Quantifying realized inbreeding in wild and captive animal populations

Most molecular measures of inbreeding do not measure inbreeding at the scale that is most relevant for understanding inbreeding depression—namely the proportion of the genome that is identical-by-descent (IBD). The inbreeding coefficient F_Ped obtained from pedigrees is a valuable estimator of IBD, but pedigrees are not always available, and cannot capture inbreeding loops that reach back in time further than the pedigree. We here propose a molecular approach to quantify the realized proportion of the genome that is IBD (propIBD), and we apply this method to a wild and a captive population of zebra finches (Taeniopygia guttata). In each of 948 wild and 1057 captive individuals we analyzed available single-nucleotide polymorphism (SNP) data (260 SNPs) spread over four different genomic regions in each population. This allowed us to determine whether any of these four regions was completely homozygous within an individual, which indicates IBD with high confidence. In the highly nomadic wild population, we did not find a single case of IBD, implying that inbreeding must be extremely rare (propIBD=0–0.00094, 95% CI). In the captive population, a five-generation pedigree strongly underestimated the average amount of realized inbreeding (F_Ped=0.013<propIBD=0.064), as expected given that pedigree founders were already related. We suggest that this SNP-based technique is generally useful for quantifying inbreeding at the individual or population level, and we show analytically that it can capture inbreeding loops that reach back up to a few hundred generations.     

Genome sharing in large pedigrees: multiple imputation of ibd for linkage detection

Our objective is the development of robust methods for assessment of evidence for linkage of loci affecting a complex trait to a marker linkage group, using data on extended pedigrees. Using Markov chain Monte Carlo (MCMC) methods, it is possible to sample realizations from the distribution of gene identity by descent (IBD) patterns on a pedigree, conditional on observed data YM at multiple marker loci. Measures of gene IBDW which capture joint genome sharing in extended pedigrees often have unknown and highly skewed distributions, particularly when conditioned on marker data. MCMC provides a direct estimate of the distribution of such measures. Let W be the IBD measure from data YM, and W* the IBD measure from pseudo-data Y*M simulated with the same data availability and genetic marker model as the true data YM, but in the absence of linkage. Then measures of the difference in distributions of W and W* provide evidence for linkage. This approach extracts more information from the data YM than either comparison to the pedigree prior distribution of W or use of statistics that are expectations of W given the data YM. A small example is presented.     

Modeling the effect of inbreeding among founders in linkage analysis

In this paper, we present a unified mathematical model for linkage analysis that allows for inbreeding among founders in all families. The identical by descent (IBD) configuration of each pedigree is modeled as a Markov process containing two parameters; the inverse inbreeding and kinship coefficient and a rate parameter proportional to the inverse expected length of chromosome segments shared IBD by two different founder haplotypes. We use hidden Markov models and define a forward-backward algorithm for computing the conditional IBD-distribution given marker data, thereby extending the multipoint method of Lander and Green [1987. Construction of multilocus genetic maps in humans, Proc. Natl. Acad. Sci. USA 84, 2363-2367] to situations where founders are inbred. Our methodology is valid for arbitrary pedigree structures. Simulation and theoretical approximations for nonparametric linkage (NPL) analysis based on affected sib pairs reveal that NPL scores are inflated and type 1 errors increased when the inbreeding coefficient or rate parameter is underestimated. When the parents are genotyped, we present a general way of modifying the score function to drastically reduce this effect.     

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.     

Pedigree and marker information requirements to monitor genetic variability

There are several measures available to describe the genetic variability of populations. The average inbreeding coefficient of a population based on pedigree information is a frequently chosen option. Due to the developments in molecular genetics it is also possible to calculate inbreeding coefficients based on genetic marker information. A simulation study was carried out involving ten sires and 50 dams. The animals were mated over a period of 20 discrete generations. The population size was kept constant. Different situations with regard to the level of polymorphism and initial allele frequencies and mating scheme (random mating, avoidance of full sib mating, avoidance of full sib and half sib mating) were considered. Pedigree inbreeding coefficients of the last generation using full pedigree or 10, 5 and 2 generations of the pedigree were calculated. Marker inbreeding coefficients based on different sets of microsatellite loci were also investigated. Under random mating, pedigree-inbreeding coefficients are clearly more closely related to true autozygosity (i.e., the actual proportion of loci with alleles identical by descent) than marker-inbreeding coefficients. If mating is not random, the demands on the quality and quantity of pedigree records increase. Greater attention must be paid to the correct parentage of the animals.     

Inbreeding as measured by isonymy, pedigrees, and population size in Törbel, Switzerland.

Törbel provides an interesting test case for the study of the relationship between inbreeding measured by pedigrees and inbreeding measured by isonymy. At the start of this investigation, we were aware that isonymy could introduce biases into the calculation of the inbreeding coefficient in either direction. However, it was expected that in Switzerland, inbreeding from isonymy would be an overestimate due to patrilocal residence and polyphyletic names. One way of dealing with this problem [13] was not to be concerned with the absolute value of inbreeding but only in the difference between estimates. Any bias introduced in the estimate itself disappears in such comparisons, so that a trend of inbreeding can be ascertained correctly. However, it was considered equally important to subject several populations to both a complete pedigree analysis and an isonymic analysis to determine the relationship between estimates of inbreeding. Despite the fact that several authors (Swedlund [18], for example) warned users of isonymy to exercise caution, the careless application of isonymy still persists. In the present study, estimates of inbreeding from isonymy were brought into line with other methods based on pedigree analysis and population size. However, it was possible to do this only in Törbel where pedigree depth was extensive and relatively complete. Similar corrections are possible only when the distribution of mono- and polyphyletic names is known and when migration data are reliable. If the trouble is taken to make these corrections, the same time and effort might as well be spent in pedigree analysis (when fairly complete ascertainment is possible) to achieve the same end result.     

Consanguinity and the sib-pair method: an approach using identity by descent between and within individuals.

To test for linkage between a trait and a marker, one can consider identical marker alleles in related individuals, for instance, sibs. For recessive diseases, it has been shown that some information may be gained from the identity by descent (IBD) of the two alleles of an affected inbred individual at the marker locus. The aim of this paper is to extend the sib-pair method of linkage analysis to the situation of sib pairs sampled from consanguineous populations. This extension takes maximum advantage of the information provided by both the IBD pattern between sibs and allelic identity within each sib of the pair. This is possible through the use of the condensed identity coefficients. Here, we propose a new test of linkage based on a chi2. We compare the performance of this test with that of the classical chi2 test based on the distribution of sib pairs sharing 0, 1, or 2 alleles IBD. For sib pairs from first-cousin matings, the proposed test can better detect the role of a disease-susceptibility (DS) locus. Its power is shown to be greater than that of the classical test, especially for models where the DS allele may be common and incompletely penetrant; that is to say for situations that may be encountered in multifactorial diseases. A study of the impact of inbreeding on the expected proportions of sib pairs sharing 0, 1, or 2 alleles IBD is also performed here. Ignoring inbreeding, when in fact inbreeding exists, increases the rate of type I errors in tests of linkage.     

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.     

Using dominance relationship coefficients based on linkage disequilibrium and linkage with a general complex pedigree to increase mapping resolution

Dominance (intralocus allelic interactions) plays often an important role in quantitative trait variation. However, few studies about dominance in QTL mapping have been reported in outbred animal or human populations. This is because common dominance effects can be predicted mainly for many full sibs, which do not often occur in outbred or natural populations with a general pedigree. Moreover, incomplete genotypes for such a pedigree make it infeasible to estimate dominance relationship coefficients between individuals. In this study, identity-by-descent (IBD) coefficients are estimated on the basis of population-wide linkage disequilibrium (LD), which makes it possible to track dominance relationships between unrelated founders. Therefore, it is possible to use dominance effects in QTL mapping without full sibs. Incomplete genotypes with a complex pedigree and many markers can be efficiently dealt with by a Markov chain Monte Carlo method for estimating IBD and dominance relationship matrices (D(RM)). It is shown by simulation that the use of D(RM) increases the likelihood ratio at the true QTL position and the mapping accuracy and power with complete dominance, overdominance, and recessive inheritance modes when using 200 genotyped and phenotyped individuals.     

Heterozygosity-fitness correlations in zebra finches: microsatellite markers can be better than their reputation

Numerous studies have reported associations between heterozygosity in microsatellite markers and fitness-related traits (heterozygosity-fitness correlations, HFCs). However, it has often been questioned whether HFCs reflect general inbreeding depression, because a small panel of microsatellite markers does not reflect very well an individual's inbreeding coefficient (F) as calculated from a pedigree. Here, we challenge this prevailing view. Because of chance events during Mendelian segregation, an individual's realized proportion of the genome that is identical by descent (IBD) may substantially deviate from the pedigree-based expectation (i.e. F). This Mendelian noise may result in a weak correlation between F and multi-locus heterozygosity, but this does not imply that multi-locus heterozygosity is a bad estimator of realized IBD. We examined correlations between 11 fitness-related traits measured in up to 1192 captive zebra finches and three measures of inbreeding: (i) heterozygosity across 11 microsatellite markers, (ii) heterozygosity across 1359 single-nucleotide polymorphism (SNP) markers and (iii) F, based on a 5th-generation pedigree. All 11 phenotypic traits showed positive relationships with measures of heterozygosity, especially traits that are most closely related to fitness. Remarkably, the small panel of microsatellite markers produced equally strong HFCs as the large panel of SNP markers. Both marker-based approaches produced stronger correlations with phenotypes than the pedigree-based F, and this did not seem to result from the shortness of our pedigree. We argue that a small panel of microsatellites with high allelic richness may better reflect an individual's realized IBD than previously appreciated, especially in species like the zebra finch, where much of the genome is inherited in large blocks that rarely experience cross-over during meiosis.     

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.     

Estimation of individual level of inbreeding using relatedness measures in haplodiploids

Although male haploidy in haplodiploid species aids purging of deleterious alleles, haplodiploid animals may nevertheless suffer significant negative effects of inbreeding. The effects may even be stronger in social Hymenoptera because the negative fitness consequences may be expressed at two levels: the individual level (inbred queens) and colony level (inbred workers). Surprisingly, in natural populations the impact of inbreeding on fitness has been studied in very few insects, and even fewer haplodiploid ones. Hence there is currently little understanding of the potential effects of inbreeding. One reason may be the difficulties in estimating inbreeding especially at the individual level, apart from the additional problems posed by haplodiploidy. In order to study the impact of inbreeding, its individual level must be estimated as precisely as possible. When the population pedigree is unknown, relatedness-based estimates of the individual inbreeding coefficient can be used to estimate inbreeding. Here we examine the relationship between inbreeding coefficients and relatedness in diploid and haplodiploid organisms, and provide guidelines for estimating inbreeding both at the individual and the colony level. Received 7 March 2005; revised 18 April 2005, accepted 20 April 2005. An erratum to this article is available at .     

Evaluation of ancestral inbreeding coefficients: Ballou’s formula versus gene dropping

Estimation of the purging of detrimental effects through inbreeding and selection is an important issue in conservation genetics opening new perspectives for the management of small populations. In 1997 Ballou proposed the ancestral inbreeding coefficient, which is calculated recursively via pedigree inbreeding coefficients, as a tool for evaluating the purging of deleterious alleles in zoo populations. The formula of Ballou assumes independence of inbreeding and ancestral inbreeding coefficients at any stage of the recursion. This study investigates the consequences of this inaccuracy on the estimation of true ancestral inbreeding, i.e. the proportion of alleles within a genome that has undergone inbreeding in the past. As an alternative we propose the estimation of ancestral inbreeding by the method of gene dropping. The methods are compared by stochastic simulation for various models with respect to mode of inheritance (neutral, detrimental and lethal alleles) and different settings for population size and initial allele frequencies. In all scenarios the proportion of alleles within a genome that has undergone inbreeding in the past was overestimated by Ballou’s formula. The overestimation was more pronounced in smaller populations but was not affected by genetic model or initial allele frequency. In contrast, the ancestral inbreeding coefficient calculated by gene dropping provided a robust estimate of ancestral inbreeding in most models and settings. A marginal overestimation was observed only in models with lethal alleles. Therefore, we recommend applying the gene dropping approach to estimate ancestral inbreeding coefficients.     

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.     

Estimating levels of inbreeding using AFLP markers

In the absence of detailed pedigree records, researchers have attempted to estimate individuals' levels of inbreeding using molecular markers, generally making use of heterozygosity measures based on microsatellite markers. Here we report and validate a method for estimating an individual's inbreeding coefficient, f, using amplified fragment length polymorphism (AFLP) markers. We use simulations to confirm that our measure scales appropriately with f when allele frequencies can be estimated from a subset of outbred individuals. We also present an approach for obtaining satisfactory estimates even in the absence of an independent set of known outbred individuals from which to estimate allele frequencies. We then test our method against empirical data from 179 wild and captive-bred old-field mice, Peromyscus polionotus subgriseus, comprising pedigree-based estimates of f, along with genetic data from 94 AFLP markers and 12 microsatellites. Inbreeding estimates based on both AFLP and microsatellite markers were found to correlate strongly with pedigree-based inbreeding coefficients. Owing to their ease of amplification in any species, AFLP markers may prove to be a valuable new tool for estimating f in natural populations and for examining correlations between heterozygosity and fitness.     

利用高密度SNP标记分析中国荷斯坦牛基因组近交

畜禽育种中传统上利用系谱信息评估群体近交程度?近年来随着高通量单核苷酸多态(single nucleotide polymorphism, SNP)检测成本降低,使利用基因组信息分析真实的基因组近交程度成为可能?本研究利用牛54 K SNP 芯片数据统计了北京地区2107头荷斯坦牛基因组上的长纯合片段(runs of homozygosity, ROH)的频率和分布,计算了2种基因组近交系数,即染色体上ROH的长度占基因组总长度的比例(Froh)及个体所有标记基因型中纯合子所占比例,即基因组纯合度(Fhom),进而分析了两种基因组近交系数之间的相关性以及基因组近交与系谱近交系数之间的相关性?结果表明,共检测到44 676个ROH片段,其长度主要分布在1~10 Mb之间?不同长度的ROH散布于个体基因组内,短ROH较长ROH更为常见?ROH在染色体上并非均匀分布,ROH频率最高的区域为10号染色体中部?两种基因组近交系数之间相关性很高(91%以上),但基因组近交与系谱近交之间的相关性较低(低于50%)?系谱完整性是影响基因组近交与系谱近交结果一致的重要因素,基因组近交系数能够反映个体真实的近交,本研究为评估群体近交水平提供了有力工具?     

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.     

Runs of homozygosity: current knowledge and applications in livestock

This review presents a broader approach to the implementation and study of runs of homozygosity (ROH) in animal populations, focusing on identifying and characterizing ROH and their practical implications. ROH are continuous homozygous segments that are common in individuals and populations. The ability of these homozygous segments to give insight into a population's genetic events makes them a useful tool that can provide information about the demographic evolution of a population over time. Furthermore, ROH provide useful information about the genetic relatedness among individuals, helping to minimize the inbreeding rate and also helping to expose deleterious variants in the genome. The frequency, size and distribution of ROH in the genome are influenced by factors such as natural and artificial selection, recombination, linkage disequilibrium, population structure, mutation rate and inbreeding level. Calculating the inbreeding coefficient from molecular information from ROH (F_ROH) is more accurate for estimating autozygosity and for detecting both past and more recent inbreeding effects than are estimates from pedigree data (F_PED). The better results of F_ROH suggest that F_ROH can be used to infer information about the history and inbreeding levels of a population in the absence of genealogical information. The selection of superior animals has produced large phenotypic changes and has reshaped the ROH patterns in various regions of the genome. Additionally, selection increases homozygosity around the target locus, and deleterious variants are seen to occur more frequently in ROH regions. Studies involving ROH are increasingly common and provide valuable information about how the genome's architecture can disclose a population's genetic background. By revealing the molecular changes in populations over time, genome‐wide information is crucial to understanding antecedent genome architecture and, therefore, to maintaining diversity and fitness in endangered livestock breeds.     

Neutral locus heterozygosity, inbreeding, and survival in Darwin's ground finches (Geospiza fortis and G. scandens)

Comprehensive long-term studies of isolated populations provide valuable comparative data that may be used to evaluate different methods for quantifying the relationship between genetic diversity and fitness. Here, we report on data collected from large and well-characterized cohorts of the two numerically dominant species of Darwin's finches on Isla Daphne Major, Galápagos, Ecuador - Geospiza fortis and G. scandens. Multilocus microsatellite (SSR) genetic diversity estimates (heterozygosity and d2) and pedigree-based estimates of the inbreeding coefficient (f) were compared to each other and to two fitness components: lifespan and recruitment. In the larger sample of G. fortis, heterozygosity (H) was correlated with both fitness components, but no relationship was detected in the smaller sample of G. scandens. Analyses of the inbreeding coefficient detected highly significant relationships between f and recruitment, but no relationship between f and overall lifespan. The d2 statistic showed no relationship to either fitness component. When the two SSR-based estimators were compared to f, d2 was correlated with f in G. fortis in the predicted direction, while in G. scandens the relationship was positive. Multilocus heterozygosity was correlated with f in G. fortis but not in the G. scandens sample. A pedigree simulation demonstrated that the variation in true autozygosity can be large among individuals with the same level of inbreeding. This observation may supplement the interpretation of patterns relevant to the local (locus-specific) and general (genome-wide) effects hypotheses, which have been proposed to explain the mechanism responsible for associations between genetic diversity and fitness.