Methods for minimizing the loss of genetic diversity in conserved populations with overlapping generations

Minimization of the average coancestry in a population has been theoretically proven to be the most efficient method to preserve genetic diversity. In the present study, based on a population genetic model, two methods to minimize the average coancestry in populations with overlapping generations were developed. For a given parental coancestry structure, the first method (OG) minimizes the average coancestry in the next generation, and the second method (LT) is designed to minimize the long-term accumulation of coancestry. The efficiencies of the two methods were examined by stochastic simulation. Compared to random choice of parents, the annual effective population sizes under the two proposed methods increased 2–3 folds. The difference among the two methods was small in a population with short generation interval. For populations with long generation intervals, the OG method showed a slightly larger annual effective size in an initial few years. However, in the subsequent years, the LT method gave a 5–15% larger annual effective size than the OG method. From these results, it is suggested that the LT method would be preferred to the OG method in most practical situations.     

Maintaining genetic diversity using molecular coancestry: the effect of marker density and effective population size

Background

The most efficient method to maintain genetic diversity in populations under conservation programmes is to optimize, for each potential parent, the number of offspring left to the next generation by minimizing the global coancestry. Coancestry is usually calculated from genealogical data but molecular markers can be used to replace genealogical coancestry with molecular coancestry. Recent studies showed that optimizing contributions based on coancestry calculated from a large number of SNP markers can maintain higher levels of diversity than optimizing contributions based on genealogical data. In this study, we investigated how SNP density and effective population size impact the use of molecular coancestry to maintain diversity.

Results

At low SNP densities, the genetic diversity maintained using genealogical coancestry for optimization was higher than that maintained using molecular coancestry. The performance of molecular coancestry improved with increasing marker density, and, for the scenarios evaluated, it was as efficient as genealogical coancestry if SNP density reached at least 3 times the effective population size.However, increasing SNP density resulted in reduced returns in terms of maintained diversity. While a benefit of 12% was achieved when marker density increased from 10 to 100 SNP/Morgan, the benefit was only 2% when it increased from 100 to 500 SNP/Morgan.

Conclusions

The marker density of most SNP chips already available for farm animals is sufficient for molecular coancestry to outperform genealogical coancestry in conservation programmes aimed at maintaining genetic diversity. For the purpose of effectively maintaining genetic diversity, a marker density of around 500 SNPs/Morgan can be considered as the most cost effective density when developing SNP chips for new species. Since the costs to develop SNP chips are decreasing, chips with 500 SNPs/Morgan should become available in a short-term horizon for non domestic species.     

Combining genetic gain and diversity by considering average coancestry in clonal selection of Norway spruce

 Genetic relationship within a population can be measured by average coancestry. This can also be expressed as an effective number which represents the relative genetic diversity of the population. The goal of breeding can be formulated to maximise genetic value minus average coancestry times a constant (the “penalty constant”). An iterative search algorithm can then be used to find the best selections for meeting this goal. Two such algorithms, one for a fixed number of selections and the other for a variable optimum number, were applied to select a mixture of field-tested Norway spruce clones with known parents. The results were compared with those from the conventional method of restricting parental contributions to the selected population as a means to control diversity. Coancestry-adjusted selection always yielded more gain than restricted selection at a given effective population size (except under circumstances where the methods were equivalent). Expressed another way, at any given level of gain, coancestry-adjusted selection maintained a larger effective population size than did restricted selection. The relative superiority of coancestry-adjusted selection declined when the effective population size approached the lowest value, that at which no penalty or restriction was applied. The method was extended by the second search algorithm to optimise the selected number of clones. The optimal number of clones can be rather large when diversity is heavily valued, but the reduction in genetic gain becomes large. Received: 7 April 1997 / Accepted: 9 June 1997     

Estimation of genetic variability of the founder population in a conservation scheme using microsatellites

In a conservation programme with genealogical records it is possible to estimate the amount of variability of the founder population from a measure of the similarity among the individuals in the current population based on microsatellite markers. Here we compare three available methods and we shown that the one based on the molecular coancestry coefficient should be preferred.     

Gain and diversity in advanced generation coastal Douglas-fir selections for seed production populations

Sublines are used in the third-generation breeding and testing of coastal Douglas-fir in British Columbia, with the original intent of selecting only one genotype per subline for production populations (e.g., seed orchards) to eliminate relatedness among parents (therein called “1/SL”). We evaluated three additional selection scenarios that did not consider the subline structure. One of the scenarios strictly selected on the basis of the highest breeding values of the trees (“TOP”); another scenario used the TOP selections, but assigned the number of ramets per selection proportionally to the selection breeding value (“LIND”); lastly, a simulated annealing technique was applied to maximize gain under explicit constraints on coancestry (“OPTS”). All three alternative selection scenarios resulted in some relatedness and coancestry among selections, but the last two provided increases in average breeding values compared to those obtained by the 1/SL scenario. Effective population sizes (and consequently inbreeding coefficients) varied among the three selection scenarios. Effects of the various selections on merchantable volume at rotation age were determined using a linear regression model based on an individual tree model (TASS), which was first run to determine the relationship between merchantable volume and inbreeding (f). LIND and TOP selections yielded the highest breeding values but, due to the increased coancestry among selections, paid a penalty in the merchantable volume determination. OPTS maximized merchantable volume at rotation age 60 after including more than 13 selections with an increase of around 3% over that obtained by the 1/SL selection scenario, with an associated increase in Ne of 50%. Other implications of the three alternative selection scenarios are discussed.     

Optimum contribution selection in large general tree breeding populations with an application to Scots pine

Development of selection methods that optimises selection differential subject to a constraint on the increase of inbreeding (or coancestry) in a population is an important part of breeding programmes. One such method that has received much attention in animal breeding is the optimum contribution (OC) dynamic selection method. We implemented the OC algorithm and applied it to a diallel progeny trial of Pinus sylvestris L. (Scots pine) focussing on two traits (total tree height and stem diameter). The OC method resulted in a higher increase in genetic gain (8–30%) compared to the genetic gain achieved using standard restricted selection method at the same level of coancestry constraint. Genetic merit obtained at two different levels of restriction on coancestry showed that the benefit of OC was highest when restriction was strict. At the same level of genetic merit, OC decreased coancestry with 56 and 39% for diameter and height, respectively, compared to the level of coancestry obtained using unrestricted truncation selection. Inclusion of a dominance term in the statistical model resulted in changes in contribution rank of trees with 7 and 13% for diameter and height, respectively, compared to results achieved by using a pure additive model. However, the genetic gain was higher for the pure additive model than for the model including dominance for both traits.     

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.     

Efficiency of the use of pedigree and molecular marker information in conservation programs

The value of molecular markers and pedigree records, separately or in combination, to assist in the management of conserved populations has been tested. The general strategy for managing the population was to optimize contributions of parents to the next generation for minimizing the global weighted coancestry. Strategies differed in the type of information used to compute global coancestries, the number and type of evaluated individuals, and the system of mating. Genealogical information proved to be very useful (at least for 10 generations of management) to arrange individuals' contributions via the minimization of global coancestry. In fact, the level of expected heterozygosity after 10 generations yielded by this strategy was 88-100% of the maximum possible improvement obtained if the genotype for all loci was known. Marker information was of very limited value if used alone. The amount and degree of polymorphism of markers to be used to compute molecular coancestry had to be high to mimic the performance of the strategy relying on pedigree, especially in the short term (for example, >10 markers per chromosome with 10 alleles each were needed if only the parents' genotype was available). When both sources of information are combined to calculate the coancestry conditional on markers, clear increases in effective population size (Ne) were found, but observed diversity levels (either gene or allelic diversity) in the early generations were quite similar to the ones obtained with pedigree alone. The advantage of including molecular information is greater when information is available on a greater number of individuals (offspring and parents vs. parents only). However, for realistic situations (i.e., large genomes) the benefits of using information on offspring are small. The same conclusions were reached when comparing the use of the different types of information (genealogical or/and molecular) to perform minimum coancestry matings.     

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.     

On the principle underlying the tabular method to compute coancestry

Summary The tabular method to compute coancestry between two individuals is based on the principle that coancestry may be computed as the average coancestry between one individual and the parents of the other, on the condition that the former individual is not a direct descendent of the latter. It follows that coancestry also may be computed as the average of the four coancestries between the parents of the two individuals, on the condition that each individual is not a direct descendent of the other. The requirement for these conditions is explained.This research was supported in part by the Illinois Agricultural Experiment Station, Hatch Projects 35-345 and 35-367     

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     

Population structure of the Trakehner Horse breed

The objective of this study was to examine the population structure of the Trakehner Horse breed. A total of 13 793 pedigree records were used for analysing the active breeding population and their ancestors dating back to 1950. Ancestors that were born before 1950 were called as base animals. The average generation interval was calculated as 10.2 years. The effective population size (Ne) was estimated by the increase in average year-wise inbreeding coefficient and average coancestry, respectively. Two methods were applied to estimate the effective population size: 1. Numerator-relationship-matrix (NRM), which did not consider missing ancestries. 2. Uncertain-parentage-matrix (UPM), which considered a probabilistic correction for unknown ancestors. There were no major differences between these two methods with respect to the rate of increase in inbreeding although the global levels using the UPM method were observed to be higher. Estimates for the inbreeding coefficients and the average coancestries varied little between both methods. The estimates of the effective population size per generation based on the rate of inbreeding ranged from 169 (NRM) to 150 (UPM) and 158 (NRM) to 144 (UPM) calculated by the average coancestry. From the early 1990s onwards, a strong increase in the rate of inbreeding was observed. This may be due to an increasing variance of the family size of sires and may be interpreted as a consequence of the growing use of artificial insemination. Analysing coancestries within and between the centrally managed regional breeding societies in Germany further revealed the Trakehner horse breed to be a genetically fragmented population with a main partition corresponding to formerly divided East and West Germany. The average rate of gene contributions (Thoroughbred (xx), Arab Horse breed (ox)) to the defined actual breeding population was calculated to be 22.3% xx-genes and 11.7% ox-genes.     

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.     

Advantages of using molecular coancestry in the removal of introgressed genetic material

Background

When introgression of undesired exogenous genetic material occurs in a population intended to remain pure, actions are necessary to recover the original background. It has been shown that genome-wide information can replace pedigree information for different objectives and is a valuable tool in the fields of genetic conservation and breeding. In this simulation study, molecular information provided by 50 000 SNP was used to minimise the molecular coancestry between individuals of an admixed population and the foreign individuals that originally introgressed a native population in order to remove the exogenous DNA.

Results

This management method, which detects the ‘purest’ individuals to be used as parents for the next generation, allowed recovery of the native genetic background to a great extent in all simulated scenarios. However, it also caused an increase in inbreeding larger than expected because of the lower number of individuals selected as parents and the higher coancestry between them. In scenarios involving several introgression events the method was more efficient than in those involving a single introgression event because part of the genetic information was mixed with the native genetic material for a shorter period.

Conclusions

Genome-wide information can be used to identify the purest individuals via the minimisation of molecular coancestry between individuals of the admixed and exogenous populations. Removal of the undesired genetic material is more efficient with a molecular-based approach than with a pedigree-based approach.     

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.     

Group coancestry-controlled selection in a Pinus sylvestris L. breeding program

 Integer Linear Programming was used to maximize genetic gain from selection at a given level of relatedness. Variances and breeding values for total height were available for 296 plus-trees of Pinus sylvestris which had been evaluated by open-pollinated progeny testing at a single test site in northern Sweden. Second-generation breeding and selection scenarios for this breeding population were evaluated using simulated data derived deterministically from normal distributions of estimated breeding values of progeny around mid-parent family means. The study considered two mating designs, assortative and non-assortative single-pair mating, and two selection criteria, individual phenotype and performance of half-sib progeny. Relatedness (group coancestry) was restricted to a level equivalent to that given by within-family selection of 2 trees per family from each of 25 families (the current standard in Sweden). Selection that allows the best-performing families to contribute a greater number of progeny was superior, both when the breeding population size was limited to 50 individuals and when it was allowed to be larger. The selected set giving the greatest average breeding value under restricted group coancestry included the best individual from families that would have been rejected under application of standard within-family selection. We made a comparison of the present value on retrieved gain between phenotypic selection and evaluation by progeny testing. Received: 24 November 1998 / Accepted: 14 December 1998     

A Monte Carlo algorithm for computing the IBD matrices using incomplete marker information

Identity-By-Descent (IBD) is a general measurement of the relationship between two groups of genes. If the two groups consist of two homologous genes, one from each individual, the IBD is called the coancestry between the two individuals. Coancestry is an important concept in both population and quantitative genetics. It is the probability that both genes are copies of the same gene in the genealogy. The average coancestry value at a random locus in a population reflects the level of population diversity, effective population size, the level of inbreeding and other attributes. Coancestry is also the building block for the covariance structure used to estimate the additive genetic variance component for a quantitative trait. There are many other types of IBD matrices, depending on the natures of the genes included in each group, and these IBD matrices vary from locus to locus. Molecular markers distributed along the genome provide information that can be used to infer these locus-specific IBD matrices. As a result, we can estimate and test the variance components of a quantitative trait contributed by these loci using the inferred IBD matrices. In this study, we develop the concept of locus-specific epistatic IBD matrices and a Monte Carlo method to infer these IBD matrices. The method is suitable for large pedigrees with arbitrary complexity and various levels of missing marker information. With these locus-specific IBD matrices, we are ready to search for quantitative trait loci along the genome in complicated pedigrees.     

Minimization of rate of inbreeding for small populations with overlapping generations

We propose a method that minimizes the rate of inbreeding (delta F) for small unselected populations with overlapping generations and several reproductive age classes. It minimizes the increase in coancestry of parents and optimizes the contribution of each selection candidate. The carrying capacity of the population is limited to a fixed number of animals per year. When survival rate equalled 100%, only animals from the oldest age class were selected, which maximized the number of parents per generation, slowed down the turnover of generations and minimized the increase of coancestry across sublines. However, the population became split into sublines separated by age classes, which substantially increased inbreeding within sublines. Sublines were prevented by a restriction of selecting at least one sire and one dam from the second-oldest age class, which resulted in an L times lower delta F, where L equals the average generation interval of sires and dams. Minimum coancestry mating resulted in lower levels of inbreeding than random mating, but delta F was approximately the same. For schemes where the oldest animals were selected, delta F increased by 18-52% compared with the proposed method.     

Genetic management of captive populations: the advantages of circular mating

We performed computer simulations to evaluate the effectiveness of circular mating as a genetic management option for captive populations. As a benchmark, we used the method proposed by Fernández and Caballero according to which parental contributions are set to produce minimum coancestry among the offspring and matings are performed so as to minimize mean pairwise coancestry (referred to as the Gc/mc method). In contrast to other methods, fitness does not vary with population size in the case of circular mating, and can be higher than under random mating. Whether circular mating is an effective method in conserving captive populations depends on the trade-off between different considerations. On the one hand, circular mating shows the highest allelic diversity and the lowest mean pairwise coancestry for all population sizes. It also shows a relatively higher efficiency of purging deleterious alleles. More importantly, circular mating can significantly increase the success probability of populations released to the wild relative to the Gc/mc method. On the other hand, circular mating has the drawback of showing high inbreeding rates and low fitness in early generations, which can result to an increase in the extinction probability of the captive populations. However, this increase is slight unless population size and litter size are both very low. Overall, if the slight increase in extinction probability can be tolerated then circular mating fulfils the primary goals of a captive breeding program, i.e., it maintains high levels of genetic diversity and increases the success probability of reintroduced populations.     

Phylogenetic inference under the pure drift model

When pairwise genetic distances are used for phylogenetic reconstruction, it is usually assumed that the genetic distance between two taxa contains information about the time after the two taxa diverged. As a result, upon an appropriate transformation if necessary, the distance usually can be fitted to a linear model such that it is expressed as the sum of lengths of all branches that connect the two taxa in a given phylogeny. This kind of distance is referred to as "additive distance." For a phylogenetic tree exclusively driven by random genetic drift, genetic distances related to coancestry coefficients (theta XY) between any two taxa are more suitable. However, these distances are fundamentally different from the additive distance in that coancestry does not contain any information about the time after two taxa split from a common ancestral population; instead, it reflects the time before the two taxa diverged. In other words, the magnitude of theta XY provides information about how long the two taxa share the same evolutionary pathways. The fundamental difference between the two kinds of distances has led to a different algorithm of evaluating phylogenetic trees when theta XY and related distance measures are used. Here we present the new algorithm using the ordinary- least-squares approach but fitting to a different linear model. This treatment allows genetic variation within a taxon to be included in the model. Monte Carlo simulation for a rooted phylogeny of four taxa has verified the efficacy and consistency of the new method. Application of the method to human population was demonstrated.