Bayesian inference for genomic imprinting underlying developmental characteristics

The identification of imprinted genes is becoming a standard procedure in searching for quantitative trait loci (QTL) underlying complex traits. When a developmental characteristic such as growth or drug response is observed at multiple time points, understanding the dynamics of gene function governing the underlying feature should provide more biological information regarding the genetic control of an organism. Recognizing that differential imprinting can be development-specific, mapping imprinted genes considering the dynamic imprinting effect can provide additional biological insights into the epigenetic control of a complex trait. In this study, we proposed a Bayesian imprinted QTL (iQTL) mapping framework considering the dynamics of imprinting effects and model multiple iQTLs with an efficient Bayesian model selection procedure. The method overcomes the limitation of likelihood-based mapping procedure, and can simultaneously identify multiple iQTLs with different gene action modes across the whole genome with high computational efficiency. An inference procedure using Bayes factors to distinguish different imprinting patterns of iQTL was proposed. Monte Carlo simulations were conducted to evaluate the performance of the method. The utility of the approach was illustrated through an analysis of a body weight growth data set in an F(2) family derived from LG/J and SM/J mouse stains. The proposed Bayesian mapping method provides an efficient and computationally feasible framework for genome-wide multiple iQTL inference with complex developmental traits.     

Selecting Informative Traits for Multivariate Quantitative Trait Locus Mapping Helps to Gain Optimal Power

A major consideration in multitrait analysis is which traits should be jointly analyzed. As a common strategy, multitrait analysis is performed either on pairs of traits or on all of traits. To fully exploit the power of multitrait analysis, we propose variable selection to choose a subset of informative traits for multitrait quantitative trait locus (QTL) mapping. The proposed method is very useful for achieving optimal statistical power for QTL identification and for disclosing the most relevant traits. It is also a practical strategy to effectively take advantage of multitrait analysis when the number of traits under consideration is too large, making the usual multivariate analysis of all traits challenging. We study the impact of selection bias and the usage of permutation tests in the context of variable selection and develop a powerful implementation procedure of variable selection for genome scanning. We demonstrate the proposed method and selection procedure in a backcross population, using both simulated and real data. The extension to other experimental mapping populations is straightforward.     

An approximate method for optimum independent culling level selection for n stages of selection with explicit solutions

Summary An approximate method with explicit solutions to apply independent culling levels for multiple traits in n-stages of selection was developed. An approximate solution was found for sequentially selected traits. Two assumptions were necessary. The first was to assume that subsequent selection would not appreciably change the mean of traits already selected, and the second was to approximate the variance of a correlated trait in a selected population with an upward biased projection. The procedure was shown to give near optimal results regardless of selection intensity or genetic correlations if phenotypic correlations among traits were low. The procedure gave poor results only for certain sequences of selection when phenotypic correlations were high. However, in those cases good results were obtained using a different sequence of selection. With high correlations, the procedure is recommended only after comparing solutions and expected genetic gain for all sequences of selection. If the expected aggregate gain for the sequence of selection desired is less than that of another order, culling points associated with the optimal ordering must be determined. Genetic gain from use of culling points is independent of order of selection. The procedure is recommended for use with computer programs that attempt to find optimal culling points to reduce computational time and to check results.Journal Paper No. 12448 of the Purdue University Agricultural Experiment Station     

Joint mapping of quantitative trait Loci for multiple binary characters

Joint mapping for multiple quantitative traits has shed new light on genetic mapping by pinpointing pleiotropic effects and close linkage. Joint mapping also can improve statistical power of QTL detection. However, such a joint mapping procedure has not been available for discrete traits. Most disease resistance traits are measured as one or more discrete characters. These discrete characters are often correlated. Joint mapping for multiple binary disease traits may provide an opportunity to explore pleiotropic effects and increase the statistical power of detecting disease loci. We develop a maximum-likelihood method for mapping multiple binary traits. We postulate a set of multivariate normal disease liabilities, each contributing to the phenotypic variance of one disease trait. The underlying liabilities are linked to the binary phenotypes through some underlying thresholds. The new method actually maps loci for the variation of multivariate normal liabilities. As a result, we are able to take advantage of existing methods of joint mapping for quantitative traits. We treat the multivariate liabilities as missing values so that an expectation-maximization (EM) algorithm can be applied here. We also extend the method to joint mapping for both discrete and continuous traits. Efficiency of the method is demonstrated using simulated data. We also apply the new method to a set of real data and detect several loci responsible for blast resistance in rice.     

Where Two Are Fighting,the Third Wins: Stronger Selection Facilitates Greater Polymorphism in Traits Conferring Competition-Dispersal Tradeoffs

A major conundrum in evolution is that, despite natural selection, polymorphism is still omnipresent in nature: Numerous species exhibit multiple morphs, namely several abundant values of an important trait. Polymorphism is particularly prevalent in asymmetric traits, which are beneficial to their carrier in disruptive competitive interference but at the same time bear disadvantages in other aspects, such as greater mortality or lower fecundity. Here we focus on asymmetric traits in which a better competitor disperses fewer offspring in the absence of competition. We report a general pattern in which polymorphic populations emerge when disruptive selection increases: The stronger the selection, the greater the number of morphs that evolve. This pattern is general and is insensitive to the form of the fitness function. The pattern is somewhat counterintuitive since directional selection is excepted to sharpen the trait distribution and thereby reduce its diversity (but note that similar patterns were suggested in studies that demonstrated increased biodiversity as local selection increases in ecological communities). We explain the underlying mechanism in which stronger selection drives the population towards more competitive values of the trait, which in turn reduces the population density, thereby enabling lesser competitors to stably persist with reduced need to directly compete. Thus, we believe that the pattern is more general and may apply to asymmetric traits more broadly. This robust pattern suggests a comparative, unified explanation to a variety of polymorphic traits in nature.     

Allometry and sexually dimorphic traits in male anurans

Allometry of secondary sexual traits has been the subject of recent debate, and the generality of positive allometry and its association with sexual selection have been recently questioned. Whereas some studies suggest an almost universal positive allometry for traits under sexual selection and isometry or a negative allometry for traits not under such pressure, other studies argue that this pattern results from the study of exaggerated (ornamental) traits. To answer the call for an examination of the allometry of less-exaggerated sexually selected traits, we have examined morphological data from 14 sexually dimorphic traits and six monomorphic traits from three anuran species. Although we found evidence of positive allometry in male secondary sexual traits of several species and populations, not all nonsexual traits were isometric or exhibited negative allometry. Furthermore, our results indicate that larger traits in the populations that we studied were not associated with greater allometric slopes. Therefore, our study is in line with the contention suggesting no specific kind of allometric pattern for sexual and nonsexual characters, and we can only advocate for further investigation of trait allometry and sexual selection to understand the complexity underlying the evolution of allometry in sexual traits.     

Predicting the response to simultaneous selection: genetic architecture and physiological constraints

A great deal is known about the evolutionary significance of body size and development time. They are determined by the nonlinear interaction of three physiological traits: two hormonal events and growth rate (GR). In this study we investigate how the genetic architecture of the underlying three physiological traits affects the simultaneous response to selection on the two life-history traits in the hawkmoth Manduca sexta. The genetic architecture suggests that when the two life-history traits are both selected in the same direction (to increase or decrease) the response to selection is primarily determined by the hormonal mechanism. When the life-history traits are selected in opposite directions (one to increase and one to decrease) the response to selection is primarily determined by factors that affect the GR. To determine how the physiological traits affect the response to selection of the life-history traits, we simulated the predicted response to 10 generations of selection. A total of 83% of our predictions were supported by the simulation. The main components of this physiological framework also exist in unicellular organisms, vertebrates, and plants and can thus provide a robust framework for understanding how underlying physiology can determine the simultaneous evolution of life-history traits.     

Stress specific correlated responses in fat content, Hsp70 and dopamine levels in Drosophila melanogaster selected for resistance to environmental stress

Studies of adaptation to stressful environments have frequently encountered cross resistance. This has prompted the hypothesis that certain adaptations confer resistance to multiple stressors. Some of the genes and mechanisms conferring stress resistance have been identified, however, the generality and basis of stress adaptation and cross resistance is still unclear. We investigated several physiological traits that have been previously linked to increased stress resistance: Hsp70 expression, fat content and dopamine levels. Additionally, we studied a behavioural trait, locomotor activity, as a proxy for the physiological state of the organisms. Physiology is the mechanistic link between resistance phenotype and underlying genetic background, and provides insights into the background and generality of cross resistance and correlated responses to selection for stress resistance. We assessed the relationship between the measured traits and stress resistance in a set of lines selected for increased resistance to several environmental stressors. We found that, although all physiological traits displayed significant differentiation among selection regimes, none were consistently associated with increased general stress resistance. This demonstrates that directional changes in Hsp70 expression level, dopamine level and fat content occur in response to the specific requirements of the different stress regimes, rather than as a general response to stress.     

Sex allocation and investment into pre- and post-copulatory traits in simultaneous hermaphrodites: the role of polyandry and local sperm competition

Sex allocation theory predicts the optimal allocation to male and female reproduction in sexual organisms. In animals, most work on sex allocation has focused on species with separate sexes and our understanding of simultaneous hermaphrodites is patchier. Recent theory predicts that sex allocation in simultaneous hermaphrodites should strongly be affected by post-copulatory sexual selection, while the role of pre-copulatory sexual selection is much less clear. Here, we review sex allocation and sexual selection theory for simultaneous hermaphrodites, and identify several strong and potentially unwarranted assumptions. We then present a model that treats allocation to sexually selected traits as components of sex allocation and explore patterns of allocation when some of these assumptions are relaxed. For example, when investment into a male sexually selected trait leads to skews in sperm competition, causing local sperm competition, this is expected to lead to a reduced allocation to sperm production. We conclude that understanding the evolution of sex allocation in simultaneous hermaphrodites requires detailed knowledge of the different sexual selection processes and their relative importance. However, little is currently known quantitatively about sexual selection in simultaneous hermaphrodites, about what the underlying traits are, and about what drives and constrains their evolution. Future work should therefore aim at quantifying sexual selection and identifying the underlying traits along the pre- to post-copulatory axis.     

A comparison of methods to calculate a total merit index using stochastic simulation

Background

Modern dairy cattle breeding goals include several production and more and more functional traits. Estimated breeding values (EBV) that are combined in the total merit index usually come from single-trait models or from multivariate models for groups of traits. In most cases, a multivariate animal model based on phenotypic data for all traits is not feasible and approximate methods based on selection index theory are applied to derive the total merit index. Therefore, the objective of this study was to compare a full multitrait animal model with two approximate multitrait models and a selection index approach based on simulated data.

Methods

Three production and two functional traits were simulated to mimic the national Austrian Brown Swiss population. The reference method for derivation of the total merit index was a multitrait evaluation based on all phenotypic data. Two of the approximate methods were variations of an approximate multitrait model that used either yield deviations or de-regressed breeding values. The final method was an adaptation of the selection index method that is used in routine evaluations in Austria and Germany. Three scenarios with respect to residual covariances were set up: residual covariances were equal to zero, or half of or equal to the genetic covariances.

Results

Results of both approximate multitrait models were very close to those of the reference method, with rank correlations of 1. Both methods were nearly unbiased. Rank correlations for the selection index method showed good results when residual covariances were zero but correlations with the reference method decreased when residual covariances were large. Furthermore, EBV were biased when residual covariances were high.

Conclusions

We applied an approximate multitrait two-step procedure to yield deviations and de-regressed breeding values, which led to nearly unbiased results. De-regressed breeding values gave even slightly better results. Our results confirmed that ignoring residual covariances when a selection index approach is applied leads to remarkable bias. This could be relevant in terms of selection accuracy. Our findings suggest that the approximate multitrait approach applied to de-regressed breeding values can be used in routine genetic evaluation.     

Selection for developmental time in bean weevil (Acanthoscelides obtectus): correlated responses for other life history traits and genetic architecture of line differentiation

In this article we investigate the direct and correlated responses to selection for developmental time in order to discern differences between lines in several preadult and adult life history traits of Acanthoscelides obtectus (Coleoptera, Bruchidae). Selection for fast development was about five times as effective as selection for slow development, as judged by realized heritabilities. The correlated responses on the following life‐history traits were studied: egg size, hatching success, embryonic developmental time, egg‐to‐adult viability, body weight, first day of egg laying, total fecundity, and longevity. Analyses of the terminal generation of selection showed that all life history traits examined, except for hatching success, were affected by selection. The findings suggest that body weight, total fecundity, and longevity traded off to preadult developmental time. Unlike the adult traits, none of the preadult traits showed negative correlations with developmental time. We also present data concerning the underlying genetic basis that produces changes in preadult developmental time, body weight, and egg‐to‐adult viability in the lines selected for fast and slow preadult developmental time. Additive‐dominance genetic architecture for both preadult developmental time and body weight was found. In addition, it appears that the responses to selection for preadult developmental time involved between 10 and 28 loci, which were correlated with at least one to four genes for body weight. Epistasis makes a significant contribution to genetic divergence between fast and slow selected lines only with respect to preadult viability. The observed levels of dominance and epistasis underscore the important role of nonadditive genetic effects to the adaptive diversifications of bean weevil populations.     

A test of the hypothesis that correlational selection generates genetic correlations

Theory predicts that correlational selection on two traits will cause the major axis of the bivariate G matrix to orient itself in the same direction as the correlational selection gradient. Two testable predictions follow from this: for a given pair of traits, (1) the sign of correlational selection gradient should be the same as that of the genetic correlation, and (2) the correlational selection gradient should be positively correlated with the value of the genetic correlation. We test this hypothesis with a meta-analysis utilizing empirical estimates of correlational selection gradients and measures of the correlation between the two focal traits. Our results are consistent with both predictions and hence support the underlying hypothesis that correlational selection generates a genetic correlation between the two traits and hence orients the bivariate G matrix.     

Selection index updating

Summary When traits become evident at different ages or there are large differences in the costs of measuring various traits, selection by independent culling levels may give a higher aggregate economic return than index selection because not all traits need to be measured on all individuals. The problems with optimum independent culling selection is that general solutions are not possible and numerical integration is needed for specific cases. Recently, Xu and Muir (1991) developed a new independent culling level procedure by use of orthogonal transformation of the original characters. With their procedure, explicit solutions for optimum truncation points are possible without numerical integration. As such, the procedure is proficient for any number of stages, and generalized theoretical comparisons of alternative breeding strategies are possible. However, their procedure was limited to the case where selection is for one character at each stage. In this paper, our previous results are extended to the general case of multi-stage index selection, called selection index updating. This procedure is called selection index updating because as traits become available in latter stages, each subsequent index contains all of the traits available up to that stage.The procedure is to develop sequential indices for each stage such that correlations among indices at different stages are zero. Optimum culling points are obtained for the updating procedure by using Xu and Muir's (1991) iterative equations. Due to the property of orthogonality of the updated indices, aggregate gain can be partitioned into gains due to various stages of selection. Partitioning of aggregate economic gain is useful to breeders who desire to adjust individual trait selection intensity based on facilities available at that stage. Methods are discussed to modify the procedure to obtain maximum aggregate economic return per unit of cost associated with obtaining measures on each trait. An application of multi-stage selection is demonstrated using a set of data for Rhode Island Red layer type chickens. A second example demonstrates the use of multi-stage selection optimized with respect to aggregate economic gain and costs associated with obtaining measurements.Journal Paper No. 12813 of the Purdue University Agricultural Experiment Station     

Effects of floral traits and plant genetic composition on pollinator behavior

Pollinator-mediated selection plays a major role in floral evolution and speciation. Floral traits that influence animal pollinator behavior are the target of pollinator-mediated selection, but can only evolve if floral phenotypes have underlying genetic variation. Thus, understanding the genetic basis of a floral trait is a crucial step in studying pollinator-mediated selection. In this study I tested the effect of quantitative trait loci (QTL) underlying floral traits on pollinator behavior in recombinant inbred lines (RILs) in the common sunflower, Helianthus annuus L. and its crop relative. The indirect effects of QTL on pollinator behavior, mediated by floral phenotypes, were analyzed for six insect visitor types using structural equation modeling (SEM) and path analysis. For three of the six visitor types (large and small bees and non-bee insects) valid models were revealed when all three levels (QTL, floral traits, and pollinator behavior) were incorporated. Nested model without genetics were validated for five of the six visitor types. The results suggest that insect behavior as a reaction to floral phenotypes is affected by the genetic architecture of floral traits. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users. Handling editor: Heikki Hokkanen     

The evolution of static allometry in sexually selected traits

Although it has been the subject of verbal theory since Darwin, the evolution of morphological trait allometries remains poorly understood, especially in the context of sexual selection. Here we present an allocation trade-off model that predicts the optimal pattern of allometry under different selective regimes. We derive a general solution that has a simple and intuitive interpretation and use it to investigate several examples of fitness functions. Verbal arguments have suggested cost or benefit scenarios under which sexual selection on signal or weapon traits may favor larger individuals with disproportionately larger traits (i.e., positive allometry). However, our results suggest that this is necessarily true only under a precisely specified set of conditions: positive allometry will evolve when the marginal fitness gains from an increase in relative trait size are greater for large individuals than for small ones. Thus, the optimal allometric pattern depends on the precise nature of net selection, and simple examples readily yield isometry, positive or negative allometry, or polymorphisms corresponding to sigmoidal scaling. The variety of allometric patterns predicted by our model is consistent with the diversity of patterns observed in empirical studies on the allometries of sexually selected traits. More generally, our findings highlight the difficulty of inferring complex underlying processes from simple emergent patterns.     

A molecular selection index method based on eigenanalysis

The traditional molecular selection index (MSI) employed in marker-assisted selection maximizes the selection response by combining information on molecular markers linked to quantitative trait loci (QTL) and phenotypic values of the traits of the individuals of interest. This study proposes an MSI based on an eigenanalysis method (molecular eigen selection index method, MESIM), where the first eigenvector is used as a selection index criterion, and its elements determine the proportion of the trait's contribution to the selection index. This article develops the theoretical framework of MESIM. Simulation results show that the genotypic means and the expected selection response from MESIM for each trait are equal to or greater than those from the traditional MSI. When several traits are simultaneously selected, MESIM performs well for traits with relatively low heritability. The main advantages of MESIM over the traditional molecular selection index are that its statistical sampling properties are known and that it does not require economic weights and thus can be used in practical applications when all or some of the traits need to be improved simultaneously.     

EXAMINING SELECTION ON THE MULTIVARIATE PHENOTYPE: PLANT RESISTANCE TO HERBIVORES

Cost–benefit theory posits that stabilizing selection, produced by a trade-off between associated costs and benefits, often maintains phenotypic traits at intermediate equilibrium values. Measurement of selection on one type of trait, resistance to herbivory, should provide evidence to test this prediction. However, most plants host more than one species of herbivore, and resistance to various herbivores may be phenotypically correlated. Consequently, selection must be measured on a multivariate phenotype, which may produce a very complex selection gradient. Canonical analysis of the matrix of quadratic coefficients of the phenotypic selection gradient is presented as a method to simplify the interpretation of the estimated multidimensional adaptive surface. Because this analytical method finds the canonical axes of second-order effects on the selection surface, it shows where nonlinear, and possibly stabilizing, selection is strongest. The resulting index traits may generate hypotheses regarding underlying resistance traits to which more than one type of herbivore responds.     

SELECTION, PREDICTION AND RESPONSE

1. The biometric approach to selection experiments has been outlined, and found to be rather deficient because it is based on excessively restrictive models which cannot take into account the complex architectures of quantitative traits as are being revealed today. 2. The nature of polygenes is discussed in detail from the theoretical point of view. In out breeding species, some form of the balanced polygenic complex is likely, showing polymorphism for the constituent genes. Although polymorphism is implicit in the argument, definitive evidence for poiymorphisms has only just appeared. 3. There is no evidence that polygenes differ from any other gene. 4. Several artificial selection experiments are described, in particular in Drosophila. By means of appropriate breeding techniques after obtaining responses to selection, genetic activity controlling quantitative traits can be located to chromosomes, and even specific loci found. Such few studies as have been carried out reveal, in general, the types of genetic architecture predicted on theoretical grounds. 5. Selection for behavioural traits is considered briefly and it appears that no new principles are needed, except that careful environmental control and objective measurement present problems. 6. The results of selection for quantitative traits in micro-organisms reveal similarities to results in higher organisms in the few cases where definitive work has been carried out. 7. Work on the simulation of models by computers has not greatly advanced selection experiment theory, mainly because, with few exceptions, linkage has been ignored. 8. The existing theory on which selection experiments are based is inadequate for several reasons. It cannot predict the rate of response to selection nor the ultimate limits to selection, the nature of correlated responses to selection, nor the nature of gene segregation underlying the observed variability. 9. Strains set up from single inseminated founder females from the same population of Drosophila have been shown to differ genetically for several quantitative traits. Therefore the base population is polymorphic for genes controlling these traits. This was exploited by carrying out directional selection on lines derived from those strains showing a high incidence of scutellar chaetae. This led to far more rapid responses to selection than lines derived from strains where the incidence of scutellar chaetae was lower. 10. Ultimately, one can envisage the selection experiment as it is known today being partly replaced by the manipulation of located genes controlling quantitative traits into certain combinations.     

Factor and principal component analyses as alternatives to index selection

Summary Selections from factor and principal component analyses were compared with those from the Smith-Hazel index when selecting for several switchgrass (Panicum virgatum L.) traits. The objective of this study was to examine several alternatives to index selection. Such procedures would potentially eliminate problems of selection associated with Smith-Hazel indices, including errors in genetic parameter estimates and difficulty in assigning relative economic weights to traits. Selection was performed on 1,280 plants that were evaluated over 2 years at 1 location, in a randomized complete block design with 4 replicates. The plants were evaluated for forage yield and several forage quality traits. The comparisons of index selection with principal factor analysis, maximum-likelihood factor analysis and principal component analysis were made for three sets of traits (five traits per set) to estimate repeatability for the comparisons. Multivariate analyses were performed on both simple and genotypic correlation matrices. Comparisons were made by computing Spearman's rank correlations between selection index plant scores and scores computed from multivariate analysis and by determining the number of plants selected in common for the selection methods. Among the three multivariate analysis methods evaluated in this study, principal component analysis had the highest correlation with index selection. The high correlation for principal component analysis of simple correlation matrices indicates the potential for using this statistical method for selection purposes. This would permit the breeder to reduce field costs (e.g., time, labor, equipment) required to obtain the genetic parameter estimates necessary to construct selection indices.