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Theory predicts that the additive genetic covariance ([Formula: see text]) matrix determines a population's short-term (in)ability to respond to directional selection-evolvability in the Hansen-Houle sense-which is typically quantified and compared via certain scalar indices called evolvability measures. Often, interest is in obtaining the averages of these measures across all possible selection gradients, but explicit formulae for most of these average measures have not been known. Previous authors relied either on approximations by the delta method, whose accuracy is generally unknown, or Monte Carlo evaluations (including the random skewers analysis), which necessarily involve random fluctuations. This study presents new, exact expressions for the average conditional evolvability, average autonomy, average respondability, average flexibility, average response difference, and average response correlation, utilizing their mathematical structures as ratios of quadratic forms. The new expressions are infinite series involving top-order zonal and invariant polynomials of matrix arguments, and can be numerically evaluated as their partial sums with, for some measures, known error bounds. Whenever these partial sums numerically converge within reasonable computational time and memory, they will replace the previous approximate methods. In addition, new expressions are derived for the average measures under a general normal distribution for the selection gradient, extending the applicability of these measures into a substantially broader class of selection regimes.

Fisher’s 1918 paper accomplished two distinct goals: unifying discrete Mendelian genetics with continuous biometric phenotypes and quantifying the variance components of variation in complex human characteristics. The former contributed to the foundation of modern quantitative genetics; the latter was adopted by social scientists interested in the pursuit of Galtonian nature-nurture questions about the biological and social origins of human behavior, especially human intelligence. This historical divergence has produced competing notions of the estimation of variance ratios referred to as heritability. Jay Lush showed that they could be applied to selective breeding on the farm, while the early twin geneticists used them as a descriptive statistic to describe the degree of genetic determination in complex human traits. Here we trace the early history (1918 to 1960) of the heritability coefficient now used by social scientists.

Fruit flies are among the most common insect pests in the world. The presence of many cryptic species and numerous fruit fly species sharing the same niche cause considerable difficulty in species identification. This study investigates the species-specific wing morphology of two fruit fly species (Bactrocera dorsalis - BD and Zeugodacus cucurbitae - ZC) using a geometric morphometric tool. Both fruit flies were collected using species-specific pheromone traps from the same niche. We detected significant wing size and shape variability within and between the species. BD wing was more symmetrical than ZC, and fluctuation asymmetry (FA) and directional asymmetry (DA) are more prominently expressed in ZC. This is the first attempt to evaluate the modularity (by using three subsets in proximal-distal wing axis), quantitative genetic and phylogenetic signal analysis of BD and ZC, and this is the first report of the geometric morphometric analysis of ZC. The highly integrative wing system was observed in both species (except the left-wing of BD). We concluded that, through the quantitative genetic analysis, BD is a highly dispersing nature than the ZC. ZC and BD evolutionary separated in a distinct morphospace, and all characters (wing shape, size, and venation pattern) are derived based on their ecological conditions. These results are interpreted in terms of the interspecific competition of two fruit fly sharing the same niche, and the different levels of phenotypic wing plasticity response reduce rivalry and promote spatial resource partitioning.

Sexual dimorphism is ubiquitous in nature but its evolution is puzzling given that the mostly shared genome constrains independent evolution in the sexes. Sex differences should result from asymmetries between the sexes in selection or genetic variation but studies investigating both simultaneously are lacking. Here, we combine a quantitative genetic analysis of body size variation, partitioned into autosomal and sex chromosome contributions and ten generations of experimental evolution to dissect the evolution of sexual body size dimorphism in seed beetles (Callosobruchus maculatus) subjected to sexually antagonistic or sex-limited selection. Female additive genetic variance (VA) was primarily linked to autosomes, exhibiting a strong intersexual genetic correlation with males ( $$r_{\mathrm{{m,f}}}^{\mathrm{a}}$$ = 0.926), while X- and Y-linked genes further contributed to the male VA and X-linked genes contributed to female dominance variance. Consistent with these estimates, sexual body size dimorphism did not evolve in response to female-limited selection but evolved by 30–50% under male-limited and sexually antagonistic selection. Remarkably, Y-linked variance alone could change dimorphism by 30%, despite the C. maculatus Y chromosome being small and heterochromatic. Our results demonstrate how the potential for sexual dimorphism to evolve depends on both its underlying genetic basis and the nature of sex-specific selection. Experimental evolution shows that sexually antagonistic selection promotes sexual body size dimorphism in the seed beetle. Dimorphism is largely explained by Y-linked genetic variance with contribution from sex-specific dominance, X-linkage and sex differences in autosomal variance.

Plant and animal populations can adapt to prolonged environmental changes if they have sufficient genetic variation in important phenological traits. The genetic regulation of annual cycles can be studied either via candidate genes or through the decomposition of phenotypic variance by quantitative genetics. Here, we combined both approaches to study the timing of migration in a long-distance migrant, the collared flycatcher (Ficedula albicollis). We found that none of the four studied candidate genes (CLOCK, NPAS2, ADCYAP1 and CREB1) had any consistent effect on the timing of six annual cycle stages of geolocator-tracked individuals. This negative result was confirmed by direct observations of males arriving in spring to the breeding site over four consecutive years. Although male spring arrival date was significantly repeatable (R = 0.24 ± 0.08 SE), most was attributable to permanent environmental effects, while the additive genetic variance and heritability were very low (h2 = 0.03 ± 0.17 SE). This low value constrains species evolutionary adaptation, and our study adds to warnings that such populations may be threatened, e.g. by ongoing climate change.

Ecologists and evolutionary biologists are well aware that natural and sexual selection do not operate on traits in isolation, but instead act on combinations of traits. This long-recognized and pervasive phenomenon is known as multivariate selection, or-in the particular case where it favours correlations between interacting traits-correlational selection. Despite broad acknowledgement of correlational selection, the relevant theory has often been overlooked in genomic research. Here, we discuss theory and empirical findings from ecological, quantitative genetic and genomic research, linking key insights from different fields. Correlational selection can operate on both discrete trait combinations and quantitative characters, with profound implications for genomic architecture, linkage, pleiotropy, evolvability, modularity, phenotypic integration and phenotypic plasticity. We synthesize current knowledge and discuss promising research approaches that will enable us to understand how correlational selection shapes genomic architecture, thereby linking quantitative genetic approaches with emerging genomic methods. We suggest that research on correlational selection has great potential to integrate multiple fields in evolutionary biology, including developmental and functional biology, ecology, quantitative genetics, phenotypic polymorphisms, hybrid zones and speciation processes.

The goals of quantitative genetics differ according to its field of application. In plant breeding, the main focus of quantitative genetics is on identifying candidates with the best genotypic value for a target population of environments. Keeping quantitative genetics current requires keeping old concepts that remain useful, letting go of what has become archaic, and introducing new concepts and methods that support contemporary breeding. The core concept of continuous variation being due to multiple Mendelian loci remains unchanged. Because the entirety of germplasm available in a breeding program is not in Hardy–Weinberg equilibrium, classical concepts that assume random mating, such as the average effect of an allele and additive variance, need to be retired in plant breeding. Doing so is feasible because with molecular markers, mixed-model approaches that require minimal genetic assumptions can be used for best linear unbiased estimation (BLUE) and prediction. Plant breeding would benefit from borrowing approaches found useful in other disciplines. Examples include reliability as a new measure of the influence of genetic versus nongenetic effects, and operations research and simulation approaches for designing breeding programs. The genetic entities in such simulations should not be generic but should be represented by the pedigrees, marker data, and phenotypic data for the actual germplasm in a breeding program. Over the years, quantitative genetics in plant breeding has become increasingly empirical and computational and less grounded in theory. This trend will continue as the amount and types of data available in a breeding program increase.

The Chinese perch (Siniperca chuatsi Basilewsky) is an endemic freshwater fish species in eastern Asian countries. The perch is mainly distributed in the Yangtze River drainage in China. The wild population of S. chuatsi has declined dramatically due to habitat degradation, anthropogenic activities and eutrophication. Unfortunately, researches regarding its genetic markers are scarce. In this study, 40 SNP markers were developed successfully from 30 individuals. The observed heterozygosity (Ho) and expected heterozygosity (He) varied from 0.4915 to 0.8734 and 0.1528 to 0.5000, respectively. The minor allele frequency ranged from 0.0667 to 0.5000. The Effective number of alleles varied from 1.1421 to 2.000. Thirty-six SNPs have been confirmed to fit Hardy–Weinberg equilibrium after Bonferroni correction (P

Evolutionary dynamics of covariation patterns in craniometric traits was studied for bats from the Myotis myotis–Myotis blythii species group (Mammalia, Chiroptera, Vespertilionidae) namely M.m.myotis, M.b.oxygnathus, M.b.omari, M.b.blythii, and M.b.altaicus. These species evolved towards increasing the size. One more species, M.dasycneme, which is phylogenetically, morphologically, and ecologically rather distant from these OTUs, also was studied for comparison with them. A set of 30 craniometric traits was studied for each of the OTUs using the quantitative genetics approaches. Phenotypic covariance matrices were used as proxies for additive genetic covariance matrices. The analysis has shown that multivariate divergence of the studied Myotis OTUs was governed by selection rather than by random drift and that these OTUs evolved in the direction close to the line of least evolutionary resistance. As overall size increases, the skull integration, respondability, and evolvability increase, while flexibility slightly decreases. Such a pattern can possibly be explained as a consequence of adaptation of M.blythii and especially M.myotis to prey on considerably large hard-shelled insects. A high cohesion of skull structures is needed for the effective functioning of their jaw apparatus. For Myotis bats with other foraging strategies (such as M. dasycneme that catches insects mainly using the claws of hind feet) this cohesion seems to be of lesser importance.

Inter-individual variation in juvenile body size can have important consequences for individual fitness, population dynamics, and adaptive evolution. In wild vertebrate populations, larger juvenile size is usually expected to be selected for. However, understanding how such selection may translate into adaptive evolution requires an understanding of the genetic underpinnings of early development and the factors modulating selection. In this study, we characterised the genetic basis of and selection pressures acting upon juvenile body size in a large insular population of feral horses on Sable Island, Canada, to gain insights into the evolution of juvenile body size in wild vertebrate populations. We used pedigree-based quantitative genetic ‘animal models’ to quantify the sources of phenotypic variation in withers-knee length, and assessed the influence of maternal age, sex, and temporal (birth year) and spatial environmental heterogeneity in modulating overwinter survival selection. We found that withers-knee length is moderately heritable and that there was a significant positive genetic correlation between males and females. There was no indication of directional selection in a pooled-sex analysis, but we did find evidence for significant sexually antagonistic selection, with a tendency for smaller body size to be favoured in males and larger body size to be favoured in females. These results suggest that juvenile body size has the potential to evolve in this population, and that selection on juvenile size may play an important role in modulating sex-specific contributions to population dynamics. However, our results also suggest that there is unlikely to be evolutionary change in the mean body size of Sable Island foals.

Better characterization of the sources of phenotypic variation in human behavioural traits-stemming from genetic and environmental influences-will allow for more informed decisions about how to approach a range of challenges arising from variation, ranging from societal issues to the treatment of diseases. In particular, understanding how the environment moderates genetic influence on phenotypes (i.e., genotype-environment interactions, or G × E) is a central component of the behavioral sciences. Yet, understanding of this phenomenon is lagging somewhat, due in part to the difficulties of detecting G × E. We discuss the logic behind one of the primary ways to detect G × E: comparing heritability estimates across environments. Then, we highlight some pitfalls, with an emphasis on how very strong G × E can sometimes be undetectable using this method when high heritability is present in multiple environments. We conclude by forwarding some initial, yet tentative, suggestions for how best to address to the problem.

Infectious diseases have a huge impact on animal health, production and welfare, and human health. Understanding the role of host genetics in disease spread is important for developing disease control strategies that efficiently reduce infection incidence and risk of epidemics. While heritable variation in disease susceptibility has been targeted in livestock breeding, emerging evidence suggests that there is additional genetic variation in host infectivity, but the potential benefits of including infectivity into selection schemes are currently unknown. A Susceptible-Infected-Recovered epidemiological model incorporating polygenic genetic variation in both susceptibility and infectivity was combined with quantitative genetics selection theory to assess the non-linear impact of genetic selection on field measures of epidemic risk and severity. Response to 20 generations of selection was calculated in large simulated populations, exploring schemes differing in accuracy and intensity. Assuming moderate genetic variation in both traits, 50% selection on susceptibility required seven generations to reduce the basic reproductive number R0 from 7.64 to the critical threshold of R0

The concept of a pan-genome refers to intraspecific diversity in genome content and structure, encompassing both genes and intergenic space. Pan-genomic studies employ a combination of de novo sequence assembly and reference-based alignment to discover and genotype structural variants. The large size and complex structure of Triticeae genomes were for a long time an obstacle for genomic research in barley and its relatives. Now that a reference genome is available, computational pipelines for high-quality sequence assembly are in place, and sequence costs continue to drop, investigations into the structural diversity of the barley genome seem within reach. Here, we review the recent progress on pan-genomics in the model grass Brachypodium distachyon, and the cereal crops rice and maize, and devise a multi-tiered strategy for a pan-genome project in barley. Our design involves: (1) the construction of high-quality de novo sequence assemblies for a small core set of representative genotypes, (2) short-read sequencing of a large diversity panel of genebank accessions to medium coverage and (3) the use of complementary methods such as chromosome-conformation capture sequencing and k-mer-based association genetics. The in silico representation of the barley pan-genome may inform about the mechanisms of structural genome evolution in the Triticeae and supplement quantitative genetics models of crop performance for better accuracy and predictive ability.

Despite extensive evidence that biodiversity promotes plant community productivity, progress towards understanding the mechanistic basis of this effect remains slow, impeding the development of predictive ecological theory and agricultural applications. Here, we analysed non-additive interactions between genetically divergent Arabidopsis accessions in experimental plant communities. By combining methods from ecology and quantitative genetics, we identify a major effect locus at which allelic differences between individuals increase the above-ground productivity of communities. In experiments with near-isogenic lines, we show that this diversity effect acts independently of other genomic regions and can be resolved to a single region representing less than 0.3% of the genome. Using plant-soil feedback experiments, we also demonstrate that allelic diversity causes genotype-specific soil legacy responses in a consecutive growing period, even after the original community has disappeared. Our work thus suggests that positive diversity effects can be linked to single Mendelian factors, and that a range of complex community properties can have a simple cause. This may pave the way to novel breeding strategies, focusing on phenotypic properties that manifest themselves beyond isolated individuals; that is, at a higher level of biological organization.

Background Advances in genotyping and phenotyping techniques have enabled the acquisition of a great amount of data. Consequently, there is an interest in multivariate statistical analyses that identify genomic regions likely to contain causal mutations affecting multiple traits (i.e., pleiotropy). As the demand for multivariate analyses increases, it is imperative that optimal tools are available to assess their performance. To facilitate the testing and validation of these multivariate approaches, we developed simplePHENOTYPES, an R/CRAN package that simulates pleiotropy, partial pleiotropy, and spurious pleiotropy in a wide range of genetic architectures, including additive, dominance and epistatic models. Results We illustrate simplePHENOTYPES’ ability to simulate thousands of phenotypes in less than one minute. We then provide two vignettes illustrating how to simulate sets of correlated traits in simplePHENOTYPES. Finally, we demonstrate the use of results from simplePHENOTYPES in a standard GWAS software, as well as the equivalence of simulated phenotypes from simplePHENOTYPES and other packages with similar capabilities. Conclusions simplePHENOTYPES is a R/CRAN package that makes it possible to simulate multiple traits controlled by loci with varying degrees of pleiotropy. Its ability to interface with both commonly-used marker data formats and downstream quantitative genetics software and packages should facilitate a rigorous assessment of both existing and emerging statistical GWAS and GS approaches. simplePHENOTYPES is also available at https://github.com/samuelbfernandes/simplePHENOTYPES.

Bacterial blight (BB, caused by Xanthomonas citri pv. malvacearum, Xcm) is a worldwide disease of cotton (Gossypium spp.). The disease has been effectively controlled through the use of BB resistant cultivars and planting of acid-delinted seed. However, a resurgence of BB has been noted in the US in recent years due to the spread of Xcm race 18 and growing of susceptible transgenic cultivars, which calls for a renewed effort to develop new BB resistant cultivars. However, there has been a paucity of information in genetics and breeding for BB resistance since the 1990s due to the lack of research efforts. This review was prepared to fill this void with an objective to provide detailed results from past qualitative and quantitative genetic studies on BB resistance, including genetic designs and specific germplasm used for conducting research. More than 20 major resistance B genes (B1 to B8, B9K, B9L, B10K, B10L, B11, B12, BIn, Bn, Bs, and more than 4 unnamed genes), with at least two polygene complexes (BSm and BDm), have been identified. One B gene may be resistant to a single or multiple Xcm races, and pyramiding of several B genes can enhance resistance to a single or multiple Xcm races. Allelic relationships among some of the genes are currently unknown. Quantitative genetics has been employed to estimate heritability, gene effects, additive and dominance variances, and effective number of genes for BB resistance. The studies suggest that the additive effect and additive variance play a predominant role in BB resistance, while the dominant effect and variance play a reduced role in resistance. Heritability estimates are moderate to high depending on environmental errors, and 1–2 effective numbers of genes have been estimated, consistent with Mendelian genetic studies. Studies in molecular mapping of several BB resistance genes (B2, B3, b6, and B12) have been conducted with the focus on B12 as it is resistant to races 1 through 19. Portable DNA markers have been developed and used in marker-assisted selection for BB resistance. Finally, areas where there is a lack of information and controversies are identified and assessed. This review provides an updated comprehensive account of the genetic basis for BB resistance in cotton.

Mastitis is one of the most prevalent and costly diseases in dairy cattle. It results in changes in milk composition and quality which are indicators of udder inflammation in absence of clinical signs. We applied structural equation modeling (SEM) - GWAS aiming to explore interrelated dependency relationships among phenotypes related to udder health, including milk yield (MY), somatic cell score (SCS), lactose (%, LACT), pH and non-casein N (NCN, % of total milk N), in a cohort of 1,158 Brown Swiss cows. The phenotypic network inferred via the Hill-Climbing algorithm was used to estimate SEM parameters. Integration of multi-trait models-GWAS and SEM-GWAS identified six significant SNPs for SCS, and quantified the contribution of MY and LACT acting as mediator traits to total SNP effects. Functional analyses revealed that overrepresented pathways were often shared among traits and were consistent with biological knowledge (e.g., membrane transport activity for pH and MY or Wnt signaling for SCS and NCN). In summary, SEM-GWAS offered new insights on the relationships among udder health phenotypes and on the path of SNP effects, providing useful information for genetic improvement and management strategies in dairy cattle.

A key step toward predicting responses to climate change is characterizing genetic variation in populations. While short-term responses will likely be shaped by currently available genetic variation, longer-term evolutionary responses will depend on the supply of novel variation by, ultimately, mutation. Studying mutational contributions to phenotypic variation can provide insights into the extent of potential variation on which selection may operate in future human-altered environments. Here we used the chemical mutagen ethyl methanesulfonate (EMS) to explore mutational contributions to phenotypic variation, integration, and plasticity to elevated carbon dioxide (eCO2) in three accessions of Arabidopsis thaliana. We found that (1) mutagenesis increased broad-sense heritabilities and variation in plasticity to eCO2 (genotype by environment interactions); (2) mutational effects varied among the three genetic backgrounds; (3) induced mutations had non-random (biased) effects on patterns of phenotypic integration. To our knowledge, this is the first study to address the effects of chemically induced mutations on phenotypic plasticity to eCO2 in a model plant. We discuss our results in light of emerging insights from theoretical and empirical quantitative genetics, suggest potential avenues of research, and identify approaches that may help advance our understanding of climate-driven evolution in plants.

Epigenetics refers to chemical modifications of chromatin or transcribed DNA that can influence gene activity and expression without changes in DNA sequence. The last 20 years have yielded breakthroughs in our understanding of epigenetic processes that impact many fields of biology. In this review, we discuss how epigenetics relates to quantitative genetics and evolution. We argue that epigenetics is important for quantitative genetics because: (1) quantitative genetics is increasingly being combined with genomics, and therefore we should expand our thinking to include cellular-level mechanisms that can account for phenotypic variance and heritability besides just those that are hard-coded in the DNA sequence; and (2) epigenetic mechanisms change how phenotypic variance is partitioned, and can thereby change the heritability of traits and how those traits are inherited. To explicate these points, we show that epigenetics can influence all aspects of the phenotypic variance formula: V(P) (total phenotypic variance) = V(G) (genetic variance) + V(E) (environmental variance) + V(GxE) (genotype-by-environment interaction) + 2COV(GE) (the genotype–environment covariance) + V(ɛ) (residual variance), requiring new strategies to account for different potential sources of epigenetic effects on phenotypic variance. We also demonstrate how each of the components of phenotypic variance not only can be influenced by epigenetics, but can also have evolutionary consequences. We argue that no sources of epigenetic effects on phenotypic variance can be easily cast aside in a quantitative genetic research program that seeks to understand evolutionary processes.

Proper cell function depends on networks of proteins that interact physically and functionally to carry out physiological processes. Thus, it seems logical that the impact of sequence variation in one protein could be significantly influenced by genetic variants at other loci in a genome. Nonetheless, the importance of such genetic interactions, known as epistasis, in explaining phenotypic variation remains a matter of debate in genetics. Recent work from our lab revealed that genes implicated from an association study of toxin tolerance in Saccharomyces cerevisiae show extensive interactions with the genetic background: most implicated genes, regardless of allele, are important for toxin tolerance in only one of two tested strains. The prevalence of background effects in our study adds to other reports of widespread genetic-background interactions in model organisms. We suggest that these effects represent many-way interactions with myriad features of the cellular system that vary across classes of individuals. Such gene-by-system interactions may influence diverse traits and require new modeling approaches to accurately represent genotype-phenotype relationships across individuals.

When individuals interact, their phenotypes may be affected not only by their own genes but also by genes in their social partners. This phenomenon is known as Indirect Genetic Effects (IGEs). In aquaculture species and some plants, however, competition not only affects trait levels of individuals, but also inflates variability of trait values among individuals. In the field of quantitative genetics, the variability of trait values has been studied as a quantitative trait in itself, and is often referred to as inherited variability. Such studies, however, consider only the genetic effect of the focal individual on trait variability and do not make a connection to competition. Although the observed phenotypic relationship between competition and variability suggests an underlying genetic relationship, the current quantitative genetic models of IGE and inherited variability do not allow for such a relationship. The lack of quantitative genetic models that connect IGEs to inherited variability limits our understanding of the potential of variability to respond to selection, both in nature and agriculture. Models of trait levels, for example, show that IGEs may considerably change heritable variation in trait values. Currently, we lack the tools to investigate whether this result extends to variability of trait values. Here we present a model that integrates IGEs and inherited variability. In this model, the target phenotype, say growth rate, is a function of the genetic and environmental effects of the focal individual and of the difference in trait value between the social partner and the focal individual, multiplied by a regression coefficient. The regression coefficient is a genetic trait, which is a measure of cooperation; a negative value indicates competition, a positive value cooperation, and an increasing value due to selection indicates the evolution of cooperation. In contrast to the existing quantitative genetic models, our model allows for co-evolution of IGEs and variability, as the regression coefficient can respond to selection. Our simulations show that the model results in increased variability of body weight with increasing competition. When competition decreases, i.e., cooperation evolves, variability becomes significantly smaller. Hence, our model facilitates quantitative genetic studies on the relationship between IGEs and inherited variability. Moreover, our findings suggest that we may have been overlooking an entire level of genetic variation in variability, the one due to IGEs.

Individuals are not merely subject to their social environments; they choose and create them, through a process called social environment (or social niche) construction. When genotypes differ in social environment-constructing behaviors, different genotypes are expected to experience different social environments. As social experience often affects behavioral development, quantitative genetics and psychology theories predict that genetic variation in social environment construction should have an important role in determining phenotypic variation; however, this hypothesis has not been tested directly. I identify multiple mechanisms of social environment construction that differ among natural genotypes of Drosophila melanogaster and investigate their consequences for the development of aggressive behavior. Male genotypes differed in the group sizes that they preferred and in their aggressive behavior; both of these behaviors influenced social experience, demonstrating that these behaviors function as social environment-constructing traits. Further, the effects of social experience-as determined in part by social environment construction-carried over to affect focal male aggression at a later time and with a new opponent. These results provide manipulative experimental support for longstanding hypotheses in psychology, that genetic variation in social environment construction has a causal role in behavioral development. More broadly, these results imply that studies of the genetic basis of complex traits should be expanded to include mechanisms by which genetic variation shapes the environments that individuals experience.

Background Increases in biological complexity and the origins of life’s hierarchical organization are described by the “major transitions” framework. A crucial component of this paradigm is that after the transition in complexity or organization, adaptation occurs primarily at the level of the new, higher-level unit. For collective-level adaptations to occur, though, collective-level traits—properties of the group, such as collective size—must be heritable. Since collective-level trait values are functions of lower-level trait values, collective-level heritability is related to particle-level heritability. However, the nature of this relationship has rarely been explored in the context of major transitions. Results We examine relationships between particle-level heritability and collective-level heritability for several functions that express collective-level trait values in terms of particle-level trait values. For clonal populations, when a collective-level trait value is a linear function of particle-level trait values and the number of particles per collective is fixed, the heritability of a collective-level trait is never less than that of the corresponding particle-level trait and is higher under most conditions. For more complicated functions, collective-level heritability is higher under most conditions, but can be lower when the environment experienced by collectives is heterogeneous. Within-genotype variation in collective size reduces collective-level heritability, but it can still exceed particle-level heritability when phenotypic variance among particles within collectives is large. These results hold for a diverse sample of biologically relevant traits. Conclusions Rather than being an impediment to major transitions, we show that, under a wide range of conditions, the heritability of collective-level traits is actually higher than that of the corresponding particle-level traits. High levels of collective-level trait heritability thus arise “for free,” with important implications not only for major transitions but for multilevel selection in general. Electronic supplementary material The online version of this article (10.1186/s12915-018-0612-6) contains supplementary material, which is available to authorized users.

Quantitative genetics approaches, and particularly animal models, are widely used to assess the genetic (co)variance of key fitness related traits and infer adaptive potential of wild populations. Despite the importance of precision and accuracy of genetic variance estimates and their potential sensitivity to various ecological and population specific factors, their reliability is rarely tested explicitly. Here, we used simulations and empirical data collected from an 11-year study on tree swallow (Tachycineta bicolor), a species showing a high rate of extra-pair paternity and a low recruitment rate, to assess the importance of identity errors, structure and size of the pedigree on quantitative genetic estimates in our dataset. Our simulations revealed an important lack of precision in heritability and genetic-correlation estimates for most traits, a low power to detect significant effects and important identifiability problems. We also observed a large bias in heritability estimates when using the social pedigree instead of the genetic one (deflated heritabilities) or when not accounting for an important cause of resemblance among individuals (for example, permanent environment or brood effect) in model parameterizations for some traits (inflated heritabilities). We discuss the causes underlying the low reliability observed here and why they are also likely to occur in other study systems. Altogether, our results re-emphasize the difficulties of generalizing quantitative genetic estimates reliably from one study system to another and the importance of reporting simulation analyses to evaluate these important issues.

In this paper we summarize recent behaviour genetic findings on happiness measured as life satisfaction (LS) and subjective wellbeing (SWB) and discuss important implications pertaining to stability and change, including the potential of individual and societal interventions. Broadly speaking, two main research strategies explore genetic and environmental influences on happiness, including quantitative and molecular genetics. Whereas molecular genetics seeks to trace the causal pathways from specific DNA variants, quantitative genetics estimates the magnitude of overall genetic and environmental influences without specifying actual DNA sequences and usually without specifying specific environmental circumstances. Molecular genetic studies have entered the happiness arena, but have shown mixed results. Most replicated findings are therefore based on quantitative genetics and derived from twin and family studies decomposing variation and co-variation into genetic, shared, and non-shared environmental sources. Recent meta-analyses of such studies report genetic influences (i.e., heritability) to account for 32–40 % of the variation in overall happiness (i.e., SWB, LS), and indicate that heritability varies across populations, subgroups, contexts and/or constructs. When exploring stable SWB levels, heritability is reported in the 70–80 % range, whereas momentary positive affect is often entirely situational. Happiness is thus heritable, stable, variable and changeable. What do these findings imply? Can happiness be raised as a platform in individuals and societies? We suggest that individual and societal interventions that target causal pathways and address both amplifying and compensatory processes (i.e., focus on developing strengths and mitigating risks)—thus providing for positive gene-environment matchmaking, are likely to be effective and longer lasting.

Correlation between study units in quantitative genetics studies often makes it difficult to compare important inferential aspects of studies. Describing the relatedness between study units is critical to capture features of pedigree studies involving heritability, including power and precision of heritability estimates. Blangero et al. (Adv Genet 81:1–31, 2012) showed that in pedigree studies the power to detect heritability is a function of the true heritability and the eigenvalues of the kinship matrix. We extend this to a more general setting which allows statements about expected precision of heritability estimates. Using two different Taylor series approximations, we summarize the relatedness in a study design by one or two parameters. These relatedness summary parameters (RSPs) are functions of the eigenvalues or log-eigenvalues of the kinship matrix. Using the RSPs based on the log-eigenvalues, we accurately approximate the expectation of the likelihood ratio test and expected confidence interval widths. We define an effective sample size of a target study as one which has the equivalent power and precision to a reference design. Using unrelated sibpairs as the reference design provides very accurate assessments of power. RSPs and effective sample sizes provide new tools for comparing studies and communicating information about relatedness in heritability studies.

Ammonia, toxic to aquaculture organisms, represents a potential problem in aquaculture systems, and the situation is exacerbated in closed and intensive shrimp farming operations, expecially for Litopenaeus vannamei. Assessing the potential for the genetic improvement of resistance to ammonia in L. vannamei requires knowledge of the genetic parameters of this trait. The heritability of resistance to ammonia was estimated using two descriptors in the present study: the survival time (ST) and the survival status at half lethal time (SS50) for each individual under high ammonia challenge. The heritability of ST and SS50 were low (0.154 4±0.044 6 and 0.147 5±0.040 0, respectively), but they were both significantly different from zero (P 0.05), suggesting that ST and SS50 could be used as suitable indicators for resistance to ammonia. There were also positive phenotypic and genetic correlation between resistance to ammonia and body weight, which means that resistance to ammonia can be enhanced by the improvement of husbandry practices that increase the body weight. The results from the present study suggest that the selection for higher body weight does not have any negative consequences for resistance to ammonia. In addition to quantitative genetics, tools from molecular genetics can be applied to selective breeding programs to improve the efficiency of selection for traits with low heritability.

Quasi-field trials (QFTs) using offspring from first-generation plus trees of Abies bornmulleriana were established on two sites in Denmark via DNA markers and parentage analysis. The aim of this study was to demonstrate an example of ad hoc breeding to make better genetic material available for Christmas tree production. Assessments of several important Christmas tree quality-associated phenotypic traits were made for all offspring individuals in delineated areas of the production stands, and moreover the best individuals in the whole production stands were identified. Postharvest needle retention was evaluated in the parent population in both 2016 and 2017. The results showed that by combining available methodology and pre-selected material, substantial genetic gain in relation to Christmas tree production in A. bornmulleriana could be achieved. Backward selection seems tempting due to its shorter time horizon for delivering improved genetic material. Postharvest needle retention evaluation can be a cheap but important last step in modifying the backward selection. We propose to combine the results based on QFTs with selective seed harvest and paternity tests to give the best possible starting point for production of clonal A. bornmulleriana plants using somatic embryogenesis (SE).

As tree species vary extensively in genome size, complexity, and resource development, reduced representation methods have been increasingly employed for the generation of population genomic data. By allowing rapid marker discovery and genotyping for thousands of genomic regions in many individuals without requiring genomic resources, restriction site-associated DNA sequencing (RADseq) methods have dramatically improved our ability to bring population genomic perspectives to non-model trees. The rapid recent increase in studies of trees utilizing RADseq suggests that it is likely to become among the most common approaches for generating genome-wide data for a variety of applications. Here we provide a practical review of RADseq and its application to research areas of tree genetics. We briefly review RADseq laboratory methods and consider analytical approaches for assembly, variant calling, and bioinformatic processing. To guide considerations for study design, we use in silico analyses of eight available tree genomes to illustrate how expected marker number and density vary across laboratory approaches and genome sizes, and to consider the ability of RADseq designs to query coding regions. We review the empirical use of RADseq for different research objectives, considering its strengths and limitations. Many studies have used RADseq data to perform genome scans for selection, although limited marker density and linkage disequilibrium will often compromise its utility for such analyses. Regardless of this limitation, RADseq offers a powerful and inexpensive technique for generating genome-wide SNP data that can greatly contribute to research spanning phylogenetic and population genetic inference, linkage mapping, and quantitative genetic parameter estimation for tree genetics.

The strategy for breeding blueberries has been based on phenotypic selection without accounting for pedigree correlation information. A central premise of classical quantitative genetics is that through knowledge of the relationships among individuals in a population, we can make inferences about breeding values (BVs), estimate genetic parameters, and support phenotypic selection. Genetic evaluations using best linear unbiased prediction (BLUP) and restricted maximum likelihood (REML) are founded on pedigree information and have been the standard method used in livestock and forest breeding. Despite theoretical and practical benefits, their application in blueberry breeding programs remains unexploited. The objective of this study was to evaluate the use of REML/BLUP in the University of Florida blueberry breeding program in order to estimate genetic parameters and predict BVs of primary selection traits. To do this, we collected phenotypic data for eight selectable traits (yield, flower bud density, fruit weight, fruit firmness, fruit diameter, fruit soluble solids, fruit pH, and fruit scar diameter) from 1996 individuals. The highest narrow-sense heritabilities were found for fruit weight, scar diameter, and yield. The majority of genetic correlations between traits were under 0.20. The largest genetic gain was achieved when selections from early stages were used as parents and the top 5% of the population was selected. Compared to traditional phenotypic selection, our results are evidencing of the importance of implementing REML/BLUP to estimate genetic parameters that help and support the breeding strategy and maximize genetic gains.

Microevolutionary projections use empirical estimates of genetic covariation between physical or psychological phenotypes and reproductive success to forecast changes in the population distributions of those phenotypes over time. The validity of these projections depends on relatively consistent heritabilities of fertility-relevant outcomes and consistent genetic covariation between fertility and other physical or psychological phenotypes across generations. However, well-documented, rapidly changing mean trends in the level and timing of fertility may have been accompanied by differences in the genetic mechanisms of fertility. Using a sample of 933 adult twin pairs from the Midlife Development in the United States study, we demonstrate that genetic influences on completed fertility and age at first birth were trivial for the 1920 to 1935 birth cohort, but rose substantially for the 1936 to 1955 birth cohort. For the 1956 to 1970 birth cohort, genetic influences on completed fertility, but not age at first birth, persisted. Because the heritability of fertility is subject to change dynamically with the social context, it is difficult to project selection pressures or the rate at which selection will occur.

Studies on quantitative genetics of foliar resistance to black pod disease in cacao could inadvertently use cocoa swollen shoot virus (CSSV) infected leaves which could bias the results especially in West Africa where the virus is prevalent. However, effects of CSSV on inheritance and heritability of foliar resistance to Phytophthora species is not known. Choice of an efficient breeding method requires an accurate estimation of genetic effects in selection schemes for foliar resistance to Phytophthora species in cacao. The objective of this study was to investigate the effect of CSSV infection on quantitative genetic parameters of foliar resistance to cocoa black pod disease in a population of 36 F1 hybrids developed by mating six cacao genotypes using a diallel method. The generated F1s and their parents were evaluated for foliar resistance to P. palmivora and P. megakarya using a randomized complete block design (RCBD) with three replications. 1A CSSV and Nsaba CSSV strains were used to infect the cacao genotypes using the patch graft method. The parents chosen showed significant variations for scores of leaf discs after inoculation with P. palmivora and P. megakarya. The leaf disc scores of CSSV infected crosses were lower than leaf disc scores of CSSV-free crosses. Genetic component analysis showed that the effects of GCA and SCA was significant for both CSSV-free and CSSV-infected crosses in resistance to P. palmivora and P. megakarya. The significant GCA and SCA for both CSSV-free and CSSV-infected crosses strongly suggest that both additive and non-additive genetic effects play an important role in the determination of inheritance of foliar resistance to Phytophthora species in cacao. There was significant variability in mean squares of GCA and SCA of CSSV-free and CSSV-infected crosses indicating that CSSV infection modifies GCA and SCA of affected plants. Narrow sense heritability was relatively low (0.31) for foliar resistance to P. palmivora and P. megakarya under CSSV-free and 1A CSSV strain infected conditions. However, heritability for foliar resistance to P. palmivora (0.43) and P. megakarya (0.36) was significantly higher under Nsaba CSSV infected condition. The modifications of mean squares of GCA and SCA and narrow sense heritability due to CSSV infection could mislead in choice of breeding methods indicating that attention must be paid to the infection status of plants when conducting quantitative genetics studies using diseased and healthy plants. CSSV status of leaf samples should be known before using them in leaf disc test. Genotypes Pa7/808 and Pound 7 had high negative GCA effects and are promising parents for enhancement of resistance to black pod disease in cacao.

Potatoes are highly heterozygous and the conventional breeding of superior germplasm is challenging, but use of a combination of MAS and EBVs can accelerate genetic gain. Cultivated potatoes are highly heterozygous due to their outbreeding nature, and suffer acute inbreeding depression. Modern potato cultivars also exhibit tetrasomic inheritance. Due to this genetic heterogeneity, the large number of target traits and the specific requirements of commercial cultivars, potato breeding is challenging. A conventional breeding strategy applies phenotypic recurrent selection over a number of generations, a process which can take over 10 years. Recently, major advances in genetics and molecular biology have provided breeders with molecular tools to accelerate gains for some traits. Marker-assisted selection (MAS) can be effectively used for the identification of major genes and quantitative trait loci that exhibit large effects. There are also a number of complex traits of interest, such as yield, that are influenced by a large number of genes of individual small effect where MAS will be difficult to deploy. Progeny testing and the use of pedigree in the analysis can provide effective identification of the superior genetic factors that underpin these complex traits. Recently, it has been shown that estimated breeding values (EBVs) can be developed for complex potato traits. Using a combination of MAS and EBVs for simple and complex traits can lead to a significant reduction in the length of the breeding cycle for the identification of superior germplasm.

Infectious diseases have a major role in evolution by natural selection and pose a worldwide concern in livestock. Understanding quantitative genetics of infectious diseases, therefore, is essential both for understanding the consequences of natural selection and for designing artificial selection schemes in agriculture. The basic reproduction ratio, R-0, is the key parameter determining risk and severity of infectious diseases. Genetic improvement for control of infectious diseases in host populations should therefore aim at reducing R-0. This requires definitions of breeding value and heritable variation for R-0, and understanding of mechanisms determining response to selection. This is challenging, as R-0 is an emergent trait arising from interactions among individuals in the population. Here we show how to define breeding value and heritable variation for R-0 for genetically heterogeneous host populations. Furthermore, we identify mechanisms determining utilization of heritable variation for R-0. Using indirect genetic effects, next-generation matrices and a SIR (Susceptible, Infected and Recovered) model, we show that an individual's breeding value for R-0 is a function of its own allele frequencies for susceptibility and infectivity and of population average susceptibility and infectivity. When interacting individuals are unrelated, selection for individual disease status captures heritable variation in susceptibility only, yielding limited response in R-0. With related individuals, however, there is a secondary selection process, which also captures heritable variation in infectivity and additional variation in susceptibility, yielding substantially greater response. This shows that genetic variation in susceptibility represents an indirect genetic effect. As a consequence, response in R-0 increased substantially when interacting individuals were genetically related.

Using large numbers of DNA markers to predict genetic merit [genomic selection (GS)] is a new frontier in plant and animal breeding programs. GS is now routinely used to select superior bulls in dairy cattle breeding. In forest trees, a few empirical proof of-concept studies suggest that GS could be successful. However, application of GS in forest tree breeding is still in its infancy. The major hurdle is lack of high throughput genotyping platforms for trees, and the high genotyping costs, though, the cost of genotyping will likely decrease in the future. There has been a growing interest in GS among tree breeders, forest geneticists, and tree improvement managers. A broad overview of pedigree reconstruction and GS is presented. Underlying reasons for failures of marker-assisted selection were summarized and compared with GS. Challenges of GS in forest tree breeding and the outlook for the future are discussed, and a GS plan for a cloned loblolly pine breeding population is presented. This review is intended for tree breeders, forest managers, scientist and students who are not necessarily familiar with genomic or quantitative genetics jargon.

The narrow genetic base of elite Upland cotton (Gossypium hirsutum L.) germplasm has been a significant impediment to sustained progress in the development of cotton cultivars to meet the needs of growers and industry in recent years. The prospect of widening the genetic base of Upland cotton by accessing the genetic diversity and fiber quality of Pima cotton (Gossypium barbadense L.) has encouraged interspecific hybridization and introgression efforts for the past century. However, success is limited due mainly to genetic barriers between the two species in the forms of divergent gene regulatory systems, accumulated gene mutations, gene order rearrangements and cryptic chromosomal structure differences that have resulted in hybrid breakdown, hybrid sterility and selective elimination of genes. The objective of this paper is to provide a mini-review in interspecific hybridization between Upland and Pima cotton relevant to breeding under the following sections: (1) qualitative genetics; (2) cytogenetic stocks; (3) quantitative genetics; (4) heterosis, and (5) introgression breeding. Case studies of successful examples are provided.

Background Genetic canalization reflects the capacity of an organism’s phenotype to remain unchanged in spite of mutations. As selection on genetic canalization is weak and indirect, whether or not genetic canalization can reasonably evolve in complex genetic architectures is still an open question. In this paper, we use a quantitative model of gene regulatory network to describe the conditions in which substantial canalization is expected to emerge in a stable environment. Results Through an individual-based simulation framework, we confirmed that most parameters associated with the network topology (complexity and size of the network) have less influence than mutational parameters (rate and size of mutations) on the evolution of genetic canalization. We also established that selecting for extreme phenotypic optima (nil or full gene expression) leads to much higher canalization levels than selecting for intermediate expression levels. Overall, constrained networks evolve less canalization than networks in which some genes could evolve freely (i.e. without direct stabilizing selection pressure on gene expression). Conclusions Taken together, these results lead us to propose a two-fold mechanism involved in the evolution of genetic canalization in gene regulatory networks: the shrinkage of mutational target (useless genes are virtually removed from the network) and redundancy in gene regulation (so that some regulatory factors can be lost without affecting gene expression). Electronic supplementary material The online version of this article (doi:10.1186/s12862-016-0801-2) contains supplementary material, which is available to authorized users.

Lithic artifacts are increasingly being used to address questions in evolutionary, i.e., historical, terms. The explicit assumption in such analyses is that lithic attributes reflect patterns of inheritance via social learning. However, both raw material and reduction factors are known to be potential sources of lithic variation. The cultural–evolutionary analysis of lithic variability must, therefore, reconcile heritable and nonheritable sources of variation under a single coherent framework. Moreover, there is a frequent assumption that conveniently measureable features, such as the relative shape of a biface at a specific point of its length, can be used as indicators of heritable variation. The use of such traits, however, is potentially questionable, especially in the light of controlled experiments that indicate that traits such as platform depths and angles influence the form of individual flakes. As such, it may be reasonable to consider whether such features represent more appropriate analytical units. Here, we contend that the solution to these problems lies in application of a “quantitative genetics” approach, which was designed to solve directly analogous problems in biology. This approach explicitly models multiple sources of variation simultaneously. Moreover, it provides a logical rationale for how evolutionary forces (e.g., drift and selection) can operate when only part of this variation is potentially heritable. We outline specifically how quantitative genetic theory can be rewritten for use with lithic artifacts. Thereafter, we provide example analyses of data, which support our case. We conclude by summarizing the merits of this framework and outline future extensions.

The analysis of phenotypic covariances among genetically related individuals is the basis for estimations of genetic and phenotypic effects on phenotypes. Beyond heritability, there are several other estimates that can be made with behavior genetic models of interest to primatologists. Some of these estimates are feasible with primate samples because they take advantage of the types of relatives available to compare in primate species and because most behaviors are expressed orders of magnitude more often and in a greater variety of contexts than morphological or life-history traits. The hypotheses that can be tested with these estimates are contrasted with hypotheses that will be difficult to achieve in primates because of sample size limitations. Feasible comparisons include the proportion of variance from interaction effects, the variation of genetic effects across environments, and the genetics of growth and development. Simulation shows that uncertainty of genetic parameters can be reduced by sampling each individual more than once. Because sample sizes are likely to remain relatively small in most primate behavior genetics, expressing uncertainty in parameter estimates is needed to move our inferences forward.

This study seeks to quantify the importance of epistatic effects on the heterosis of maize using complex pedigrees in a single model of the so-called bi-, tri-, and tetra-alleles in an analysis with and without information from microsatellite markers. To this end, 51 inbred lines were sampled from different backgrounds, obtaining 6 double cross hybrids, 14 triple cross hybrids, and 58 single cross hybrids, for a total of 78 hybrids. Seventy-nine microsatellite markers were used in the genotyping of the 51 lines. These markers were distributed throughout the 10 linkage groups in maize. This information was used to construct an information matrix on kinship. The mixed models and restricted maximum likelihood approaches were used to estimate additive, dominant and epistatic effects. It was observed that the dominant by dominant epistasis was the most important effect related to genetic control of the heterosis in maize. Also, our study demonstrated that it is possible to exploit a large amount of information when we jointly analyze simple, double, and three-way cross hybrids under the same model. Using this approach, it is possible to dissect heterosis into several components and to adopt the best crossbreeding strategy based on the importance of each component. Additionally, it was possible to verify that the use of molecular markers improves the accuracy of calculating the epistatic and dominance effects. Thus, using the current state-of-art in quantitative genetics and statistical methods the concept of crossbreeding can be expanded to frontiers that are far beyond the traditional general and specific combining ability.

The power of genome-wide association studies (GWAS) rests on several foundations: (i) there is a significant amount of additive genetic variation, (ii) individual causal polymorphisms often have sizable effects and (iii) they segregate at moderate-to-intermediate frequencies, or will be effectively 'tagged' by polymorphisms that do. Each of these assumptions has recently been questioned. (i) Why should genetic variation appear additive given that the underlying molecular networks are highly nonlinear? (ii) A new generation of relatedness-based analyses directs us back to the nearly infinitesimal model for effect sizes that quantitative genetics was long based upon. (iii) Larger effect causal polymorphisms are often low frequency, as selection might lead us to expect. Here, we review these issues and other findings that appear to question many of the foundations of the optimism GWAS prompted. We then present a roadmap emerging as one possible future for quantitative genetics. We argue that in future GWAS should move beyond purely statistical grounds. One promising approach is to build upon the combination of population genetic models and molecular biological knowledge. This combined treatment, however, requires fitting experimental data to models that are very complex, as well as accurate capturing of the uncertainty of resulting inference. This problem can be resolved through Bayesian analysis and tools such as approximate Bayesian computation-a method growing in popularity in population genetic analysis. We show a case example of anterior-posterior segmentation in Drosophila, and argue that similar approaches will be helpful as a GWAS augmentation, in human and agricultural research.

The additive genetic variance with respect to absolute fitness, VA(W), divided by mean absolute fitness, , sets the rate of ongoing adaptation. Fisher's key insight yielding this quantitative prediction of adaptive evolution, known as the Fundamental Theorem of Natural Selection, is well appreciated by evolutionists. Nevertheless, extremely scant information about VA(W) is available for natural populations. Consequently, the capacity for fitness increase via natural selection is unknown. Particularly in the current context of rapid environmental change, which is likely to reduce fitness directly and, consequently, the size and persistence of populations, the urgency of advancing understanding of immediate adaptive capacity is extreme. We here explore reasons for the dearth of empirical information about VA(W), despite its theoretical renown and critical evolutionary role. Of these reasons, we suggest that expectations that VA(W) is negligible, in general, together with severe statistical challenges of estimating it, may largely account for the limited empirical emphasis on it. To develop insight into the dynamics of VA(W) in a changing environment, we have conducted individual-based genetically explicit simulations. We show that, as optimizing selection on a trait changes steadily over generations, VA(W) can grow considerably, supporting more rapid adaptation than would the VA(W) of the base population. We call for direct evaluation of VA(W) and in support of prediction of rates adaptive evolution, and we advocate for the use of aster modeling as a rigorous basis for achieving this goal.

Seven growth-related traits were measured to assess the selection response and genetic parameters of the growth of Pacific white shrimp, Litopenaeus vannamei, which had been domesticated in tanks for more than four generations. Phenotypic and genetic parameters were evaluated and fitted to an animal model. Realized response was measured from the difference between the mean growth rates of selected and control families. Realized heritability was determined from the ratio of the selection responses and selection differentials. The animal model heritability estimate over generations was 0.44±0.09 for body weight (BW), and ranged from 0.21±0.08 to 0.37±0.06 for size traits. Genetic correlations of phenotypic traits were more variable (0.51–0.97), although correlations among various traits were high (>0.83). Across generations, BW and size traits increased, while selection response and heritability gradually decreased. Selection responses were 12.28%-23.35% for harvest weight and 3.58%–13.53% for size traits. Heritability estimates ranged from 0.34±0.09 to 0.48±0.15 for harvest weight and 0.17±0.01–0.38±0.11 for size traits. All phenotypic and genetic parameters differed between various treatments. To conclude, the results demonstrated a potential for mass selection of growth traits in L. vannamei. A breeding scheme could use this information to integrate the effectiveness constituent traits into an index to achieve genetic progress.

The objectives of this study were to implement a Bayesian framework for mixed models analysis in crop species breeding and to exploit alternatives for informative prior elicitation. Bayesian inference for genetic evaluation in annual crop breeding was illustrated with the first two half-sib selection cycles in a popcorn population. The Bayesian framework was based on the Just Another Gibbs Sampler software and the R2jags package. For the first cycle, a non-informative prior for the inverse of the variance components and an informative prior based on meta-analysis were used. For the second cycle, a non-informative prior and an informative prior defined as the posterior from the non-informative and informative analyses of the first cycle were used. Regarding the first cycle, the use of an informative prior from the meta-analysis provided clearly distinct results relative to the analysis with a non-informative prior only for the grain yield. Regarding the second cycle, the results for the expansion volume and grain yield showed differences among the three analyses. The differences between the non-informative and informative prior analyses were restricted to variance components and heritability. The correlations between the predicted breeding values from these analyses were almost perfect.

A recent discussion in this journal (Dingemanse et al. Behav Ecol Sociobiol 66: 1543–1548, 2012; Garamszegi and Herczeg Behav Ecol Socibiol 66:1651–1658, 2012) deals with a core issue in animal personality research: Can animal personality research quantify correlated behaviors on the between-individual level, or is this too demanding in terms of design and analysis of the data, and should behavioral ecologists therefore take the “individual gambit” and work on the phenotypic level only. Taking this gambit implies accepting that the between-individual correlation in behavioral traits (which is the correlation of interest) may be masked by a residual correlation of different magnitude or sign. Understanding (co)variances on different levels is the main thrust of quantitative genetics, and animal personality research can make good use of the plethora of ideas and analytical approaches developed in this field. I, here, outline reasons why the “individual gambit” may or may not work out and its relationship to the quantitative genetic “phenotypic gambit”. I especially emphasize the meaning of residuals and phenotypic plasticity which has not been fully appreciated in the debate thus far. I conclude that instead of a priori assuming that between-individual correlations are captured sufficiently well by the phenotypic correlation, animal personality researchers should set up more ambitious data collection and analysis designs to critically test this conjectured equality.

Chantier qualité GA; Although the effects of linkage disequilibrium (LD) on partition of genetic variance have received attention in quantitative genetics, there has been little discussion on how this phenomenon affects attribution of variance to a given locus. This paper reinforces the point that standard metrics used for assessing the contribution of a locus to variance can be misleading when there is linkage LD and that factors such as distribution of effects and of allelic frequencies over loci, or existence of frequency-dependent effects, play a role as well. An apparently new metric is proposed for measuring how much of the variability is contributed by a locus when LD exists. Effects of intervening factors, such as type and extent of LD, number of loci, distribution of effects, and of allelic frequencies over loci, as well as a model for generating frequency-dependent effects, are illustrated via hypothetical simulation scenarios. Implications on the interpretation of genome-wide association studies (GWAS), as typically carried out in human genetics, where single marker regression and the assumption of a sole quantitative trait locus (QTL) are common, are discussed. It is concluded that the standard attributions to variance contributed by a single QTL from a GWAS analysis may be misleading, conceptually and statistically, when a trait is complex and affected by sets of many genes in linkage disequilibrium. Yet another factor to consider in the "missing heritability" saga?.

Along with the development and integration of molecular genetics and quantitative genetics, many quantitative trait locus (QTL) mapping studies have been conducted using different mapping populations in various crop species. Existing QTLs can be used for marker-assisted breeding and map-based cloning, whereas the false-positive QTLs are no use. The purpose of this study is to evaluate the suitability of different mapping procedures for data from different genetic models. In this study, four types of recombinant inbred lines (RILs) with different genetic models, viz. additive QTLs (Model I), additive and epistatic QTLs (Model II), additive QTLs and QTL × environment interaction (Model III), additive, epistatic QTLs and QTL × environment interaction (Model IV), were simulated by computer. Six types of QTL mapping procedures, viz. CIM, MIMF, MIMR, ICIM, MQM and NWIM, on four kinds of QTL mapping software, viz. WinQTL Cartographer Version 2.5, IciMapping Version 2.0, MapQTL Version 5.0 and QTLnetwork Version 2.0, were used for screening QTLs of the simulated RILs. The results showed that different mapping procedures have different suitability for different genetic models. CIM and MQM can only screen Model I data. MIMR, MIMF and ICIM can only screen Model I and Model II data. NWIM can screen all four models’ data. It can be concluded that different genetic models’ data have different most suitable mapping procedures. In practical experiments where the genetic model of the data is unknown, a multiple model mapping strategy should be used, that is a full model scanning with complex model procedure followed by verification with other procedures corresponding to the scanning results.

This commentary highlights multivariate tools that have been used by evolutionary biologists in the study of syndromes and their evolution and discusses the insights that these methods provide into evolutionary pro- cesses relative to the metric 'syndrome deviation' that has recently been proposed by Herczeg and Garamszegi (Behav Ecol Sociobiol 66:161-169, 2012). We clarify that non-zero phenotypic correlations arise from the joint influ- ences of within- and between-individual correlations, whereas only non-zero between-individual correlations repre- sent behavioural syndromes, and discuss how acknowledge- ment of this subtle difference between phenotypic and between-individual correlations affects the applicability of syndrome deviation for the study of behavioural syndromes.

The physiological requirements of reproduction are predicted to generate a link between energy, physiology and life history traits. Simultaneously, low maintenance costs, measured by energy consumption, are expected to be advantageous. Here we investigated fitness relatedness of traits by estimating genetic correlations between, and inbreeding depression for, body mass, basal metabolic rate (BMR) and other life history characters in a wild rodent, Myodes glareolus. The narrow-sense heritability of absolute and mass corrected BMRs were high for females (h 2 = 0.48 and 0.42) but low and non-significant for males (0.32 and 0.09). A significant positive genetic correlation between BMR and litter size suggests that traits connected to female fecundity might favour higher metab- olism (i.e. support increased intake hypothesis). However, the estimates of inbreeding depression indicate that, while higher values of body mass and female litter size could be positively associated with overall fitness, the association between BMR and overall fitness in bank voles would be negative (i.e. support compensation hypothesis). This result sug- gests that the advantages of larger litters and larger body mass might be evolutionary constrained by high costs of maintenance of those traits, as reflected by the level of basal metabolism.