Seed Dispersal as a Maternally Influenced Character: Mechanistic Basis of Maternal Effects and Selection on Maternal Characters in an Annual Plant

Maternal influences on progeny characters affect phenotypic correlations between characters expressed in maternal and progeny generations and consequently influence evolutionary responses to selection. Net selection on maternally influenced characters depends on selection both on the progeny character and on the maternal characters that influence it. I used seed dispersal in Cakile edentula as a system in which to identify the mechanisms of environmentally mediated maternal effects and to determine how selection on maternal characters alters the adaptive value of dispersal. In C. edentula, maternal morphology responds to conspecific density experienced by the mother. Maternal morphology in turn affects offspring (seed) dispersal and density and thereby offspring morphology and fitness. I estimated the magnitude of density-mediated maternal effects on dispersal and identified their mechanism by characterizing the plasticity of maternal morphology to density. I also measured density-dependent selection on maternal characters that influence dispersal. Maternal plasticity to density was caused by both allometric and nonallometric variation in morphology, and this plasticity resulted in a negative correlation between maternal and progeny density. Such negative maternal effects are expected to retard responses to selection. Maternal morphology influenced maternal fitness, in part through the relationship of fitness to maternal plant size and in part through size-independent fitness effects. Maternal phenotypes that promote dispersal, and thereby increase progeny fitness, were associated with decreased maternal fitness. Selection on dispersal at the level of progeny favors increased dispersal; maternal influences on dispersal, however, not only cause a greatly reduced adaptive value of dispersal but lead to the prediction of a slower response to selection.     

UNIFICATION OF REGRESSION‐BASED METHODS FOR THE ANALYSIS OF NATURAL SELECTION

Regression analyses are central to characterization of the form and strength of natural selection in nature. Two common analyses that are currently used to characterize selection are (1) least squares–based approximation of the individual relative fitness surface for the purpose of obtaining quantitatively useful selection gradients, and (2) spline‐based estimation of (absolute) fitness functions to obtain flexible inference of the shape of functions by which fitness and phenotype are related. These two sets of methodologies are often implemented in parallel to provide complementary inferences of the form of natural selection. We unify these two analyses, providing a method whereby selection gradients can be obtained for a given observed distribution of phenotype and characterization of a function relating phenotype to fitness. The method allows quantitatively useful selection gradients to be obtained from analyses of selection that adequately model nonnormal distributions of fitness, and provides unification of the two previously separate regression‐based fitness analyses. We demonstrate the method by calculating directional and quadratic selection gradients associated with a smooth regression‐based generalized additive model of the relationship between neonatal survival and the phenotypic traits of gestation length and birth mass in humans.     

Context dependence in complex adaptive landscapes: frequency and trait‐dependent selection surfaces within an adaptive radiation of Caribbean pupfishes

The adaptive landscape provides the foundational bridge between micro‐ and macroevolution. One well‐known caveat to this perspective is that fitness surfaces depend on ecological context, including competitor frequency, traits measured, and resource abundance. However, this view is based largely on intraspecific studies. It is still unknown how context‐dependence affects the larger features of peaks and valleys on the landscape which ultimately drive speciation and adaptive radiation. Here, I explore this question using one of the most complex fitness landscapes measured in the wild in a sympatric pupfish radiation endemic to San Salvador Island, Bahamas by tracking survival and growth of laboratory‐reared F2 hybrids. I present new analyses of the effects of competitor frequency, dietary isotopes, and trait subsets on this fitness landscape. Contrary to expectations, decreasing competitor frequency increased survival only among very common phenotypes, whereas less common phenotypes rarely survived despite few competitors, suggesting that performance, not competitor frequency, shapes large‐scale features of the fitness landscape. Dietary isotopes were weakly correlated with phenotype and growth, but did not explain additional survival variation. Nonlinear fitness surfaces varied substantially among trait subsets, revealing one‐, two‐, and three‐peak landscapes, demonstrating the complexity of selection in the wild, even among similar functional traits.     

Relative Fitness, Teleology, and the Adaptive Landscape

The metaphor of the adaptive landscape, introduced by Sewall Wright in 1932, has played, and continues to play, a central role in much evolutionary thought. I argue that the use of this metaphor is tied to a teleological view of the evolutionary process, in which natural selection directs evolution toward an improved future state. I argue further that the use of “relative fitnesses” standardized to an arbitrary value, which is closely connected with the metaphor of an adaptive landscape, produces a disconnect between the mean fitness of a population and any real property of that population. This allows for a vague and ill-defined improvement to occur under the influence of selection. Instead, I suggest that relative fitnesses should be standardized by the mean absolute fitness (expected population growth rate), so that they express the expected rate of increase in frequency, rather than number. Under this definition, the mean relative fitness of all populations is always 1.0, and never changes as long as the population continues to exist.     

Extracting characteristic properties of fitness landscape from in vitro molecular evolution: a case study on infectivity of fd phage to E.coli

We have developed a methodology for extracting characteristic properties of a fitness landscape of interest by analyzing fitness data on an in vitro molecular evolution. The in vitro evolution is required to be conducted as the following "adaptive walk": a single parent sequence generates N mutant sequences as its offsprings, and the fittest individual among the N offsprings will become a new parent in the next generation. N is the library size of mutants to be screened in a single generation. Our theory of the adaptive walk on the "NK landscape" suggests the following: the adaptive walker starting from a random sequence climbs the landscape easily in an early stage, and then reaches a stationary phase in which the mutation-selection-random drift balance sets in. The stationary fitness value is nearly proportional to square root of ln N. Our analysis is performed from the following points: (1) stationary fitness values, (2) time series of fitness in the transitional state, (3) mutant's fitness distribution, and (4) the strength of selection pressure. Applying our methodology, we analyzed experimental data on the in vitro evolution of a random polypeptide (139 amino acids) toward acquiring infectivity (= ability to infect) of fd phage. As a result, we estimated that k is about 27 in this system, indicating that an arbitrary residue in a sequence is affected from other 23% residues. In this article, we demonstrated that the experimental data is consistent with our theoretical equations quantitatively, and that our methodology for extracting characteristic properties of a fitness landscape may be effective.     

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor,II

In our previous report [Aita, T., Morinaga, S., Hosimi, Y., 2004. Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor I. Bull. Math. Biol. 66, 1371–1403], an analogy between thermodynamics and adaptive walks on a Mt. Fuji-type fitness landscape in an artificial selection system was presented. Introducing the ‘free fitness’ as the sum of a fitness term and an entropy term and ‘evolutionary force’ as the gradient of free fitness on a fitness coordinate, we demonstrated that the adaptive walk (=evolution) is driven by the evolutionary force in the direction in which free fitness increases. In this report, we examine the effect of various modifications of the original model on the properties of the adaptive walk. The modifications were as follows: first, mutation distance d was distributed obeying binomial distribution; second, the selection process obeyed the natural selection protocol; third, ruggedness was introduced to the landscape according to the NK model; fourth, a noise was included in the fitness measurement. The effect of each modification was described in the same theoretical framework as the original model by introducing ‘effective’ quantities such as the effective mutation distance or the effective screening size.     

Is seasonal variation in leaf traits adaptive for the annual plant Dicerandra linearifolia?

Empirical studies of phenotypic plasticity have often relied on the plausibility that a plastic response to the environment would increase fitness in order to diagnose the response as adaptive. I conducted a test of the hypothesis that seasonal variation in leaf traits is an adaptive response to seasonal variation in environmental conditions faced by the annual plant Dicerandralinearifolia. This species exhibits variation in leaf morphology and anatomy in response to temperature that is consistent with the expectations for adaptive plasticity. I examined variation in the size, thickness and density of stomata of leaves that develop in summer and winter and used analysis of phenotypic selection during winter and summer seasons to test the hypothesis that seasonal variation in these traits is adaptive. Regression analyses of estimated dry mass (as a proxy for fitness) on leaf traits revealed no evidence supporting the adaptive hypothesis. Selection favoured individuals with large and thick leaves in both winter and summer, and density of stomata had little or no effect on estimated relative fitness in any season. Correspondence between seasonal variation in leaf thickness and density of stomata and expectations for adaptive plasticity appears to be purely fortuitous. Seasonal variation in leaf traits may persist simply because there is no selection against individuals in which these traits vary. My results underscore the importance of definitive tests of the hypothesis of adaptation to distinguish adaptive plasticity from neutral or nonadaptive phenotypic plasticity.     

Thermodynamical interpretation of an adaptive walk on a Mt. Fuji-type fitness landscape: Einstein relation-like formula holds in a stochastic evolution

We have theoretically studied the statistical properties of adaptive walks (or hill-climbing) on a Mt. Fuji-type fitness landscape in the multi-dimensional sequence space through mathematical analysis and computer simulation. The adaptive walk is characterized by the "mutation distance" d as the step-width of the walker and the "population size" N as the number of randomly generated d-fold point mutants to be screened. In addition to the fitness W, we introduced the following quantities analogous to thermodynamical concepts: "free fitness" G(W) is identical with W+T x S(W), where T is the "evolutionary temperature" T infinity square root of d/lnN and S(W) is the entropy as a function of W, and the "evolutionary force" X is identical with d(G(W)/T)/dW, that is caused by the mutation and selection pressure. It is known that a single adaptive walker rapidly climbs on the fitness landscape up to the stationary state where a "mutation-selection-random drift balance" is kept. In our interpretation, the walker tends to the maximal free fitness state, driven by the evolutionary force X. Our major findings are as follows: First, near the stationary point W*, the "climbing rate" J as the expected fitness change per generation is described by J approximately L x X with L approximately V/2, where V is the variance of fitness distribution on a local landscape. This simple relationship is analogous to the well-known Einstein relation in Brownian motion. Second, the "biological information gain" (DeltaG/T) through adaptive walk can be described by combining the Shannon's information gain (DeltaS) and the "fitness information gain" (DeltaW/T).     

Exploring variation in fitness surfaces over time or space

As the number of studies estimating selection on multiple traits has increased in recent years, fitness surfaces have become a fundamental tool for understanding multivariate selection and evolution. However, rigorous statistical comparisons of multivariate selection surfaces over time or space have been limited to parametric analyses of selection coefficients estimated using a quadratic regression model. Although parametric comparisons are useful when selection is approximately linear or quadratic in nature, they are limited when confronting the complex nature of rugged fitness surfaces. Here, I present a novel solution to comparing nonparametric fitness surfaces over time or space. Using a Tucker3 tensor decomposition, which is essentially a higher order principal components analysis, I show how major features of fitness surfaces can be compared statistically. Combined with a bootstrap algorithm, I develop three statistical tests that identify (1) differences in the shape of nonparametric fitness surfaces, (2) differences in the contribution of each surface to variation in fitness across time or space, and (3) specific areas of the surfaces (trait combinations) that vary significantly over time or space. I illustrate the tensor decomposition and statistical analyses using idealized fitness surfaces.     

Visualizing fitness landscapes

Fitness landscapes are a classical concept for thinking about the relationship between genotype and fitness. However, because the space of genotypes is typically high-dimensional, the structure of fitness landscapes can be difficult to understand and the heuristic approach of thinking about fitness landscapes as low-dimensional, continuous surfaces may be misleading. Here, I present a rigorous method for creating low-dimensional representations of fitness landscapes. The basic idea is to plot the genotypes in a manner that reflects the ease or difficulty of evolving from one genotype to another. Such a layout can be constructed using the eigenvectors of the transition matrix describing the evolution of a population on the fitness landscape when mutation is weak. In addition, the eigendecomposition of this transition matrix provides a new, high-level view of evolution on a fitness landscape. I demonstrate these techniques by visualizing the fitness landscape for selection for the amino acid serine and by visualizing a neutral network derived from the RNA secondary structure genotype-phenotype map.     

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

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 gamma matrix, and modeling the evolution of populations on an adaptive landscape.     

Divergent selection drives the adaptive radiation of crossbills

Abstract Knowledge of how phenotype influences fitness is necessary if we are to understand the basis of natural selection and how natural selection contributes to adaptive radiations. Here I quantify selection on a wild population of red crossbills ( Loxia curvirostra complex) in the South Hills, Idaho. Bill depth is the target of selection and selection on bill depth is stabilizing. I then show how fitness is related to both bill depth and performance. I use these and previously published relationships to estimate a fitness surface for five species of red crossbills that are part of an ongoing adaptive radiation in western North America. The fitness surface for crossbills has distinct peaks and valleys, with each crossbill species residing on or very near the summits. This work strongly supports a key tenet of the ecological theory of adaptive radiations; namely, divergent selection for utilizing alternative resources is the ultimate cause of adaptive radiations.     

Evolution in the real world: stochastic variation and the determinants of fitness in Carlina vulgaris

Empirical studies of life histories often ignore stochastic variation, despite theoretical demonstrations of its potential impact on life-history evolution. Here we use a novel approach to explore the effects of stochastic variation on life-history evolution and estimate the selection pressures operating on the monocarpic perennial Carlina vulgaris, in which flowering may be delayed by up to eight years. The approach is novel in that we use modern theoretical techniques to estimate selection pressures and the fitness landscape from a fully parameterised individual-based model. These approaches take into account temporal variation in demographic rates and density dependence. Analysis of 16 years' data revealed significant temporal variation in growth, mortality, and recruitment in our study population. Flowering was strongly size dependent and, unusually for such a species, also age dependent. Individual-based models of the flowering strategy, parameterized using field data, consistently underestimated the size at flowering, when temporal variation in demographic rates was ignored. In contrast, models that incorporated temporal variation in growth, mortality, and recruitment predicted sizes at flowering not significantly different from those observed in the field. Temporal variation in mortality, which had the largest effect on the flowering strategy, selected for increased size at flowering. An analytical approximation is presented to explain this result, extending the "1-year look-ahead criterion" presented in Rees et al. (2000). A fitness landscape generated by following the fate of rare mutant invaders with a broad range of alternative flowering strategies demonstrated that the observed parameters were adaptive. However, the fitness landscape reveals that approximately equal fitness is achieved by a broad range of strategies, providing a mechanism for the maintenance of genetic variation. To understand how the different parameters that defined our models determine the fitness of rare mutants, we numerically estimated the elasticities and sensitivities of mutant fitness. This demonstrated strong selection on a number of the parameters. Elasticities and sensitivities estimated in constant and random environments were significantly positively correlated, and both were negatively related to the standard error of the parameter. This last result is surprising and, we argue, reflects the genetic and phenotypic responses to selection.     

Thermoregulation, Flight, and the Evolution of Wing Pattern in Pierid Butterflies: The Topography of Adaptive Landscapes

SYNOPSIS. This paper describes a case study of adaptation, constraint,and evolutionary innovation in pierid butterflies. I developa framework for discussing these issues that focuses on thequestions: What is the form of the adaptive landscape relatingfitness to phenotypic characters? How do such landscapes differfor evolutionarily related groups? I examine the evolution ofwing pigment patterns and thermoregulatory behavior for butterfliesin two subfamilies in the family Pieridae, with three principalresults. First, I show that thermoregulation can be an importantcomponent of fitness in pierids, and that wing color and thermoregulatorybehavior are important phenotypic characters determining thermoregulatoryperformance and the adaptive landscape. Second, I show how limitson possible variation in wing color and behavior constrain evolutionwithin one subfamily of pierids, and how these constraints areset by the physical and biochemical mechanisms of adaptation.Third, I show how evolutionary innovation may have resultedfrom the addition of a new, behavioral dimension to the landscape,and how this addition has altered the functional interrelationsamong various elements of the wing color pattern. I suggestthat comparative analyses of the form and determinants of theadaptive landscape may be useful in identifying evolutionaryinnovations, and complement theoretical analyses of evolutionarydynamics on such fitness surfaces.     

Strong Epistatic Selection on the RNA Secondary Structure of HIV

A key question in evolutionary genomics is how populations navigate the adaptive landscape in the presence of epistasis, or interactions among loci. This problem can be directly addressed by studying the evolution of RNA secondary structures, for which there is constraint to maintain pairing between Watson-Crick (WC) sites. Replacement of a nucleotide at one site of a WC pair reduces fitness by disrupting binding, which can be restored via a compensatory replacement at the interacting site. Here, I present the first genome-scale analysis of epistasis on the RNA secondary structure of human immunodeficiency virus type 1 (HIV-1). Comparison of polymorphism frequencies at ancestrally conserved sites reveals that selection against replacements is ∼2.7 times stronger at WC than at non-WC sites, such that nearly 50% of constraint can be attributed to epistasis. However, almost all epistatic constraint is due to selection against conversions of WC pairs to unpaired (UP) nucleotides, whereas conversions to GU wobbles are only slightly deleterious. This disparity is also evident in pairs with second-site compensatory replacements; conversions from UP nucleotides to WC pairs increase median fitness by ∼4.2%, whereas conversions from GU wobbles to WC pairs only increase median fitness by ∼0.3%. Moreover, second-site replacements that convert UP nucleotides to GU wobbles also increase median fitness by ∼4%, indicating that such replacements are nearly as compensatory as those that restore WC pairing. Thus, WC peaks of the HIV-1 epistatic adaptive landscape are connected by high GU ridges, enabling the viral population to rapidly explore distant peaks without traversing deep UP valleys.     

Adaptive landscapes in evolving populations of Pseudomonas fluorescens

The repeatability of adaptive evolution depends on the ruggedness of the underlying adaptive landscape. We contrasted the relative ruggedness of two adaptive landscapes by measuring the variance in fitness and metabolic phenotype within and among genetically distinct strains of Pseudomonas fluorescens in two environments differing only in the carbon source provided (glucose vs. xylose). Fitness increased in all lines, plateauing in one environment but not the other. The pattern of variance in fitness among replicate lines was unique to the selection environment; it increased over the course of the experiment in xylose but not in glucose. Metabolic phenotypes displayed two results: (1) populations adapted via changes that were distinctive to their selection environment, and (2) endpoint phenotypes were less variable in glucose than in xylose. These results indicate that although the response to selection is highly repeatable at the level of fitness, the underlying genetic routes taken were different for each environment and more variable in xylose. We suggest that this reflects a more rugged adaptive landscape in xylose compared to glucose. Our study demonstrates the utility of using replicate selection lines with different evolutionary starting points to try and quantify the relative ruggedness of adaptive landscapes.     

The population genetics of adaptation on correlated fitness landscapes: the block model

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.     

Natural selection, evolvability and bias due to environmental covariance in the field in an annual plant

Estimates of the form and magnitude of natural selection based on phenotypic relationships between traits and fitness measures can be biased when environmental factors influence both relative fitness and phenotypic trait values. I quantified genetic variances and covariances, and estimated linear and quadratic selection coefficients, for seven traits of an annual plant grown in the field. For replicates of 50 paternal half-sib families, coefficients of selection were calculated both for individual phenotypic values of the traits and for half-sib family mean values. The potential for evolutionary response was supported by significant heritability and phenotypic directional selection for several traits but contradicted by the absence of significant genetic variation for fitness estimates and evidence of bias in phenotypic selection coefficients due to environmental covariance for at least two of the traits analysed. Only studies of a much wider range of organisms and traits will reveal the frequency and extent of such bias.     

AN ADAPTIVE WALK BY HUMAN IMMUNODEFICIENCY VIRUS TYPE 1 THROUGH A FLUCTUATING FITNESS LANDSCAPE

The mutational landscape model of adaptive sequence evolution has been used to explain an unexpected strong positive linear relationship between marginal fitness and mean site‐specific amino acid frequency in the functionally important HIV‐1 gp120 V3 protein region. The model predicts a positive linear relationship between the probability that a particular beneficial allele, among several, is the next to spread to fixation during an adaptive walk, its transition probability, and the allele's selection coefficient. Here, stochastic simulation is used to confirm the intuition that the linear relationship between transition probabilities and selection coefficients, predicted by the model, should, under fluctuating selection, produce a linear relationship between allele frequency, averaged across populations, and fitness. In addition, these relationships hold for the effective population size and mutation rate of HIV‐1 and for the moderately strong selection observed for V3. A survey of the strength of mutation for diverse organisms suggests that these relationships may be widely applicable.     

Morphology and escape performance of tiger salamander larvae (Ambystoma tigrinum mavortium)

The ability of an individual to escape predators is an important component of fitness. Several adaptive explanations of body shape variation in amphibians hypothesize relationships between swimming performance and morphology, but these ideas have rarely been tested. Here we investigate bivariate and multivariate relationships between natural variation in morphology and performance. We used high-speed video to examine fast-starts associated with escape responses in small tiger salamander larvae (Ambystoma tigrinum). Our results indicate that performance is influenced by interactions among aspects of morphology, physiology, and behavior. Relationships between morphometric variables and velocity could be detected with multivariate, but not bivariate statistical analyses. In particular, relationships between morphology and velocity depend on tail beat frequency (potentially a measure of effort or vigor). Relationships between morphology and acceleration were detected with bivariate analyses, but multivariate analysis suggests that acceleration performance, too, depends on interactions between morphology and tail beat frequency. We found a positive relationship between tail area and propulsive performance, which supports adaptive interpretations of variation in larval tail shape within and between amphibian species.