A reappraisal of Bateman's classic study of intrasexual selection

Bateman's (1948) study showing greater variances in number of mates and reproductive success in male than female Drosophila melanogaster is a foundational paper in sexual selection. Here we show for the first time that his methods had flaws, including the elimination of genetic variance, sampling biases, miscalculations of fitness variances, statistical pseudo-replication, and selective presentation of data. We conclude that Bateman's results are unreliable, his conclusions are questionable, and his observed variances are similar to those expected under random mating. Despite our analysis, we do not intend this article as a criticism of Bateman; he accomplished his work without modern computational tools, and his approach was groundbreaking emphasizing the significance of fitness variance for sexual selection. However, this reanalysis has implications for what counts as evidence for sexual selection and we believe that our concerns should be of interest to contemporary students of sexual selection. We call for repetitions of Bateman's study using modern statistical and molecular methods.     

Critical Assessment of the C-Optimality Design Criteria for Estimating the Median Effective Dose in Quantal Dose-Response Curves

In this paper the properties of C-optimal designs constructed for estimating the median effective dose within the framework of two-parametric linear logistic models are critically assessed. It is well known that this design criterion which is based on the first-order variance approximation of the exact variance of the maximum likelihood estimate of the ED50 leads to a one-point design where the maximum likelihood theory breaks down. The single dose used in this design is identical with the true but unknown value of the ED50. It will be shown, that at this one-point design the asymptotic variance does not exist. A two-point design in the neighbourhood of the one-point design which is symmetrical about the ED50 and associated with a small dose-distance would be nearly optimal, but extremely nonrobust if the best guess of the ED50 differs from the true value. In this situation the asymptotic variance of the two-point design converging towards the one-point design tends to infinity. Moreover, taking in consideration, that for searching an optimal design the exact variance is of primary interest and the asymptotic variance serves only as an approximation of the exact variance, we calculate the exact variance of the estimator from balanced, symmetric 2-point designs in the neighbourhood of the limiting 1-point design for various dose distances and initial best guesses of the ED50. We compare the true variance of the estimate of the ED50 with the asymptotic variance and show that the approximations generally do not represent suitable substitutes for the exact variance even in case of unrealistically large sample sizes. Kalish (1990) proposed a criterion based on the second-order asymptotic variance of the maximum likelihood estimate of the ED50 to overcome the degenerated 1-point design as the solution of the optimization procedure. In fact, we are able to show that this variance approximation does not perform substantially better than the first–order variance. From these considerations it follows, that the C-optimality criterion is not useful in this estimation problem. Other criteria like the F-optimality should be used.     

A New Algorithm for Explicit Determination of Variance Component Estimations in Mixed Models and Mixed Classifications of Balanced ANOVA

This paper deals with the balanced case of the analysis of variance. The use of a classification function leads to an easy determination of all possible sources of variation of any mixed classification. For mixed models a new method is derived, which allows to represent explicit the ANOVA-estimations of the variance components respectively the estimation of the mean sum of squares of the fixed effects for all sources of variation. Thereby the corresponding F-quotients and the approximate confidence intervals of variance components are received in a simple way.     

RISK OF POPULATION EXTINCTION FROM FIXATION OF NEW DELETERIOUS MUTATIONS

The fixation of new deleterious mutations is analyzed for a randomly mating population of constant size with no environmental or demographic stochasticity. Mildly deleterious mutations are far more important in causing loss of fitness and eventual extinction than are lethal and semilethal mutations in populations with effective sizes, N_e, larger than a few individuals. If all mildly deleterious mutations have the same selection coefficient, s against heterozygotes and 2s against homozygotes, the mean time to extinction, , is asymptotically proportional to for 4N_es > 1. Nearly neutral mutations pose the greatest risk of extinction for stable populations, because the magnitude of selection coefficient that minimizes is about ? = 0.4/N_e. The influence of variance in selection coefficients among mutations is analyzed assuming a gamma distribution of s, with mean and variance . The mean time to extinction increases with variance in selection coefficients if is near ?, but can decrease greatly if is much larger than ?. For a given coefficient of variation of , the mean time to extinction is asymptotically proportional to for . When s is exponentially distributed, (c = 1) is asymptotically proportional to . These results in conjunction with data on the rate and magnitude of mildly deleterious mutations in Drosophila melanogaster indicate that even moderately large populations, with effective sizes on the order of N_e = 10³, may incur a substantial risk of extinction from the fixation of new mutations.     

Parent-of-origin effects cause genetic variation in pig performance traits

In order to assess the relative importance of genomic imprinting for the genetic variation of traits economically relevant for pork production, a data set containing 21 209 records from Large White pigs was analysed. A total of 33 traits for growth, carcass composition and meat quality were investigated. All traits were recorded between 1997 and 2006 at a test station in Switzerland and the pedigree included 15 747 ancestors. A model with two genetic effects for each animal was applied: the first corresponds to a paternal and the second to a maternal expression pattern of imprinted genes. The imprinting variance was estimated as the sum of both corresponding genetic variances per animal minus twice the covariance. The null hypothesis of no imprinting was tested by a restricted maximum likelihood ratio test with two degrees of freedom. Genomic imprinting significantly contributed to the genetic variance of 19 traits. The proportion of the total additive genetic variance that could be attributed to genomic imprinting was of the order between 5% and 19%.     

Natural selection and inheritance of breeding time and clutch size in the collared flycatcher

Many characteristics of organisms in free-living populations appear to be under directional selection, possess additive genetic variance, and yet show no evolutionary response to selection. Avian breeding time and clutch size are often-cited examples of such characters. We report analyses of inheritance of, and selection on, these traits in a long-term study of a wild population of the collared flycatcher Ficedula albicollis. We used mixed model analysis with REML estimation ("animal models") to make full use of the information in complex multigenerational pedigrees. Heritability of laying date, but not clutch size, was lower than that estimated previously using parent-offspring regressions, although for both traits there was evidence of substantial additive genetic variance (h2 = 0.19 and 0.29, respectively). Laying date and clutch size were negatively genetically correlated (rA = -0.41 +/- 0.09), implying that selection on one of the traits would cause a correlated response in the other, but there was little evidence to suggest that evolution of either trait would be constrained by correlations with other phenotypic characters. Analysis of selection on these traits in females revealed consistent strong directional fecundity selection for earlier breeding at the level of the phenotype (beta = -0.28 +/- 0.03), but little evidence for stabilising selection on breeding time. We found no evidence that clutch size was independently under selection. Analysis of fecundity selection on breeding values for laying date, estimated from an animal model, indicated that selection acts directly on additive genetic variance underlying breeding time (beta = -0.20 +/- 0.04), but not on clutch size (beta = 0.03 +/- 0.05). In contrast, selection on laying date via adult female survival fluctuated in sign between years, and was opposite in sign for selection on phenotypes (negative) and breeding values (positive). Our data thus suggest that any evolutionary response to selection on laying date is partially constrained by underlying life-history trade-offs, and illustrate the difficulties in using purely phenotypic measures and incomplete fitness estimates to assess evolution of life-history trade-offs. We discuss some of the difficulties associated with understanding the evolution of laying date and clutch size in natural populations.     

Dominance Genetic Variance for Traits Under Directional Selection in Drosophila serrata

In contrast to our growing understanding of patterns of additive genetic variance in single- and multi-trait combinations, the relative contribution of nonadditive genetic variance, particularly dominance variance, to multivariate phenotypes is largely unknown. While mechanisms for the evolution of dominance genetic variance have been, and to some degree remain, subject to debate, the pervasiveness of dominance is widely recognized and may play a key role in several evolutionary processes. Theoretical and empirical evidence suggests that the contribution of dominance variance to phenotypic variance may increase with the correlation between a trait and fitness; however, direct tests of this hypothesis are few. Using a multigenerational breeding design in an unmanipulated population of Drosophila serrata, we estimated additive and dominance genetic covariance matrices for multivariate wing-shape phenotypes, together with a comprehensive measure of fitness, to determine whether there is an association between directional selection and dominance variance. Fitness, a trait unequivocally under directional selection, had no detectable additive genetic variance, but significant dominance genetic variance contributing 32% of the phenotypic variance. For single and multivariate morphological traits, however, no relationship was observed between trait–fitness correlations and dominance variance. A similar proportion of additive and dominance variance was found to contribute to phenotypic variance for single traits, and double the amount of additive compared to dominance variance was found for the multivariate trait combination under directional selection. These data suggest that for many fitness components a positive association between directional selection and dominance genetic variance may not be expected.     

Comparing the Powers of the Wald-Wolfowitz and Kolmogorov-Smirnov Tests

The Wald-Wolfowitz test and the Kolmogorov-Smirnov test are two well-known tests which can be used to test for differences between two population distributions, where these distributions could differ in means, variances or shapes. This paper compares the simulated power of the Wald-Wolfowitz test to that of the Kolmogorov-Smirnov test in several situations. Differences in location only, differences in variance only, and differences in both location and variance are considered. In most cases, equal sample sizes of 10 and 20 are used.     

楸树无性系离体培养特性差异研究

对选育的5个楸树无性系(004-1、1-3、2-6、015-1、1-4)进行组织培养比较研究,以明确楸树无性系再生芽增殖和生根培养中遗传因素及外界条件的影响。结果表明:楸树不同无性系是影响瓶苗生长的主要因素,继代培养无性系间的方差分量在93.89%～98.16%,芽增殖系数、增殖芽数、芽长、叶数、茎段基部愈伤组织横向膨大、茎段基部愈伤组织纵向膨大在不同无性系间达到极显著水平;生根率、生根数和根长无性系间差异极显著,方差分量分别为92.97%、88.75%、96.25%。5个无性系生长性状以004-1表现最好,增殖系数为10.74,生根率为61.11%,移栽成活率为74.44%,无性系1-4最弱。     

Nearest neighbour adjustment and linear variance models in plant breeding trials

This paper reviews methods for nearest neighbour analysis that adjust for local trend in one dimension. Such methods are commonly used in plant breeding and variety testing. The focus is on simple differencing methods, including first differences and the Papadakis method. We discuss mixed model representations of these methods on the scale of the observed data. Modelling observed data has a number of practical advantages compared to differencing, for example the facility to conveniently compute adjusted cultivar means. Most models considered involve a linear variance-covariance structure and can be represented as state-space models. The reviewed methods and models are exemplified using three datasets.     

Effect of mass selection on the within-family genetic variance in finite populations

Summary The adequacy of an expression for the withinfamily genetic variance under pure random drift in an additive infinitesimal model was tested via simulation in populations undergoing mass selection. Two hundred or one thousand unlinked loci with two alleles at initial frequencies of 1/2 were considered. The size of the population was 100 (50 males and 50 females). Full-sib matings were carried out for 15 generations with only one male and one female chosen as parents each generation, either randomly or on an individual phenotypic value. In the unselected population, results obtained from 200 replicates were in agreement with predictions. With mass selection, within-family genetic variance was overpredicted by theory from the 12th and 4th generations for the 1,000 and 200 loci cases, respectively. Taking into account the observed change in gene frequencies in the algorithm led to a much better agreement with observed values. Results for the distribution of gene frequencies and the withinlocus genetic covariance are presented. It is concluded that the expression for the within-family genetic variance derived for pure random drift holds well for mass selection within the limits of an additive infinitesimal model.     

Analysis of lambing distribution in the Ripollesa sheep breed. II. Environmental and genetic sources of variation

Seasonal reproduction patterns are typically observed in small ruminants and are a major limitation for production efficiency in most meat- and dairy-type production systems. Indeed, selection for reduced seasonality could be an appealing strategy for the small ruminant industry worldwide, although its genetic background has been poorly analyzed. One of the main limitations relied on the availability of appropriate analytical tools to cope with the circular (i.e. year-round) pattern of lambing and kidding data. The recent development of a heteroskedastic circular mixed model provided the statistical tool to go deeply into the knowledge of seasonality in small ruminants. In this study, 26 005 lambing distribution records from 4764 Ripollesa ewes collected in 20 purebred flocks were analyzed. The model accounted for systematic (lambing interval and ewe age), permanent environmental (flock-year-season and ewe) and additive genetic sources of variation influencing both mean and dispersion pattern (i.e. heteroskedasticity). Systematic effects suggested that first-lambing ewes and short lambing intervals delayed lambing date (~30 days) and increased dispersion of the lambing period. Nevertheless, this was partially compensated by ewe age, given that youngest females tended to concentrate the lambing peak. Flock-year-season, permanent ewe and additive genetic sources of variation reached moderate variance components for direct (and residual) effects on lambing distribution, they being 0.119 (0.156), 0.092 (0.132) and 0.195 (0.170) radians², respectively. Moreover, all 95% credibility intervals were placed far from the null estimate. Covariances between direct and residual effects where high and positive for additive genetic (posterior mean, 0.814) and permanent ewe effects (posterior mean, 0.917), whereas it was not relevant for flock-year-season. Selection for direct additive genetic effects should be able to advance or delay the lambing peak, whereas selection applied on residual additive genetic effects should increase or reduce seasonality (i.e. concentrate or flatten the lambing peak). Moreover, the positive and relevant genetic covariance between direct and residual effects also suggested correlated genetic responses. As example, genetic selection for earlier lambing peaks must also reduce seasonality, whereas selection for narrower lambing seasons may originate a delay in the lambing peak. These results must be viewed as the first attempt to analyze systematic, environmental and genetic sources of variation of lambing distribution within the circular paradigm, they providing a reliable characterization of these effects within the context of an heteroskedastic model.     

Can dominance genetic variance be ignored in evolutionary quantitative genetic analyses of wild populations?

Accurately estimating genetic variance components is important for studying evolution in the wild. Empirical work on domesticated and wild outbred populations suggests that dominance genetic variance represents a substantial part of genetic variance, and theoretical work predicts that ignoring dominance can inflate estimates of additive genetic variance. Whether this issue is pervasive in natural systems is unknown, because we lack estimates of dominance variance in wild populations obtained in situ. Here, we estimate dominance and additive genetic variance, maternal variance, and other sources of nongenetic variance in eight traits measured in over 9000 wild nestlings linked through a genetically resolved pedigree. We find that dominance variance, when estimable, does not statistically differ from zero and represents a modest amount (2-36%) of genetic variance. Simulations show that (1) inferences of all variance components for an average trait are unbiased; (2) the power to detect dominance variance is low; (3) ignoring dominance can mildly inflate additive genetic variance and heritability estimates but such inflation becomes substantial when maternal effects are also ignored. These findings hence suggest that dominance is a small source of phenotypic variance in the wild and highlight the importance of proper model construction for accurately estimating evolutionary potential.     

Factor analysis models for structuring covariance matrices of additive genetic effects: a Bayesian implementation

Multivariate linear models are increasingly important in quantitative genetics. In high dimensional specifications, factor analysis (FA) may provide an avenue for structuring (co)variance matrices, thus reducing the number of parameters needed for describing (co)dispersion. We describe how FA can be used to model genetic effects in the context of a multivariate linear mixed model. An orthogonal common factor structure is used to model genetic effects under Gaussian assumption, so that the marginal likelihood is multivariate normal with a structured genetic (co)variance matrix. Under standard prior assumptions, all fully conditional distributions have closed form, and samples from the joint posterior distribution can be obtained via Gibbs sampling. The model and the algorithm developed for its Bayesian implementation were used to describe five repeated records of milk yield in dairy cattle, and a one common FA model was compared with a standard multiple trait model. The Bayesian Information Criterion favored the FA model.     

A Generalization of the GMANOVA-Model

It is shown that in some experimental designs the MANOVA- and the GMANOVA-model are too restrictive either to yield all hypothesis tests of interest or to reflect all known features of the design. An extension of these models is derived by relating the response vectors with the unknown model parameters by linear equations which may be completely different for each of the p components of the response vector and for each of the n independent vectors. For situations, in which a Wishart-distributed estimator for the underlying common covariance matrix is attainable, a test for any s-dimensional linear hypothesis on the model parameters is derived.     

菊花离体快速繁殖的研究

用MS基本培养基附加植物生长调节剂,进行了菊花离体快速繁殖试验。以幼叶为外植体在附加不同生长素的培寿基上诱导愈伤组织后进行分化培养。结果表明,2.OppmNAA上的愈伤组织诱导率最高,0.5ppmBA上的不定芽分化率最高。用不同浓度NAA与BA的组合进行分化试验,其方差分析结果说明0.1ppmNAA+0.5ppmBA是分化培养的最佳激素组合。无根苗在MS无激素培寿基上诱导生根,28天后移栽成活率达到85％。     

Genetic parameters for test day milk yields of first lactation Holstein cows by random regression models

Covariance components for test day milk yield using 263 390 first lactation records of 32 448 Holstein cows were estimated using random regression animal models by restricted maximum likelihood. Three functions were used to adjust the lactation curve: the five-parameter logarithmic Ali and Schaeffer function (AS), the three-parameter exponential Wilmink function in its standard form (W) and in a modified form (W*), by reducing the range of covariate, and the combination of Legendre polynomial and W (LEG+W). Heterogeneous residual variance (RV) for different classes (4 and 29) of days in milk was considered in adjusting the functions. Estimates of RV were quite similar, rating from 4.15 to 5.29 kg². Heritability estimates for AS (0.29 to 0.42), LEG+W (0.28 to 0.42) and W* (0.33 to 0.40) were similar, but heritability estimates used W (0.25 to 0.65) were highest than those estimated by the other functions, particularly at the end of lactation. Genetic correlations between milk yield on consecutive test days were close to unity, but decreased as the interval between test days increased. The AS function with homogeneous RV model had the best fit among those evaluated.     

QTL mapping in outbred half-sib families using Bayesian model selection

In this article, we propose a model selection method, the Bayesian composite model space approach, to map quantitative trait loci (QTL) in a half-sib population for continuous and binary traits. In our method, the identity-by-descent-based variance component model is used. To demonstrate the performance of this model, the method was applied to map QTL underlying production traits on BTA6 in a Chinese half-sib dairy cattle population. A total of four QTLs were detected, whereas only one QTL was identified using the traditional least square (LS) method. We also conducted two simulation experiments to validate the efficiency of our method. The results suggest that the proposed method based on a multiple-QTL model is efficient in mapping multiple QTL for an outbred half-sib population and is more powerful than the LS method based on a single-QTL model.     

On the Probability of a Negative Estimator of Heteroscedasticity in the Random Coefficient Model

In the estimation of a linear regression model with random coefficients, sometimes negative estimates of variances of random coefficients are obtained–an undesirable feature. In this paper we have obtained the asymptotic bounds of the probability of obtaining negative estimators. A simple illustration is also provided for the purpose.