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Trait Mean (trait + mean)
Selected AbstractsEFFECTS OF GENETIC DRIFT ON VARIANCE COMPONENTS UNDER A GENERAL MODEL OF EPISTASISEVOLUTION, Issue 10 2004N.H. Barton Abstract We analyze the changes in the mean and variance components of a quantitative trait caused by changes in allele frequencies, concentrating on the effects of genetic drift. We use a general representation of epistasis and dominance that allows an arbitrary relation between genotype and phenotype for any number of diallelic loci. We assume initial and final Hardy-Weinberg and linkage equilibrium in our analyses of drift-induced changes. Random drift generates transient linkage disequilibria that cause correlations between allele frequency fluctuations at different loci. However, we show that these have negligible effects, at least for interactions among small numbers of loci. Our analyses are based on diffusion approximations that summarize the effects of drift in terms of F, the inbreeding coefficient, interpreted as the expected proportional decrease in heterozygosity at each locus. For haploids, the variance of the trait mean after a population bottleneck is var(,z,) =where n is the number of loci contributing to the trait variance, VA(1)=VA is the additive genetic variance, and VA(k) is the kth-order additive epistatic variance. The expected additive genetic variance after the bottleneck, denoted (V*A), is closely related to var(,z,); (V*A) (1 ,F)Thus, epistasis inflates the expected additive variance above VA(1 ,F), the expectation under additivity. For haploids (and diploids without dominance), the expected value of every variance component is inflated by the existence of higher order interactions (e.g., third-order epistasis inflates (V*AA)). This is not true in general with diploidy, because dominance alone can reduce (V*A) below VA(1 ,F) (e.g., when dominant alleles are rare). Without dominance, diploidy produces simple expressions: var(,z,)==1 (2F) kVA(k) and (V*A) = (1 ,F)k(2F)k-1VA(k) With dominance (and even without epistasis), var(,z,)and (V*A) no longer depend solely on the variance components in the base population. For small F, the expected additive variance simplifies to (V*A)(1 ,F) VA+ 4FVAA+2FVD+2FCAD, where CAD is a sum of two terms describing covariances between additive effects and dominance and additive × dominance interactions. Whether population bottlenecks lead to expected increases in additive variance depends primarily on the ratio of nonadditive to additive genetic variance in the base population, but dominance precludes simple predictions based solely on variance components. We illustrate these results using a model in which genotypic values are drawn at random, allowing extreme and erratic epistatic interactions. Although our analyses clarify the conditions under which drift is expected to increase VA, we question the evolutionary importance of such increases. [source] COMPARING STRENGTHS OF DIRECTIONAL SELECTION: HOW STRONG IS STRONG?EVOLUTION, Issue 10 2004Joe Hereford Abstract The fundamental equation in evolutionary quantitative genetics, the Lande equation, describes the response to directional selection as a product of the additive genetic variance and the selection gradient of trait value on relative fitness. Comparisons of both genetic variances and selection gradients across traits or populations require standardization, as both are scale dependent. The Lande equation can be standardized in two ways. Standardizing by the variance of the selected trait yields the response in units of standard deviation as the product of the heritability and the variance-standardized selection gradient. This standardization conflates selection and variation because the phenotypic variance is a function of the genetic variance. Alternatively, one can standardize the Lande equation using the trait mean, yielding the proportional response to selection as the product of the squared coefficient of additive genetic variance and the mean-standardized selection gradient. Mean-standardized selection gradients are particularly useful for summarizing the strength of selection because the mean-standardized gradient for fitness itself is one, a convenient benchmark for strong selection. We review published estimates of directional selection in natural populations using mean-standardized selection gradients. Only 38 published studies provided all the necessary information for calculation of mean-standardized gradients. The median absolute value of multivariate mean-standardized gradients shows that selection is on average 54% as strong as selection on fitness. Correcting for the upward bias introduced by taking absolute values lowers the median to 31%, still very strong selection. Such large estimates clearly cannot be representative of selection on all traits. Some possible sources of overestimation of the strength of selection include confounding environmental and genotypic effects on fitness, the use of fitness components as proxies for fitness, and biases in publication or choice of traits to study. [source] Functional trait variation and sampling strategies in species-rich plant communitiesFUNCTIONAL ECOLOGY, Issue 1 2010Christopher Baraloto Summary 1. ,Despite considerable interest in the application of plant functional traits to questions of community assembly and ecosystem structure and function, there is no consensus on the appropriateness of sampling designs to obtain plot-level estimates in diverse plant communities. 2. ,We measured 10 plant functional traits describing leaf and stem morphology and ecophysiology for all trees in nine 1-ha plots in terra firme lowland tropical rain forests of French Guiana (N = 4709). 3. ,We calculated, by simulation, the mean and variance in trait values for each plot and each trait expected under seven sampling methods and a range of sampling intensities. Simulated sampling methods included a variety of spatial designs, as well as the application of existing data base values to all individuals of a given species. 4. ,For each trait in each plot, we defined a performance index for each sampling design as the proportion of resampling events that resulted in observed means within 5% of the true plot mean, and observed variance within 20% of the true plot variance. 5. ,The relative performance of sampling designs was consistent for estimations of means and variances. Data base use had consistently poor performance for most traits across all plots, whereas sampling one individual per species per plot resulted in relatively high performance. We found few differences among different spatial sampling strategies; however, for a given strategy, increased intensity of sampling resulted in markedly improved accuracy in estimates of trait mean and variance. 6. ,We also calculated the financial cost of each sampling design based on data from our ,every individual per plot' strategy and estimated the sampling and botanical effort required. The relative performance of designs was strongly positively correlated with relative financial cost, suggesting that sampling investment returns are relatively constant. 7. ,Our results suggest that trait sampling for many objectives in species-rich plant communities may require the considerable effort of sampling at least one individual of each species in each plot, and that investment in complete sampling, though great, may be worthwhile for at least some traits. [source] Longitudinal data analysis in pedigree studiesGENETIC EPIDEMIOLOGY, Issue S1 2003W. James Gauderman Abstract Longitudinal family studies provide a valuable resource for investigating genetic and environmental factors that influence long-term averages and changes over time in a complex trait. This paper summarizes 13 contributions to Genetic Analysis Workshop 13, which include a wide range of methods for genetic analysis of longitudinal data in families. The methods can be grouped into two basic approaches: 1) two-step modeling, in which repeated observations are first reduced to one summary statistic per subject (e.g., a mean or slope), after which this statistic is used in a standard genetic analysis, or 2) joint modeling, in which genetic and longitudinal model parameters are estimated simultaneously in a single analysis. In applications to Framingham Heart Study data, contributors collectively reported evidence for genes that affected trait mean on chromosomes 1, 2, 3, 5, 8, 9, 10, 13, and 17, but most did not find genes affecting slope. Applications to simulated data suggested that even for a gene that only affected slope, use of a mean-type statistic could provide greater power than a slope-type statistic for detecting that gene. We report on the results of a small experiment that sheds some light on this apparently paradoxical finding, and indicate how one might form a more powerful test for finding a slope-affecting gene. Several areas for future research are discussed. Genet Epidemiol 25 (Suppl. 1):S18,S28, 2003. © 2003 Wiley-Liss, Inc. [source] |