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     

Open-nucleus breeding strategies compared with population-wide positive assortative mating

This study compares population-wide positive assortative mating (PAM) with open-nucleus breeding with an elite and main population when more effort is allocated to parents of the elite. A companion study showed that PAM is advantageous when testing effort is independent of parental value. In the present study, unbalanced testing was imposed by varying the number of crosses or the number of genotypes per cross. These unbalanced alternatives are compared with PAM, where the testing effort was varied so that better parents were mated more frequently. More effort allocated to parents of higher rank increased the additive effect and the additive variance and only slightly altered the group coancestry and inbreeding in the breeding population (BP) compared with completely balanced scenarios. Of particular interest to the breeder, large enhancement of the additive variance in the BP contributed to higher gains in the production population (PP). These simulations demonstrate that population-wide PAM leads to higher genetic gains compared with open-nucleus alternatives at any desired target level of diversity in the PP. This is true for both balanced (part I) and unbalanced distribution of testing effort (part II).     

Positive assortative mating with family size as a function of predicted parental breeding values

While other investigations have described benefits of positive assortative mating (PAM) for forest tree breeding, the allocation of resources among mates in these studies was either equal or varied, using schemes corresponding only to parental rank (i.e., more resources invested in higher-ranking parents). In this simulation study, family sizes were proportional to predicted midparent BLUP values. The distribution of midparent BLUP values was standardized by a constant, which was varied to study the range of distributions of family size. Redistributing progenies from lower- to higher-ranking families to a point where an equal number of progenies were still selected out of each family to the next generation caused minimal change in group coancestry and inbreeding in the breeding population (BP), while the additive genetic response and variance in the BP were both greatly enhanced. This generated additional genetic gains for forest plantations by selecting more superior genotypes from the BP (compared to PAM with equal family sizes) for production of improved regeneration materials. These conclusions were verified for a range of heritability under a polygenic model and under a mixed-inheritance model with a QTL contributing to the trait variation.     

Single versus subdivided population strategies in breeding against an adverse genetic correlation

In advanced conifer breeding programmes, the simultaneous genetic improvement of adversely correlated traits constitutes a major challenge. Population subdivision strategies have been proposed to deal with breeding objective uncertainty, to reduce inbreeding depression in production populations and to reduce genetic correlation adversity. We used Monte Carlo simulations based on a finite locus model to study the effect of a two-breeding-population strategy applying selection for each trait in each breeding population on the genetic correlation and on genetic gains in breeding populations (BP) and the production population (PP) within a time frame of ten generations. A single-BP and a two-subline strategy both applying multitrait index selection with equal trait weights were used as references. Two BP strategy simulations indicated that simultaneous genetic gain for the two traits could be achieved in the PP despite adverse pleiotropy. The adversity of the genetic correlations decreased in BPs of the two-BP strategy, in contrast to single-BP and subline strategies, but the adversity reduction came at the cost of a lower rate of aggregated (summed) genetic gain in the PP for the two-BP strategy compared to the single-BP or subline strategies. The subline strategy exhibited increased genetic gain in the PP at equal levels of inbreeding as intended. Two BP strategies could be useful to develop breeds specialised on different traits and to simultaneously reduce adverse genetic correlations. However, if the aggregated genetic gain should be maximised, the single-BP strategy appears a better choice.     

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.     

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     

The impact of recombination on short-term selection gain in plant breeding experiments

Recombination is a requirement for response to selection, but researchers still debate whether increasing recombination beyond normal levels will result in significant gains in short-term selection. We tested this hypothesis, in the context of plant breeding, through a series of simulation experiments comparing short-term selection response (≤20 cycles) between populations with normal levels of recombination and similar populations with unconstrained recombination (i.e., free recombination). We considered additive and epistatic models and examined a wide range of values for key design variables: selection cycles, QTL number, heritability, linkage phase, selection intensity and population size. With few exceptions, going from normal to unconstrained levels of recombination produced only modest gains in response to selection (≈11 % on average). We then asked how breeders might capture some of this theoretical gain by increasing recombination through either (1) extra rounds of mating or (2) selection of highly recombinant individuals via use of molecular markers/maps. All methods tested captured less than half of the potential gain, but our analysis indicates that the most effective method is to select for increased recombination and the trait simultaneously. This recommendation is based on evidence of a favorable interaction between trait selection and the impact of recombination on selection gains. Finally, we examined the relative contributions of the two components of meiotic recombination, chromosome assortment and crossing over, to short-term selection gain. Depending primarily on the presence of trait selection pressure, chromosome assortment alone accounted for 40–75 % of gain in response to short-term selection.     

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.     

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.     

Using semidefinite programming to optimize unequal deployment of genotypes to a clonal seed orchard

Tree breeders must often consider the conservation of genetic diversity, while at the same time, maximizing response to selection. In the case of seed orchards, the buyer of seed wants maximum performance, while satisfying a restriction, sometimes legislated, on the diversity deployed to the forest. Optimal selection will not completely avoid kinship but rather maximize gain while imposing a constraint on average relatedness. Here, we present the application of semidefinite programming (SDP) as a flexible approach to optimize the deployment of genotypes to a clonal seed orchard. We formulate the selection problem as an SDP, where average breeding value is to be maximized, while imposing constraints on relatedness, as well as maximum and minimum contributions from each candidate. An open-source solver, SDPA, was embedded into a tool designed to make the optimization of seed orchards by SDP simple and flexible. Case studies optimizing seed orchards for Scots pine and loblolly pine illustrate how this flexibility can be used to impose additional constraints on the scion material available from some candidate genotypes and optimize selection even when related candidates have varying degrees of coancestry among them. Additional situations where SDP can be employed are discussed.     

Comparison of selection methods for optimizing genetic gain and gene diversity in a red pine (<Emphasis Type="Italic">Pinus resinosa</Emphasis> Ait.) seedling seed orchard

Four selection methods, individual selection (IS), family selection (FS), family plus within-family selection (FWFS) and combined selection (CS), were used to estimate genetic gain [E(g)] for stem volume and gene diversity (GD) for ten theoretical selection intensities in a 108-family, 12-year-old red pine seedling seed orchard. Estimated genetic gain for stem volume ranged from 4.6% to 11.8% across all selection methods and intensities with CS consistently having the highest gains and FS the lowest for any given selection intensity. Genetic diversity ranged from 0.9797 to 0.9954 across all selection methods and intensities. Individual selection was the best selection method for retaining GD, especially at the higher selection intensities, while FWFS was more efficient at the lowest selection intensity. An optimization point, which maximized E(g) and GD relative to each other, was calculated for each selection method. In all cases the optimization point indicated that both E(g) and GD would be favorably high when optimized relative to each other. The implications for volume gain, genetic diversity and potential inbreeding in red pine, a species with inherently low levels of genetic variation, are discussed.Communicated by D.B. Neale     

Within and among family variation of orchard and wild-stand progeny of interior spruce in British Columbia

A common garden study was conducted with seedlings of the interior spruce complex [Picea glauca (Monch) Voss and Picea. engelmannii Parry and their hybrids], comparing seedling height growth using open-pollinated orchard families and wild-stand (WS) families from the same breeding zone. Phenotypic variances of three bulked orchard seedlots and three WS seedlots did not differ. Orchard seedlots had generally higher within-family variance components than WS families. To examine year-to-year variation in orchard seedlots, three seedlots, composed of the same 18 orchard families collected in three different years, were evaluated in the same common garden study. Family mean heights within the three crop years were statistically not different; however, large rank changes in family mean heights and family variances were observed. This study shows that orchard seed derived from breeding programs does not reduce phenotypic variability in commercial plantations. In spite of the moderate to high selection intensities applied to the selection of orchard parents, large amounts of phenotypic variation are maintained because of the lack of coancestry in the orchard pollen cloud and large temporal variation in mating success and fecundity of the various parents contributing to the crop.     

Prospects for genomic selection in conifer breeding: a simulation study of Cryptomeria japonica

Genomic selection (GS) can be a powerful technology in conifer breeding because conifers have long generation intervals, protracted evaluation times, and high costs of breeding inputs. To elucidate the potential of GS for conifer breeding, we simulated 60-year breeding programs in Cryptomeria japonica with and without GS. In conifers, the rapid decay of linkage disequilibrium (LD) can constitute a severe barrier to application of GS. For overcoming that barrier, we proposed an idea to leverage a seed orchard system, which has been used commonly in conifers, because some degree of LD exists in progenies derived from the limited number of elite trees in a seed orchard. The base population used for simulations consisted of progenies from 25 elite trees. Results show that GS breeding (GSB) done without model updating outperformed phenotypic selection breeding (PSB) during the first 30 years, but the genetic gain achieved over the 60 years was smaller in GSB than in PSB. However, GSB with model updating outperformed PSB over the 60 years. The genetic gain achieved over the 60 years of GSB with model updating was nearly twice that of PSB. Advantages of GSB over PSB prevailed, even for a low heritability polygenic trait. The number of markers necessary for efficient GS was a realistic level (e.g., one in every 1 cM), although higher marker density engendered higher accuracy of selection. These results suggest that GS can be useful in C. japonica breeding. Updating of the prediction model was, however, indispensable for attaining the large genetic gain.     

Levels of genetic diversity at different stages of the domestication cycle of interior spruce in British Columbia

Concerns over the reductionist nature of the domestication of forest-tree species focus on the possibility of potential genetic erosion during this process. To address these concerns, genetic diversity assessments in a breeding zone the Province of British Columbia “interior” spruce (Picea glauca×engelmanni) program was conducted using allozyme markers. Genetic-variation comparisons were made between natural and production (seed orchard) populations as well as seed and seedling crops produced from the same breeding zone’s seed orchard. The natural population sample consisted of a total of 360 trees representing three stands within each of three watersheds present in the Shuswap-Adams low-elevation zone of interior British Columbia. Small amounts of genetic differentiation were observed among the nine natural populations (4%) and this was attributable to extensive gene flow Consequently, the sum of these nine populations was considered as a baseline for the genetic variation present in the breeding zone. The comparisons between the seed orchard and the breeding zone produced a similar percentage of polymorphic loci while the expected hetrozygosity (0.207 vs 0.210) and the average number of alleles per locus (2.7 vs 2.4) were slightly lower in the seed orchard. A total of seven natural populations’ rare alleles were not present in the orchard population, while one allele was unique to the orchard. The %P increased to 70.6% in the seedlot, but dropped to the natural populations level (64.7%) in the plantation. The observed increase in %P was a result of pollen contamination in the orchard. It is suspected that the reduction in the plantation was caused by an unintentional selection in the nursery. Simulated roguing in the orchard did not drastically reduce even if up to 50% of the orchard’s clones were rogued. However, roguing was associated with a reduction in the average number of alleles per locus (i.e., sampling effect). Received: 2 January 1996 / Accepted: 24 May 1996     

Bias in the prediction of genetic gain due to mass and half-sib selection in random mating populations

The prediction of gains from selection allows the comparison of breeding methods and selection strategies, although these estimates may be biased. The objective of this study was to investigate the extent of such bias in predicting genetic gain. For this, we simulated 10 cycles of a hypothetical breeding program that involved seven traits, three population classes, three experimental conditions and two breeding methods (mass and half-sib selection). Each combination of trait, population, heritability, method and cycle was repeated 10 times. The predicted gains were biased, even when the genetic parameters were estimated without error. Gain from selection in both genders is twice the gain from selection in a single gender only in the absence of dominance. The use of genotypic variance or broad sense heritability in the predictions represented an additional source of bias. Predictions based on additive variance and narrow sense heritability were equivalent, as were predictions based on genotypic variance and broad sense heritability. The predictions based on mass and family selection were suitable for comparing selection strategies, whereas those based on selection within progenies showed the largest bias and lower association with the realized gain.     

A comparison of the effect of genetic improvement, seed source and seedling seed orchard variables on progeny growth in Eucalyptus nitens in South Africa

Eucalyptus nitens is an important forestry species grown for pulp and paper production in the temperate, summer-rainfall regions of South Africa. A tree improvement programme has been ongoing at the Institute for Commercial Forestry Research for two decades, but genetic improvement in the species has been slow due to delayed and infrequent flowering and seed production. Three trials were established, firstly, to quantify the gains that have been made in the first generation of improvement in the breeding programme and, secondly, to establish whether a number of seed source and orchard variables influence the performance of the progeny. These variables were the amount of flowering trees in the seed orchard, year of seed collection, seed orchard origin and composition of seed orchard bulks. Diameter at breast height and tree heights were measured in the trials at between 87 and 97 months after establishment, and timber volumes and survival were calculated. Improved seed orchard bulks performed significantly better (p?<?0.01) than unimproved controls in the field trials. Genetic gains ranging from 23.2 to 164.8 m³?ha^?1 were observed over the unimproved commercial seed. There were significant differences (p?<?0.01) in progeny growth between the levels of seed orchard flowering, with higher levels of flowering (≥40 %) producing substantially greater progeny growth than lower flowering levels (≤20 %). The seed orchard had no effect on progeny growth in this trial series. This suggests that seed collected from any of the four seed orchards tested will produce trees with significant improvement in growth.     

Genetic diversity in a seed production population vs. natural populations of Sitka Spruce

Isozyme analysis was applied to estimate the level of variation and the genetic structure of a seed-production population (i.e., seed orchard) and 10 range-wide natural populations of Sitka spruce (Picea sitchensis (Bong.) Carr.). Gene diversity and heterozygosity estimates were comparatively high in both the seed orchard and the natural populations studied. The seed orchard population showed a significantly higher number of alleles per locus and percentage of polymorphic loci. Though not significant, mean heterozygosity of the seed orchard was higher than that observed for all natural populations. Genetic distance analysis indicated that the seed-orchard population was genetically similar to three natural populations from which the parent trees were selected. Parent trees sampling breadth has been identified as the major cause for the observed increased level. The impact of recurrent selection and seed orchard biology and management on maintaining the genetic diversity is discussed.     

马尾松不同改良水平子代群体遗传多样性研究

该研究以马尾松三个不同改良水平的良种生产群体子代为材料,用天然群体作为对照,采用16对SSR引物对试验群体进行遗传多样性分析,并探究遗传改良对马尾松林分遗传多样性的影响。结果表明:马尾松天然群体、母树林子代、1代种子园子代及1.5代种子园子代的Shannon多样性指数(I)分别为0.53、0.53、0.53、0.46;观测杂合度(Ho)分别为0.36、0.36、0.39、0.35;期望杂合度(He)分别为0.32、0.32、0.33、0.27。在这三项主要遗传多样性指标上,马尾松母树林、1代种子园及1.5代种子园的子代之间无显著差异。由此说明,在广西马尾松的遗传改良进程中,遗传多样性并未因改良选择而受到明显的影响。良种人工林与天然林相比较,马尾松良种人工林在三项主要指标上无明显下降,说明广西三类主要的良种群体都具有较好的群体缓冲能力和个体缓冲能力。该研究结果对于科学制定马尾松育种策略具有重要意义,为马尾松高世代育种研究提供了重要的理论依据。     

Optimization of selection for growth in Menz Sheep while minimizing inbreeding depression in fitness traits

The genetic trends in fitness (inbreeding, fertility and survival) of a closed nucleus flock of Menz sheep under selection during ten years for increased body weight were investigated to evaluate the consequences of selection for body weight on fitness. A mate selection tool was used to optimize in retrospect the actual selection and matings conducted over the project period to assess if the observed genetic gains in body weight could have been achieved with a reduced level of inbreeding. In the actual selection, the genetic trends for yearling weight, fertility of ewes and survival of lambs were 0.81 kg, –0.00026% and 0.016% per generation. The average inbreeding coefficient remained zero for the first few generations and then tended to increase over generations. The genetic gains achieved with the optimized retrospective selection and matings were highly comparable with the observed values, the correlation between the average breeding values of lambs born from the actual and optimized matings over the years being 0.99. However, the level of inbreeding with the optimized mate selections remained zero until late in the years of selection. Our results suggest that an optimal selection strategy that considers both genetic merits and coancestry of mates should be adopted to sustain the Menz sheep breeding program.     

Effect of genomic prediction on response to selection in forest tree breeding

Through stochastic simulations, estimates of breeding values accuracies and response to selection were assessed under traditional pedigree-based and genomic-based evaluation methods. More specifically, several key parameters such as the trait’s heritability (0.2 and 0.6), the number of QTLs underlying the trait (100 to 200), and the marker density (1 to 10 SNPs/cM) were evaluated. Additionally, impact of two contrasting mating designs (partial diallel vs. single-pair mating) was investigated. Response to selection was then assessed in a seed production population (seed orchard consisting of unrelated selections) for different effective population sizes (N_e?=?5 to 25). The simulated candidate population comprised a fixed size of 2050 individuals with fast linkage disequilibrium decay, generally found in forest tree populations. Following the genetic/genomic evaluation, top-ranked individuals were selected to meeting the predetermined effective population size in target production population. The combination of low h², high N_e, and dense marker coverage resulted at maximum relative genomic prediction efficiency and the most efficient exploitation of the Mendelian sampling term (within-family additive genetic variance). Since genomic prediction of breeding values constitutes the methodological foundation of genomic selection, our results can be used to address important questions when similar scenarios are considered.