Half-sib Design Research Articles

Localization of a quantitative trait locus via a Bayesian approach.

A Bayesian approach to the direct mapping of a quantitative trait locus (QTL), fully utilizing information from multiple linked gene markers, is presented in this paper. The joint posterior distribution (a mixture distribution modeling the linkage between a biallelic QTL and N gene markers) is computationally challenging and invites exploration via Markov chain Monte Carlo methods. The parameter's complete marginal posterior densities are obtained, allowing a diverse range of inferences. Parameters estimated include the QTL genotype probabilities for the sires and the offspring, the allele frequencies for the QTL, and the position and additive and dominance effects of the QTL. The methodology is applied through simulation to a half-sib design to form an outbred pedigree structure where there is an entire class of missing information. The capacity of the technique to accurately estimate parameters is examined for a range of scenarios.

Quantitative genetics of ultrasonic advertisement signalling in the lesser waxmoth Achroia grisella (Lepidoptera: pyralidae).

Males of the lesser waxmoth Achroia grisella (Lepidoptera: Pyralidae) produce ultrasonic advertisement signals attractive to females within several metres. Previous studies showed that females prefer male signals that are louder, delivered at a faster rate, and have a greater asynchrony between pulses produced by the right and left wings. These three signal characters vary considerably within populations but are repeatable within individuals. Breeding experiments employing half-sib designs were conducted on both collectively and individually reared moths to determine genetic variance within and covariance among these signal characters. Heritabilities of all signal characters were significant among collectively reared moths. Heritabilities for signal rate and right-left wing asynchrony interval were not significant, however, among individually reared moths, suggesting the presence of significant nonadditive genetic variance or common environmental variation. Development time was also significantly heritable, but only under individual rearing. The only significant genetic correlation was between signal rate and length of the right-left wing asynchrony and this was negative. Our findings on heritability of signal characters are consistent with a coevolutionary sexual selection mechanism, but the absence of signal x development genetic correlation fails to support specifically a good-genes mechanism. The variation in heritability among conditions suggests that environmental variance may be high, and may render selection on signal characters by female choice ineffective. Thus, additive genetic variance for these characters may be maintained in the presence of directional female choice.

Quantitative genetics of ultrasonic advertisement signalling in the lesser waxmoth Achroia grisella (Lepidoptera: Pyralidae)

Males of the lesser waxmoth Achroia grisella (Lepidoptera: Pyralidae) produce ultrasonic advertisement signals attractive to females within several metres. Previous studies showed that females prefer male signals that are louder, delivered at a faster rate, and have a greater asynchrony between pulses produced by the right and left wings. These three signal characters vary considerably within populations but are repeatable within individuals. Breeding experiments employing half-sib designs were conducted on both collectively and individually reared moths to determine genetic variance within and covariance among these signal characters. Heritabilities of all signal characters were significant among collectively reared moths. Heritabilities for signal rate and right–left wing asynchrony interval were not significant, however, among individually reared moths, suggesting the presence of significant nonadditive genetic variance or common environmental variation. Development time was also significantly heritable, but only under individual rearing. The only significant genetic correlation was between signal rate and length of the right–left wing asynchrony and this was negative. Our findings on heritability of signal characters are consistent with a coevolutionary sexual selection mechanism, but the absence of signal × development genetic correlation fails to support specifically a good-genes mechanism. The variation in heritability among conditions suggests that environmental variance may be high, and may render selection on signal characters by female choice ineffective. Thus, additive genetic variance for these characters may be maintained in the presence of directional female choice.

Power to detect QTL in a free‐living polygynous population

Evolutionary biologists attempting to detect quantitative trait loci (QTL) in natural populations have thus far had to carry out some kind of cross with their study organism. Such techniques often increase the probability of detecting linkage, but are impossible or undesirable in many populations. A potential way of overcoming this problem is to carry out linkage studies in large complex pedigrees. In this paper we contrast the power to detect linkage in a complex pedigree of red deer (Cervus elaphus) with that of the widely used half-sib design. When a QTL of magnitude 1 phenotypic standard deviation is segregating and completely linked to a marker, the extended pedigree has power of 0.67, whereas the half-sib design has power of just 0.21. We conclude that detecting QTL may be possible in intensively studied natural populations, provided detailed life history data and good pedigree information are available.

Power to detect QTL in a free-living polygynous population.

Evolutionary biologists attempting to detect quantitative trait loci (QTL) in natural populations have thus far had to carry out some kind of cross with their study organism. Such techniques often increase the probability of detecting linkage, but are impossible or undesirable in many populations. A potential way of overcoming this problem is to carry out linkage studies in large complex pedigrees. In this paper we contrast the power to detect linkage in a complex pedigree of red deer (Cervus elaphus) with that of the widely used half-sib design. When a QTL of magnitude 1 phenotypic standard deviation is segregating and completely linked to a marker, the extended pedigree has power of 0.67, whereas the half-sib design has power of just 0.21. We conclude that detecting QTL may be possible in intensively studied natural populations, provided detailed life history data and good pedigree information are available.

WITHIN-SEASON VARIABILITY OF PUPAL PERIOD IN THE AUTUMNAL MOTH: A BET-HEDGING STRATEGY?

Pupal period is highly variable in Epirrita autumnata (Lepidoptera, Geometridae) lasting from about one to over three months. We aimed to find proximate and ultimate explanations for the high variability, including the possibility that variation in eclosion time represents a diversified bet-hedging strategy. Patterns of variation in pupal period, both among and within populations, were analyzed in several common environment experiments, including one with a half-sib design. We further assessed possible selective forces on eclosion date and its variance using an empirical simulation model. Latitudinal among-population differences in pupal period were shown to have a genetic basis. Within populations, there was a considerable among-sibship variance in this trait that suggests high heritabilities of pupal period. The environmental component of the variance was unlikely to result from a deterministic reaction norm, neither adaptive nor constraint-based, and may thus represent a type of variance on which a bet-hedging strategy can be based. Importantly, there were significant among-sibship differences in the variance itself, and a significant sire effect on offspring variability in the half-sib design. This suggests a possibility for the variance in pupal period to be selected for as such, and for increased random environmental variance (a bet-hedging strategy) to evolve via natural selection. We assumed that seasonal changes in night temperatures and predation rate determine the optimal timing of adult flight period in E. autumnata. Results of modeling suggested that there are apparently flat fitness profiles in relation to eclosion date, which is the probable reason for maintenance of high genetic diversity in pupal period. Unpredictable temperature during adult flight period has a potential to select for high variance in eclosion dates, although the selective pressure appears to be weak. Genetic variance in variance of pupal period may thus be largely selectively neutral in the studied system.

A Bayesian approach to ordering gene markers.

A technique is presented whereby a marker map can be constructed using resource family data with an entire class of missing data. The focus is on a half-sib design where there is only information on a single parent and its progeny. A Bayesian approach is utilised with solutions obtained via a Markov chain Monte Carlo algorithm. Features of the approach include the capacity to determine parameters for the ungenotyped dam population, the ability to incorporate published information and its reliability, and the production of posterior densities and the consequent deduction of a wide range of inferences. These features are demonstrated through the analysis of simulated and experimental data.

Casein polymorphism and relation between milk production traits

Casein polymorphism and relation between milk production traits

Regression on markers with uncertain allele transmission for QTL mapping in half-sib designs

Recently, regression of phenotype on marker genotypes was described for quantitative trait loci (QTL) mapping in F populations and shown to be equivalent to regression interval mapping (RIM). In this study, regression on markers was extended to half-sib designs with uncertain marker allele transmission, and properties of QTL parameters were examined analytically. In this method, offspring phenotypes are first regressed on the probability of transmission of a given allele from the common parent at flanking marker loci. Resulting regression coefficients can then be interpreted based on an assumed genetic model. With presence of a single QTL in the marker interval, it was shown that expected values of regression coefficients for the flanking markers contained all information about position and effect of the QTL and were independent of the probability of marker allele transmission. Through simulation, it was shown that regression of phenotype on marker allele transmission probabilities is equivalent to RIM under the same assumed genetic model. Regression on marker genotypes is computationally less time consuming than QTL interval mapping, as it eliminates the need to search for the best QTL position across marker intervals. This can form the basis for more efficient methods of analysis with more complex models, including threshold or logistic models for the analysis of categorical traits. © Inra/Elsevier, Paris genetic marker / QTL mapping / half-sib design

Regression on markers with uncertain allele transmission for QTL mapping in half-sib designs

Regression on markers with uncertain allele transmission for QTL mapping in half-sib designs

Power of a chromosomal test to detect genetic variation using genetic markers

The power of a backcross design to detect genetic variation associated with a single chromosome was investigated. A simple chromosomal test was suggested in which the phenotypic observations are regressed onto genotypic information from multiple markers. It was shown that the optimum marker spacing depends on the underlying genetic structure and chromosome length. A sparse marker map, with markers approximately every 50 cM, is sufficient to detect chromosomal variation if the nature of the genetic variance is coupled polygenes, whereas the optimum marker spacing to detect a single QTL somewhere on the chromosome is slightly denser, about 20–40 cM. Although the method was demonstrated for line crosses, it can equally be applied to other populations, for example four-way crosses and half-sib designs.

Power of a chromosomal test to detect genetic variation using genetic markers

The power of a backcross design to detect genetic variation associated with a single chromosome was investigated. A simple chromosomal test was suggested in which the phenotypic observations are regressed onto genotypic information from multiple markers. It was shown that the optimum marker spacing depends on the underlying genetic structure and chromosome length. A sparse marker map, with markers approximately every 50 cM, is sufficient to detect chromosomal variation if the nature of the genetic variance is coupled polygenes, whereas the optimum marker spacing to detect a single QTL somewhere on the chromosome is slightly denser, about 20–40 cM. Although the method was demonstrated for line crosses, it can equally be applied to other populations, for example four-way crosses and half-sib designs.

Blood Groups and Milk and Type Traits in Dairy Cattle: After Forty Years of Research

This study addresses the utility of 11 blood groups as selection aids in Holstein breeding schemes and considers issues inherent to the approach of resolving quantitative variation into components that are due to quantitative trait loci. The data consisted of predicted transmitting abilities of 22,614 bulls, first lactation information on 1,924,171 cows, and type scores on 447,800 cows. Linear models were fitted under male half-sib designs, female half-sib designs, and granddaughter designs as well as under the assumption of direct effects of the markers. The evolution of allele frequencies through time was determined, and previous research results were synthesized according to criteria of consistency of biological significance. The inconsistency of results across studies and analytical designs alludes to the importance of the intrinsic nonadditivity of genetic and biological phenomena to quantitative trait locus detection and marker-assisted selection. In our analyses, three associations met the criteria of consistency—a C blood group effect on rump angle, an L effect on milk yield and composition traits, and an S effect on milk fat yield. The M locus appears to be directly associated with effects on milk and protein yields. An enhanced understanding of the biochemical and physiological bases of quantitative genetics should be a long-term objective of this type of genetic analysis.

A Two-Stage Half-Sib Design for Mapping Quantitative Trait Loci in Food Animals

Daughter and granddaughter half-sib designs for mapping quantitative trait loci were modified to increase experimental power. This new design includes a two-stage procedure, in contrast to conventional one-step half-sib designs. In stage 1, a few progeny of each sire are genotyped for marker loci. Based on the analyses of stage 1 data, some sires are chosen to continue genotyping more progeny for stage 2. When multiple chromosomes are under investigation, chromosomes and sires for stage 2 are selected based on the analysis of stage 1 data. Sire selection results in increased frequency of heterozygous genotypes of interest in stage 2 if the markers are linked to those genes. Chromosome selection can increase the proportion of chromosomes with segregating quantitative trait loci in stage 2 if not all of the chromosomes evaluated in stage 1 have segregating quantitative trait loci. Numerical results indicated that two-stage half-sib designs are generally more powerful than conventional designs when 1) the noncentrality parameter is moderate or larger, 2) larger quantitative trait loci are mapped using tightly linked markers in larger families, and 3) variation is large in numbers and sizes of segregating quantitative trait loci among the chromosomes evaluated in stage 1.

Genetic Mapping of Quantitative Trait Loci Controlling Growth and Wood Quality Traits in Eucalyptus grandis Using a Maternal Half-sib Family and RAPD Markers

Quantitative trait loci (QTL) mapping of forest productivity traits was performed using an open pollinated half-sib family of Eucalyptus grandis. For volume growth, a sequential QTL mapping approach was applied using bulk segregant analysis (BSA), selective genotyping (SG) and cosegregation analysis (CSA). Despite the low heritability of this trait and the heterogeneous genetic background employed for mapping, BSA detected one putative QTL and SG two out of the three later found by CSA. The three putative QTL for volume growth were found to control 13.7% of the phenotypic variation, corresponding to an estimated 43.7% of the genetic variation. For wood specific gravity five QTL were identified controlling 24.7% of the phenotypic variation corresponding to 49% of the genetic variation. Overlapping QTL for CBH, WSG and percentage dry weight of bark were observed. A significant case of digenic epistasis was found, involving unlinked QTL for volume. Our results demonstrate the applicability of the within half-sib design for QTL mapping in forest trees and indicate the existence of major genes involved in the expression of economically important traits related to forest productivity in Eucalyptus grandis. These findings have important implications for marker-assisted tree breeding.

Nonadditive genetic structuring of morphometric variation in relation to a population bottleneck

The genetic architectures of four morphometric traits in the housefly, Musca domestica L., were analysed using a paternal half-sib design on a large outbred base population and on two populations each established with two pairs of flies from the base population. By including parents with the offspring in the analysis, phenotypic variance was subdivided into components for additive, dominance, additive-by-additive epistasis and environmental variation. In relation to the nonbottlenecked base population, narrow sense hertitability was lower in the bottle-necked populations, largely because of an increase in the level of the environmental component of variance. Averaged over the four traits in the nonbottlenecked base population, nonadditive components contributed nearly 60 per cent of the phenotypic variance, with more than half of this being attributable to epistasis. Two of the four traits showed reduced additive genetic variance in the bottlenecked lines, whereas two of the traits showed increased additive genetic variance. A major difference in the genetic architecture between traits showing these two disparate bottleneck effects was the presence of epistasis in the nonbottlenecked base population for the traits which showed an increase in the additive component. Overall, there was a significant positive relationship between the initial percentage contribution of epistasis in the base population and the gain in the additive component in the bottleneck lines, as predicted by models incorporating additive-by-additive epistasis.

EVOLUTION OF FLORAL TRAITS IN A HERMAPHRODITIC PLANT: FIELD MEASUREMENTS OF HERITABILITIES AND GENETIC CORRELATIONS.

Genetic variances, heritabilities, and genetic correlations of floral traits were measured in the monocarpic perennial Ipomopsis aggregata (Polemoniaceae). A paternal half-sib design was employed to generate seeds in each of four years, and seeds were planted back in the field near the parental site. The progeny were followed for up to eight years to estimate quantitative genetic parameters subject to natural levels of environmental variation over the entire life cycle. Narrow-sense heritabilities of 0.2-0.8 were detected for the morphometric traits of corolla length, corolla width, stigma position, and anther position. The proportion of time spent by the protandrous flowers in the pistillate phase ("proportion pistillate") also exhibited detectable heritability of near 0.3. In contrast, heritability estimates for nectar reward traits were low and not significantly different from zero, due to high environmental variance between and within flowering years. The estimates of genetic parameters were combined with phenotypic selection gradients to predict evolutionary responses to selection mediated by the hummingbird pollinators. One trait, corolla width, showed the potential for a rapid response to ongoing selection through male function, as it experienced both direct selection, by influencing pollen export, and relatively high heritability. Predicted responses were lower for proportion pistillate and corolla length, even though these traits also experienced direct selection. Stigma position was expected to respond positively to indirect selection of proportion pistillate but negatively to selection of corolla length, with the net effect sensitive to variation in the selection estimates. Anther position also was not directly selected but could respond to indirect selection of genetically correlated traits.

Methodology and accuracy of estimation of quantitative trait loci parameters in a half-sib design using maximum likelihood.

Maximum likelihood methods were developed for estimation of the six parameters relating to a marker-linked quantitative trait locus (QTL) segregating in a half-sib design, namely the QTL additive effect, the QTL dominance effect, the population mean, recombination between the marker and the QTL, the population frequency of the QTL alleles, and the within-family residual variance. The method was tested on simulated stochastic data with various family structures under two genetic models. A method for predicting the expected value of the likelihood was also derived and used to predict the lower bound sampling errors of the parameter estimates and the correlations between them. It was found that standard errors and confidence intervals were smallest for the population mean and variance, intermediate for QTL effects and allele frequency, and highest for recombination rate. Correlations among standard errors of the parameter estimates were generally low except for a strong negative correlation (r = -0.9) between the QTL's dominance effect and the population mean, and medium positive and negative correlations between the QTL's additive effect and, respectively, recombination rate (r = 0.5) and residual variance (r = -0.6). The implications for experimental design and method of analysis on power and accuracy of marker-QTL linkage experiments were discussed.

Quantitative Genetics of Behavioral and Physiological Response to Permethrin in Diamondback Moth (Lepidoptera: Plutellidae)

Insects may survive insecticide applications by physiological mechanisms that permit tolerance of an acquired dose or behavioral mechanisms that reduce the dose acquired. We investigated the genetic basis of physiological and behavioral responses to the pyrethroid permethrin within four diamondback moth, Plutella xylostella (L.), populations with different average levels of tolerance. Using a half-sib design, variance components and heritabilities of the two characters and the genetic correlation between them were calculated for each population. In all four populations, additive genetic variances and heritabilities for physiological tolerance to permethrin were highly significant. In contrast, heritabilities for behavioral avoidance of permethrin were low and significant in only one population, although additive genetic variances were similar to those for tolerance. The phenotypic and genetic correlations between these two characters varied among the populations from essentially zero to strongly significant. All correlations were negative in form, with behaviorally responsive families tending to be less physiologically tolerant and unresponsive families tending to be more physiologically tolerant. The magnitude of the correlation was related to the amount of additive variation in the population ; significant correlations between physiological tolerance and behavioral avoidance occurred in populations with relatively high levels of additive variation for both characters. Implications for the evolution of insecticide resistance and applications for resistance management are discussed, as are parallels with oviposition preference-larval performance studies.

Linkage information content and efficiency of full-sib and half-sib designs for gene mapping

The accuracy of a genetic map depends on the amount of linkage information contained in the data set used for construction of the map. The amount of linkage information is related to the designs employed for linkage analysis. The purpose of this study was to provide general formulations for various genotyping schemes and family structures in order to evaluate the amount of linkage information in a data set. Linkage information content (LIC) was defined as the frequency of fully informative gametes, which are gametes from doubly heterozygous parents with known linkage phases. Depending on the design, LIC is based on two generations if the parental phases are determined statistically, or three generations if the parental phases are determined genetically. Different schemes were considered in deriving LIC: (1) genotyping of one parent or two parents, and (2) genotyping of two or three generation families. The LIC for a full-sib design was found to be generally greater than for a half-sib design but requires typing a large number of individuals when at least one locus has only two alleles. The efficiency of the full-sib design is reduced significantly if a sex-specific linkage map is sought.