Molecular and pedigree measures of relatedness provide similar estimates of inbreeding depression in a bottlenecked population

Individual‐based estimates of the degree of inbreeding or parental relatedness from pedigrees provide a critical starting point for studies of inbreeding depression, but in practice wild pedigrees are difficult to obtain. Because inbreeding increases the proportion of genomewide loci that are identical by descent, inbreeding variation within populations has the potential to generate observable correlations between heterozygosity measured using molecular markers and a variety of fitness related traits. Termed heterozygosity‐fitness correlations (HFCs), these correlations have been observed in a wide variety of taxa. The difficulty of obtaining wild pedigree data, however, means that empirical investigations of how pedigree inbreeding influences HFCs are rare. Here, we assess evidence for inbreeding depression in three life‐history traits (hatching and fledging success and juvenile survival) in an isolated population of Stewart Island robins using both pedigree‐ and molecular‐derived measures of relatedness. We found results from the two measures were highly correlated and supported evidence for significant but weak inbreeding depression. However, standardized effect sizes for inbreeding depression based on the pedigree‐based kin coefficients (k) were greater and had smaller standard errors than those based on molecular genetic measures of relatedness (RI), particularly for hatching and fledging success. Nevertheless, the results presented here support the use of molecular‐based measures of relatedness in bottlenecked populations when information regarding inbreeding depression is desired but pedigree data on relatedness are unavailable.     

The imprecision of heterozygosity-fitness correlations hinders the detection of inbreeding and inbreeding depression in a threatened species

In nonpedigreed wild populations, inbreeding depression is often quantified through the use of heterozygosity-fitness correlations (HFCs), based on molecular estimates of relatedness. Although such correlations are typically interpreted as evidence of inbreeding depression, by assuming that the marker heterozygosity is a proxy for genome-wide heterozygosity, theory predicts that these relationships should be difficult to detect. Until now, the vast majority of empirical research in this area has been performed on generally outbred, nonbottlenecked populations, but differences in population genetic processes may limit extrapolation of results to threatened populations. Here, we present an analysis of HFCs, and their implications for the interpretation of inbreeding, in a free-ranging pedigreed population of a bottlenecked species: the endangered takahe (Porphyrio hochstetteri). Pedigree-based inbreeding depression has already been detected in this species. Using 23 microsatellite loci, we observed only weak evidence of the expected relationship between multilocus heterozygosity and fitness at individual life-history stages (such as survival to hatching and fledging), and parameter estimates were imprecise (had high error). Furthermore, our molecular data set could not accurately predict the inbreeding status of individuals (as 'inbred' or 'outbred', determined from pedigrees), nor could we show that the observed HFCs were the result of genome-wide identity disequilibrium. These results may be attributed to high variance in heterozygosity within inbreeding classes. This study is an empirical example from a free-ranging endangered species, suggesting that even relatively large numbers (>20) of microsatellites may give poor precision for estimating individual genome-wide heterozygosity. We argue that pedigree methods remain the most effective method of quantifying inbreeding in wild populations, particularly those that have gone through severe bottlenecks.     

Estimating relatedness and inbreeding using molecular markers and pedigrees: the effect of demographic history

Estimates of inbreeding and relatedness are commonly calculated using molecular markers, although the accuracy of such estimates has been questioned. As a further complication, in many situations, such estimates are required in populations with reduced genetic diversity, which is likely to affect their accuracy. We investigated the correlation between microsatellite‐ and pedigree‐based coefficients of inbreeding and relatedness in laboratory populations of Drosophila melanogaster that had passed through bottlenecks to manipulate their genetic diversity. We also used simulations to predict expected correlations between marker‐ and pedigree‐based estimates and to investigate the influence of linkage between loci and null alleles. Our empirical data showed lower correlations between marker‐ and pedigree‐based estimates in our control (nonbottleneck) population than were predicted by our simulations or those found in similar studies. Correlations were weaker in bottleneck populations, confirming that extreme reductions in diversity can compromise the ability of molecular estimates to detect recent inbreeding events. However, this result was highly dependent on the strength of the bottleneck and we did not observe or predict any reduction in correlations in our population that went through a relatively severe bottleneck of N = 10 for one generation. Our results are therefore encouraging, as molecular estimates appeared robust to quite severe reductions in genetic diversity. It should also be remembered that pedigree‐based estimates may not capture realized identity‐by‐decent and that marker‐based estimates may actually be more useful in certain situations.     

Inbreeding coefficient and heterozygosity–fitness correlations in unhatched and hatched song sparrow nestmates

Heterozygosity–fitness correlations use molecular measures of heterozygosity as proxy estimates of individual inbreeding coefficients (f) to examine relationships between inbreeding and fitness traits. Heterozygosity–fitness correlations partly depend on the assumption that individual heterozygosity and f are strongly and negatively correlated. Although theory predicts that this relationship will be strongest when mean f and variance in f are high, few studies of heterozygosity–fitness correlations include estimates of f based on pedigrees, which allow for more thorough examinations of the relationship between f, heterozygosity and fitness in nature. We examined relationships between pedigree‐based estimates of f, multilocus heterozygosity (MLH) and the probability of survival to hatch in song sparrow nestmates. f and MLH were weakly, but significantly negatively correlated. Inbreeding coefficient predicted the probability of survival to hatch. In contrast, MLH did not predict the probability of survival to hatch nor did it account for residual variation in survival to hatch after statistically controlling for the effects of f. These results are consistent with the expectation that heterozygosity–f correlations will be weak when mean and variance in f are low. Our results also provide empirical support for recent simulation studies, which show that variation in MLH among siblings with equal f can be large and may obscure MLH–fitness relationships.     

Marker-assisted estimation of quantitative genetic parameters in rainbow trout,Oncorhynchus mykiss

Estimation of quantitative genetic parameters conventionally requires known pedigree structure. However, several methods have recently been developed to circumvent this requirement by inferring relationship structure from molecular marker data. Here, two such marker-assisted methodologies were used and compared in an aquaculture population of rainbow trout (Oncorhynchus mykiss). Firstly a regression-based model employing estimates of pairwise relatedness was applied, and secondly a Markov Chain Monte Carlo (MCMC) procedure was employed to reconstruct full-sibships and hence an explicit pedigree. While both methods were effective in detecting significant components of genetic variance and covariance for size and spawning time traits, the regression model resulted in estimates that were quantitatively unreliable, having both significant bias and low precision. This result can be largely attributed to poor performance of the pairwise relatedness estimator. In contrast, genetic parameters estimated from the reconstructed pedigree showed close agreement with ideal values obtained from the true pedigree. Although not significantly biased, parameters based on the reconstructed pedigree were underestimated relative to ideal values. This was due to the complex structure of the true pedigree in which high numbers of half-sibling relationships resulted in inaccurate partitioning of full-sibships, and additional unrecognized relatedness between families.     

Multilocus heterozygosity and inbreeding in the Siberian jay

Because of its common negative association with fitness, inbreeding is a major concern in conservation biology. Traditionally it has been measured as individual inbreeding coefficient calculated from the pedigree, but recently multilocus heterozygosity estimates have become commonly used as proxies. However, theoretical and simulation studies have cast doubt on the validity of these surrogates especially when they are based on only a few molecular markers. Yet, empirical studies reporting the correlation between multilocus heterozygosity and inbreeding coefficient are rare. We studied this relationship in a wild Siberian jay (Perisoreus infaustus) population subject to a long-term field study over 30 years. The correlations between inbreeding coefficient and the employed heterozygosity measures—standardized heterozygosity and internal relatedness—based on 21 microsatellite loci were weak. These results together with results from theoretical and simulation studies caution against use of multilocus heterozygosity estimates to study inbreeding in natural populations.     

How many SNPs are enough?

Since the days of allozyme analysis, we have been enamored with the idea that if we just had enough polymorphic mendelian loci, we could gauge the inbreeding level of individuals by measuring heterozygosity and simultaneously measure the degree of genetic relatedness between pairs of individuals. Given Mendel’s Laws, we have always known that we would need numerous independently segregating loci to achieve any reasonable degree of accuracy. Santure et al. (2010, this issue) use a 771 marker SNP panel to assess heterozygosity levels and to assess pairwise relatedness, and compare both with theoretical expectations obtained from a carefully recorded pedigree of a zebra finch breeding colony, as a function of increasing numbers of SNP markers. They also compare the SNP results with those from a 20‐locus microsatellite panel, showing that adding SNPs to a fairly large microsatellite panel improves accuracy, but given an existing panel of 125 SNPs, little is to be gained by adding microsatellites. They show that the accuracy available for estimating individual levels of inbreeding is somewhat limited. They also show that the average pairwise relatedness measures bracket pedigree relationship very nicely, but the variances for individual pairs remain substantial, even with a very large panel.     

Partial genotyping at polymorphic markers can improve heritability estimates in sibling groups

Accurate estimates of heritability () are necessary to assess adaptive responses of populations and evolution of fitness‐related traits in changing environments. For plants, estimates generally rely on maternal progeny designs, assuming that offspring are either half‐sibs or unrelated. However, plant mating systems often depart from half‐sib assumptions, this can bias estimates. Here, we investigate how to accurately estimate in nonmodel species through the analysis of sibling designs with a moderate genotyping effort. We performed simulations to investigate how microsatellite marker information available for only a subset of offspring can improve estimates based on maternal progeny designs in the presence of nonrandom mating, inbreeding in the parental population or maternal effects. We compared the basic family method, considering or not adjustments based on average relatedness coefficients, and methods based on the animal model. The animal model was used with average relatedness information, or with hybrid relatedness information: associating one‐generation pedigree and family assumptions, or associating one‐generation pedigree and average relatedness coefficients. Our results highlighted that methods using marker‐based relatedness coefficients performed as well as pedigree‐based methods in the presence of nonrandom mating (i.e. unequal male reproductive contributions, selfing), offering promising prospects to investigate in situ heritabilities in natural populations. In the presence of maternal effects, only the use of pairwise relatednesses through pedigree information improved the accuracy of estimates. In that case, the amount of father‐related offspring in the sibling design is the most critical. Overall, we showed that the method using both one‐generation pedigree and average relatedness coefficients was the most robust to various ecological scenarios.     

swinger: a user‐friendly computer program to establish captive breeding groups that minimize relatedness without pedigree information

Captive breeding programmes are often a necessity for the continued persistence of a population or species. They typically have the goal of maintaining genetic diversity and minimizing inbreeding. However, most captive breeding programmes have been based on the assumption that the founding breeders are unrelated and outbred, even though in situ anthropogenic impacts often mean these founders may have high relatedness and substantial inbreeding. In addition, polygamous group‐breeding species in captivity often have uncertain pedigrees, making it difficult to select the group composition for subsequent breeding. Molecular‐based estimates of relatedness and inbreeding may instead be used to select breeding groups (≥two individuals) that minimize relatedness and filter out inbred individuals. swinger constructs breeding groups based on molecular estimates of relatedness and inbreeding. The number of possible combinations of breeding groups quickly becomes intractable by hand. swinger was designed to overcome this major issue in ex situ conservation biology. The user can specify parameters within swinger to reach breeding solutions that suit the mating system of the target species and available resources. We provide evidence of the efficiency of the software with an empirical example and using simulations. The only data required are a typical molecular marker data set, such as a microsatellite or SNP data set, from which estimates of inbreeding and pairwise relatedness may be obtained. Such molecular data sets are becoming easier to gather from non‐model organisms with next‐generation sequencing technology. swinger is an open‐source software with a user‐friendly interface and is available at http://www.molecularecology.flinders.edu.au/molecular-ecology-lab/software/swinger/swinger/ and https://github.com/Yuma248/Swinger .     

Pedigrees and microsatellites among endangered ungulates: what do they tell us?

Relationships between pedigree coefficients of inbreeding and molecular metrics are generally weak, suggesting that measures of heterozygosity estimated using microsatellites may be poor surrogates of genome-wide inbreeding. We compare three endangered species of gazelles ( Gazella ) with different degrees of threat in their natural habitats, for which captive breeding programmes exist. For G. dorcas, the species with the largest founding population, the highest and most recent number of founding events, the correlation between pedigree coefficient of inbreeding and molecular metrics was higher than for outbred populations of mammals, probably because it has both higher mean f and variance. For the two species with smaller founding populations, conventional assumptions about founders, i.e. outbred and unrelated, are unrealistic. When realistic assumptions about the founders were made, clear relationships between pedigree coefficients of inbreeding and molecular metrics were revealed for G. cuvieri. This population had a small founding population, but it did experience admixture years later; thus, the relationship between inbreeding and molecular metrics in G. cuvieri is very similar to the expected values but lower than in G. dorcas . In contrast, no relationship was found for G. dama mhorr which had a much smaller founding population than had been previously assumed, which probably had high levels of inbreeding and low levels of genetic variability, and no admixture. In conclusion, the strength of the association between pedigree coefficient of inbreeding and molecular metrics among endangered species depends on the level of inbreeding and genetic variability present in the founding population, its size and its history.     

Rhh: an R extension for estimating multilocus heterozygosity and heterozygosity-heterozygosity correlation

Individual multilocus heterozygosity estimates based on a limited number of loci are expected to correlate only weakly with the inbreeding level of an individual. Before using multilocus heterozygosity estimates in studies of inbreeding, their ability to capture information on inbreeding in the given setting should be tested. A convenient method for this is to compute the heterozygosity-heterozygosity correlation, i.e. the mean correlation between multilocus heterozygosity estimates calculated from random samples of loci, which should be positive if multilocus heterozygosity carries a signature of inbreeding. Rhh is an extension package for the statistical software r that estimates this correlation and calculates three measures of individual multilocus heterozygosity: homozygosity by loci, internal relatedness and standardized heterozygosity. The extension package is available through the CRAN (http://cran.r-project.org) and has a homepage at http://www.helsinki.fi/biosci/egru/research/software.     

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.     

INBREEDING INFLUENCES WITHIN‐BROOD HETEROZYGOSITY‐FITNESS CORRELATIONS (HFCS) IN AN ISOLATED PASSERINE POPULATION

Molecular estimates of inbreeding may be made using genetic markers such as microsatellites, however the interpretation of resulting heterozygosity‐fitness correlations (HFCs) with respect to inbreeding depression is not straightforward. We investigated the relationship between pedigree‐determined inbreeding coefficients (f) and HFCs in a closely monitored, reintroduced population of Stewart Island robins (Petroica australis rakiura) on Ulva Island, New Zealand. Using a full sibling design, we focused on differences in juvenile survival associated specifically with individual sibling variation in standardized multilocus heterozygosity (SH) when expected f was identical. We found that within broods, siblings with higher SH at microsatellite loci experienced a higher probability of juvenile survival. This effect, however, was detected primarily within broods that experienced inbreeding or when inbreeding had occurred in their pedigree histories (i.e., at the parents’ level). Thus we show, for the first time in a wild population, that the strength of an HFC is partially dependent on the presence of inbreeding events in the recent pedigree history. Our results illustrate the importance of realized effects of inbreeding on genetic variation and fitness and the value of full‐sibling designs for the study of HFCs in the context of small, inbred populations.     

Immigration prevents inbreeding in a growing colony of a long‐lived and philopatric seabird

Mating between close relatives can have deleterious effects on reproductive success or offspring fitness, which should favour the evolution of active or passive inbreeding avoidance mechanisms. In birds, evidence for active inbreeding avoidance by kin‐discriminative mate choice is scarce; many studies describe random mating in relation to kinship and thus support passive inbreeding avoidance by natal dispersal. However, most studies were conducted in island populations of short‐lived passerines with fast alternation of generations. In this study, we present inbreeding estimates based on pedigree data from a 16‐year study in a coastal colony of Common Terns Sterna hirundo, a long‐lived seabird with delayed sexual maturation and low rates of extra‐pair paternity. Incestuous mating was rare (four of 2387 pairs), even if partially accounting for incomplete pedigrees. Although the average relatedness of observed pairs was lower than would be expected from random pairing, the inbreeding coefficient did not differ from random mating. Hence, we found no clear evidence for active inbreeding avoidance by kin‐discriminative mate choice, and the low level of inbreeding seems to be related to the high immigration rate in the colony and thus to be maintained passively by dispersal.     

Quantitative Genetics Model as the Unifying Model for Defining Genomic Relationship and Inbreeding Coefficient

The traditional quantitative genetics model was used as the unifying approach to derive six existing and new definitions of genomic additive and dominance relationships. The theoretical differences of these definitions were in the assumptions of equal SNP effects (equivalent to across-SNP standardization), equal SNP variances (equivalent to within-SNP standardization), and expected or sample SNP additive and dominance variances. The six definitions of genomic additive and dominance relationships on average were consistent with the pedigree relationships, but had individual genomic specificity and large variations not observed from pedigree relationships. These large variations may allow finding least related genomes even within the same family for minimizing genomic relatedness among breeding individuals. The six definitions of genomic relationships generally had similar numerical results in genomic best linear unbiased predictions of additive effects (GBLUP) and similar genomic REML (GREML) estimates of additive heritability. Predicted SNP dominance effects and GREML estimates of dominance heritability were similar within definitions assuming equal SNP effects or within definitions assuming equal SNP variance, but had differences between these two groups of definitions. We proposed a new measure of genomic inbreeding coefficient based on parental genomic co-ancestry coefficient and genomic additive correlation as a genomic approach for predicting offspring inbreeding level. This genomic inbreeding coefficient had the highest correlation with pedigree inbreeding coefficient among the four methods evaluated for calculating genomic inbreeding coefficient in a Holstein sample and a swine sample.     

Heterozygosity–fitness correlations in a wild mammal population: accounting for parental and environmental effects

HFCs (heterozygosity–fitness correlations) measure the direct relationship between an individual's genetic diversity and fitness. The effects of parental heterozygosity and the environment on HFCs are currently under‐researched. We investigated these in a high‐density U.K. population of European badgers (Meles meles), using a multimodel capture–mark–recapture framework and 35 microsatellite loci. We detected interannual variation in first‐year, but not adult, survival probability. Adult females had higher annual survival probabilities than adult males. Cubs with more heterozygous fathers had higher first‐year survival, but only in wetter summers; there was no relationship with individual or maternal heterozygosity. Moist soil conditions enhance badger food supply (earthworms), improving survival. In dryer years, higher indiscriminate mortality rates appear to mask differential heterozygosity‐related survival effects. This paternal interaction was significant in the most supported model; however, the model‐averaged estimate had a relative importance of 0.50 and overlapped zero slightly. First‐year survival probabilities were not correlated with the inbreeding coefficient (f); however, small sample sizes limited the power to detect inbreeding depression. Correlations between individual heterozygosity and inbreeding were weak, in line with published meta‐analyses showing that HFCs tend to be weak. We found support for general rather than local heterozygosity effects on first‐year survival probability, and g2 indicated that our markers had power to detect inbreeding. We emphasize the importance of assessing how environmental stressors can influence the magnitude and direction of HFCs and of considering how parental genetic diversity can affect fitness‐related traits, which could play an important role in the evolution of mate choice.     

Relatedness and inclusive fitness with inbreeding.

Relatedness arising in kin selection theory is measured by a variable taking as values two pedigree indices in populations with inbreeding when selection is weak. This variable reduces to a single pedigree index when inbreeding is caused by partial selfing or partial sib-mating. General inclusive fitness formulations of kin selection models based on such a variable of relatedness are proposed.     

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.     

A MARKER-BASED METHOD FOR INFERENCES ABOUT QUANTITATIVE INHERITANCE IN NATURAL POPULATIONS

A marker-based method for studying quantitative genetic characters in natural populations is presented and evaluated. The method involves regressing quantitative trait similarity on marker-estimated relatedness between individuals. A procedure is first given for estimating the narrow sense heritability and additive genetic correlations among traits, incorporating shared environments. Estimation of the actual variance of relatedness is required for heritability, but not for genetic correlations. The approach is then extended to include isolation by distance of environments, dominance, and shared levels of inbreeding. Investigations of statistical properties show that good estimates do not require great marker polymorphism, but rather require significant variation of actual relatedness; optimal allocation generally favors sampling many individuals at the expense of assaying fewer marker loci; when relatedness declines with physical distance, it is optimal to restrict comparisons to within a certain distance; the power to estimate shared environments and inbreeding effects is reasonable, but estimates of dominance variance may be difficult under certain patterns of relationship; and any linkage of markers to quantitative trait loci does not cause significant problems. This marker-based method makes possible studies with long-lived organisms or with organisms difficult to culture, and opens the possibility that quantitative trait expression in natural environments can be analyzed in an unmanipulative way.     

The effect of using approximate gametic variance covariance matrices on marker assisted selection by BLUP

Under additive inheritance, the Henderson mixed model equations (HMME) provide an efficient approach to obtaining genetic evaluations by marker assisted best linear unbiased prediction (MABLUP) given pedigree relationships, trait and marker data. For large pedigrees with many missing markers, however, it is not feasible to calculate the exact gametic variance covariance matrix required to construct HMME. The objective of this study was to investigate the consequences of using approximate gametic variance covariance matrices on response to selection by MABLUP. Two methods were used to generate approximate variance covariance matrices. The first method (Method A) completely discards the marker information for individuals with an unknown linkage phase between two flanking markers. The second method (Method B) makes use of the marker information at only the most polymorphic marker locus for individuals with an unknown linkage phase. Data sets were simulated with and without missing marker data for flanking markers with 2, 4, 6, 8 or 12 alleles. Several missing marker data patterns were considered. The genetic variability explained by marked quantitative trait loci (MQTL) was modeled with one or two MQTL of equal effect. Response to selection by MABLUP using Method A or Method B were compared with that obtained by MABLUP using the exact genetic variance covariance matrix, which was estimated using 15 000 samples from the conditional distribution of genotypic values given the observed marker data. For the simulated conditions, the superiority of MABLUP over BLUP based only on pedigree relationships and trait data varied between 0.1% and 13.5% for Method A, between 1.7% and 23.8% for Method B, and between 7.6% and 28.9% for the exact method. The relative performance of the methods under investigation was not affected by the number of MQTL in the model.