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.     

Optimization of combined genetic gain and diversity for collection and deployment of seed orchard crops

Genetic gain and diversity of seed orchards’ crops are determined by the number of parents, their breeding values and relatedness, within-orchard pollination efficiency, and level of pollen contamination. These parameters can be manipulated at establishment by varying clonal representation (e.g., linear deployment), during orchard development by genetic thinning, or by selective harvesting. Since clonal fecundities are known to vary both within and among years, then each seed crop has a unique genetic composition and, therefore, crops should be treated on a yearly basis. Here we present an optimization protocol that maximizes crop’s genetic gain at any desired genetic diversity through the selection of a subset of the crop that meets both parameters. The genetic gain is maximized within the biological limit set by each clone’s seed-cone production and effective population size is used as a proxy to genetic diversity whereby any relationship among clones is considered. The optimization was illustrated using 3 years’ reproductive output data from a first-generation western larch seed orchard and was tested under various scenarios including actual male and female reproductive output and male reproductive output assumed to be either equal to that of female or a function of clonal representation. Furthermore, various levels of co-ancestry were assigned to the orchard’s clones in supplementary simulations. Following the optimization, all solutions were effective in creating custom seedlots with different gain and diversity levels and provided the means to estimate the genetic properties of composite seedlots encompassing the remaining “unused” seed from a number of years.     

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.     

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     

Prediction of genetic gain and gene diversity in seed orchard crops under alternative management strategies

Genetic gain and the gene diversity of seed crops from clonal seed orchards were formulated considering genetic selection, fertility variation and pollen contamination, and compared for five different management strategies. Genetic response was studied as a function of orchard management tactics. Management variables included the proportion of clones left after genetic thinning and/or selective seed harvesting. Formulae were derived to calculate gene diversity (expressed as group coancestry or status number) based on the sex ratio in an orchard population. The influence of having different sets of clones serving as seed parents, or pollen parents, or as both, was analysed. In addition, the impact on genetic gain and the gene diversity of seed crops was studied quantitatively as a function of the quantity and quality of gene flow from outside the orchard. The negative impact of fertility variation among orchard genotypes on the gene diversity of the seed crop was quantified. Numerical examples were given to illustrate the impact of orchard management alternatives on genetic gain and gene diversity. The formulae and results of this study can be used for identifying favourable alternatives for the management of seed orchards. Received: 16 December 2000 / Accepted: 13 March 2001     

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.     

Positive assortative mating with selection restrictions on group coancestry enhances gain while conserving genetic diversity in long-term forest tree breeding

Selection and mating principles in a closed breeding population (BP) were studied by computer simulation. The BP was advanced, either by random assortment of mates (RAM), or by positive assortative mating (PAM). Selection was done with high precision using clonal testing. Selection considered both genetic gain and gene diversity by "group-merit selection", i.e. selection for breeding value weighted by group coancestry of the selected individuals. A range of weights on group coancestry was applied during selection to vary parent contributions and thereby adjust the balance between gain and diversity. This resulted in a series of scenarios with low to high effective population sizes measured by status effective number. Production populations (PP) were selected only for gain, as a subset of the BP. PAM improved gain in the PP substantially, by increasing the additive variance (i.e. the gain potential) of the BP. This effect was more pronounced under restricted selection when parent contributions to the next generation were more balanced with within-family selection as the extreme, i.e. when a higher status effective number was maintained in the BP. In that case, the additional gain over the BP mean for the clone PP and seed PPs was 32 and 84% higher, respectively, for PAM than for RAM in generation 5. PAM did not reduce gene diversity of the BP but increased inbreeding, and in that way caused a departure from Hardy-Weinberg equilibrium. The effect of inbreeding was eliminated by recombination during the production of seed orchard progeny. Also, for a given level of inbreeding in the seed orchard progeny or in a mixture of genotypes selected for clonal deployment, gain was higher for PAM than for RAM. After including inbreeding depression in the simulation, inbreeding was counteracted by selection, and the enhancement of PAM on production population gain was slightly reduced. In the presence of inbreeding depression the greatest PP gain was achieved at still higher levels of status effective number, i.e. when more gene diversity was conserved in the BP. Thus, the combination of precise selection and PAM resulted in close to maximal short-term PP gain, while conserving maximal gene diversity in the BP.Communicated by O. Savolainen     

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.     

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.     

Change in genetic size of small-closed populations: Lessons from a domestic mammal population

The aim of this study was to monitor changes in genetic size of a small-closed population of Iranian Zandi sheep, by using pedigree information from animals born between 1991 and 2005. The genetic size was assessed by using measures based on the probability of identity-by-descend of genes (coancestry, f, and effective population size, N(e) ), as well as measures based on probability of gene origin (effective number of founders, f(e) , effective number of founder genomes, f(g) , and effective number of non-founder genomes, f(ne) ). Average coancestry, or the degree of genetic similarity of individuals, increased from 0.81% to 1.44% during the period 1993 to 2005, at the same time that N(e) decreased from 263 to 93. The observed trend for f(e) was irregular throughout the experiment in a way that f(e) was 68, 87, 77, 92, and 80 in 1993, 1996, 1999, 2002, and 2005, respectively. Simultaneously, f(g) , the most informative effective number, decreased from 61 to 35. The index of genetic diversity (GD) which was obtained from estimates of f(g) , decreased about 2% throughout the period studied. In addition, a noticeable reduction was observed in the estimates of f(ne) from 595 in 1993 to 61 in 2005. The higher than 1 ratio of f(e) to f(g) indicated the presence of bottlenecks and genetic drift in the development of this population of Zandi sheep. From 1993 to 1999, f(ne) was much higher than f(e) , thereby indicating that with respect to loss of genetic diversity, the unequal contribution of founders was more important than the random genetic drift in non-founder generations. Subsequently, random genetic drift in non-founder generations was the major reason for f(e) > f(ne) . The minimization of average coancestry in new reproductive individuals was recommended as a means of preserving the population against a further loss in genetic diversity.     

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     

Expected gain and status number following restricted individual and combined-index selection.

Imposition of restrictions on number of individuals selected from a family and number of families from which superior individuals are selected could markedly alter the consequences of individual and combined-index selection. Predicted genetic gain and diversity measured as status number following selection were studied to draw general conclusions. Selection and its prediction were applied to two sets of real-life data. Theoretical prediction gave results close to those from factual selection. Gain and status number varied with initial family number and size, sib type, heritability, selection proportion, restriction type and intensity, and selection criteria. Proper restriction on the number of individuals selected can control the reduction of status number to an acceptable level, particularly when breeding values are used as the selection criterion. Restriction on the number of families selected would effectively improve the gain efficiency of selection based on phenotypic values. Choosing combinations of both restrictions might produce higher gain without the loss of status number. Given constant population size, family number should be large enough to ensure that restricted selection will yield higher gain and status number.     

Gains from the clonal and the clonal seed-orchard options compared for tree breeding programs

Summary Gains expected from clonal propagation of selections for plantation from a breeding population were compared with those expected from seed propagation via clonal seed-orchards of selections from the same breeding population. Assumptions were made about numbers of clones selected, size of the breeding population, relative sizes of additive and dominance genetic variance components and time required for various operations. Even when dominance variance is zero, considerable extra gain is obtained by the clonal option over the seed-orchard option; mostly due to the shorter time between selection in the breeding population and field planting. When dominance variance equals additive variance, the advantage of the clonal option due to time saved is approximately equal to the advantage due to genetics (i.e. use of more of the additive variance, use of non-additive variance and greater precision of selection). This means that there is a substantial gain to be made simply by getting superior genotypes into plantations more quickly via the clonal option. The gains obtainable through the use of clonal forestry may also be obtained through seed orchards, but some decades later. In no case was the seed-orchard option superior to the clonal option in terms of the gains obtained. No clonal propagation program can advance without a strong sexually-based breeding program to supply it with improved genotypes. The opportunity for improvement comes from genetic recombination.     

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.     

Gene and QTL detection in a three-way barley cross under selection by a mixed model with kinship information using SNPs

Quantitative trait locus (QTL) detection is commonly performed by analysis of designed segregating populations derived from two inbred parental lines, where absence of selection, mutation and genetic drift is assumed. Even for designed populations, selection cannot always be avoided, with as consequence varying correlation between genotypes instead of uniform correlation. Akin to linkage disequilibrium mapping, ignoring this type of genetic relatedness will increase the rate of false-positives. In this paper, we advocate using mixed models including genetic relatedness, or ‘kinship’ information for QTL detection in populations where selection forces operated. We demonstrate our case with a three-way barley cross, designed to segregate for dwarfing, vernalization and spike morphology genes, in which selection occurred. The population of 161 inbred lines was screened with 1,536 single nucleotide polymorphisms (SNPs), and used for gene and QTL detection. The coefficient of coancestry matrix was estimated based on the SNPs and imposed to structure the distribution of random genotypic effects. The model incorporating kinship, coancestry, information was consistently superior to the one without kinship (according to the Akaike information criterion). We show, for three traits, that ignoring the coancestry information results in an unrealistically high number of marker–trait associations, without providing clear conclusions about QTL locations. We used a number of widely recognized dwarfing and vernalization genes known to segregate in the studied population as landmarks or references to assess the agreement of the mapping results with a priori candidate gene expectations. Additional QTLs to the major genes were detected for all traits as well.     

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.     

Effective size and F-statistics of subdivided populations for sex-linked loci.

For a population subdivided into an arbitrary number (s) of subpopulations, each consisting of different numbers of separate sexes, with arbitrary distributions of family size and variable migration rates by males (dm) and females (df), the recurrence equations for inbreeding coefficient and coancestry between individuals within and among subpopulations for a sex-linked locus are derived and the corresponding expressions for asymptotic effective size are obtained by solving the recurrence equations. The usual assumptions are made which are stable population size and structure, discrete generations, the island migration model, and without mutation and selection. The results show that population structure has an important effect on the inbreeding coefficients in any generation, asymptotic effective size, and F-statistics. Gene exchange among subpopulations inhibits inbreeding in initial generations but increases inbreeding in later generations. The larger the migration rate, the greater the final inbreeding coefficients and the smaller the effective size. Thus if the inbreeding coefficient is to be restricted to a specific value within a given number of generations, the appropriate population structure (the values of s, dm, and df) can be obtained by using the recurrence equations. It is shown that the greater the extent of subdivision (large s, small dm and df), the larger the effective size. For a given subdivided population, the effective size for a sex-linked locus may be larger or smaller than that for an autosomal locus, depending on the sex ratio, variance and covariance of family size, and the extend of subdivision. For the special case of a single unsubdivided population, our recurrence equations for inbreeding coefficient and coancestry and formulas for effective size reduce to the simple expressions derived by previous authors.     

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.     

Is linear deployment of clones optimal under different clonal outcrossing contributions in seed orchards?

Self-pollen seldom results in vital genotypes and can thus be regarded as unimportant. Large-sized clones (clones with many ramets) are more exposed to self-pollen and spread more self-pollen and thus contribute relatively less than small-sized clones. The size of clones required to maximize genetic gain at given diversity, considering that only outcrossing contributes to successful gametes, was derived for tested clones intended to establish a Norway spruce (Picea abies) seed orchard. The derived optimal deployment was compared with linear deployment according to Lindgren and Matheson (Silvae Genet 35:173–177, 1986), where the size of a clone is deployed proportional to its breeding value. The study covered a range of effective numbers between 5 and 50. The results suggest that linear deployment is a good approximation to optimal deployment when only outcrossing is considered. The difference between the two strategies is decreased by increasing clone number and is negligible except at low effective numbers.     

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.