Genome-Wide Estimates of Coancestry,Inbreeding and Effective Population Size in the Spanish Holstein Population

Estimates of effective population size in the Holstein cattle breed have usually been low despite the large number of animals that constitute this breed. Effective population size is inversely related to the rates at which coancestry and inbreeding increase and these rates have been high as a consequence of intense and accurate selection. Traditionally, coancestry and inbreeding coefficients have been calculated from pedigree data. However, the development of genome-wide single nucleotide polymorphisms has increased the interest of calculating these coefficients from molecular data in order to improve their accuracy. In this study, genomic estimates of coancestry, inbreeding and effective population size were obtained in the Spanish Holstein population and then compared with pedigree-based estimates. A total of 11,135 animals genotyped with the Illumina BovineSNP50 BeadChip were available for the study. After applying filtering criteria, the final genomic dataset included 36,693 autosomal SNPs and 10,569 animals. Pedigree data from those genotyped animals included 31,203 animals. These individuals represented only the last five generations in order to homogenise the amount of pedigree information across animals. Genomic estimates of coancestry and inbreeding were obtained from identity by descent segments (coancestry) or runs of homozygosity (inbreeding). The results indicate that the percentage of variance of pedigree-based coancestry estimates explained by genomic coancestry estimates was higher than that for inbreeding. Estimates of effective population size obtained from genome-wide and pedigree information were consistent and ranged from about 66 to 79. These low values emphasize the need of controlling the rate of increase of coancestry and inbreeding in Holstein selection programmes.     

Methods to estimate effective population size using pedigree data: Examples in dog,sheep, cattle and horse

Background

Effective population sizes of 140 populations (including 60 dog breeds, 40 sheep breeds, 20 cattle breeds and 20 horse breeds) were computed using pedigree information and six different computation methods. Simple demographical information (number of breeding males and females), variance of progeny size, or evolution of identity by descent probabilities based on coancestry or inbreeding were used as well as identity by descent rate between two successive generations or individual identity by descent rate.

Results

Depending on breed and method, effective population sizes ranged from 15 to 133 056, computation method and interaction between computation method and species showing a significant effect on effective population size (P < 0.0001). On average, methods based on number of breeding males and females and variance of progeny size produced larger values (4425 and 356, respectively), than those based on identity by descent probabilities (average values between 93 and 203). Since breeding practices and genetic substructure within dog breeds increased inbreeding, methods taking into account the evolution of inbreeding produced lower effective population sizes than those taking into account evolution of coancestry. The correlation level between the simplest method (number of breeding males and females, requiring no genealogical information) and the most sophisticated one ranged from 0.44 to 0.60 according to species.

Conclusions

When choosing a method to compute effective population size, particular attention should be paid to the species and the specific genetic structure of the population studied.     

Fine decomposition of the inbreeding and the coancestry coefficients by using the tabular method

In this paper we describe a simple algorithm to decompose both inbreeding and coancestry coefficients. The decomposition is performed in pieces coming from each ancestor, including the founders and the Mendelian sampling terms of non-founders. The original algorithm presented here replaces the conventional tabular method formulae with an original set of recursive formulas. We illustrate the procedure with two small examples, including the pedigree of the bull Comet. The procedure was also tested with simulated pedigrees and it succeeded in analyzing the impact of successive bottlenecks into the average coancestry of the current cohort. Finally, we analyzed the origin of the current coancestry of the Asian Wild Horse population. The average coancestry of the current cohort was around 0.17 and the most relevant ancestors were the direct descendants of Woburn/7 and Mongolia/0, which converged in the Askania reintroduced population in Ukraine after surviving World War II.     

Estimation of genealogical coancestry in plant species using a pedigree reconstruction algorithm and application to an oil palm breeding population

Key message

Explicit pedigree reconstruction by simulated annealing gave reliable estimates of genealogical coancestry in plant species, especially when selfing rate was lower than 0.6, using a realistic number of markers. Genealogical coancestry information is crucial in plant breeding to estimate genetic parameters and breeding values. The approach of Fernández and Toro (Mol Ecol 15:1657–1667, 2006) to estimate genealogical coancestries from molecular data through pedigree reconstruction was limited to species with separate sexes. In this study it was extended to plants, allowing hermaphroditism and monoecy, with possible selfing. Moreover, some improvements were made to take previous knowledge on the population demographic history into account. The new method was validated using simulated and real datasets. Simulations showed that accuracy of estimates was high with 30 microsatellites, with the best results obtained for selfing rates below 0.6. In these conditions, the root mean square error (RMSE) between the true and estimated genealogical coancestry was small (<0.07), although the number of ancestors was overestimated and the selfing rate could be biased. Simulations also showed that linkage disequilibrium between markers and departure from the Hardy–Weinberg equilibrium in the founder population did not affect the efficiency of the method. Real oil palm data confirmed the simulation results, with a high correlation between the true and estimated genealogical coancestry (>0.9) and a low RMSE (<0.08) using 38 markers. The method was applied to the Deli oil palm population for which pedigree data were scarce. The estimated genealogical coancestries were highly correlated (>0.9) with the molecular coancestries using 100 markers. Reconstructed pedigrees were used to estimate effective population sizes. In conclusion, this method gave reliable genealogical coancestry estimates. The strategy was implemented in the software MOLCOANC 3.0.     

Optimization of selection contribution and mate allocations in monoecious tree breeding populations

Background

The combination of optimized contribution dynamic selection and various mating schemes was investigated over seven generations for a typical tree breeding scenario. The allocation of mates was optimized using a simulated annealing algorithm for various object functions including random mating (RM), positive assortative mating (PAM) and minimization of pair-wise coancestry between mates (MCM) all combined with minimization of variance in family size and coancestry. The present study considered two levels of heritability (0.05 and 0.25), two restrictions on relatedness (group coancestry; 1 and 2%) and two maximum permissible numbers of crosses in each generation (100 and 400). The infinitesimal genetic model was used to simulate the genetic architecture of the trait that was the subject of selection. A framework of the long term genetic contribution of ancestors was used to examine the impacts of the mating schemes on population parameters.

Results

MCM schemes produced on average, an increased rate of genetic gain in the breeding population, although the difference between schemes was small but significant after seven generations (up to 7.1% more than obtained with RM). In addition, MCM reduced the level of inbreeding by as much as 37% compared with RM, although the rate of inbreeding was similar after three generations of selection. PAM schemes yielded levels of genetic gain similar to those produced by RM, but the increase in the level of inbreeding was substantial (up to 43%).

Conclusion

The main reason why MCM schemes yielded higher genetic gains was the improvement in managing the long term genetic contribution of founders in the population; this was achieved by connecting unrelated families. In addition, the accumulation of inbreeding was reduced by MCM schemes since the variance in long term genetic contributions of founders was smaller than in the other schemes. Consequently, by combining an MCM scheme with an algorithm that optimizes contributions of the selected individuals, a higher long term response is obtained while reducing the risk within the breeding program.     

Interrelations between effective population size and other pedigree tools for the management of conserved populations

Genetic parameters widely used to monitor genetic variation in conservation programmes, such as effective number of founders, founder genome equivalents and effective population size, are interrelated in terms of coancestries and variances of contributions from ancestors to descendants. A new parameter, the effective number of non-founders, is introduced to describe the relation between effective number of founders and founder genome equivalents. Practical recommendations for the maintenance of genetic variation in small captive populations are discussed. To maintain genetic diversity, minimum coancestry among individuals should be sought. This minimizes the variances of contributions from ancestors to descendants in all previous generations. The method of choice of parents and the system of mating should be independent of each other because a clear-cut recommendation cannot be given on the latter.     

Comparative Analysis of Genome Diversity in Bullmastiff Dogs

Management and preservation of genomic diversity in dog breeds is a major objective for maintaining health. The present study was undertaken to characterise genomic diversity in Bullmastiff dogs using both genealogical and molecular analysis. Genealogical analysis of diversity was conducted using a database consisting of 16,378 Bullmastiff pedigrees from year 1980 to 2013. Additionally, a total of 188 Bullmastiff dogs were genotyped using the 170,000 SNP Illumina CanineHD Beadchip. Genealogical parameters revealed a mean inbreeding coefficient of 0.047; 142 total founders (f); an effective number of founders (f_e) of 79; an effective number of ancestors (f_a) of 62; and an effective population size of the reference population of 41. Genetic diversity and the degree of genome-wide homogeneity within the breed were also investigated using molecular data. Multiple-locus heterozygosity (MLH) was equal to 0.206; runs of homozygosity (ROH) as proportion of the genome, averaged 16.44%; effective population size was 29.1, with an average inbreeding coefficient of 0.035, all estimated using SNP Data. Fine-scale population structure was analysed using NETVIEW, a population analysis pipeline. Visualisation of the high definition network captured relationships among individuals within and between subpopulations. Effects of unequal founder use, and ancestral inbreeding and selection, were evident. While current levels of Bullmastiff heterozygosity, inbreeding and homozygosity are not unusual, a relatively small effective population size indicates that a breeding strategy to reduce the inbreeding rate may be beneficial.     

Inbreeding and genetic structure in the endangered Sorraia horse breed: implications for its conservation and management

The Sorraia horse is a closed breed with reduced effective population size and considered in critical maintained risk status. The breed exists in 2 main breeding populations, one in Portugal and one in Germany, with a smaller population size. A set of 22 microsatellite loci was used to examine genetic diversity and structure of the Sorraia horse breed and to compare individual inbreeding coefficient F, estimated from pedigree data, with individual heterozygosity and mean d(2). The Sorraia horse shows lower levels of microsatellite diversity when compared with other horse breeds. Due to management strategies, there are clear differences in the genetic structure of the 2 main Sorraia horse populations. Individual heterozygosity was shown to be a good estimator, used together with or as an alternative to inbreeding coefficient, in predicting fitness and evaluating the inbreeding level of the Sorraia horse. The information gathered in this study, combined with information available from previous studies, offers an important and wide information base for the future development of an effective breeding management of the Sorraia horse in order to preserve this endangered breed.     

BREEDING SYSTEM AND GENETIC VARIANCE IN THE MONOGAMOUS,SEMI-SOCIAL SHREW,CROCIDURA RUSSULA

The population-genetic consequences of monogamy and male philopatry (a rare breeding system in mammals) were investigated using microsatellite markers in the semisocial and anthropophilic shrew Crocidura russula. A hierarchical sampling design over a 16-km geographical transect revealed a large genetic diversity (h = 0.813) with significant differentiation among subpopulations (F_ST = 5–6%), which suggests an exchange of 4.4 migrants per generation. Demic effective-size estimates were very high, due both to this limited gene inflow and to the inner structure of subpopulations. These were made of 13–20 smaller units (breeding groups), comprising an estimate of four breeding pairs each. Members of the same breeding groups displayed significant coancestries (F_LS = 9–10%), which was essentially due to strong male kinship: syntopic males were on average related at the half-sib level. Female dispersal among breeding groups was not complete (~39%), and insufficient to prevent inbreeding. From our results, the breeding strategy of C. russula seems less efficient than classical mammalian systems (polygyny and male dispersal) in disentangling coancestry from inbreeding, but more so in retaining genetic variance.     

A note on the rationale for estimating genealogical coancestry from molecular markers

Background

Genetic relatedness or similarity between individuals is a key concept in population, quantitative and conservation genetics. When the pedigree of a population is available and assuming a founder population from which the genealogical records start, genetic relatedness between individuals can be estimated by the coancestry coefficient. If pedigree data is lacking or incomplete, estimation of the genetic similarity between individuals relies on molecular markers, using either molecular coancestry or molecular covariance. Some relationships between genealogical and molecular coancestries and covariances have already been described in the literature.

Methods

We show how the expected values of the empirical measures of similarity based on molecular marker data are functions of the genealogical coancestry. From these formulas, it is easy to derive estimators of genealogical coancestry from molecular data. We include variation of allelic frequencies in the estimators.

Results

The estimators are illustrated with simulated examples and with a real dataset from dairy cattle. In general, estimators are accurate and only slightly biased. From the real data set, estimators based on covariances are more compatible with genealogical coancestries than those based on molecular coancestries. A frequently used estimator based on the average of estimated coancestries produced inflated coancestries and numerical instability. The consequences of unknown gene frequencies in the founder population are briefly discussed, along with alternatives to overcome this limitation.

Conclusions

Estimators of genealogical coancestry based on molecular data are easy to derive. Estimators based on molecular covariance are more accurate than those based on identity by state. A correction considering the random distribution of allelic frequencies improves accuracy of these estimators, especially for populations with very strong drift.     

The accuracy of a heritability estimator using molecular information

The heritability of a quantitative trait is a key parameter to quantify the genetic variation present in a population. Although estimates of heritability require accurate information on the genetic relationship among individuals, pedigree data is generally lacking in natural populations. Nowadays, the increasing availability of DNA markers is making possible the estimation of coancestries from neutral molecular information. In 1996, K. Ritland developed an approach to estimate heritability from the regression of the phenotypic similarity on the marker-based coancestry. We carried out simulations to analyze the accuracy of the estimates of heritability obtained by this method using information from a variable number of neutral codominant markers. Because the main application of the estimator is on populations with no family structure, such as natural populations, its accuracy was tested under this scenario. However, the method was also investigated under other scenarios, in order to test the influence of different factors (family structure, assortative mating and phenotypic selection) on the precision. Our results suggest that the main factor causing a directional bias in the estimated heritability is the presence of phenotypic selection, and that very noisy estimates are obtained in the absence of a familiar structure and for small population sizes. The estimated heritabilities from marker-based coancestries showed lower accuracy than the estimated heritabilities from genealogical coancestries. However, a large amount of bias occurred even in the most favourable situation where genealogical coancestries are known. The results also indicate that the molecular markers are more suitable to infer coancestry than inbreeding.     

Pedigree estimation of the (sub) population contribution to the total gene diversity: the horse coat colour case

A method to quantify the contribution of subpopulations to genetic diversity in the whole population was assessed using pedigree information. The standardization of between- and within-subpopulation mean coancestries was developed to account for the different coat colour subpopulation sizes in the Spanish Purebred (SPB) horse population. The data included 166264 horses registered in the SPB Studbook. Animals born in the past 11 years (1996 to 2006) were selected as the 'reference population' and were grouped according to coat colour into eight subpopulations: grey (64 836 animals), bay (33 633), black (9414), chestnut (1243), buckskin (433), roan (107), isabella (57) and white (37). Contributions to the total genetic diversity were first assessed in the existing subpopulations and later compared with two scenarios with equal subpopulation size, one with the mean population size (13 710) and another with a low population size (100). Ancestor analysis revealed a very similar origin for the different groups, except for six ancestors that were only present in one of the groups likely to be responsible for the corresponding colour. The coancestry matrix showed a close genetic relationship between the bay and chestnut subpopulations. Before adjustment, Nei's minimum distance showed a lack of differentiation among subpopulations (particularly among the black, chestnut and bay subpopulations) except for isabella and white individuals, whereas after adjustment, white, roan and grey individuals appeared less differentiated. Standardization showed that balancing coat colours would contribute preserving the genetic diversity of the breed. The global genetic diversity increased by 12.5% when the subpopulations were size standardized, showing that a progressive increase in minority coats would be profitable for the genetic diversity of this breed. The methodology developed could be useful for the study of the genetic structure of subpopulations with unbalanced sizes and to predict their genetic importance in terms of their contribution to genetic variability.     

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

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

Pedigree analysis in the Polish Red cattle population

The objective of this study was to describe the population structure and inbreeding level of the population of Polish Red Cattle (PRC). The structure of the breed was analysed in the context of the existing genetic resources conservation programme. The level of genetic diversity and the effective population size were also determined. The analyses were carried out based on pedigree records of 9 170 animals. Data and pedigree information were collected during the time period of 1950–2014. Records were collected by the National Research Institute of Animal Production in Balice, Poland. The population structure was analysed using the CFC programme. All the animals were grouped into five classes according to their inbreeding coefficient: the first class included non-inbred animals; and the next classes included inbred animals 0% < F ≤ 5%, 5% < F ≤ 10%, 10% < F ≤ 20%, 20% < F ≤ 30% or F > 30%. The average inbreeding in PRC population was 4% and there were 2 182 (23.8%) inbred animals. The study also included the determination of ancestral paths for the PRC population. The longest ancestral path (LAP) consisted of 12 generations (three animals) while only 229 animals (2.53%) had an LAP comprising at least 10 generations. Therefore, a need exists, particularly in PRC as a small local breed, to manage selection and mating decisions to control future coancestry and inbreeding, which would lead to better handling of the effective population size. The study results showed the possibility of disrupting the balance of the structure of a small population like PRC. Hence, endangered populations need to be monitored on a continuous basis.     

Genetic diversity and variability in Alpine sheep breeds

The aim of this study was to analyze, through the use of microsatellite molecular markers, the genetic diversity and variability of nine Alpine sheep breeds reared in Italy (Bergamasca, Biellese, Schwarzbraunes Bergschaf, Tiroler Bergschaf, and Schnalserschaf), Germany (Brillenschaf and Weisses Bergschaf) and Slovenia (Bovška and Jezerzkǒ-Solčavska), and one Italian crossbreed population. Allelic richness was rather high in each breed highlighting a considerable genetic diversity. However, the study evidenced a significant departure from Hardy–Weinberg equilibrium in all analyzed breeds caused by a heterozygote deficiency. Such lack seems to be caused both to the presence of population substructure within breed and to a rather high level of inbreeding. The genetic differentiation among breed was rather low (F_ST = 0.057) but significant. The clustering analysis performed with STRUCTURE detected the presence of eight clusters; Schwarzbraunes Bergschaf and Tiroler Bergschaf were grouped together and Biellese and Bergamasca as well, evidencing a high similarity of their genetic make up. Reynolds’ genetic distance estimates confirmed the close relationship between these pairs of breeds. Moreover, Bovška, Jezerzkǒ-Solčavska and Brillenschaf resulted rather similar as expected according to their region of origin and to their common ancestors. Molecular coancestry confirmed as well such findings, suggesting that the studied breeds had origin from different ancestral populations. Concluding, microsatellite resulted a useful tool to investigate breed variability and to characterize Alpine sheep breeds. Obtained findings suggest the need to set up a conservation plan aiming to safeguard and increase the genetic variability of the studied breeds compromised by the high level of inbreeding. Microsatellites genotyping could help to monitor breed variability and to organize matings.     

Inbreeding depression and genetic load in laboratory metapopulations of the butterfly Bicyclus anynana

Abstract.— We investigated the effects of inbreeding on various fitness components and their genetic load in laboratory metapopulations of the butterfly Bicyclus anynana . Six metapopulations each consisted of four subpopulations with breeding population sizes of N = 6 or N = 12 and migration rate of m = 0 or m = 0.33. Metapopulations were maintained for seven generations during which coancestries and pedigrees were established. Individual inbreeding coefficients at the F₇ were calculated and ranged between 0.01 and 0.51. Even though considerable purging had occurred during inbreeding, the genetic load remained higher than that of many outbreeding species: approximately two lethal equivalents were detected for egg sterility, one for zygote survival, one for juvenile survival, and one for longevity. Severe inbreeding depression occurred after seven generations of inbreeding, which jeopardized the metapopulation survival. This finding suggests that the purging of genetic load by intentional inbreeding cannot be recommended for the genetic conservation of species with a high number of lethal.     

Controlling genetic variability by mathematical programming in a selection scheme on an open-pollinated population in Eucalyptus globulus

A model using integer quadratic mathematical programming has been developed to control the inbreeding level (or genetic diversity) through group coancestry in a selection programme for a forestry population structured in terms of maternal families coming from different locations. A method to calculate the average group coancestry between- and within-families for these open-pollinated populations is also proposed. This model has been applied to data from a breeding programme of Australian Eucalyptus globulus. The strategy proved to be effective as reductions of up to 50% for the group coancestry of the selected individuals were reached with a loss of only 5% of the maximum attainable selection differential (corresponding to truncation selection). Received: 14 October 1999 / Accepted: 26 July 2000     

Mating schemes for optimum contribution selection with constrained rates of inbreeding

The effect of non-random mating on genetic response was compared for populations with discrete generations. Mating followed a selection step where the average coancestry of selected animals was constrained, while genetic response was maximised. Minimum coancestry (MC), Minimum coancestry with a maximum of one offspring per mating pair (MC1) and Minimum variance of the relationships of offspring (MVRO) mating schemes resulted in a delay in inbreeding of about two generations compared with Random, Random factorial and Compensatory mating. In these breeding schemes where selection constrains the rate of inbreeding, ΔF, the improved family structure due to non-random mating increased genetic response. For schemes with ΔF constrained to 1.0% and 100 selection candidates, genetic response was 22% higher for the MC1 and MVRO schemes compared with Random mating schemes. For schemes with a less stringent constraint on ΔF or more selection candidates, the superiority of the MC1 and MVRO schemes was smaller (5–6%). In general, MC1 seemed to be the preferred mating method, since it almost always yielded the highest genetic response. MC1 mainly achieved these high genetic responses by avoiding extreme relationships among the offspring, i.e. fullsib offspring are avoided, and by making the contributions of ancestors to offspring more equal by mating least related animals.     

Effect of non-random mating on genomic and BLUP selection schemes

Background

The risk of long-term unequal contribution of mating pairs to the gene pool is that deleterious recessive genes can be expressed. Such consequences could be alleviated by appropriately designing and optimizing breeding schemes i.e. by improving selection and mating procedures.

Methods

We studied the effect of mating designs, random, minimum coancestry and minimum covariance of ancestral contributions on rate of inbreeding and genetic gain for schemes with different information sources, i.e. sib test or own performance records, different genetic evaluation methods, i.e. BLUP or genomic selection, and different family structures, i.e. factorial or pair-wise.

Results

Results showed that substantial differences in rates of inbreeding due to mating design were present under schemes with a pair-wise family structure, for which minimum coancestry turned out to be more effective to generate lower rates of inbreeding. Specifically, substantial reductions in rates of inbreeding were observed in schemes using sib test records and BLUP evaluation. However, with a factorial family structure, differences in rates of inbreeding due mating designs were minor. Moreover, non-random mating had only a small effect in breeding schemes that used genomic evaluation, regardless of the information source.

Conclusions

It was concluded that minimum coancestry remains an efficient mating design when BLUP is used for genetic evaluation or when the size of the population is small, whereas the effect of non-random mating is smaller in schemes using genomic evaluation.