The danger of applying the breeder's equation in observational studies of natural populations

The breeder's equation, which predicts evolutionary change when a phenotypic covariance exists between a heritable trait and fitness, has provided a key conceptual framework for studies of adaptive microevolution in nature. However, its application requires strong assumptions to be made about the causation of fitness variation. In its univariate form, the breeder's equation assumes that the trait of interest is not correlated with other traits having causal effects on fitness. In its multivariate form, the validity of predicted change rests on the assumption that all such correlated traits have been measured and incorporated into the analysis. Here, we (i) highlight why these assumptions are likely to be seriously violated in studies of natural, rather than artificial, selection and (ii) advocate wider use of the Robertson–Price identity as a more robust, and less assumption‐laden, alternative to the breeder's equation for applications in evolutionary ecology.     

COMPARING STRENGTHS OF DIRECTIONAL SELECTION: HOW STRONG IS STRONG?

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.     

NATURAL HERITABILITIES: CAN THEY BE RELIABLY ESTIMATED IN THE LABORATORY?

The validity of the assumption, that laboratory estimates of heritabilities will tend to overestimate natural heritabilities, due to a reduction in environmental variability and thus the phenotypic variance of traits, is examined. One hundred sixty-five field estimates of narrow sense heritabilities derived from the literature are compared with 189 estimates from laboratory studies on wild, outbred animal populations derived from the data set of Mousseau and Roff. The results indicate that 84% of field heritabilities are significantly different from zero and that for morphological, behavioral, and life-history traits there are no significant differences between laboratory and field estimates of heritability. Unexpectedly, mean heritabilities for morphological and life-history traits are actually higher in the field than in the lab. Twenty-two cases were found for which both laboratory and natural heritabilities had been estimated on the same traits. For this subset of the data, laboratory heritabilities tended to be higher than field estimates, but the difference was not significant. Also, the correlation between lab and field estimates was high (r = 0.6, P < 0.001), and the regression slope did not differ significantly from one. The major implications of this study are that laboratory estimates of heritability should generally provide reasonable estimations of both the magnitude and the significance of heritabilities in nature.     

Estimating evolutionary parameters when viability selection is operating

Some individuals die before a trait is measured or expressed (the invisible fraction), and some relevant traits are not measured in any individual (missing traits). This paper discusses how these concepts can be cast in terms of missing data problems from statistics. Using missing data theory, I show formally the conditions under which a valid evolutionary inference is possible when the invisible fraction and/or missing traits are ignored. These conditions are restrictive and unlikely to be met in even the most comprehensive long-term studies. When these conditions are not met, many selection and quantitative genetic parameters cannot be estimated accurately unless the missing data process is explicitly modelled. Surprisingly, this does not seem to have been attempted in evolutionary biology. In the case of the invisible fraction, viability selection and the missing data process are often intimately linked. In such cases, models used in survival analysis can be extended to provide a flexible and justified model of the missing data mechanism. Although missing traits pose a more difficult problem, important biological parameters can still be estimated without bias when appropriate techniques are used. This is in contrast to current methods which have large biases and poor precision. Generally, the quantitative genetic approach is shown to be superior to phenotypic studies of selection when invisible fractions or missing traits exist because part of the missing information can be recovered from relatives.     

EVOLUTIONARY ECOLOGY OF DATURA STRAMONIUM L. IN CENTRAL MEXICO: NATURAL SELECTION FOR RESISTANCE TO HERBIVOROUS INSECTS

It has been assumed that herbivores constitute a selective agent for the evolution of plant resistance. However, few studies have tested this hypothesis. In this study, we look at the annual weed Datura stramonium for evidence of current natural selection for resistance to herbivorous insects. Paternal half-sib families obtained through controlled crosses were exposed to herbivores under natural conditions. The plants were damaged by two folivorous insects: the tobacco flea beetle Epitrix parvula and the grasshopper Sphenarium purpurascens. Selection was estimated using a multiple-regression analysis of plant size and of damage by the two herbivores on plant fitness measured as fruit production for both individual phenotypes and family breeding values (genetic analysis). Directional phenotypic selection was detected for both larger plant size and lower resistance to the flea beetles, whereas stabilizing phenotypic selection was revealed for resistance to S. purpurascens. However, performing the same analyses on the breeding values of the characters revealed directional and stabilizing selection only for plant size. Thus, no agreement existed between the results of the two types of analyses, nor was there any detectable potential for genetic change in the studied population because of selection on herbivore resistance. The narrow-sense heritability of every trait studied was small (all <0.1) and not different from zero. The potential for evolutionary response to natural selection for higher resistance to herbivores in the studied population of D. stramonium is probably limited by lack of genetic variation. Natural selection acts on phenotypes, and the detection of phenotypic selection on resistance to herbivores confirms their ecological importance in determining plant fitness. However, evolutionary inferences based solely on phenotypic selection analyses must be interpreted with caution.     

数量遗传学理论框架下的进化生态学研究：以动物模型的运用为例

目前,生态学家越来越关注深入的生物学问题,例如,1)理解生态和进化过程的互作和关系;2)种群中一个重要的表型特征,受遗传基因影响多大?即其可遗传程度,表示该性状的进化潜能;3)基因是怎样影响表型性状,及其对应的个体适合度以及种群动态?4)决定多个重要表型性状的基因之间关系和互作如何?随着生物统计软件尤其是线性混合模型的发展,结合经典数量遗传学的理论,发展出了针对上述问题的动物模型(Animal Model),使得我们可以对野外种群进行上述研究。本文首先介绍了经典数量遗传学的重要概念,随后在其理论框架下,举例介绍了动物模型的操作和使用,最后探讨和展望了利用数量遗传学方法进行进化生态学研究的前景。     

QUANTITATIVE GENETICS OF BRYOZOAN PHENOTYPIC EVOLUTION. II. ANALYSIS OF SELECTION AND RANDOM CHANGE IN FOSSIL SPECIES USING RECONSTRUCTED GENETIC PARAMETERS

The roles of natural selection and random genetic change in the punctuated phenotypic evolution of eight Miocene-Pliocene tropical American species of the cheilostome bryozoan Metrarabdotos are analyzed by quantitative genetic methods. Trait heritabilities and genetic covariances reconstructed by partitioning within- and among-colony phenotypic variance are similar to those previously obtained for living species of the cheilostome Stylopoma using breeding data. The hypothesis that differences in skeletal morphology between species of Metrarabdotos are entirely due to mutation and genetic drift cannot be rejected for reasonable rates of mutation maintained for periods brief enough to account for the geologically abrupt appearances of these species in the fossil record. Except for one pair of species, separated by the largest morphologic distance, directional selection acting alone would require unrealistically high rates of selective mortality to be maintained for these periods. Thus, directional selection is not strongly implicated in the divergence of Metrarabdotos species. Within species, rates of net phenotypic change are slow enough to require stabilizing selection, but mask large, relatively rapid fluctuations, all of which, however, can be attributed to chance departures from the mean phenotype by mutation and genetic drift, rather than to tracking environmental fluctuation by directional selection. The results are consistent with genetic models involving shifts between multiple adaptive peaks on which phenotypes remain more or less static through long-term stabilizing selection. Regardless of the degree to which directional selection may be involved in peak shifts, phenotypic differentiation is thus related to processes different than the pervasive stabilizing selection acting within species.     

Understanding and using quantitative genetic variation

Quantitative genetics, or the genetics of complex traits, is the study of those characters which are not affected by the action of just a few major genes. Its basis is in statistical models and methodology, albeit based on many strong assumptions. While these are formally unrealistic, methods work. Analyses using dense molecular markers are greatly increasing information about the architecture of these traits, but while some genes of large effect are found, even many dozens of genes do not explain all the variation. Hence, new methods of prediction of merit in breeding programmes are again based on essentially numerical methods, but incorporating genomic information. Long-term selection responses are revealed in laboratory selection experiments, and prospects for continued genetic improvement are high. There is extensive genetic variation in natural populations, but better estimates of covariances among multiple traits and their relation to fitness are needed. Methods based on summary statistics and predictions rather than at the individual gene level seem likely to prevail for some time yet.