Prediction of genetic values of quantitative traits with epistatic effects in plant breeding populations

Though epistasis has long been postulated to have a critical role in genetic regulation of important pathways as well as provide a major source of variation in the process of speciation, the importance of epistasis for genomic selection in the context of plant breeding is still being debated. In this paper, we report the results on the prediction of genetic values with epistatic effects for 280 accessions in the Nebraska Wheat Breeding Program using adaptive mixed least absolute shrinkage and selection operator (LASSO). The development of adaptive mixed LASSO, originally designed for association mapping, for the context of genomic selection is reported. The results show that adaptive mixed LASSO can be successfully applied to the prediction of genetic values while incorporating both marker main effects and epistatic effects. Especially, the prediction accuracy is substantially improved by the inclusion of two-locus epistatic effects (more than onefold in some cases as measured by cross-validation correlation coefficient), which is observed for multiple traits and planting locations. This points to significant potential in using non-additive genetic effects for genomic selection in crop breeding practices.     

Social cues affect quantitative genetic variation and covariation in animal personality traits

The social environment is expected to have substantial effects on behavior, and as a consequence, its heritability and evolvability. We investigated these effects by exposing Australian field crickets (Teleogryllus oceanicus) to either silence or recordings of male acoustic sexual signals. We used a combined pedigree and full‐sib/half‐sib breeding design to estimate the repeatability, heritability, and evolvability of behaviors related to boldness, exploration, and activity. All behaviors measured were significantly repeatable in both social environments. Additionally, most behaviors showed significant heritabilities in the two environments. We found no difference in repeatabilities between the silent and the acoustic environment but did find significant differences in the heritabilities and evolvabilities between these environments. There was a high degree of similarity between the phenotypic covariance matrices across the two environments, while the genotypic covariance matrices were highly dissimilar. Reflecting this, we found significant genotype‐by‐environment interactions for most of the behaviors. Lastly, we found that the repeatable aspect of behavior (“personality”) was significantly heritable for most behaviors, but that these heritabilities were higher in the acoustic than in the silent environment. We conclude that the social environment can have a significant impact on the heritability and evolvability of behavior, and argue that evolutionary inferences from phenotypic studies should be made with caution.     

Evolution of genetic variation for selected traits in successive breeding populations of maritime pine

Directional selection impacts a trait distribution by shifting its mean and reducing its variance. The change of variance is of major importance as the response to selection in subsequent generations is highly dependent of the genetic variability available in the population. In this contribution, evolution of genetic variation was investigated through the first breeding populations of the French maritime pine (Pinus pinaster Ait.) breeding program. We considered three populations: P0 (the forest where plus trees were initially selected), G0 (the plus tree population) and G1 (the population composed of trees selected in the progenies of G0). Analyses focused on the following selected traits: total height (H), girth at 1.30 m (D) and stem deviation to verticality (S). More than 150,000 trees from 25 tests of three distinct populations were studied with an individual genetic model. Accurate genetic parameters were obtained by taking all relationships between trees into account. For H and D, we found a strong decrease of the genetic variation from P0 to G0 corresponding to the initial selection of plus trees, which constitutes the base population of the breeding program. Then, despite the second step of selection applied, no appreciable evolution arose from comparisons between G0 and G1 for these traits. For S, the evolution is less significant as phenotypic variation slightly increased, possibly due to changes of silvicultural practices.     

Spatially structured genetic variation in a broadcast spawning bivalve: quantitative vs. molecular traits

Understanding the origin, maintenance and significance of phenotypic variation is one of the central issues in evolutionary biology. An ongoing discussion focuses on the relative roles of isolation and selection as being at the heart of genetically based spatial variation. We address this issue in a representative of a taxon group in which isolation is unlikely: a marine broadcast spawning invertebrate. During the free-swimming larval phase, dispersal is potentially very large. For such taxa, small-scale population genetic structuring in neutral molecular markers tends to be limited, conform expectations. Small-scale differentiation of selective traits is expected to be hindered by the putatively high gene flow. We determined the geographical distribution of molecular markers and of variation in a shell shape measure, globosity, for the bivalve Macoma balthica (L.) in the western Dutch Wadden Sea and adjacent North Sea in three subsequent years, and found that shells of this clam are more globose in the Wadden Sea. By rearing clams in a common garden in the laboratory starting from the gamete phase, we show that the ecotypes are genetically different; heritability is estimated at 23%. The proportion of total genetic variation that is between sites is much larger for the morphological additive genetic variation (QST = 0.416) than for allozyme (FST = 0.000-0.022) and mitochondrial DNA cytochrome-c-oxidase-1 sequence variation (phiST = 0.017). Divergent selection must be involved and intraspecific spatial genetic differentiation in marine broadcast spawners is apparently not constrained by low levels of isolation.     

Effects of a founder event and supplementary introductions on genetic variation in a captive breeding population of the endangered Spanish killifish

Twelve polymorphic allozyme loci were employed to assess the genetic change in a captive breeding population of the endangered killifish Aphanius baeticus in the Doñana National Park, south‐western Spain. The initial founder event did not significantly reduce the allelic richness or the expected heterozygosity. No genetic bottleneck signature was detected by tests for deviation from mutation‐drift equilibrium. The F _ST between the wild source and captive population, however, was relatively high (0·053 or 0·122 when excluding or including the locus IDHP‐1 * respectively), after just two to three generations in captivity. Two generations after the incorporation of 68 new wild specimens (greater than five generations after founding) decreased the genetic differences and the F _ST(0·041 excluding IDHP‐1 *). The restoration efforts appeared to be helpful and the study of 12 polymorphic loci and a sensitive parameter such as F _ST were useful for monitoring genetic changes in captivity. Nonetheless, future monitoring should include additional highly polymorphic loci (microsatellites) to achieve higher power to detect genetic change. Such restoration and monitoring efforts should help to avoid rapid inbreeding, adaptation to captivity, and to maintain the long‐term evolutionary potential in small isolated populations.     

Effect of low stressful temperature on genetic variation of five quantitative traits in Drosophila melanogaster

A half-sib analysis was used to investigate genetic variation for three morphological traits (thorax length, wing length and sternopleural bristle number) and two life-history traits (developmental time and larva-to-adult viability) in Drosophila melanogaster reared at a standard (25 degrees C) and a low stressful (13 degrees C) temperature. Both phenotypic and environmental variation showed a significant increase under stressful conditions in all traits. For estimates of genetic variation, no statistically significant differences were found between the two environments. Narrow heritabilities tended to be higher at 13 degrees C for sternopleural bristle number and viability and at 25 degrees C for wing length and developmental time, whereas thorax length did not show any trend. However, the pattern of genetic variances and evolvability indices (coefficient of genetic variation and evolvability), considered in the context of literature evidence, indicated the possibility of an increase in additive genetic variation for the morphological traits and viability and in nonadditive genetic variation for developmental time. The data suggest that the effect of stressful temperature may be trait-specific and this warns against generalizations about the behaviour of genetic variation under extreme conditions.     

Elevation induced variation in the breeding traits of a nectar-feeding non-flying mammal

Factors that influence reproduction in nectar-feeding non-flying mammals are poorly described. We investigated factors that may influence the breeding traits of the eastern pygmy-possum (Cercartetus nanus), a small (25 g) nectar-feeding marsupial from eastern Australia. Females at our coastal site produced 1–3 litters (frequently of 5–6 young) over an 8-month period within the flowering period of the dominant food plant (Banksia ericifolia). The number of lactating females over time was highly correlated (R?=?0.9) with the abundance of flowers on B. ericifolia, suggesting that flower availability has a substantial influence on breeding. To assess the generality of these findings and investigate whether elevation or latitude influence breeding in this species, we examined the breeding traits previously described at three other locations. Females on the tableland 70 km away produced one litter of 3–4 young over a 4-month period within the flowering period of B. ericifolia, the dominant food plant. At other coastal and tableland locations 500 km away, coastal females produced larger numbered litters more often than tableland females. A hypothesis relating to minimum temperature appears the most plausible explanation for this pattern that reflects elevation but not latitude. The mean minimum temperature drops below 5 °C for 2–5 months each year at the tableland locations but not at all at the coastal locations. Low temperatures are known to reduce nectar secretion in the dominant food plants. Thus, although the breeding traits of the eastern pygmy-possum are influenced by flowering in their dominant food plants, low temperature appears to impose a constraint on reproductive output.     

SASQuant: a SAS software program to estimate genetic effects and heritabilities of quantitative traits in populations consisting of 6 related generations

Plant breeders are interested in the analysis of phenotypic data to measure genetic effects and heritability of quantitative traits and predict gain from selection. Measurement of phenotypic values of 6 related generations (parents, F(1), F(2), and backcrosses) allows for the simultaneous analysis of both Mendelian and quantitative traits. In 1997, Liu et al. released a SAS software based program (SASGENE) for the analysis of inheritance and linkage of qualitative traits. We have developed a new program (SASQuant) that estimates gene effects (Hayman's model), genetic variances, heritability, predicted gain from selection (Wright's and Warner's models), and number of effective factors (Wright's, Mather's, and Lande's models). SASQuant makes use of traditional genetic models and allows for their easy application to complex data sets. SASQuant is freely available and is intended for scientists studying quantitative traits in plant populations.     

RFLP approach to breeding for quantitative traits in plants—a critique

A number of recent papers suggest that use of RFLPs as markers offers a clear advantage in breeding for improvement in quantitative traits (QTs). The concepts underlying establishment of linkage between RFLP markers and QT loci stem from three papers on tomato published during 1987–1991. Essentially, continuously varying QT phenotypes are assigned to RFLP genotype classes, which can be considered to be determined by a single, diallelic gene with codominant alleles. Linkage is inferred through statistical analysis. Similarly, interaction between markers and QT is also tested by an analysis of variance. Here, the statistical methods employed in these three papers to detect linkage are critically evaluated, especially because subsequent investigations take the concepts developed in these papers as proven. In this paper, we examine the three fundamental papersde novo. We scrutinize the methods employed and the inferences drawn to bring to light what we believe are conceptual drawbacks.     

The value of gametoclonal variation in breeding for quantitative traits in flue-cured tobacco (Nicotiana tabacum L.)

Summary In tobacco (Nicotiana tabacum L.), anther-derived doubled haploid populations have been shown to exhibit large amounts of unexpected genetic variation and a severe depression in cured leaf yield when compared to conventionally inbred genotypes from comparable sources. A previous study had predicted that the yield depression observed in a doubled haploid population-derived from a near homozygous cultivar, NC95, might be overcome through a recurrent selection program. In the current study, progress from three cycles of full-sib family selection for improved yield in an anther-culture derived population of NC95 was measured, as well as the remaining genetic variation within the population. A design II experiment was conducted in the population following three cycles of selection. Results indicate that the NC95 yield level has been recovered in the third selection cycle population. Although most of the genetic variation in the population appears to be exhausted, the additive genetic variance among maternal half-sib families for yield is significant, and it appears that continued yield improvement can be made through recurrent selection. Significant additive-genetic variance for yield was found among maternal half-sib families but was essentially zero among the paternal half-sib families, suggesting that remaining genetic variation is not being transmitted through pollen. One possible explanation results from the phenomenon of DNA amplification that can occur during the anther culture process, and that may enable extraordinary recombinational events and reduce the viability of male gametes.     

Heritable variation and genetic correlation of quantitative traits within and between ecotypes of Avena barbata

We examined heritable variation for quantitative traits within and between naturally occurring mesic and xeric ecotypes of the slender wild oat (Avena barbata), and in 188 recombinant inbred lines derived from a cross between the ecotypes. We measured a suite of seedling and adult traits in the greenhouse, as well as performance-related traits in field sites native to the two ecotypes. Although the ecotypes were genetically diverged for most traits, few traits showed significant heritable variation within either ecotype. In contrast, considerable heritable variation was released in the recombinant progeny of the cross, and transgressive segregation was apparent in all traits. Heritabilities were substantially greater in the greenhouse than in the field, and this was associated with an increase in environmental variance in the field, rather than a decrease in genetic variance. Strong genetic correlations were evident among the recombinants, such that 22 measured traits could be well represented by only seven underlying factors, which accounted for 80% of the total variation. The primary axis of variation in the greenhouse described a trade-off between vegetative and reproductive allocation, mediated by the date of first flowering, and fitness was strongly correlated with this trade-off. Other factors in the greenhouse described variation in size and in seedling traits. Lack of correlation among these factors represents the release of multivariate trait variation through recombination. In the field, a separate axis of variation in overall performance was found for each year/site combination. Performance was significantly correlated across field environments, but not significantly correlated between greenhouse and field.     

Estimating the genetic architecture of quantitative traits

Understanding and estimating the structure and parameters associated with the genetic architecture of quantitative traits is a major research focus in quantitative genetics. With the availability of a well-saturated genetic map of molecular markers, it is possible to identify a major part of the structure of the genetic architecture of quantitative traits and to estimate the associated parameters. Multiple interval mapping, which was recently proposed for simultaneously mapping multiple quantitative trait loci (QTL), is well suited to the identification and estimation of the genetic architecture parameters, including the number, genomic positions, effects and interactions of significant QTL and their contribution to the genetic variance. With multiple traits and multiple environments involved in a QTL mapping experiment, pleiotropic effects and QTL by environment interactions can also be estimated. We review the method and discuss issues associated with multiple interval mapping, such as likelihood analysis, model selection, stopping rules and parameter estimation. The potential power and advantages of the method for mapping multiple QTL and estimating the genetic architecture are discussed. We also point out potential problems and difficulties in resolving the details of the genetic architecture as well as other areas that require further investigation. One application of the analysis is to improve genome-wide marker-assisted selection, particularly when the information about epistasis is used for selection with mating.     

Mutation load and mutation-selection-balance in quantitative genetic traits

Haldane (1937) showed that the reduction of equilibrium mean fitness in an infinite population due to recurrent deleterious mutations depends only on the mutation rate but not on the harmfulness of mutants. His analysis, as well as more recent ones (cf. Crow 1970), ignored back mutation. The purpose of the present paper is to extend these results to arbitrary mutation patterns among alleles and to quantitative genetic traits. We derive first-order approximations for the equilibrium mean fitness (and the mutation load) and determine the order of the error term. For a metric trait under mutation-stabilizing-selection balance our result differs qualitatively from that of Crow and Kimura (1964), whose analysis is based on a Gaussian assumption. Our general approach also yields a mathematical proof that the variance under the usual mutation-stabilizing-selection model is, to first order, µ/s (the house-of-cards approximation) as µ/s tends to zero. This holds for arbitrary mutant distributions and does not require that the population mean coincide with the optimum. We show how the mutant distribution determines the order of the error term, and thus the accuracy of the house-of-cards approximation. Upper and lower bounds to the equilibrium variance are derived that deviate only to second order as µ/s tends to zero. The multilocus case is treated under the assumption of global linkage equilibrium.     

Developing a breeding strategy to exploit quantitative variation in symbiotic nitrogen fixation

Summary This paper examines evidence which quantifies the relative importance of legume and Rhizobium genotypes as determinants of phenotypic variation in symbiotic nitrogen fixation. It demonstrates potentially large and unpredictable effects of the Rhizobium genotype. The likely importance of such effects on crop yield is considered. The information is then used to assess ways in which legume breeding programmes may be altered to encompass the effects of genetic variation in Rhizobium.     

Large-scale geographic patterns of genetic variation in Melica nutans, a widespread Eurasian woodland grass

 The geographic distribution of allozyme variation within the Eurasian boreo-nemoreal woodland grass Melica nutans L. has been investigated together with a minor subset of other Melica species. Twenty alleles were found at nine polymorphic loci in M. nutans. Allelic richness was highest in areas central in the species' European distribution, i.e. in southern Fennoscandia. High population densities, reducing the effects of genetic drift, as well as accumulation of variation through long-distance gene-flow from different marginal populations, is proposed to explain high allelic richness in this area. Several alleles showed geographic patterns in distribution and frequency variation. However, these patterns were not congruent, e.g. some alleles appear to have migrated to northern Europe from the south-west whereas others may have spread from the east. Genetic distances between geographic regions, each consisting of 2–6 populations, were generally low between all Fennoscandian, Russian and Siberian regions, but much higher between western and continental European regions. On the population level, cluster analysis grouped populations from Siberia, Russia, coastal and lowland areas in Fennoscandia and British Cumbria into one subcluster whereas other subclusters contained mainly south-west European populations or populations from almost throughout the distribution range. A scenario with several independent glacial refugia in central Europe, south-western Siberia and possibly western Norway, and subsequent colonisation of Fennoscandia mainly from the east, but with some long-distance gene-flow from central Europe, is proposed. Received April 3, 2002; accepted September 17, 2002 Published online: December 11, 2002     

Integrating candidate gene and quantitative genetic approaches to understand variation in timing of breeding in wild tit populations

Two commonly used techniques for estimating the effect of genes on traits in wild populations are the candidate gene approach and quantitative genetic analyses. However, whether these two approaches measure the same underlying processes remains unresolved. Here, we use these two methods to test whether they are alternative or complementary approaches to understanding genetic variation in the timing of reproduction - a key trait involved in adaptation to climate change - in wild tit populations. Our analyses of the candidate gene Clock show weak correlates with timing variables in blue tits, but no association in great tits, confirming earlier results. Quantitative genetic analyses revealed very low levels of both direct (female) and indirect (male) additive genetic variation in timing traits for both species, in contrast to previous studies on these traits, and much lower than generally assumed. Hence, neither method suggests strong genetic effects on the timing of breeding in birds, and further work should seek to assess the generality of these conclusions. We discuss how differences in the genetic control of traits, species life-history and confounding environmental variables may determine how useful integrating these two techniques is to understand the phenotypic variation in wild populations.     

Patterns of genetic variation within a captive population of Amur tigerPanthera tigris altaica

Eight founders and thirty-one descendants were sampled as the Founder group and the Offspring group respectively from a captive population of Amur tigerPanthera tigris altaica Temminck, 1844 for population genetic analysis with RAPD and ISSR markers. Integrated with demographic data during the initial recovery stage, results showed: (1) increasing the population size (N) and the effective population size (N _e) greatly retard lose of genetic variation induced mainly by genetic drift and selection; (2) recombination and admixture could cause the Offspring group (5.711%) and the Founder group (10.383%) to hold different linkage disequilibrium (LD); (3) further Ohta’s variance analysis indicated genetic drift (87.3%) and epistatic selection (12.7%) maintained LD in population, whereas GENEDROP analysis supported epistatic selection largely derived from artificial selection of managers; (4) both Tajima’s test and Fu’s test confirmed the statistic neutrality of genetic markers used, moreover the positive value of Tajima’sD (0.090) together with the result that π (25.286) was bigger than ϑ (24.898) revealed the Founder group was admixture population, while the negative Tajima’sD value (−0.053) together with the result that π (23.679) was less than ϑ (23.912) disclosed the Offspring group experienced selective sweep.     

Genotype matrix mapping: searching for quantitative trait loci interactions in genetic variation in complex traits.

In order to reveal quantitative trait loci (QTL) interactions and the relationship between various interactions in complex traits, we have developed a new QTL mapping approach, named genotype matrix mapping (GMM), which searches for QTL interactions in genetic variation. The central approach in GMM is the following. (1) Each tested marker is given a virtual matrix, named a genotype matrix (GM), containing intersecting lines and rows equal to the total allele number for that marker in the population analyzed. (2) QTL interactions are then estimated and compared through virtual networks among the GMs. To evaluate the contribution of marker combinations to a quantitative phenotype, the GMM method divides the samples into two non-overlapping subclasses, S(0) and S(1); the former contains the samples that have a specific genotype pattern to be evaluated, and the latter contains samples that do not. Based on this division, the F-measure is calculated as an index of significance. With the GMM method, we extracted significant marker combinations consisting of one to three interacting markers. The results indicated there were multiple QTL interactions affecting the phenotype (flowering date). GMM will be a valuable approach to identify QTL interactions in genetic variation of a complex trait within a variety of organisms.     

Patterns of quantitative genetic variation in multiple dimensions

A fundamental question for both evolutionary biologists and breeders is the extent to which genetic correlations limit the ability of populations to respond to selection. Here I view this topic from three perspectives. First, I propose several nondimensional statistics to quantify the genetic variation present in a suite of traits and to describe the extent to which correlations limit their selection response. A review of five data sets suggests that the total variation differs substantially between populations. In all cases analyzed, however, the “effective number of dimensions” is less than two: more than half of the total genetic variation is explained by a single combination of traits. Second, I consider how patterns of variation affect the average evolutionary response to selection in a random direction. When genetic variation lies in a small number of dimensions but there are a large number of traits under selection, then the average selection response will be reduced substantially from its potential maximum. Third, I discuss how a low genetic correlation between male fitness and female fitness limits the ability of populations to adapt. Data from two recent studies of natural populations suggest this correlation can diminish or even erase any genetic benefit to mate choice. Together these results suggest that adaptation (in natural populations) and genetic improvement (in domesticated populations) may often be as much constrained by patterns of genetic correlation as by the overall amount of genetic variation.