Stevan J. Arnold

On the measurement of natural and sexual selection : theory

The aim of this paper is to illustrate an approach to the empirical measurement of selection that is directly related to formal evolutionary theory. Recent field studies have demonstrated that it is feasible to measure fitness in natural populations. The most successful studies have yielded accurate tallies of survivorship, mating success and fertility (e.g., Tinkle, 1965; Howard, 1979; Downhower and Brown, 1980; Lennington, 1980; Kluge, 1981; Clutton-Brock et al., 1982). Despite this success, no concensus has been reached on how to analyze the data and relate them to evolutionary theory. We present here a mode of data analysis that describes selection in useful, theoretical terms, so that field or experimental results will have a tangible relationship to equations for evolutionary change. Multivariate, polygenic theory (Lande, 1979, 1980, 1981; Bulmer, 1980) is particularly useful as a conceptual framework because it is concerned with the evolution of continuously distributed traits such as those commonly studied in laboratory and field situations. Multivariate equations have been used for many years by plant and animal breeders in order to impose selection and predict its impact (Smith, 1936; Hazel, 1943; Dickerson et al., 1954, 1974; Yamada, 1977), but this quantitative genetic theory has only recently been applied to evolutionary problems. Definitions and Aims. -It is critical to distinguish between selection and evolutionary response to selection (Fisher, 1930; Haldane, 1954). Selection causes observable changes within a generation in the means, variances and covariances of phenotypic distributions. Thus selection can be described in purely phenotypic terms without recourse to the inheritance of characters. In contrast, evolutionary response to selection, for example, the change in phenotypic mean from one generation to the next, certainly does depend on inheritance. In the following sections we show how knowledge of inheritance can be combined with purely phenotypic measures of selection to predict evolutionary response to selection. By distinguishing between selection and response to selection we can measure selection on characters whose mode of inheritance may be unknown and make prediction of evolutionary response a separate issue. Thus knowledge of inheritance is essential for complete

On the measurement of natural and sexual selection: applications

In this paper, we use measures of selection developed by quantitative geneticists and some new results (Arnold and Wade, 1984) to analyze multiple episodes of selection in natural populations of amphibians, reptiles, and insects. These examples show how different methods of data collection influence the potential for relating field observations to formal evolutionary theory. We adhere to the Darwinian tradition of distinguishing between natural and sexual selection (Darwin, 1859, 1871; Ghiselin, 1974). We view sexual selection as selection arising from variance in mating success and natural selection as arising from variance in other components of fitness. The justification for this formal distinction is developed by Wade (1979), Lande (1980), Wade and Arnold (1980), Arnold and Houck (1982) and Arnold (1 983 a). (We define mating success as the number of mates that bear progeny given survival of the mating organsim to sexual maturity. We do not equate mating success with mere copulatory success.) The utility of the distinction between sexual and natural selection is that the two forms of selection may often act in opposite directions on particular characters (Darwin, 1859, 1871). While we find the distinction between these two forms of selection useful, the difference is not crucial to our analysis. The essential point is that the recognition of selection episodes permits analysis of selection that may change in magnitude and direction during the life cycle. Defining Fitness Components. -The key first step in the analysis of data is to define multiplicative components of fitness so that selection can be partitioned into parts corresponding to these components or episodes of selection. Using an animal example, if the number of offspring zygotes is taken as total fitness, we can define the following components of fitness: viability (survivorship to sexual maturity), mating success (the number of mates) and fertility per mate (the average number of zygotes produced per mate). These components of fitness are defined so that their product gives total fitness. As a second example, consider the components of fitness in a plant in which yield (seeds/plant) is taken as the measure of total fitness (Primack and Antonovics, 1981). We might define the following components of fitness: number of stems per plant, average number of inflorescences per stem, average number of seed capsules per inflorescence, and average number of seeds per capsule. Again, these four fitness components are defined so that their product gives total fitness. We will need to measure each component of fitness and each character on each individual in order to partition selection into parts corresponding to the separate episodes of selection or to the separate components of fitness. Thus in the animal example, we need to measure the viability, mating success and fertility of each individual. With this accomplished we can estimate the separate forces of viability, sexual and fertility selection on each phenotypic character. In addition we can calculate the opportunities of selection corresponding to these three episodes and covariances between the different kinds of selection. In the plant example, we might begin with the intuition that larger plants have a greater yield. Using our methodology we can reword and extend this intuition. We can not only test the proposition of

Constraints on Phenotypic Evolution

Constraints on phenotypic evolution can take a variety of forms. Constraints can arise from inheritance, selection, development, and design limits. Contemporary visions of the evolutionary process often focus on one or two of these varieties and ignore the others. A unifying framework that considers all four major varieties of constraint is emerging within the discipline of quantitative genetics. I attempt to sketch that emerging framework and summarize recent efforts toward unification. Although couched in the technical language of quantitative genetics, the ongoing search for a common framework promises a rapprochement among the approaches of optimality theorists, population geneticists, and developmental biologists.

Visualizing multivariate selection

Recent developments in quantitative‐genetic theory have shown that natural selection can be viewed as the multivariate relationship between fitness and phenotype. This relationship can be described by a multidimensional surface depicting fitness as a function of phenotypic traits. We examine the connection between this surface and the coefficients of phenotypic selection that can be estimated by multiple regression and show how the interpretation of multivariate selection can be facilitated through the use of the method of canonical analysis. The results from this analysis can be used to visualize the surface implied by a set of selection coefficients. Such a visualization provides a compact summary of selection coefficients, can aid in the comparison of selection surfaces, and can help generate testable hypotheses as to the adaptive significance of the traits under study. Further, we discuss traditional definitions of directional, stabilizing, and disruptive selection and conclude that selection may be more usefully classified into two general modes, directional and nonlinear selection, with stabilizing and disruptive selection as special cases of nonlinear selection.

The intensity of sexual selection in relation to male sexual behaviour, female choice, and sperm precedence.

Abstract In this paper we define sexual selection on males as the variance in numbers of mates per male and show how the intensity of this selection is affected by male sexual behaviour, female choice, sex ratio, and modes of sperm precedence. This definition coincides with Darwins conception of sexual selection but differs from some post-Darwinian views. For systems of single-male paternity, we show that the intensity of total selection on male reproductive success equals the intensity of natural selection on female fertility, times the sex ratio, plus the intensity of sexual selection on males. The absolute intensity of sexual selection is unaffected by the system of sperm precedence. The application of the results to field studies is discussed.

ANIMAL MATING SYSTEMS: A SYNTHESIS BASED ON SELECTION THEORY

Following principles used by A. J. Bateman, we identify the relationship between fecundity and mating success as the central feature in the operation of mating systems. Using selection theory from the field of quantitative genetics, we define the sexual selection gradient as the average slope of the relationship between fecundity and mating success and show how it can be estimated from data. We argue that sexual selection gradients are the key to understanding how the intensity of sexual selection is affected by mate provisioning, parental investment, and sex ratio.

HOT ROCKS AND NOT-SO-HOT ROCKS: RETREAT-SITE SELECTION BY GARTER SNAKES AND ITS THERMAL CONSEQUENCES'

Studies of behavioral thermoregulation ofectotherms have typically focused only on active animals. However, most temperate-zone ectotherms actually spend more time sequestered in retreats (e.g., under rocks) than active above ground. We documented retreat-site selection during summer by gravid garter snakes (Thamnophis elegans) at Eagle Lake in northeastern California, USA. To explore the thermal consequences of retreat-site selection, we measured potential body temperatures in retreats and combined these with data on thermal tolerances, thermal preferences, and thermal dependence of metabolism and digestion. Garter snakes at Eagle Lake usually retreated under rocks of intermediate thickness (20-30 cm) even though both thinner and thicker rocks were available. Empirical and biophysical analyses of temperatures under rocks of various sizes and shapes demonstrated that rock thickness had the dominant effect on potential Tb available to snakes and in turn on thermal physiology. Snakes selecting thin rocks ( 40 cm thick) or remaining at the bottom of deep burrows would not experience such extreme Tb, but neither would they warm to Tb in their preferred range. However, snakes selecting intermediate-thickness rocks would never overheat but would achieve preferred Tb for long periods-far longer than if they remained on the ground surface or moved up and down within a burrow. Interestingly, snakes selecting burrows or intermediate-thickness rocks may be able to have either the highest energy gain or the lowest overall metabolic rate, depending on the particular Tb they select. Medium-thickness rocks, the size rocks normally selected by the snakes, offer them a variety of suitable thermoregulatory opportunities.

The adaptive landscape as a conceptual bridge between micro- and macroevolution

An adaptive landscape concept outlined by G.G. Simpson constitutes the major conceptual bridge between the fields of micro- and macroevolutionary study. Despite some important theoretical extensions since 1944, this conceptual bridge has been ignored in many empirical studies. In this article, we review the status of theoretical work and emphasize the importance of models for peak movement. Although much theoretical work has been devoted to evolution on stationary, unchanging landscapes, an important new development is a focus on the evolution of the landscape itself. We also sketch an agenda of empirical issues that is inspired by theoretical developments.

ESTIMATING NONLINEAR SELECTION GRADIENTS USING QUADRATIC REGRESSION COEFFICIENTS: DOUBLE OR NOTHING?

Abstract The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the γ matrix, and modeling the evolution of populations on an adaptive landscape.

HIERARCHICAL COMPARISON OF GENETIC VARIANCE-COVARIANCE MATRICES. I. USING THE FLURY HIERARCHY

The comparison of additive genetic variance‐covariance matrices (G‐matrices) is an increasingly popular exercise in evolutionary biology because the evolution of the G‐matrix is central to the issue of persistence of genetic constraints and to the use of dynamic models in an evolutionary time frame. The comparison of G‐matrices is a nontrivial statistical problem because family structure induces nonindependence among the elements in each matrix. Past solutions to the problem of G‐matrix comparison have dealt with this problem, with varying success, but have tested a single null hypothesis (matrix equality or matrix dissimilarity). Because matrices can differ in many ways, several hypotheses are of interest in matrix comparisons. Flury (1988) has provided an approach to matrix comparison in which a variety of hypotheses are tested, including the two extreme hypotheses prevalent in the evolutionary literature. The hypotheses are arranged in a hierarchy and involve comparisons of both the principal components (eigenvectors) and eigenvalues of the matrix. We adapt Flurys hierarchy of tests to the problem of comparing G‐matrices by using randomization testing to account for nonindependence induced by family structure. Software has been developed for carrying out this analysis for both genetic and phenotypic data. The method is illustrated with a garter snake test case.