Trade-offs are a core component of many evolutionary models, particularly those dealing with the evolution of life histories. In the present paper, we identify four topics of key importance for studies of the evolutionary biology of trade-offs. First, we consider the underlying concept of 'constraint'. We conclude that this term is typically used too vaguely and suggest that 'constraint' in the sense of a bias should be clearly distinguished from 'constraint' in the sense of proscribed combinations of traits or evolutionary trajectories. Secondly, we address the utility of the acquisition-allocation model (the 'Y-model'). We find that, whereas this model and its derivatives have provided new insights, a misunderstanding of the pivotal equation has led to incorrect predictions and faulty tests. Thirdly, we ask how trade-offs are expected to evolve under directional selection. A quantitative genetic model predicts that, under weak or short-term selection, the intercept will change but the slope will remain constant. Two empirical tests support this prediction but these are based on comparisons of geographic populations: more direct tests will come from artificial selection experiments. Finally, we discuss what maintains variation in trade-offs noting that at present little attention has been given to this question. We distinguish between phenotypic and genetic variation and suggest that the latter is most in need of explanation. We suggest that four factors deserving investigation are mutation-selection balance, antagonistic pleiotropy, correlational selection and spatio-temporal variation, but as in the other areas of research on trade-offs, empirical generalizations are impeded by lack of data. Although this lack is discouraging, we suggest that it provides a rich ground for further study and the integration of many disciplines, including the emerging field of genomics.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1420-9101.2006.01255.x

The evolution of trade-offs: where are we?

An absence of genetic variance in traits under selection is perhaps the oldest explanation for a limit to evolutionary change, but has also been the most easily dismissed. We review a range of theoretical and empirical results covering single traits to more complex multivariate systems, and show that an absence of genetic variance may be more common than is currently appreciated. From a single-trait perspective, we highlight that it is becoming clear that some trait types do not display significant levels of genetic variation, and we raise the possibility that species with restricted ranges may differ qualitatively from more widespread species in levels of genetic variance in ecologically important traits. A common misconception in many life-history studies is that a lack of genetic variance in single traits, and genetic constraints as a consequence of bivariate genetic correlations, are different causes of selection limits. We detail how interpretations of bivariate patterns are unlikely to demonstrate genetic limits to selection in many cases. We advocate a multivariate definition of genetic constraints that emphasizes the presence (or otherwise) of genetic variance in the multivariate direction of selection. For multitrait systems, recent results using longer term studies of organisms, in which more is understood concerning what traits may be under selection, have indicated that selection may exhaust genetic variance, resulting in a limit to the selection response.

A reassessment of genetic limits to evolutionary change

There is increasing interest in determining the extent to which multiple characters related to drug sensitivity are influenced by common genes. The principal method for testing for the existence of such genetic correlations has been examination of pairs of mouse or rat lines selectively bred for sensitivity or resistance to a single behavioral effect of a drug. When a pair of selected lines is found to differ significantly on some trait other than the one on which they were selected, it is commonly concluded that significant genetic correlation between the traits exists, implying the action of a common set of genes on the two responses. In addition, results from comparisons of lines of animals selected for trait X and tested for trait Y may be compared with results from lines selected for trait Y and tested for trait X. As the number of correlated responses in selected lines increases, it becomes more important to adhere to sensible, consensual guidelines for interpreting such line differences. The principles underlying phenotypic and genotypic correlational analyses with selected lines are discussed. A scheme is presented to allow standardization across laboratories of inferences about the relative strength of genetic association from experiments with selected lines. Statistical and practical experimental issues are addressed. Estimates of genetic correlations may also be derived from the correlation of mean trait values across a panel of inbred strains. Existing data have sometimes found estimates of genetic correlations made with one approach to be inconsistent with those estimated in other ways. Possible reasons for this are discussed. Finally, the relationship between phenotypic correlations and genetic correlations is discussed. Phenotypic and genetic correlations for a pair of traits may differ widely, and may even be opposite in sign. Both are characteristic of the population from which they are sampled. Phenotypic correlations estimated within selected lines may change over time, as the additive genetic variance in the selected trait is exhausted. A specific example of this phenomenon is given.

Estimation of Genetic Correlation: Interpretation of Experiments Using Selectively Bred and Inbred Animals

Stabilizing selection has been predicted to change genetic variances and covariances so that the orientation of the genetic variance-covariance matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic variance, more than 99% of the genetic variance was orientated 74.9 degrees away from the vector of linear sexual selection, suggesting that open-ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear (convex) selection. Associating the eigenstructure of G with vectors of linear and nonlinear selection may provide a way of determining what long-term changes in G may be generated by the processes of natural and sexual selection.

/pdf/orientation-of-the-genetic-variance-covariance-matrix-and-2cl0j55cr4.pdf

Orientation of the genetic variance-covariance matrix and the fitness surface for multiple male sexually selected traits.

A knowledge of the magnitude of genetic variability and covariability of quantitative traits in natural populations and an understanding of the action of forces that maintain variation and those that lead to change are fundamental to the study of evolutionary biology. Artificial selection experiments, in which known strong forces are applied to laboratory or field populations over a greatly curtailed evolutionary timescale, have been and continue to be an important source of information on the genetics of quantitative characters and their effects on fitness.

https://www.jstor.org/stable/pdfplus/2097290.pdf

Artificial Selection Experiments

The pattern of changes of the genetic covariance between two characters on selection was examined in an effort to explain the asymmetry of correlated responses in two traits, or of the same trait in two environments, frequently observed in experimental results.The algebraic conclusions were further examined by model selection experiments using a computer. The computer was programmed to calculate the change in gene frequency from generation to generation and to calculate from it the expected changes in genetic variances and covariance as selection proceeded. This procedure was carried out with several models of gene effects and gene frequencies.Asymmetry of the genetic covariance, and consequently of the correlated responses, resulted when the relative change in gene frequency at the loci contributing positively and negatively to the covariance depended on the trait selected. The conditions necessary for the development of asymmetry were examined and the results suggest that any symmetry found in an experiment is perhaps more surprising than asymmetry. Probably the most frequent contribution to asymmetry in practice will be from loci contributing negatively to the covariance and having frequencies other than 0·5.Accurate prediction of correlated response over many generations is therefore not possible without prior knowledge of the composition of the genetic covariance, as well as its magnitude. The validity of existing theory for the prediction of correlated responses is likely to be much poorer than for the prediction of direct responses. Predictions would then have to be based on the genetic parameters estimated in each generation.

Some observations on asymmetrical correlated responses to selection.

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Some observations on asymmetrical correlated responses to selection.