THE EVOLUTION OF PHENOTYPIC CORRELATIONS AND “DEVELOPMENTAL MEMORY”

Development introduces structured correlations among traits that may constrain or bias the distribution of phenotypes produced. Moreover, when suitable heritable variation exists, natural selection may alter such constraints and correlations, affecting the phenotypic variation available to subsequent selection. However, exactly how the distribution of phenotypes produced by complex developmental systems can be shaped by past selective environments is poorly understood. Here we investigate the evolution of a network of recurrent nonlinear ontogenetic interactions, such as a gene regulation network, in various selective scenarios. We find that evolved networks of this type can exhibit several phenomena that are familiar in cognitive learning systems. These include formation of a distributed associative memory that can “store” and “recall” multiple phenotypes that have been selected in the past, recreate complete adult phenotypic patterns accurately from partial or corrupted embryonic phenotypes, and “generalize” (by exploiting evolved developmental modules) to produce new combinations of phenotypic features. We show that these surprising behaviors follow from an equivalence between the action of natural selection on phenotypic correlations and associative learning, well‐understood in the context of neural networks. This helps to explain how development facilitates the evolution of high‐fitness phenotypes and how this ability changes over evolutionary time.     

A POPULATION GENETIC THEORY OF CANALIZATION

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a “canalization limit” is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V_e). The rate of decrease of mutational variance V_m is found to be less than 10% of the initial V_m. From this result it is concluded that characters with typical mutational variances of about 10^–3 V_e are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of macroevolutionary patterns are discussed.     

GENOTYPE-ENVIRONMENT INTERACTION AND THE EVOLUTION OF PHENOTYPIC PLASTICITY

Studies of spatial variation in the environment have primarily focused on how genetic variation can be maintained. Many one-locus genetic models have addressed this issue, but, for several reasons, these models are not directly applicable to quantitative (polygenic) traits. One reason is that for continuously varying characters, the evolution of the mean phenotype expressed in different environments (the norm of reaction) is also of interest. Our quantitative genetic models describe the evolution of phenotypic response to the environment, also known as phenotypic plasticity (Gause, 1947), and illustrate how the norm of reaction (Schmalhausen, 1949) can be shaped by selection. These models utilize the statistical relationship which exists between genotype-environment interaction and genetic correlation to describe evolution of the mean phenotype under soft and hard selection in coarse-grained environments. Just as genetic correlations among characters within a single environment can constrain the response to simultaneous selection, so can a genetic correlation between states of a character which are expressed in two environments. Unless the genetic correlation across environments is ± 1, polygenic variation is exhausted, or there is a cost to plasticity, panmictic populations under a bivariate fitness function will eventually attain the optimum mean phenotype for a given character in each environment. However, very high positive or negative correlations can substantially slow the rate of evolution and may produce temporary maladaptation in one environment before the optimum joint phenotype is finally attained. Evolutionary trajectories under hard and soft selection can differ: in hard selection, the environments with the highest initial mean fitness contribute most individuals to the mating pool. In both hard and soft selection, evolution toward the optimum in a rare environment is much slower than it is in a common one. A subdivided population model reveals that migration restriction can facilitate local adaptation. However, unless there is no migration or one of the special cases discussed for panmictic populations holds, no geographical variation in the norm of reaction will be maintained at equilibrium. Implications of these results for the interpretation of spatial patterns of phenotypic variation in natural populations are discussed.     

PERSPECTIVE: COMPLEX ADAPTATIONS AND THE EVOLUTION OF EVOLVABILITY

The problem of complex adaptations is studied in two largely disconnected research traditions: evolutionary biology and evolutionary computer science. This paper summarizes the results from both areas and compares their implications. In evolutionary computer science it was found that the Darwinian process of mutation, recombination and selection is not universally effective in improving complex systems like computer programs or chip designs. For adaptation to occur, these systems must possess “evolvability,” i.e., the ability of random variations to sometimes produce improvement. It was found that evolvability critically depends on the way genetic variation maps onto phenotypic variation, an issue known as the representation problem. The genotype-phenotype map determines the variability of characters, which is the propensity to vary. Variability needs to be distinguished from variations, which are the actually realized differences between individuals. The genotype-phenotype map is the common theme underlying such varied biological phenomena as genetic canalization, developmental constraints, biological versatility, developmental dissociability, and morphological integration. For evolutionary biology the representation problem has important implications: how is it that extant species acquired a genotype-phenotype map which allows improvement by mutation and selection? Is the genotype-phenotype map able to change in evolution? What are the selective forces, if any, that shape the genotype-phenotype map? We propose that the genotype-phenotype map can evolve by two main routes: epistatic mutations, or the creation of new genes. A common result for organismic design is modularity. By modularity we mean a genotype-phenotype map in which there are few pleiotropic effects among characters serving different functions, with pleiotropic effects falling mainly among characters that are part of a single functional complex. Such a design is expected to improve evolvability by limiting the interference between the adaptation of different functions. Several population genetic models are reviewed that are intended to explain the evolutionary origin of a modular design. While our current knowledge is insufficient to assess the plausibility of these models, they form the beginning of a framework for understanding the evolution of the genotype-phenotype map.     

SHORT-TERM EVOLUTION IN THE SIZE AND SHAPE OF PEA APHIDS

Phenotypic evolution in contemporary populations can generally be witnessed only when novel selective forces produce rapid evolution. Examples of conditions that have led to rapid evolution include drastic environmental change, invasion of a new predator, or a host-range expansion. In cyclical parthenogens, however, yearly cycles of phenotypic evolution may occur due to the loss of adaptation during recombination in the sexual phase (genetic slippage), permitting an opportunity to observe adaptive evolutionary change in contemporary populations that are not necessarily subject to new patterns of natural selection. In insect herbivores, comparative studies suggest that morphological features that aid individuals in remaining on the plant or exploiting it as a food source are likely targets for selection. Here, we estimated the genetic variability of morphological traits in a cyclical parthenogen, the pea aphid (Acyrthosiphon pisum), to determine the potential for their evolution and we tested the hypothesis that size and/or shape evolves by clonal selection during one season of parthenogenetic reproduction. Genetic variation in a set of morphological traits was estimated using laboratory-reared descendents of clones collected from a single alfalfa field in May 1988 and April 1989 (henceforth, the “early” collections). In both years, there was significant clonal heritability early in the season both for overall morphology and for several individual aspects of size and shape. Because the course of short-term evolutionary change in the multivariate phenotype is a function of patterns of genetic covariance among characters, genetic correlations between size and 12 shape variables were also estimated for these early collections. A comparison between the mean phenotype of each early collection and that of a corresponding “late” collection made from the same field seven to eight clonal generations later in the same years revealed qualitatively similar changes in the average multivariate morphological phenotypes between the time periods in both years, although the difference was only significant for the 1989 samples. The pattern of genetic correlations that we estimated early in the 1989 season between overall size and various shape variables suggests that the observed short-term evolutionary changes in shape could have been due to natural selection acting only to increase overall size. We tested this hypothesis by estimating selection on size using a separate data set in which both demographic and morphological variables were measured on individuals reared under field conditions. Highly significant regressions of individual relative fitness on size were found for two major fitness components. Thus, it is likely that the evolutionary change in morphology that we observed is attributable to natural selection, possibly acting primarily through body size. A shift back to smaller size between the late 1988 and early 1989 collections from the same field suggests that either a cost of recombination or opposing selective forces during overwintering may produce persistent yearly cycles of morphological evolution in this cyclically parthenogenetic species.     

THE EVOLUTION OF COSTLY MATE PREFERENCES II. THE “HANDICAP” PRINCIPLE

We use a general additive quantitative genetic model to study the evolution of costly female mate choice by the “handicap” principle. Two necessary conditions must be satisfied for costly preference to evolve. The conditions are (i) biased mutation pressure on viability and (ii) a direct relationship between the degree of expression of the male mating character and viability. These two conditions explain the success and failure of previous models of the “handicap” principle. Our model also applies to other sources of fitness variation like migration and host-parasite coevolution, which cause effects equivalent to biased mutation.     

The influence of variation and of developmental constraints on the rate of multivariate phenotypic evolution

A model of multivariate phenotypic evolution is analysed under the assumption that all characters have the same variance or at least constant ratios of variance. The rate of evolution is examined as a function of the amount of phenotypic variance in a variety of adaptive landscapes (fitness functions). It is demonstrated that the effect of variation depends on the type of adaptive landscape. In “well behaved” adaptive landscapes the rate of evolution can theoretically increase without limits, depending on the amount of heritable phenotypic variation. However, in other adaptive landscapes there are upper limits to the rate of evolution which cannot be exceeded if phenotypic variation is developmentally unconstrained, i. e. if it is the same for all characters. Further it is shown that the maximal rate of evolution becomes small if the number of characters becomes large. Fitness functions of this type are called malignant. It is argued that malignant fitness functions are more adequate models for the evolution of typical organismic systems, because they are models of functionally interdependent characters. It is concluded that there are upper limits to the rate of phenotypic evolution if the variation of functionally interdependent characters is developmentally unconstrained. The possible role of developmental constraints in adaptive phenotypic evolution is discussed.     

THE DYNAMICS OF NICHE EVOLUTION UPON ABRUPT ENVIRONMENTAL CHANGE

Abrupt environmental changes are of particular interest to understand how species can quickly evolve at the boundary of their current niche. In particular the “sliding niche” model, wherein a niche shifts globally toward the new condition, has been used in understanding and modeling this process. Here, we investigate the dynamics of relative fitness change in four evolutionary replicates of Escherichia coli populations exposed to an extreme pH shift. We analyzed these changes at generations 500, 1000, and 2000 to determine whether niche global deformations fully capture the temporal dynamics of niche evolution. Strikingly, this analysis reveals that fitness variations can indeed be attributed to simple and global deformation of an underlying simple niche template. Analysis from two experimental replicates displays a transient increase in niche width, consistent with recent theory considering plasticity evolution in the context of an abrupt environmental change. We term this scenario the “sidestep niche model.”     

EVOLUTION OF VARIATION AND VARIABILITY UNDER FLUCTUATING,STABILIZING, AND DISRUPTIVE SELECTION

How variation and variability (the capacity to vary) may respond to selection remain open questions. Indeed, effects of different selection regimes on variational properties, such as canalization and developmental stability are under debate. We analyzed the patterns of among‐ and within‐individual variation in two wing‐shape characters in populations of Drosophila melanogaster maintained under fluctuating, disruptive, and stabilizing selection for more than 20 generations. Patterns of variation in wing size, which was not a direct target of selection, were also analyzed. Disruptive selection dramatically increased phenotypic variation in the two shape characters, but left phenotypic variation in wing size unaltered. Fluctuating and stabilizing selection consistently decreased phenotypic variation in all traits. In contrast, within‐individual variation, measured by the level of fluctuating asymmetry, increased for all traits under all selection regimes. These results suggest that canalization and developmental stability are evolvable and presumably controlled by different underlying genetic mechanisms, but the evolutionary responses are not consistent with an adaptive response to selection on variation. Selection also affected patterns of directional asymmetry, although inconsistently across traits and treatments.     

SPERM COMPETITION AND THE EVOLUTION OF SEMINAL FLUID COMPOSITION

Male ejaculates include large amounts of seminal fluid proteins (Sfps) that influence male sperm competitive success. In spite of their diverse proximate functions, Sfps involved in sperm competition increase male fitness in one of three ways: (1) “avoidance” proteins help males avoid sperm competition, (2) “defense” proteins help males defend their sperm from displacement by the female's subsequent mate, and (3) “offense” proteins aid males in displacing sperm of preceding males. Here, we present a population genetic model of the evolution of allocation of finite resources by males to the three kinds of Sfps. We analyze the influence of relative efficiencies of different Sfps, of plasticity in resource allocation, and of differences in viability costs of Sfps. We find that in absence of plasticity or different viability costs, equal investment in defense and offense Sfps evolves, irrespective of their relative efficiency. In all cases, males evolve to invest more in avoidance when avoidance proteins are increasingly efficient, and when offense is more efficient than defense. Differences in viability costs result in lower investment in costly proteins, whereas plasticity has complex effects, influencing both the optimal seminal fluid composition and maintenance of variation in investment in these proteins across populations.     

EVOLUTION IN FLUCTUATING ENVIRONMENTS: DECOMPOSING SELECTION INTO ADDITIVE COMPONENTS OF THE ROBERTSON–PRICE EQUATION

We analyze the stochastic components of the Robertson–Price equation for the evolution of quantitative characters that enables decomposition of the selection differential into components due to demographic and environmental stochasticity. We show how these two types of stochasticity affect the evolution of multivariate quantitative characters by defining demographic and environmental variances as components of individual fitness. The exact covariance formula for selection is decomposed into three components, the deterministic mean value, as well as stochastic demographic and environmental components. We show that demographic and environmental stochasticity generate random genetic drift and fluctuating selection, respectively. This provides a common theoretical framework for linking ecological and evolutionary processes. Demographic stochasticity can cause random variation in selection differentials independent of fluctuating selection caused by environmental variation. We use this model of selection to illustrate that the effect on the expected selection differential of random variation in individual fitness is dependent on population size, and that the strength of fluctuating selection is affected by how environmental variation affects the covariance in Malthusian fitness between individuals with different phenotypes. Thus, our approach enables us to partition out the effects of fluctuating selection from the effects of selection due to random variation in individual fitness caused by demographic stochasticity.     

GENERALISTS,SPECIALISTS, AND THE EVOLUTION OF PHENOTYPIC PLASTICITY IN SYMPATRIC POPULATIONS OF DISTINCT SPECIES

The evolution of phenotypic plasticity is studied in a model with two reproductively isolated “species” in a coarse-grained environment, consisting of two types of habitats. A quantitative genetic model for selection was constructed, in which habitats differ in the optimal value for a focal trait, and with random dispersal among habitats. The main interest was to study the effects of different selection regimes. Three cases were investigated: (1) without any limits to plasticity; (2) without genetic variation for plasticity; and (3) with a fitness cost for phenotypically plastic reactions. In almost all cases a generalist strategy to exploit both habitats emerged. Without any limits to plasticity, optimal adaptive reactions evolved. Without any genetic variation for plasticity, a compromise strategy with an intermediate, fixed phenotype evolved, whereas in the presence of costs a plastic compromise between the demands of the habitats and the costs associated with plasticity was found. Specialization and phenotypic differentiation was only found when selection within habitats was severe and optimal phenotypes for different habitats were widely different. Under soft selection (local regulation of population numbers in each habitat) the specialists coexisted; under hard selection (global regulation of population numbers) one specialist outcompeted the other. The prevalent evolutionary outcome of compromises rather than specialization implies that costs or constraints are not necessarily detectable as local adaptation in transplantation or translocation experiments.     

FITNESS SENSITIVITY AND THE CANALIZATION OF LIFE-HISTORY TRAITS

Canalization is an abstract term that describes unknown developmental mechanisms that reduce phenotypic variation. A trait can be canalized against environmental perturbations (e.g., changes in temperature or nutrient quality), or genetic perturbations (e.g., mutations or recombination); this paper is about genetic canalization. Stabilizing selection should improve the canalization of traits, and the degree of canalization should be positively correlated with the traits' impact on fitness. Experiments testing this idea should measure the canalization of a series of traits whose impact on fitness is known or can be inferred, exclude differences among traits in the number of loci and alleles segregating as an explanation for the pattern of variability found, and distinguish between canalization against genetic and environmental variation. These conditions were met by three experiments within which the variation of fitness components among Drosophila melanogaster lines was measured and among which the genetic contribution to the variation among lines was clearly different. The canalization of the traits increased with their impact on fitness and did not depend on the degree of genetic differences among lines. That the flies used had been transformed by a P-element insert suggests that canalization was also effective against novel genetic variation. The results reported here cannot be explained by the classical hypothesis of reduction in the number of loci segregating for traits with greater impact on fitness and confirm that traits with greater impact on fitness are more strongly canalized. This pattern of canalization reveals an underappreciated role for development in microevolution. There is differential genetic canalization of fitness components in D. melanogaster.     

MULTIDIMENSIONAL ADAPTIVE EVOLUTION OF A FEED‐FORWARD NETWORK AND THE ILLUSION OF COMPENSATION

When multiple substitutions affect a trait in opposing ways, they are often assumed to be compensatory, not only with respect to the trait, but also with respect to fitness. This type of compensatory evolution has been suggested to underlie the evolution of protein structures and interactions, RNA secondary structures, and gene regulatory modules and networks. The possibility for compensatory evolution results from epistasis. Yet if epistasis is widespread, then it is also possible that the opposing substitutions are individually adaptive. I term this possibility an adaptive reversal. Although possible for arbitrary phenotype‐fitness mappings, it has not yet been investigated whether such epistasis is prevalent in a biologically realistic setting. I investigate a particular regulatory circuit, the type I coherent feed‐forward loop, which is ubiquitous in natural systems and is accurately described by a simple mathematical model. I show that such reversals are common during adaptive evolution, can result solely from the topology of the fitness landscape, and can occur even when adaptation follows a modest environmental change and the network was well adapted to the original environment. The possibility of adaptive reversals warrants a systems perspective when interpreting substitution patterns in gene regulatory networks.     

EVOLUTION OF INFLORESCENCE DESIGN: THEORY AND DATA

Very low fruit set in milkweeds and other flowering plants often has been attributed to greater sexual selection on inflorescence size via male, rather than female, reproductive success. Although this explanation has been generally accepted, alternate explanations have been presented, and recently the “male function” or “pollen donation” hypothesis has been sharply criticized. In this paper, we make the distinction between selection on total flower number and on the size of inflorescence units, both of which have been termed “inflorescence size.” We present an ESS model for the evolution of inflorescence design that considers reproductive success through male and female function. The model predicts that selection will balance the proportional changes in female and male reproductive success resulting from changes in inflorescence-unit size. We conducted a field study of selection on the size of inflorescence units (umbels) by manipulating umbel size and number in a natural population of Asclepias tuberosa, in southeastern Arizona, during two reproductive seasons. We found that the male fitness function reached a maximum at an intermediate umbel size in both years (although not significantly different from the smallest umbel size in either year), whereas the female fitness function was highest for the smallest umbel size in one year, but was constant across umbel sizes in the other year. We also found that pollinator visitation rate corresponded well with male, but not female, function, and that between-year variation in the male reproductive success of different umbel sizes corresponded with variation in the composition of the pollinator pool. Our empirical results, when inserted in the model, predict ESS umbel sizes similar to those observed in the study population and the species throughout its range.     

SOLVING THE PARADOX OF STASIS: SQUASHED STABILIZING SELECTION AND THE LIMITS OF DETECTION

Despite the potential for rapid evolution, stasis is commonly observed over geological timescales—the so‐called “paradox of stasis.” This paradox would be resolved if stabilizing selection were common, but stabilizing selection is infrequently detected in natural populations. We hypothesize a simple solution to this apparent disconnect: stabilizing selection is hard to detect empirically once populations have adapted to a fitness peak. To test this hypothesis, we developed an individual‐based model of a population evolving under an invariant stabilizing fitness function. Stabilizing selection on the population was infrequently detected in an “empirical” sampling protocol, because (1) trait variation was low relative to the fitness peak breadth; (2) nonselective deaths masked selection; (3) populations wandered around the fitness peak; and (4) sample sizes were typically too small. Moreover, the addition of negative frequency‐dependent selection further hindered detection by flattening or even dimpling the fitness peak, a phenomenon we term “squashed stabilizing selection.” Our model demonstrates that stabilizing selection provides a plausible resolution to the paradox of stasis despite its infrequent detection in nature. The key reason is that selection “erases its traces”: once populations have adapted to a fitness peak, they are no longer expected to exhibit detectable stabilizing selection.     

The differential genetic and environmental canalization of fitness components in Drosophila melanogaster

Canalization describes the process by which phenotypic variation is reduced by developmental mechanisms. A trait can be canalized against environmental or genetic perturbations. Stabilizing selelction should favor improved canalization, and the degree of a trait's canalization should be positively correlated with its impact on fitness. Here we report, for Drosophila melanogaster, measurements of environmental canalization for five fitness components. We compare them with measurements of genetic canalization, and we discuss the impact of inbreeding on both. In three experiments we measured the variation of fitness components within lines nested within temperature, treatment, and experiment. Lines differed in the position of a P element insert or in genetic background. Within lines flies were genetically nearly identical. We designated trait variation within lines as environmental canalization. The canalization of the traits increased with their impact on fitness, and the pattern was similar to that found for the canalization of fitness components against genetic differences, measured as the variation among lines nested within temperature, treatment, and experiment. This suggests that developmental mechanisms buffer the phenotype against both genetic and environmental disturbance. The results also suggest, less strongly, that inbreeding weakens canalization.     

Short‐term insurance versus long‐term bet‐hedging strategies as adaptations to variable environments

Understanding how organisms adapt to environmental variation is a key challenge of biology. Central to this are bet‐hedging strategies that maximize geometric mean fitness across generations, either by being conservative or diversifying phenotypes. Theoretical models have identified environmental variation across generations with multiplicative fitness effects as driving the evolution of bet‐hedging. However, behavioral ecology has revealed adaptive responses to additive fitness effects of environmental variation within lifetimes, either through insurance or risk‐sensitive strategies. Here, we explore whether the effects of adaptive insurance interact with the evolution of bet‐hedging by varying the position and skew of both arithmetic and geometric mean fitness functions. We find that insurance causes the optimal phenotype to shift from the peak to down the less steeply decreasing side of the fitness function, and that conservative bet‐hedging produces an additional shift on top of this, which decreases as adaptive phenotypic variation from diversifying bet‐hedging increases. When diversifying bet‐hedging is not an option, environmental canalization to reduce phenotypic variation is almost always favored, except where the tails of the fitness function are steeply convex and produce a novel risk‐sensitive increase in phenotypic variance akin to diversifying bet‐hedging. Importantly, using skewed fitness functions, we provide the first model that explicitly addresses how conservative and diversifying bet‐hedging strategies might coexist.     

PHYLOGENETIC ANALYSES OF THE CORRELATED EVOLUTION OF CONTINUOUS CHARACTERS: A SIMULATION STUDY

We use computer simulation to compare the statistical properties of several methods that have been proposed for estimating the evolutionary correlation between two continuous traits, and define alternative evolutionary correlations that may be of interest. We focus on Felsenstein's (1985) method and some variations of it and on several “minimum evolution” methods (of which the procedure of Huey and Bennett [1987] is a special case), as compared with a nonphylogenetic correlation. The last, a simple correlation of trait values across the tips of a phylogeny, virtually always yields inflated Type I error rates, relatively low power, and relatively poor estimates of evolutionary correlations. We therefore cannot recommend its use. In contrast, Felsenstein's (1985) method yields acceptable significance tests, high power, and good estimates of what we term the input correlation and the standardized realized evolutionary correlation, given complete phylogenetic information and knowledge of the rate and mode of character change (e.g., gradual and proportional to time [“Brownian motion”] or punctuational, with change only at speciation events). Inaccurate branch length information may affect any method adversely, but only rarely does it cause Felsenstein's (1985) method to perform worse than do the others tested. Other proposed methods generally yield inflated Type I error rates and have lower power. However, certain minimum evolution methods (although not the specific procedure used by Huey and Bennett [1987]) often provide more accurate estimates of what we term the unstandardized realized evolutionary correlation, and their use is recommended when estimation of this correlation is desired. We also demonstrate how correct Type I error rates can be obtained for any method by reference to an empirical null distribution derived from computer simulations, and provide practical suggestions on choosing an analytical method, based both on the evolutionary correlation of interest and on the availability of branch lengths and knowledge of the model of evolutionary change appropriate for the characters being analyzed. Computer programs that implement the various methods and that will simulate (correlated) character evolution along a known phylogeny are available from the authors on request. These programs can be used to test the effectiveness of any new methods that might be proposed, and to check the generality of our conclusions with regard to other phylogenies.     

THE EVOLUTION OF MATERNAL CHARACTERS

We develop quantitative-genetic models for the evolution of multiple traits under maternal inheritance, in which traits are transmitted through non-Mendelian as well as Mendelian mechanisms, and maternal selection, in which the fitness of offspring depends on their mother's phenotype as well as their own. Maternal inheritance results in time lags in the evolutionary response to selection. These cause a population to evolve for an indefinite number of generations after selection ceases and make the rate and direction of evolution change even when the strength of selection and parameters of inheritance remain constant. The rate and direction of evolution depend on the inheritance of traits that are not under selection, unlike under classical Mendelian inheritance. The models confirm earlier findings that the response to selection can be larger or smaller than what is possible with simple Mendelian inheritance, and even in a direction opposite to what selection favors. Maternal selection, in which a mother's phenotype influences her offspring's fitness, is frequency-dependent and can cause a population to evolve maladaptively away from a fitness peak, regardless of whether traits are transmitted by Mendelian or maternal inheritance. Maternal selection differs from other forms of selection in that its force depends not only on the fitness function but also on the phenotypic resemblance of parents and offspring.