it had the highest correlations with DNA similarity, was the most conservative approach, and incorporated all field data. The analyses indicated that estimating relatedness using DNA profiles remains problematic, therefore we compared mean kinship, a measure of genetic importance, with mean DNA profile similarity to determine if genetic importance among individuals could be determined via use of DNA profiles alone. The significant correlation suggests this method may provide more information about population structure than was previously thought. Thus, DNA profiles can provide a reasonable explanation for founder relatedness and mean DNA profile similarity may be helpful in determining relative genetic importance of individuals when detailed pedigrees are absent.     

The aunt and uncle effect: an empirical evaluation of the confounding influence of full sibs of parents on pedigree reconstruction.

This study used simulations and a known two-generation pedigree of chinook salmon (Oncorhynchus tshawytscha) to evaluate the effect of full sibs of parents on pedigree reconstruction. Parentage analysis was conducted on 100 parent pair-offspring relationships from pedigrees with unrelated (simulation) and related (chinook salmon) candidate parents. Parentage assignment success for the chinook salmon was lower than in the simulated populations. For example, the six most variable loci (mean H(E) = 0.87) provided a mean of 97% unambiguous assignments in the simulated population and 67% unambiguous assignments for the chinook salmon. Estimates of the pairwise relatedness coefficient ((xy)) for most nonexcluded false parents and true parents of chinook salmon offspring exceeded 0.50. These results support the conclusion that closely related candidate parents decrease the power of genetic markers for pedigree reconstruction based on exclusion. Ambiguous parentage may be resolved using single parent- and parent pair-offspring likelihood analysis, however, these methods should be used with caution and they are not replacements for using more loci when many candidate parents are full sibs.     

Fine-scale genetic structure and dispersal in cooperatively breeding apostlebirds

In cooperatively breeding species, restricted dispersal of offspring leads to clustering of closely related individuals, increasing the potential both for indirect genetic benefits and inbreeding costs. In apostlebirds (Struthidea cinerea), philopatry by both sexes results in the formation of large (up to 17 birds), predominantly sedentary breeding groups that remain stable throughout the year. We examined patterns of relatedness and fine-scale genetic structure within a population of apostlebirds using six polymorphic microsatellite loci. We found evidence of fine-scale genetic structure within the study population that is consistent with behavioural observations of short-distance dispersal, natal philopatry by both sexes and restricted movement of breeding groups between seasons. Global F(ST) values among breeding groups were significantly positive, and the average level of pairwise relatedness was significantly higher for individuals within groups than between groups. For individuals from different breeding groups, geographical distance was negatively correlated with pairwise relatedness and positively correlated with pairwise F(ST). However, when each sex was examined separately, this pattern was significant only among males, suggesting that females may disperse over longer distances. We discuss the potential for kin selection to influence the evolution and maintenance of cooperative breeding in apostlebirds. Our results demonstrate that spatial genetic structural analysis offers a useful alternative to field observations in examining dispersal patterns of cooperative breeders.     

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.     

Data depth, data completeness, and their influence on quantitative genetic estimation in two contrasting bird populations

Evolutionary biologists increasingly use pedigree‐based quantitative genetic methods to address questions about the evolutionary dynamics of traits in wild populations. In many cases, phenotypic data may have been collected only for recent parts of the study. How does this influence the performance of the models used to analyse these data? Here we explore how data depth (number of years) and completeness (number of observations) influence estimates of genetic variance and covariance within the context of an existing pedigree. Using long‐term data from the great tit Parus major and the mute swan Cygnus olor, species with different life‐histories, we examined the effect of manipulating the amount of data included on quantitative genetic parameter estimates. Manipulating data depth and completeness had little influence on estimated genetic variances, heritabilities, or genetic correlations, but (as expected) did influence confidence in these estimates. Estimated breeding values in the great tit were not influenced by data depth but were in the mute swan, probably because of differences in pedigree structure. Our analyses suggest the ‘rule of thumb’ that data from 3 years and a minimum of 100 individuals per year are needed to estimate genetic parameters with acceptable confidence, and that using pedigree data is worthwhile, even if phenotypes are only available toward the tips of the pedigree.     

A screen for identifying genes interacting with armadillo, the Drosophila homolog of beta-catenin

Applications of quantitative genetics and conservation genetics often require measures of pairwise relationships between individuals, which, in the absence of known pedigree structure, can be estimated only by use of molecular markers. Here we introduce methods for the joint estimation of the two-gene and four-gene coefficients of relationship from data on codominant molecular markers in randomly mating populations. In a comparison with other published estimators of pairwise relatedness, we find these new "regression" estimators to be computationally simpler and to yield similar or lower sampling variances, particularly when many loci are used or when loci are hypervariable. Two examples are given in which the new estimators are applied to natural populations, one that reveals isolation-by-distance in an annual plant and the other that suggests a genetic basis for a coat color polymorphism in bears.     

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.     

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.