Toward reconciling inferences concerning genetic variation in senescence in Drosophila melanogaster.

Standard models for senescence predict an increase in the additive genetic variance for log mortality rate late in the life cycle. Variance component analysis of age-specific mortality rates of related cohorts is problematic. The actual mortality rates are not observable and can be estimated only crudely at early ages when few individuals are dying and at late ages when most are dead. Therefore, standard quantitative genetic analysis techniques cannot be applied with confidence. We present a novel and rigorous analysis that treats the mortality rates as missing data following two different parametric senescence models. Two recent studies of Drosophila melanogaster, the original analyses of which reached different conclusions, are reanalyzed here. The two-parameter Gompertz model assumes that mortality rates increase exponentially with age. A related but more complex three-parameter logistic model allows for subsequent leveling off in mortality rates at late ages. We find that while additive variance for mortality rates increases for late ages under the Gompertz model, it declines under the logistic model. The results from the two studies are similar, with differences attributable to differences between the experiments.     

Genetic evaluation and selection response for growth in meat-type quail through random regression models using B-spline functions and Legendre polynomials

The objective was to estimate (co)variance functions using random regression models (RRM) with Legendre polynomials, B-spline function and multi-trait models aimed at evaluating genetic parameters of growth traits in meat-type quail. A database containing the complete pedigree information of 7000 meat-type quail was utilized. The models included the fixed effects of contemporary group and generation. Direct additive genetic and permanent environmental effects, considered as random, were modeled using B-spline functions considering quadratic and cubic polynomials for each individual segment, and Legendre polynomials for age. Residual variances were grouped in four age classes. Direct additive genetic and permanent environmental effects were modeled using 2 to 4 segments and were modeled by Legendre polynomial with orders of fit ranging from 2 to 4. The model with quadratic B-spline adjustment, using four segments for direct additive genetic and permanent environmental effects, was the most appropriate and parsimonious to describe the covariance structure of the data. The RRM using Legendre polynomials presented an underestimation of the residual variance. Lesser heritability estimates were observed for multi-trait models in comparison with RRM for the evaluated ages. In general, the genetic correlations between measures of BW from hatching to 35 days of age decreased as the range between the evaluated ages increased. Genetic trend for BW was positive and significant along the selection generations. The genetic response to selection for BW in the evaluated ages presented greater values for RRM compared with multi-trait models. In summary, RRM using B-spline functions with four residual variance classes and segments were the best fit for genetic evaluation of growth traits in meat-type quail. In conclusion, RRM should be considered in genetic evaluation of breeding programs.     

Quantitative genetic tests of recent senescence theory: age-specific mortality and male fertility in Drosophila melanogaster

Quantitative genetic models of aging predict that additive genetic variance for fitness components should increase with age. However, recent studies have found that at very late ages, the genetic variance components decline. This decline may be due to an age-related drop in reproductive effort. If genetic variance in reproductive effort affects the genetic variance in mortality, the decline in reproductive effort at late ages should lead to a decrease in the genetic variance in mortality. To test this, we carried out a large-scale quantitative genetic analysis of age-specific mortality and fertility in virgin male Drosophila melanogaster. As in earlier studies, we found that the additive variance for age-specific mortality and fertility declined at late ages. Also, recent theoretical developments provide new predictions to distinguish between the mutation accumulation (MA) and antagonistic pleiotropy (AP) models of senescence. The deleterious effects of inbreeding are expected to increase with age under MA, but not under AP. This prediction was supported for both age-specific mortality and male fertility. Under AP, the ratio of dominance to additive variance is expected to decline with age. This predicition, too, was supported by the data analyzed here. Taken together, these analyses provide support for both the models playing a role in the aging process. We argue that the time has come to move beyond a simple comparison of these genetic models, and to think more deeply about the evolutionary causes and consequences of senescence.     

Multivariate character process models for the analysis of two or more correlated function-valued traits

Various methods, including random regression, structured antedependence models, and character process models, have been proposed for the genetic analysis of longitudinal data and other function-valued traits. For univariate problems, the character process models have been shown to perform well in comparison to alternative methods. The aim of this article is to present an extension of these models to the simultaneous analysis of two or more correlated function-valued traits. Analytical forms for stationary and nonstationary cross-covariance functions are studied. Comparisons with the other approaches are presented in a simulation study and in an example of a bivariate analysis of genetic covariance in age-specific fecundity and mortality in Drosophila. As in the univariate case, bivariate character process models with an exponential correlation were found to be quite close to first-order structured antedependence models. The simulation study showed that the choice of the most appropriate methodology is highly dependent on the covariance structure of the data. The bivariate character process approach proved to be able to deal with quite complex nonstationary and nonsymmetric cross-correlation structures and was found to be the most appropriate for the real data example of the fruit fly Drosophila melanogaster.     

Ontogenetic patterns in heritable variation for body size: using random regression models in a wild ungulate population

Body size is an important determinant of fitness in many organisms. While size will typically change over the lifetime of an individual, heritable components of phenotypic variance may also show ontogenetic variation. We estimated genetic (additive and maternal) and environmental covariance structures for a size trait (June weight) measured over the first 5 years of life in a natural population of bighorn sheep Ovis canadensis. We also assessed the utility of random regression models for estimating these structures. Additive genetic variance was found for June weight, with heritability increasing over ontogeny because of declining environmental variance. This pattern, mirrored at the phenotypic level, likely reflects viability selection acting on early size traits. Maternal genetic effects were significant at ages 0 and 1, having important evolutionary implications for early weight, but declined with age being negligible by age 2. Strong positive genetic correlations between age-specific traits suggest that selection on June weight at any age will likely induce positively correlated responses across ontogeny. Random regression modeling yielded similar results to traditional methods. However, by facilitating more efficient data use where phenotypic sampling is incomplete, random regression should allow better estimation of genetic (co)variances for size and growth traits in natural populations.     

Demographic variance in heterogeneous populations: matrix models and sensitivity analysis

The demographic consequences of stochasticity in processes such as survival and reproduction are modulated by the heterogeneity within the population. Therefore, to study effects of stochasticity on population growth and extinction risk, it is critical to use structured population models in which the most important sources of heterogeneity (e.g. age, size, developmental stage) are incorporated as i‐state variables. Demographic stochasticity in heterogeneous populations has often been studied using one of two approaches: multitype branching processes and diffusion approximations. Here, we link these approaches, through the demographic stochasticity in age‐ or stage‐structured matrix population models. We derive the demographic variance, σ²_d, which measures the per capita contribution to the variance in population growth increment, and we show how it can be decomposed into contributions from transition probabilities and fertility across ages or stages. Furthermore, using matrix calculus we derive the sensitivity of σ²_d to age‐ or stage‐specific mortality and fertility. We apply the methods to an extensive set of data from age‐classified human populations (long‐term time‐series for Sweden, Japan and the Netherlands; two hunter–gatherer populations, and the high‐fertility Hutterites), and to a size‐classified population of the herbaceous plant Calathea ovandensis. For the human populations our analysis reveals substantial temporal changes in the demographic variance as well as its main components across age. These new methods provide a powerful approach for calculating the demographic variance for any structured model, and for analyzing its main components and sensitivities. This will make possible new analyses of demographic variance across different kinds of heterogeneity in different life cycles, which will in turn improve our understanding of mechanisms underpinning extinction risk and other important biological outcomes.     

Estimating Modifying Effect of Age on Genetic and Environmental Variance Components in Twin Models

Twin studies have been adopted for decades to disentangle the relative genetic and environmental contributions for a wide range of traits. However, heritability estimation based on the classical twin models does not take into account dynamic behavior of the variance components over age. Varying variance of the genetic component over age can imply the existence of gene–environment (G × E) interactions that general genome-wide association studies (GWAS) fail to capture, which may lead to the inconsistency of heritability estimates between twin design and GWAS. Existing parametric G × E interaction models for twin studies are limited by assuming a linear or quadratic form of the variance curves with respect to a moderator that can, however, be overly restricted in reality. Here we propose spline-based approaches to explore the variance curves of the genetic and environmental components. We choose the additive genetic, common, and unique environmental variance components (ACE) model as the starting point. We treat the component variances as variance functions with respect to age modeled by B-splines or P-splines. We develop an empirical Bayes method to estimate the variance curves together with their confidence bands and provide an R package for public use. Our simulations demonstrate that the proposed methods accurately capture dynamic behavior of the component variances in terms of mean square errors with a data set of >10,000 twin pairs. Using the proposed methods as an alternative and major extension to the classical twin models, our analyses with a large-scale Finnish twin data set (19,510 MZ twins and 27,312 DZ same-sex twins) discover that the variances of the A, C, and E components for body mass index (BMI) change substantially across life span in different patterns and the heritability of BMI drops to ∼50% after middle age. The results further indicate that the decline of heritability is due to increasing unique environmental variance, which provides more insights into age-specific heritability of BMI and evidence of G × E interactions. These findings highlight the fundamental importance and implication of the proposed models in facilitating twin studies to investigate the heritability specific to age and other modifying factors.     

Race differences in pubic symphyseal aging patterns in the male

A well-documented multiracial sample of 704 male pubic bones allows for rigorous testing for racial differences in pubic symphyseal metamorphosis. The relationship between estimated age (using a modified Todd six-stage system) and age is examined as a function of race (White, Black, Mexican). One set of analyses incorporates linear regression models, while a second set does not impose such structure on the relationship. The latter analyses incorporate analysis of variance and related procedures. Significant differences in age are found across racial groups; it is seen that Blacks and Mexicans with advanced pubic symphyseal patterns tend to have lower ages than Whites. We do not address the question of causality, which may involve genetic factors and/or environmental variables such as diet, alcoholism, or drug abuse.     

Accelerating the domestication of trees using genomic selection: accuracy of prediction models across ages and environments

? Genomic selection is increasingly considered vital to accelerate genetic improvement. However, it is unknown how accurate genomic selection prediction models remain when used across environments and ages. This knowledge is critical for breeders to apply this strategy in genetic improvement. ? Here, we evaluated the utility of genomic selection in a Pinus taeda population of c. 800 individuals clonally replicated and grown on four sites, and genotyped for 4825 single-nucleotide polymorphism (SNP) markers. Prediction models were estimated for diameter and height at multiple ages using genomic random regression best linear unbiased predictor (BLUP). ? Accuracies of prediction models ranged from 0.65 to 0.75 for diameter, and 0.63 to 0.74 for height. The selection efficiency per unit time was estimated as 53-112% higher using genomic selection compared with phenotypic selection, assuming a reduction of 50% in the breeding cycle. Accuracies remained high across environments as long as they were used within the same breeding zone. However, models generated at early ages did not perform well to predict phenotypes at age 6 yr. ? These results demonstrate the feasibility and remarkable gain that can be achieved by incorporating genomic selection in breeding programs, as long as models are used at the relevant selection age and within the breeding zone in which they were estimated.     

The influence of environmentally induced heterogeneity on age-specific genetic variance for mortality rates

Using parametric models that describe the increase in mortality rates with age, we demonstrate that environmentally induced heterogeneity among genetically identical individuals is sufficient to generate biased estimates of age-specific genetic variance. Although the magnitude of the bias may change with age, one general trend emerges: the true genetic variance at the oldest ages is likely to be dramatically underestimated. Our results are robust to different manifestations of heterogeneity and suggest that such a bias is a general feature of these models. We note that age-dependent estimates of genetic variance for characters that are correlated with mortality (either genetically or environmentally) can be expected to be similarly affected. The results are independent of sample size and suggest that the bias may be more widespread in the literature than is currently appreciated. Our results are discussed with reference to existing data on mortality variance in Drosophila melanogaster.     

Random regression analyses using B-spline functions to model growth of Nellore cattle

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.     

Structured antedependence models for genetic analysis of repeated measures on multiple quantitative traits

Simultaneous analysis of correlated traits that change with time is an important issue in genetic analyses. Several methodologies have already been proposed for the genetic analysis of longitudinal data on single traits, in particular random regression and character process models. Although the latter proved, in most cases, to compare favourably to alternative approaches for analysis of single function-valued traits, they do not allow a straightforward extension to the multivariate case. In this paper, another methodology (structured antedependence models) is proposed, and methods are derived for the genetic analysis of two or more correlated function-valued traits. Multivariate analyses are presented of fertility and mortality in Drosophila and of milk, fat and protein yields in dairy cattle. These models offer a substantial flexibility for the correlation structure, even in the case of complex non-stationary patterns, and perform better than multivariate random regression models, with fewer parameters.     

An exploration of the genetic and environmental etiology of heart rate in infancy and middle childhood.

Heart rate was recorded on 210 MZ and 174 DZ same sex twin pairs participating in the MacArthur Longitudinal Twin Study (MALTS) at age 14, 20, 24, 36 months and 7 years. Heart rate was monitored in the laboratory at all ages. At ages 14 to 36 months, heart rate was monitored prior to a set of cognitive tasks. At age 7 years heart rate was recorded during a mood-eliciting videotaped presentation. At this age only heart rate monitored during neutral portions of the presentation were used. Mean heart rate declines substantially across this age range, but is similar in boys and girls and for MZ and DZ twins at each age. Heart rate is moderately correlated across all time points suggesting that individual differences in heart rate are relatively stable over this age range. Multivariate genetic and environmental models were fitted to the raw data. In general, genetic factors contribute to the stability of individual differences over time. Shared and non-shared environment factors tended to be occasion specific, with non-shared environment contributing substantially to the individual variation at each age. Shared environment and non-shared environment also contributed a modicum to the stability across time. Thus, individual differences in resting heart rate is a relatively stable, heritable trait from infancy to early childhood.     

On the maintenance of genetic variation: global analysis of Kimura's continuum-of-alleles model

Methods of functional analysis are applied to provide an exact mathematical analysis of Kimura's continuum-of-alleles model. By an approximate analysis, Kimura obtained the result that the equilibrium distribution of allelic effects determining a quantitative character is Gaussian if fitness decreases quadratically from the optimum and if production of new mutants follows a Gaussian density. Lande extended this model considerably and proposed that high levels of genetic variation can be maintained by mutation even when there is strong stabilizing selection. This hypothesis has been questioned recently by Turelli, who published analyses and computer simulations of some multiallele models, approximating the continuum-of-alleles model, and reviewed relevant data. He found that the Kimura and Lande predictions overestimate the amount of equilibrium variance considerably if selection is not extremely weak or mutation rate not extremely high. The present analysis provides the first proof that in Kimura's model an equilibrium in fact exists and, moreover, that it is globally stable. Finally, using methods from quantum mechanics, estimates of the exact equilibrium variance are derived which are in best accordance with Turelli's results. This shows that continuum-of-alleles models may be excellent approximations to multiallele models, if analysed appropriately.     

The evolution of age-specific mortality rates in Drosophila melanogaster: genetic divergence among unselected lines.

Age-specific effects of spontaneous mutations on mortality rates in Drosophila are inferred from three large demographic experiments. Data were collected from inbred lines that were allowed to accumulate spontaneous mutations for 10, 19, and 47 generations. Estimates of age-specific mutational variance for mortality were based on data from all three experiments, totalling approximately 225,000 flies, using a model developed for genetic analysis of age-dependent traits (the character process model). Both within- and among-generation analyses suggest that the input of genetic variance is greater for early life mortality rates than for mortality at older ages. In females, age-specific mutational variances ranged over an order of magnitude from 5.96 x 10(-3) at 2 wk posteclosion to 0.02 x 10(-3) at 7 wk. The male data show a similar pattern. Age-specific genetic variances were substantially less at generation 47 than at generation 19-an unexplained observation that is likely due to block effects. Mutational correlations among mortality rates at different ages tend to increase with the accumulation of new mutations. Comparison of the mutation-accumulation lines at generations 19 and 47 with their respective control lines suggests little age-specific mutational bias.     

Data and theory point to mainly additive genetic variance for complex traits

The relative proportion of additive and non-additive variation for complex traits is important in evolutionary biology, medicine, and agriculture. We address a long-standing controversy and paradox about the contribution of non-additive genetic variation, namely that knowledge about biological pathways and gene networks imply that epistasis is important. Yet empirical data across a range of traits and species imply that most genetic variance is additive. We evaluate the evidence from empirical studies of genetic variance components and find that additive variance typically accounts for over half, and often close to 100%, of the total genetic variance. We present new theoretical results, based upon the distribution of allele frequencies under neutral and other population genetic models, that show why this is the case even if there are non-additive effects at the level of gene action. We conclude that interactions at the level of genes are not likely to generate much interaction at the level of variance.     

Do the genetic or environmental determinants of anxiety and depression change with age? A longitudinal study of Australian twins.

Because the determinants of anxiety and depression in late adolescence and early adulthood may differ from those in later life, we investigated the temporal stability and magnitude of genetic and environmental correlates of symptoms of anxiety and depression across the life span. Data were collected from a population-based Australian sample of 4364 complete twin pairs and 777 singletons aged 20 to 96 years who were followed-up over three studies between 1980 and 1996. Each study contained the 14-item self-report DSSI/sAD scale which was used to measure recently experienced symptoms of anxiety and depression. Symptom scores were then divided and assigned to age intervals according to each subject's age at time of participation. We fitted genetic simplex models to take into account the longitudinal nature of the data. For male anxiety and depression, the best fitting simplex models comprised a single genetic innovation at age 20 which was transmitted, and explained genetic variation in anxiety and depression at ages 30, 40, 50 and 60. Most of the lifetime genetic variation in female anxiety and depression could also be explained by innovations at age 20 which were transmitted to all other ages; however, there were also smaller age-dependent genetic innovations at 30 for anxiety and at 40 and 70 for depression. Although the genetic determinants of anxiety and depression appear relatively stable across the lifespan for males and females, there is some evidence to support additional mid-life and late age gene action in females for depression. The fact that midlife onset for anxiety occurs one decade before depression is also consistent with a causal relationship (anxiety leading to depression) between these conditions. These findings have significance for large scale depression prevention projects.     

作物品种间杂种优势遗传分析的新方法

本文提出了分析双列杂交试验资料的两个遗传模型。第一个模型包括加性、显性和母体效应;第二个模型只包括简单的加性和显性效应。还介绍了分析杂种优势、估算遗传方差分量以及预测遗传效应值的相应统计分析方法。用所介绍的遗传模型和分析方法以及常用的Griffing配合力分析方法,分析了棉花6个品种双列杂交的产量性状,并进一步比较了不同方法的分析结果。采用本文所介绍的遗传模型和分析方法,可以克服用Griffing的配合力模型及其方法分析杂种优势和配合力遗传表现所存在的局限性。     

The best in all possible worlds? A quantitative genetic study of geographic variation in the meadow vole,Microtus pennsylvanicus

The meadow vole, Microtus pennsylvanicus , is the most widely distributed Microtus species in North America. Across its range, it shows marked demographic differences, experiences a large range of climatic conditions, and varies considerably in body size and life-history characteristics. To study the genetic basis of the geographic variation in size and life history of this species, we subjected three populations, one from central Canada and two from eastern Canada, to quantitative genetic analysis in the lab. We studied the variance and covariance of several size and growth variables as well as age and size at maturity by means of population crosses, full-sib analysis, and parent-offspring regressions. We found that the phenotypic differences among these populations are almost entirely due to environmental effects. However, within populations, additive genetic and maternal effects explain most of the variation. We discuss possible explanations for the lack of genetic differences among the populations and speculate that a similar reaction norm is maintained in all populations through heterogeneity in the temporal or spatial environment that the populations experience. The heterogeneity may be mediated through population density fluctuations, climatic variation, or variation in site productivity. Thus, we hypothesize that M. pennsylvanicus has evolved to be the best in all possible worlds rather than in one actual world. This study highlights the crucial importance of maternal and environmental effects on the size, growth, and life history of small rodents.     

Selecting an appropriate genetic evaluation model for selection in a developing dairy sector

This study aimed to identify genetic evaluation models (GEM) to accurately select cattle for milk production when only limited data are available. It is based on a data set from the Pakistani Sahiwal progeny testing programme which includes records from five government herds, each consisting of 100 to 350 animals, with lactation records dating back to 1968. Different types of GEM were compared, namely: (1) multivariate v. repeatability model when using the first three lactations, (2) an animal v. a sire model, (3) different fixed effects models to account for effects such as herd, year and season; and (4) fitting a model with genetic parameters fixed v. estimating the genetic parameters as part of the model fitting process. Two methods were used for the comparison of models. The first method used simulated data based on the Pakistani progeny testing system and compared estimated breeding values with true breeding values. The second method used cross-validation to determine the best model in subsets of actual Australian herd-recorded data. Subsets were chosen to reflect the Pakistani data in terms of herd size and number of herds. Based on the simulation and the cross-validation method, the multivariate animal model using fixed genetic parameters was generally the superior GEM, but problems arise in determining suitable values for fixing the parameters. Using mean square error of prediction, the best fixed effects structure could not be conclusively determined. The simulation method indicated the simplest fixed effects structure to be superior whereas in contrast, the cross-validation method on actual data concluded that the most complex one was the best. In conclusion it is difficult to propose a universally best GEM that can be used in any data set of this size. However, some general recommendations are that it is more appropriate to estimate the genetic parameters when evaluating for selection purposes, the animal model was superior to the sire model and that in the Pakistani situation the repeatability model is more suitable than a multivariate.