Impact of reconstructed pedigrees on progeny-test breeding values in red spruce

Pedigrees reconstructed through DNA marker assigned paternities in polymix (PMX) and open pollinated (OP) progeny tests were analyzed using mixed models to test the effect of unequal male reproductive success and pedigree errors on quantitative genetic parameters. The reconstructed pedigree increased heritabilities in the larger PMX test. Increased heritability resulted from adding the paternities to the pedigree per se, not by correcting the male reproductive bias by specifying the exact pedigree. Removing hypothesized pedigree errors had no effect on quantitative parameters, either because the magnitude of the errors was too small (PMX) or the progeny test was too small to detect variance components reliably (OP). Although there was no advantage in backwards selection, the increased additive variance, heritabilities and accuracy of progeny with assigned paternities in the pedigree, should permit forward selection of offspring with greater genetic gain and complete control of coancestry for future breeding decisions. Some possible breeding population structures with the new genetic information are discussed.     

Polymix breeding with parental analysis of progeny: an alternative to full-sib breeding and testing

Implementation of most traditional full-sib crossing and testing designs is logistically difficult, costly, and genetic gain is constrained by resource availability. An alternative to full-sib crossing and testing can ameliorate all these constraints. The alternative solution is to apply a pollen mix (PMX) of many male parents rather than a single pollen for each cross. PMX breeding is easy to implement, ensures good estimates of breeding values of the parent being pollinated, and provides for increased genetic gain opportunity because of the significantly increased number of effective parental combinations tested. However, PMX breeding has found limited use because inbreeding and pedigree control is lost. The development of relatively inexpensive molecular markers allows for the paternity analysis of progeny, thus allowing full pedigree control. We call this system PMX breeding with parental analysis (PMX/WPA). The feasibility of PMX/WPA was evaluated in a loblolly pine (Pinus taeda) third-generation population of 45 select individuals, among which there was considerable relatedness. All parental trees were genotyped at seven chloroplast and three nuclear microsatellite loci. Unique fingerprints were obtained for all 45 individuals, but unambiguous paternal determinations for progeny from a complete pollen mix would not be possible due largely to relatedness in the breeding population. The inclusion of more markers and/or the creation of polmixes and breeding groups that avoid relatedness would resolve this problem. Three PMX/WPA scenarios are described and compared with conventional full-sib breeding and testing systems: (1) paternity analysis of only the forward (next generation) selection candidates in each generation, (2) paternal genotyping of all progeny test individuals in PMX crosses and using those data to construct the effective full-sib crosses for statistical analysis, and (3) like #2 except mixing seed of the several PMX crosses for ease of greenhouse rearing and progeny testing and then doing maternal and paternal analysis. Received: 27 October 2000 / Accepted: 5 March 2001     

Comparison of genetic parameters from marker-based relationship, sibship, and combined models in Scots pine multi-site open-pollinated tests

Nine microsatellite DNA markers (simple sequence repeats, SSRs) were used to estimate pairwise relationships among 597 Scots pine (Pinus sylvestris) trees as well as to generate a sibship structure for quantitative genetic parameters’ estimation comparison. The studied trees were part of an open-pollinated progeny test of 102 first-generation parents. Three methods were used to estimate variance components and heritabilities, namely, structured pedigree (half- and full-sib), marker-based pairwise relationships (four pairwise estimators), and a combined pedigree and marker-based relationship. In each of the three methods, the same animal model was used to compute variances except when marker-based relationship was used wherein we substituted the average numerator relationship matrix (i.e., pedigree-based matrix) with that computed based on markers’ pairwise relationships. Our results showed a high correlation in estimated breeding values between the pedigree (full-sib) and the combined marker-pedigree estimates. The marker-based relationship method produced high correlations when individual site data were analyzed. In contrast, the marker-based relationship method resulted in a significant decrease in both variance estimation and their standard errors which were in concordance with earlier published results; however, no estimates were produced when across-site analyses were attempted. We concluded that the combined pedigree method is the best approach as it represents the historical (pairwise) and contemporary (pedigree) relationships among the tested individuals, a situation that cannot be attained by any of the used methods individually. This method is dependent on the number and informativeness of the markers used.     

Polymix breeding with paternity analysis in Populus: a test for differential reproductive success (DRS) among pollen donors

Polymix breeding with paternity analysis (PMX/WPA) has been proposed as an alternative to traditional full-sib breeding and testing schemes. To fully capture the benefits of PMX/WPA, differential reproductive success (DRS) of pollen parents used in the polymix must be modest. DRS was evaluated in an operational test of PMX/WPA for a hybrid poplar breeding program. A 16-parent pollen polymix (Populus nigra L.) was used to pollinate seven clones of Populus deltoides (Bartr. ex. Marshall) under greenhouse breeding conditions. Progeny were grown out briefly and randomly sampled (357) prior to out-planting in field trials. Twenty-eight simple sequence repeat (SSR) loci were evaluated and 15 were selected for genetic characterization in small populations of three Populus spp (P. nigra, P. deltoides, and P. balsamifera spp trichocarpa Torr. & Gray). Seven loci were ultimately selected for paternity analysis of progeny. The average exclusion probability of the seven loci in P. nigra was 0.604; combined, the theoretical exclusion probability was 0.9999. However, only 95% of sampled progeny were unambiguously assigned a single paternal parent. Missing data likely accounted for most of the ambiguity. DRS was statistically significant though not prohibitive for practical utility of PMX/WPA as a breeding system. Of the 112 potential crosses in this study, 92 were represented. Eight of the 16 pollen parents contributed 83% of the progeny. Good pollen vigor, as measured by germination percent, did not ensure paternal success, but poor vigor was associated with lack of paternal success. PMX/WPA appears to be logistically and economically attractive for hybrid poplar breeding and testing.     

How do misassigned paternities affect the estimation of heritability in the wild?

Studies of birds have recently played an important role in the increasing success of quantitative genetics applied to natural populations. However, these studies mostly base their pedigree relationships on social information, despite the known widespread genetic polygamy in avian species. Here, we study the influence of misassigned paternities, combined with the effect of pedigree size and depth, on the estimation of heritability. First, we compute simulations of a polygenic trait for two levels of heritability (0.1 and 0.4), several extra-pair paternity rates (ranging from 5% to 40%), and varying sample sizes (20, 50 and 100 broods) or pedigree depth (2 or 4 generations). We compare heritability estimates from the social and the genetic pedigree, running a restricted maximum-likelihood 'animal model'. Social pedigree underestimates heritability by an average of 0-17% for 5-20% extra-pair paternities and by up to 18% for 40% extra-pair paternities and a heritability of 0.4. Second, we identifyied extra-pair offspring using microsatellite loci in two populations of blue tits (Parus caeruleus) showing high levels of extra-pair paternities (15% and 25% of extra-pair offspring). We compare heritabilities of tarsus length and body mass estimated with pedigrees of increasing accuracy. These analyses suggest that the bias induced by misassigned paternities on heritability estimation depends on the level of heritability and the rate of paternity error. Typical rates of extra-pair paternities in birds (around 20% of offspring) should result in an underestimation of heritability of less than 15% when estimated over a minimum of 100 broods.     

Prediction of response with overlapping generations accounting for multistage selection

Summary A generalization of Hill's equations predicting response to selection is developed that accounts for multiple stage selection in either or both sexes. The method accounts for the flow of genes for animals selected at later stages. This allows for the use of genetic gains from later stages, which explains the reduction in variance due to previous selection. Genetic gains from different selection differentials in each reproductive pathway are incorporated into the equations. The asymptotic response to a single cycle of selection is shown to agree with classical selection theory.The method is applied to a dairy progeny testing scheme representative of an artificial insemination organization in the USA. Two models were compared: (1) the first model accounted for two-stage selection of males, the first stage being based on pedigree information and the second stage on both pedigree and progeny test information; and (2) the second model assumed single-stage male selection. Selection was based on milk volume, milk fat, and milk protein yields. The predicted asymptotic rates for a single cycle of selection were overestimated by 6% and the cumulative response to continuous selection over 20 years was overestimated by 8% by assuming singlestage male selection.Journal Paper No. J14146 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa; Project No. 1053     

Genotype by environment interaction for adult body weights of shrimp Penaeus vannamei when grown at low and high densitie

Shrimp is one of few marine species cultured worldwide for which several selective breeding programs are being conducted. One environmental factor that can affect the response to selection in breeding programs is the density at which the shrimp are cultured (low-medium-high). Phenotypic plasticity in the growth response to different densities might be accompanied by a significant genotype by environment interaction, evidenced by a change in heritabilities between environments and by a genetic correlation less than one for a unique trait between environments. Our goal was to understand whether different growth densities affect estimates of those genetic parameters for adult body weight (BW) in the Pacific white shrimp (Penaeus vannamei). BW heritabilities were significantly different between environments, with the largest at high density. These differences resulted from both an increased additive genetic variance and a decreased environmental variance when grown at high density. The genetic correlation between BWs at the two environmental conditions was significantly less than one. Whereas these results might be suggestive for carrying out shrimp selective breeding for BW under high density conditions, further understanding of genetic correlations between growth and reproductive traits within a given environment is necessary, as there are indications of reduced reproductive fitness for shrimp grown at high densities.     

Quantitative genetic variance associated with chromosomal markers in segregating populations

Summary Use of chromosomal markers can accelerate genetic progress for quantitative traits in pedigree selection programs by providing early information on Mendelian segregation effects for individual progeny. Potential effectiveness of selection using markers is determined by the amount of additive genetic variance traced from parents to progeny by the markers. Theoretical equations for the amount of additive genetic variance associated with a marker were derived at the individual level and for a segregating population in joint linkage equilibrium. Factors considered were the number of quantitative trait loci linked to the marker, their individual effects, and recombination rates with the marker. Subsequently, the expected amount of genetic variance associated with a marker in a segregating population was derived. In pedigree selection programs in segregating populations, a considerable fraction of the genetic variance on a chromosome is expected to be associated with a marker located on that chromosome. For an average chromosome in the bovine, this fraction is approximately 40% of the Mendelian segregation variance contributed by the chromosome. The effects of interference and position of the marker on this expectation are relative small. Length of the chromosome has a large effect on the expected variance. Effectiveness of MAS is, however, greatly reduced by lack of polymorphism at the marker and inaccuracy of estimation of chromosome substitution effects. The size of the expected amount of genetic variance associated with a chromosomal marker indicates that, even when the marker is not the active locus, large chromosome substitution effects are not uncommon in segregating populations.     

EVOLUTIONARY PREDICTABILITY IN NATURAL POPULATIONS: DO MATING SYSTEM AND NONADDITIVE GENETIC VARIANCE INTERACT TO AFFECT HERITABILITIES IN PLANTAGO LANCEOLATA?

Quantitative genetics has been an immensely powerful tool in manipulating the phenotypes of domesticated plants and animals. Much of the predictive power of quantitative genetics depends on the breeder's control over the context in which phenotype and mating are being expressed. In the natural world, these contexts are often difficult to describe, let alone control. We are left, therefore, with a poor understanding of the limits of quantitative genetics in natural populations. One of the crucial contextual elements for assessing breeding value is the genetic background in which an individual's genes are being assessed. When interacting genes are polymorphic within a population, the degree of mating among relatives can influence the correlations among mates and the predictions of a response to selection. Population structure can strongly influence the degree to which dominance and epistasis influences additive genetic variance and heritability. The extent of inbreeding can also influence heritabilities through its effect on the environmental component of phenotypic variance. The applicability of standard quantitative genetic breeding designs to the measurement of heritabilities in natural populations therefore depends in part on: (1) the mating system of the population; and (2) the importance of gene interactions in determining phenotypic variation. We tested for an effect of mating structure on the partitioning of phenotypic variance and heritability by comparing two breeding designs in a common environment. Both breeding designs used 139 pollen parents taken from mapped locations in a population of Plantago lanceolata L., and crossed to 280 seed parents from the same population. One design was random-mating, the second was biased toward near-neighbor matings to an extent determined by field measure of pollen-mediated gene flow distances. The offspring were grown randomly mixed in a common garden. Nine traits were measured: central corm diameter, number of leaves, area of the most recently fully expanded leaf, density of hairs (cm^-2) on the leaves, dry weight per unit leaf area, photosynthetic capacity, transpiration rates, water use efficiency, and reproductive dry weight. Heritabilities and variance components from the two designs were compared using randomization tests. None of the variance components or the heritabilities differed significantly between breeding designs at the 0.05 level. The test could distinguish differences between the heritabilities measured in the two breeding designs as small as 0.11, on average. Thus, for the degree of inbreeding normally exhibited in P. lanceolata there is insufficient gene interaction present within populations to influence the partitioning of variance between additive and nonadditive components or to influence heritability estimates to a meaningful extent. We suggest that for Plantago other sources of variation in heritability estimates, such as maternal effects and genotype × environment interactions, are more important influences than the interaction between inbreeding and gene interactions, and standard heritability estimate based on random breeding is as accurate as one taking the natural mating structure into account.     

Data depth, data completeness, and their influence on quantitative genetic estimation in two contrasting bird populations

Evolutionary biologists increasingly use pedigree‐based quantitative genetic methods to address questions about the evolutionary dynamics of traits in wild populations. In many cases, phenotypic data may have been collected only for recent parts of the study. How does this influence the performance of the models used to analyse these data? Here we explore how data depth (number of years) and completeness (number of observations) influence estimates of genetic variance and covariance within the context of an existing pedigree. Using long‐term data from the great tit Parus major and the mute swan Cygnus olor, species with different life‐histories, we examined the effect of manipulating the amount of data included on quantitative genetic parameter estimates. Manipulating data depth and completeness had little influence on estimated genetic variances, heritabilities, or genetic correlations, but (as expected) did influence confidence in these estimates. Estimated breeding values in the great tit were not influenced by data depth but were in the mute swan, probably because of differences in pedigree structure. Our analyses suggest the ‘rule of thumb’ that data from 3 years and a minimum of 100 individuals per year are needed to estimate genetic parameters with acceptable confidence, and that using pedigree data is worthwhile, even if phenotypes are only available toward the tips of the pedigree.     

Multienvironment genomic variance decomposition analysis of open-pollinated Interior spruce (<Emphasis Type="Italic">Picea glauca</Emphasis> x <Emphasis Type="Italic">engelmannii</Emphasis>)

The advantages of open-pollinated (OP) family testing over controlled crossing (i.e., structured pedigree) are the potential to screen and rank a large number of parents and offspring with minimal cost and efforts; however, the method produces inflated genetic parameters as the actual sibling relatedness within OP families rarely meets the half-sib relatedness assumption. Here, we demonstrate the unsurpassed utility of OP testing after shifting the analytical mode from pedigree- (ABLUP) to genomic-based (GBLUP) relationship using phenotypic tree height (HT) and wood density (WD) and genotypic (30k SNPs) data for 1126 38-year-old Interior spruce (Picea glauca (Moench) Voss x P. engelmannii Parry ex Engelm.) trees, representing 25 OP families, growing on three sites in Interior British Columbia, Canada. The use of the genomic realized relationship permitted genetic variance decomposition to additive, dominance, and epistatic genetic variances, and their interactions with the environment, producing more accurate narrow-sense heritability and breeding value estimates as compared to the pedigree-based counterpart. The impact of retaining (random folding) vs. removing (family folding) genetic similarity between the training and validation populations on the predictive accuracy of genomic selection was illustrated and highlighted the former caveats and latter advantages. Moreover, GBLUP models allowed breeding value prediction for individuals from families that were not included in the developed models, which was not possible with the ABLUP. Response to selection differences between the ABLUP and GBLUP models indicated the presence of systematic genetic gain overestimation of 35 and 63% for HT and WD, respectively, mainly caused by the inflated estimates of additive genetic variance and individuals’ breeding values given by the ABLUP models. Extending the OP genomic-based models from single to multisite made the analysis applicable to existing OP testing programs.     

Patterns of male reproductive success in a highly promiscuous whale species: the endangered North Atlantic right whale

Parentage analyses of baleen whales are rare, and although mating systems have been hypothesized for some species, little data on realized male reproductive success are available and the patterns of male reproductive success have remained elusive for most species. Here we combine over 20 years of photo-identification data with high-resolution genetic data for the majority of individual North Atlantic right whales to assess paternity in this endangered species. There was significant skew in male reproductive success compared to what would be expected if mating was random (P < 0.001). The difference was due to an excess of males assigned zero paternities, a deficiency of males assigned one paternity, and an excess of males assigned as fathers for multiple calves. The variance in male reproductive success was high relative to other aquatically mating marine mammals, but was low relative to mammals where the mating system is based on resource- and/or mate-defence polygyny. These results are consistent with previous data suggesting that the right whale mating system represents one of the most intense examples of sperm competition in mammals, but that sperm competition on its own does not allow for the same degree of polygyny as systems where males can control access to resources and/or mates. The age distribution of assigned fathers was significantly biased towards older males (P < 0.05), with males not obtaining their first paternity until approximately 15 years of age, which is almost twice the average age of first fertilization in females (8 years), suggesting that mate competition is preventing younger males from reproducing. The uneven distribution of paternities results in a lower effective population size in this species that already has one of the lowest reported levels of genetic diversity, which may further inhibit reproductive success through mate incompatibility of genetically similar individuals.     

A framework for power and sensitivity analyses for quantitative genetic studies of natural populations, and case studies in Soay sheep (Ovis aries)

Studies of the quantitative genetics of natural populations have contributed greatly to evolutionary biology in recent years. However, while pedigree data required are often uncertain (i.e. incomplete and partly erroneous) and limited, means to evaluate the effects of such uncertainties have not been developed. We have therefore developed a general framework for power and sensitivity analyses of such studies. We propose that researchers first generate a set of pedigree data that they wish to use in a quantitative genetic study, as well as data regarding errors that occur in that pedigree. This pedigree is then permuted using the data regarding errors to generate hypothetical 'true' and 'assumed' pedigrees that differ so as to mimic pedigree errors that might occur in the study system under consideration. Phenotypic data are then simulated across the true pedigree (according to user-defined genetic and environmental covariance structures), before being analysed with standard quantitative genetic techniques in conjunction with the 'assumed' pedigree data. To illustrate this approach, we conducted power and sensitivity analyses in a well-known study of Soay sheep (Ovis aries). We found that, although the estimation of simple genetic (co)variance structures is fairly robust to pedigree errors, some potentially serious biases were detected under more complex scenarios involving maternal effects. Power analyses also showed that this study system provides high power to detect heritabilities as low as about 0.09. Given this range of results, we suggest that such power and sensitivity analyses could greatly complement empirical studies, and we provide the computer program PEDANTICS to aid in their application.     

Heritability of female extra-pair paternity rate in song sparrows (Melospiza melodia)

The forces driving the evolution of extra-pair reproduction in socially monogamous animals remain widely debated and unresolved. One key hypothesis is that female extra-pair reproduction evolves through indirect genetic benefits, reflecting increased additive genetic value of extra-pair offspring. Such evolution requires that a female's propensity to produce offspring that are sired by an extra-pair male is heritable. However, additive genetic variance and heritability in female extra-pair paternity (EPP) rate have not been quantified, precluding accurate estimation of the force of indirect selection. Sixteen years of comprehensive paternity and pedigree data from socially monogamous but genetically polygynandrous song sparrows (Melospiza melodia) showed significant additive genetic variance and heritability in the proportion of a female's offspring that was sired by an extra-pair male, constituting major components of the genetic architecture required for extra-pair reproduction to evolve through indirect additive genetic benefits. However, estimated heritabilities were moderately small (0.12 and 0.18 on the observed and underlying latent scales, respectively). The force of selection on extra-pair reproduction through indirect additive genetic benefits may consequently be relatively weak. However, the additive genetic variance and non-zero heritability observed in female EPP rate allow for multiple further genetic mechanisms to drive and constrain mating system evolution.     

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.     

Predicting breeding values and genetic components using generalized linear mixed models for categorical and continuous traits in walnut (<Emphasis Type="Italic">Juglans regia</Emphasis>)

Genetic components for economically important traits in walnut (Juglans regia) were estimated for the first time using historical pedigree and heirloom phenotypic data from the walnut breeding program at the University of California, Davis. The constructed pedigree is composed of ~ 15,000 individuals and is derived from current and historic phenotypic records dating back > 50 years and located across California. To predict the additive genetic values of individuals under selection, generalized linear mixed models (GLMM), implemented with MCMCglmm, were developed. Several repeatability models were established to obtain the best model and predict the genetic parameters for each trait. Repeatability for yield, harvest date, extra-light kernel color (ELKC), and lateral bearing were predicted at 0.82, 0.98, 0.63, and 0.96, respectively, and average narrow-sense heritabilities were 0.54, 0.77, 0.49, and 0.75, respectively. Each individual in the pedigree was ranked by its estimated breeding value (EBV). The genetic trend showed specific patterns for each trait, and real genetic improvement was found over time. The completed pedigree built here, the estimated breeding values, and the ranking of individuals according to their breeding values, can be used to guide future crossing designs in the walnut breeding program and future implementation of genomic selection methods in walnut.     

Maturational costs of reproduction due to clutch size and ontogenetic conflict as revealed in the invisible fraction

Reproduction is thought to entail costs, but assessing survival costs associated with maturation as organisms express reproductive genes for the first time is problematic because many will die prior to expressing a phenotype. We quantified selection acting on this invisible fraction by measuring selection on predicted breeding values for clutch size estimated from a multigenerational pedigree of side-blotched lizards in which clutch size was heritable (h2=0.25+/-0.04). The survival effects of predicted breeding values for clutch size during maturation, however, differed between males and females indicating ontogenetic conflict. Increased mortality during maturation was associated with lower predicted breeding values for clutch size for females, but higher predicted breeding values for males who do not produce a clutch. Genetic correlations between clutch size and male and female survival were consistent with calculated selection differentials. Experimental yolk removal did not affect progeny survival during maturation, indicating that selection on maturing progeny was not due to confounding yolk-volume maternal effects, and hormone manipulations confirmed clutch size as the target of viability selection during maturation. Such episodes of selection prior to phenotypic expression of the trait will have important consequences for the evolution of reproductive investment.     

Estimating heritabilities and genetic correlations: comparing the 'animal model' with parent-offspring regression using data from a natural population

Quantitative genetic parameters are nowadays more frequently estimated with restricted maximum likelihood using the 'animal model' than with traditional methods such as parent-offspring regressions. These methods have however rarely been evaluated using equivalent data sets. We compare heritabilities and genetic correlations from animal model and parent-offspring analyses, respectively, using data on eight morphological traits in the great reed warbler (Acrocephalus arundinaceus). Animal models were run using either mean trait values or individual repeated measurements to be able to separate between effects of including more extended pedigree information and effects of replicated sampling from the same individuals. We show that the inclusion of more pedigree information by the use of mean traits animal models had limited effect on the standard error and magnitude of heritabilities. In contrast, the use of repeated measures animal model generally had a positive effect on the sampling accuracy and resulted in lower heritabilities; the latter due to lower additive variance and higher phenotypic variance. For most trait combinations, both animal model methods gave genetic correlations that were lower than the parent-offspring estimates, whereas the standard errors were lower only for the mean traits animal model. We conclude that differences in heritabilities between the animal model and parent-offspring regressions were mostly due to the inclusion of individual replicates to the animal model rather than the inclusion of more extended pedigree information. Genetic correlations were, on the other hand, primarily affected by the inclusion of more pedigree information. This study is to our knowledge the most comprehensive empirical evaluation of the performance of the animal model in relation to parent-offspring regressions in a wild population. Our conclusions should be valuable for reconciliation of data obtained in earlier studies as well as for future meta-analyses utilizing estimates from both traditional methods and the animal model.     

Direct and indirect genetic effects on reproductive investment in a grasshopper

A fundamental part of the quantitative genetic theory deals with the partitioning of the phenotypic variance into additive genetic and environmental components. During interaction with conspecifics, the interaction partner becomes a part of the environment from the perspective of the focal individual. If the interaction effects have a genetic basis, they are called indirect genetic effects (IGEs) and can evolve along with direct genetic effects. Sexual reproduction is a classic context where potential conflict between males and females can arise from trade‐offs between current and future investments. We studied five female fecundity traits, egg length and number, egg pod length and number and latency to first egg pod, and estimated the direct and IGEs using a half‐sib breeding design in the grasshopper Chorthippus biguttulus. We found that the male IGEs were an order of magnitude lower than the direct genetic effects and were not significantly different from zero. However, there was some indication that IGEs were larger shortly after mating, consistent with the idea that IGEs fade with time after interaction. Female direct heritabilities were moderate to low. Simulation shows that the variance component estimates can appear larger with less data, calling for care when interpreting variance components estimated with low power. Our results illustrate that the contribution of male IGEs is overall low on the phenotypic variance of female fecundity traits. Thus, even in the relevant context of sexual conflict, the influence of male IGEs on the evolutionary trajectory of female reproductive traits is likely to be small.     

Optimising two-stage independent culling selection in tree and animal breeding

Summary Theory is given for a simple practical method of predicting gain from two-stage independent culling, where stage 1 of selection is for individual performance and stage 2 is for either progeny performance only, or an index combining individual and progeny performance. Expected gain is determined as a direct function of heritabilities, genetic correlations, selection intensities and progeny-testing capacity. Results show the effect these parameters can have on proportions selected at each stage and, if multiple selection criteria are used, traits selected for first. Methods are discussed in the context of tree and animal breeding, with an example taken from forestry.