Variation,selection and evolution of function-valued traits

We describe an emerging framework for understanding variation, selection and evolution of phenotypic traits that are mathematical functions. We use one specific empirical example – thermal performance curves (TPCs) for growth rates of caterpillars – to demonstrate how models for function-valued traits are natural extensions of more familiar, multivariate models for correlated, quantitative traits. We emphasize three main points. First, because function-valued traits are continuous functions, there are important constraints on their patterns of variation that are not captured by multivariate models. Phenotypic and genetic variation in function-valued traits can be quantified in terms of variance-covariance functions and their associated eigenfunctions: we illustrate how these are estimated as well as their biological interpretations for TPCs. Second, selection on a function-valued trait is itself a function, defined in terms of selection gradient functions. For TPCs, the selection gradient describes how the relationship between an organism's performance and its fitness varies as a function of its temperature. We show how the form of the selection gradient function for TPCs relates to the frequency distribution of environmental states (caterpillar temperatures) during selection. Third, we can predict evolutionary responses of function-valued traits in terms of the genetic variance-covariance and the selection gradient functions. We illustrate how non-linear evolutionary responses of TPCs may occur even when the mean phenotype and the selection gradient are themselves linear functions of temperature. Finally, we discuss some of the methodological and empirical challenges for future studies of the evolution of function-valued traits.     

Sexual dimorphism in the quantitative-genetic architecture of floral, leaf, and allocation traits in Silene latifolia

Many species exhibit sexual dimorphism in a variety of characters, and the underlying genetic architecture of dimorphism potentially involves sex-specific differences in the additive-genetic variance-covariance matrix (G) of dimorphic traits. We investigated the quantitative-genetic structure of dimorphic traits in the dioecious plant Silene latifolia by estimating G (including within-sex matrices, G(m), G(f), and the between-sex variance-covariance matrix, B), and the phenotypic variance-covariance matrix (P) for seven traits. Flower number was the most sexually dimorphic trait, and was significantly genetically correlated with all traits within each sex. Negative genetic correlations between flower size and number suggested a genetic trade-off in investment, but positive environmental correlations between the same traits resulted in no physical evidence for a trade-off in the phenotype. Between-sex genetic covariances for homologous traits were always greater than 0 but smaller than 1, showing that some, but not all, of the variation in traits is caused by genes or alleles with sex-limited expression. Using common principal-components analysis (CPCA), a maximum-likelihood (ML) estimation approach, and element-by-element comparison to compare matrices, we found that G(m) and G(f) differed significantly in eigenstructure because of dissimilarity in covariances involving leaf traits, suggesting the presence of variation in sex-limited genes with pleiotropic effects and/or linkage between sex-limited loci. The sex-specific structure of G is expected to cause differences in the correlated responses to selection within each sex, promoting the further evolution and maintenance of dimorphism.     

A general model of functional constraints on phenotypic evolution

A general model of the functional constraints on the rate and direction of phenotypic evolution is developed using a decomposition of the Lande-Arnold model of multivariate phenotypic evolution. The important feature of the model is the F matrix of performance coefficients reflecting the causal relationship between morphophysiological (m-p) and functional performance traits. The structure of F, which reflects the functional architecture of the organism, constrains the shape of the adaptive landscape and thus the rate and direction of m-p trait evolution. The rate of m-p trait evolution is a function of the pattern of coefficients in a row of F. The sums and variances of these rows are related to current concepts of evolvability. The direction of m-p trait evolution through m-p trait space is a function of the functional covariances among m-p traits. The functional covariance between a pair of m-p traits is a measure of how much the traits function together and is computed as the covariance between rows of F. Finally, it is shown that genetic covariances between m-p traits and performance traits are a function of the F matrix, but a G matrix that includes these covariances cannot be used to model functional constraints effectively.     

Genetic covariances promote climatic adaptation in Australian Drosophila*

Evolutionary potential for adaptation hinges upon the orientation of genetic variation for traits under selection, captured by the additive genetic variance-covariance matrix (G), as well as the evolutionary stability of G. Yet studies that assess both the stability of G and its alignment with selection are extraordinarily rare. We evaluated the stability of G in three Drosophila melanogaster populations that have adapted to local climatic conditions along a latitudinal cline. We estimated population- and sex-specific G matrices for wing size and three climatic stress-resistance traits that diverge adaptively along the cline. To determine how G affects evolutionary potential within these populations, we used simulations to quantify how well G aligns with the direction of trait divergence along the cline (as a proxy for the direction of local selection) and how genetic covariances between traits and sexes influence this alignment. We found that G was stable across the cline, showing no significant divergence overall, or in sex-specific subcomponents, among populations. G also aligned well with the direction of clinal divergence, with genetic covariances strongly elevating evolutionary potential for adaptation to climatic extremes. These results suggest that genetic covariances between both traits and sexes should significantly boost evolutionary responses to environmental change.     

Variation in continuous reaction norms: quantifying directions of biological interest

Thermal performance curves are an example of continuous reaction norm curves of common shape. Three modes of variation in these curves--vertical shift, horizontal shift, and generalist-specialist trade-offs--are of special interest to evolutionary biologists. Since two of these modes are nonlinear, traditional methods such as principal components analysis fail to decompose the variation into biological modes and to quantify the variation associated with each mode. Here we present the results of a new method, template mode of variation (TMV), that decomposes the variation into predetermined modes of variation for a particular set of thermal performance curves. We illustrate the method using data on thermal sensitivity of growth rate in Pieris rapae caterpillars. The TMV model explains 67% of the variation in thermal performance curves among families; generalist-specialist trade-offs account for 38% of the total between-family variation. The TMV method implemented here is applicable to both differences in mean and patterns of variation, and it can be used with either phenotypic or quantitative genetic data for thermal performance curves or other continuous reaction norms that have a template shape with a single maximum. The TMV approach may also apply to growth trajectories, age-specific life-history traits, and other function-valued traits.     

The B-matrix harbors significant and sex-specific constraints on the evolution of multicharacter sexual dimorphism

The extent to which sexual dimorphism can evolve within a population depends on an interaction between sexually divergent selection and constraints imposed by a genetic architecture that is shared between males and females. The degree of constraint within a population is normally inferred from the intersexual genetic correlation, r(mf) . However, such bivariate correlations ignore the potential constraining effect of genetic covariances between other sexually coexpressed traits. Using the fruit fly Drosophila serrata, a species that exhibits mutual mate preference for blends of homologous contact pheromones, we tested the impact of between-sex between-trait genetic covariances using an extended version of the genetic variance-covariance matrix, G, that includes Lande's (1980) between-sex covariance matrix, B. We find that including B greatly reduces the degree to which male and female traits are predicted to diverge in the face of divergent phenotypic selection. However, the degree to which B alters the response to selection differs between the sexes. The overall rate of male trait evolution is predicted to decline, but its direction remains relatively unchanged, whereas the opposite is found for females. We emphasize the importance of considering the B-matrix in microevolutionary studies of constraint on the evolution of sexual dimorphism.     

Feeding, growth, and the thermal environment of cabbage white caterpillars, Pieris rapae L

Laboratory studies of temperature effects on short-term feeding and growth rates were combined with field data on thermal environments to explore the consequences of temperature variation for growth of caterpillars of the cabbage white butterfly, Pieris rapae. Mean short-term (24-h) consumption and growth rates of fourth-instar P. rapae feeding on collard leaves increased continuously with increasing temperatures between 10 degrees and 35 degrees C, peaked at 35 degrees C, and declined rapidly with temperatures above 35 degrees C. Physical models can mimic temperatures of real fifth-instar caterpillars under collard leaves within 1 degrees -2 degrees C in sunny summer conditions in Seattle, Washington. Continuous recordings of operative temperatures of model caterpillars in a collard garden suggest that, at the timescale of the duration of the fifth instar (5-8 d in the field), P. rapae caterpillars frequently experience temperatures spanning a 25 degrees C range, they spend most of their time at temperatures well below those that maximize growth, and they encounter substantial variation in the frequency distribution of operative temperatures between time periods. Combining these data on growth rate as a function of temperature and the distribution of operative temperatures in the field, I illustrate how growth rates at higher temperatures can make disproportionate contributions to the overall mean growth rates even when higher temperatures are relatively infrequent. Fluctuating thermal conditions may generate variable patterns of selection on reaction norms for growth rate in the field.     

Quantitative genetic variation for thermal performance curves within and among natural populations of Drosophila serrata

Thermal performance curves (TPCs) provide a powerful framework for studying the evolution of continuous reaction norms and for testing hypotheses of thermal adaptation. Although featured heavily in comparative studies, the framework has been comparatively underutilized for quantitative genetic tests of thermal adaptation. We assayed the distribution of genetic (co)variance for TPC (locomotor activity) within and among three natural populations of Drosophila serrata and performed replicated tests of two hypotheses of thermal adaptation--that 'hotter is better' and that a generalist-specialist trade-off underpins the evolution of thermal sensitivity. We detected significant genetic variance within, and divergence among, populations. The 'hotter is better' hypothesis was not supported as the genetic correlations between optimal temperature (T(opt)) and maximum performance (z(max)) were consistently negative. A pattern of variation consistent with a generalist-specialist trade-off was detected within populations and divergence among populations indicated that performance curves were narrower and had higher optimal temperatures in the warmer, but less variable tropical population.     

Thermal adaptation in the fungal pathogen Mycosphaerella graminicola

Genetic differentiation in thermal adaptation can result from a trade-off between the performance of organisms across different temperatures or from the accumulation of deleterious mutations. In this experiment, we assayed thermal sensitivity of 138 genetically distinct Mycosphaerella graminicola isolates sampled from five host populations in four locations under two temperature regimes (22 and 15 °C) and found significant differences in growth rate and response to temperature among populations. On average, genetic differentiation accounted for more than 50% of phenotypic variation in thermal adaptation while plasticity contributed less than a quarter of phenotypic variation. Populations originating from warm places performed better under the high-temperature regime and had a larger positive response to increasing temperature. Pairwise population differentiation (Q(ST) ) in temperature sensitivity, measured by taking the ratio of growth rates at 22 to 15 °C, was positively and significantly correlated to the pairwise difference in annual mean temperature at the collection sites. Because overall Q(ST) in temperature sensitivity was significantly higher than overall G(ST) in neutral restriction fragment length polymorphism loci, we believe that the primary mechanism underlying this thermal adaptation is antagonistic pleiotropy. Our results indicate that temperature sensitivity is a better indicator of thermal adaptation than growth rate at individual temperatures.     

Plasticity of size and growth in fluctuating thermal environments: comparing reaction norms and performance curves

Ectothermic animals exhibit two distinct kinds of plasticityin response to temperature: Thermal performance curves (TPCs),in which an individual's performance (e.g., growth rate) variesin response to current temperature; and developmental reactionnorms (DRNs), in which the trait value (e.g., adult body sizeor development time) of a genotype varies in response to developmentaltemperatures experienced over some time period during development.Here we explore patterns of genetic variation and selectionon TPCs and DRNs for insects in fluctuating thermal environments.First, we describe two statistical methods for partitioningtotal genetic variation into variation for overall size or performanceand variation in plasticity, and apply these methods to availabledatasets on DRNs and TPCs for insect growth and size. Our resultsindicate that for the datasets we considered, genetic variationin plasticity represents a larger proportion of the total geneticvariation in TPCs compared to DRNs, for the available datasets.Simulations suggest that estimates of the genetic variationin plasticity are strongly affected by the number and rangeof temperatures considered, and by the degree of nonlinearityin the TPC or DRN. Second, we review a recent analysis of fieldselection studies which indicates that directional selectionfavoring increased overall size is common in many systems—thatbigger is frequently fitter. Third, we use a recent theoreticalmodel to examine how selection on thermal performance curvesrelates to environmental temperatures during selection. Themodel predicts that if selection acts primarily on adult sizeor development time, then selection on thermal performance curvesfor larval growth or development rates is directly related tothe frequency distribution of temperatures experienced duringlarval development. Using data on caterpillar temperatures inthe field, we show that the strength of directional selectionon growth rate is predicted to be greater at the modal (mostfrequent) temperatures, not at the mean temperature or at temperaturesat which growth rate is maximized. Our results illustrate someof the differences in genetic architecture and patterns of selectionbetween thermal performance curves and developmental reactionnorms.     

Influence of temperature on the development, reproduction and longevity of Ceratothripoides claratris (Thysanoptera: Thripidae) on tomatoes

Ceratothripoides claratris (Shumsher) is a serious pest attacking tomatoes in Thailand. Temperature-dependent development of C. claratris was studied at seven constant temperatures, i.e. 22, 25, 27, 30, 34, 35 and 40 degrees C. Pre-adult survivorship was greatest (95%) at 25 and 30 degrees C and shortest at 22 degrees C. Egg-to-adult time decreased within the range of 20 to 30 degrees C and at 34 degrees C it started to increase. The lower thermal threshold for egg-to-adult development was estimated at 16 and 18 degrees C by linear regression and the modified Logan model, respectively. The optimum temperature for egg-to-adult development was estimated at 32-33 degrees C by the modified Logan model. The influence of temperature on reproduction and longevity of C. claratris was determined at 25, 30 and 35 and 40 degrees C. Both inseminated and virgin females failed to reproduce at 40 degrees C. Virgin females produced only male offspring, confirming arrhenotoky. The sex ratio of the offspring of fertilized females was strongly female-biased, except at 25 degrees C. Mean total fecundity per female and mean daily total fecundity per female were highest for both virgin and inseminated females at 30 degrees C. Female longevity was longest at 25 degrees C and shortest at 40 degrees C. Male longevity was longest at 30 degrees C and shortest at 40 degrees C. The net reproductive rate (R0) and intrinsic rate of natural increase (rm) was greatest at 30 degrees C while, mean generation time (G) and the doubling time (t) were highest at 25 degrees C. The finite rate of increase (lambda) was fairly constant (1.1-1.5 days) over the three temperatures tested. The pest potential of C. claratris for tropical Asia is discussed.     

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

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.     

HOMOGENEITY OF THE GENETIC VARIANCE-COVARIANCE MATRIX FOR ANTIPREDATOR TRAITS IN TWO NATURAL POPULATIONS OF THE GARTER SNAKE THAMNOPHIS ORDINOIDES

Quantitative genetic models of evolution rely on the genetic variance-covariance matrix to predict the phenotypic response to selection. Both prospective and retrospective studies of phenotypic evolution across generations rely on assumptions about the constancy of patterns of genetic covariance through time. In the absence of robust theoretical predictions about the stability of genetic covariances, this assumption must be tested with empirical comparisons of genetic parameters among populations and species. Genetic variance-covariance matrices were estimated for a suite of antipredator traits in two populations of the northwestern garter snake, Thamnophis ordinoides. The characters studied include color pattern and antipredator behaviors that interact to facilitate escape from predators. Significant heritabilities for all traits were detected in both populations. Genetic correlations and covariances were found among behaviors in both populations and between color pattern and behavior in one of the populations. Phenotypic means differed among populations, but pairwise comparisons revealed no heterogeneity of genetic parameters between the populations. The structure of the genetic variance-covariance matrix has apparently not changed significantly during the divergence of these two populations.     

Influence of white light on production of aflatoxins and anthraquinones in Aspergillus parasiticus.

The effect of continuous light and continuous darkness on the growth of Aspergillus parasiticus and on the production of aflatoxin, averufin, versicolorin A, and versicolorin C by Aspergillus parasiticus were determined at six different temperatures with six replicates for each experiment. No growth was observed at 15 degrees C in the light, although slight growth was observed at this temperature in the dark. No aflatoxins or anthraquinones were produced in the light or dark at 35 and 40 degrees C, although growth was good at these temperatures. Differences in aflatoxins and anthraquinones for cultures grown in light and in dark were consistent at each temperature. Higher mean quantities of these secondary metabolites were produced in the light at 20 and 25 degrees C; lower mean quantities were produced in the light at 30 degrees C. The ranges of values overlapped considerably, but in all cases the differences between temperatures were significant.     

Study of temperature-growth interactions of entomopathogenic fungi with potential for control of Varroa destructor (Acari: Mesostigmata) using a nonlinear model of poikilotherm development

AIMS: To investigate the thermal biology of entomopathogenic fungi being examined as potential microbial control agents of Varroa destructor, an ectoparasite of the European honey bee Apis mellifera. METHODS AND RESULTS: Colony extension rates were measured at three temperatures (20, 30 and 35 degrees C) for 41 isolates of entomopathogenic fungi. All of the isolates grew at 20 and 30 degrees C but only 11 isolates grew at 35 degrees C. Twenty-two isolates were then selected on the basis of appreciable growth at 30-35 degrees C (the temperature range found within honey bee colonies) and/or infectivity to V. destructor, and their colony extension rates were measured at 10 temperatures (12.5-35 degrees C). This data were then fitted to Schoolfield et al. [J Theor Biol (1981)88:719-731] re-formulation of the Sharpe and DeMichele [J Theor Biol (1977)64:649-670] model of poikilotherm development. Overall, this model accounted for 87.6-93.9% of the data variance. Eleven isolates exhibited growth above 35 degrees C. The optimum temperatures for extension rate ranged from 22.9 to 31.2 degrees C. Only three isolates exhibited temperature optima above 30 degrees C. The super-optimum temperatures (temperature above the optimum at which the colony extension rate was 10% of the maximum rate) ranged from 31.9 to 43.2 degrees C. CONCLUSIONS: The thermal requirements of the isolates examined against V. destructor are well matched to the temperatures in the broodless areas of honey bee colonies, and a proportion of isolates, should also be able to function within drone brood areas. SIGNIFICANCE AND IMPACT OF THE STUDY: Potential exists for the control of V. destructor with entomopathogenic fungi in honey bee colonies. The methods employed in this study could be utilized in the selection of isolates for microbial control prior to screening for infectivity and could help in predicting the activity of a fungal control agent of V. destructor under fluctuating temperature conditions.     

Seasonal and artificially elevated temperatures influence bioenergetic allocation patterns in the common pond snail, Physella virgata

Allocation of organic carbon (OC) to primary energetic pathways was estimated under seasonal and artificially elevated ambient temperatures for a field population of a freshwater pulmonate snail, Physella virgata. Allocation to respiration increased with temperature. Snails allocated most assimilated OC to reproduction within their natural temperature range (15 degrees -35 degrees C), where assimilation efficiencies remained relatively stable at 25%-35%. However, in artificially heated waters exceeding 35 degrees C, declining assimilation rates and increasing respiratory demands inhibited allocation to reproduction and growth. At the species' 40 degrees C upper thermal limit, assimilation efficiencies fell below 10%, while average consumption levels more than doubled relative to snails unaffected by the thermal effluent. Ambient temperature substantially influenced OC allocation over P. virgata's natural temperature range and negatively affected growth and reproduction at temperatures approaching or exceeding maximum natural levels.     

Critical thermal limits depend on methodological context

A full-factorial study of the effects of rates of temperature change and start temperatures was undertaken for both upper and lower critical thermal limits (CTLs) using the tsetse fly, Glossina pallidipes. Results show that rates of temperature change and start temperatures have highly significant effects on CTLs, although the duration of the experiment also has a major effect. Contrary to a widely held expectation, slower rates of temperature change (i.e. longer experimental duration) resulted in poorer thermal tolerance at both high and low temperatures. Thus, across treatments, a negative relationship existed between duration and upper CTL while a positive relationship existed between duration and lower CTL. Most importantly, for predicting tsetse distribution, G. pallidipes suffer loss of function at less severe temperatures under the most ecologically relevant experimental conditions for upper (0.06 degrees C min(-1); 35 degrees C start temperature) and lower CTL (0.06 degrees C min(-1); 24 degrees C start temperature). This suggests that the functional thermal range of G. pallidipes in the wild may be much narrower than previously suspected, approximately 20-40 degrees C, and highlights their sensitivity to even moderate temperature variation. These effects are explained by limited plasticity of CTLs in this species over short time scales. The results of the present study have broad implications for understanding temperature tolerance in these and other terrestrial arthropods.     

Quantitative genetics of temperature performance curves of Neurospora crassa

Earth's temperature is increasing due to anthropogenic CO emissions; and organisms need either to adapt to higher temperatures, migrate into colder areas, or face extinction. Temperature affects nearly all aspects of an organism's physiology via its influence on metabolic rate and protein structure, therefore genetic adaptation to increased temperature may be much harder to achieve compared to other abiotic stresses. There is still much to be learned about the evolutionary potential for adaptation to higher temperatures, therefore we studied the quantitative genetics of growth rates in different temperatures that make up the thermal performance curve of the fungal model system Neurospora crassa. We studied the amount of genetic variation for thermal performance curves and examined possible genetic constraints by estimating the G -matrix. We observed a substantial amount of genetic variation for growth in different temperatures, and most genetic variation was for performance curve elevation. Contrary to common theoretical assumptions, we did not find strong evidence for genetic trade-offs for growth between hotter and colder temperatures. We also simulated short-term evolution of thermal performance curves of N. crassa, and suggest that they can have versatile responses to selection.     

Evolution and stability of the G-matrix on a landscape with a moving optimum

In quantitative genetics, the genetic architecture of traits, described in terms of variances and covariances, plays a major role in determining the trajectory of evolutionary change. Hence, the genetic variance-covariance matrix (G-matrix) is a critical component of modern quantitative genetics theory. Considerable debate has surrounded the issue of G-matrix constancy because unstable G-matrices provide major difficulties for evolutionary inference. Empirical studies and analytical theory have not resolved the debate. Here we present the results of stochastic models of G-matrix evolution in a population responding to an adaptive landscape with an optimum that moves at a constant rate. This study builds on the previous results of stochastic simulations of G-matrix stability under stabilizing selection arising from a stationary optimum. The addition of a moving optimum leads to several important new insights. First, evolution along genetic lines of least resistance increases stability of the orientation of the G-matrix relative to stabilizing selection alone. Evolution across genetic lines of least resistance decreases G-matrix stability. Second, evolution in response to a continuously changing optimum can produce persistent maladaptation for a correlated trait, even if its optimum does not change. Third, the retrospective analysis of selection performs very well when the mean G-matrix (G) is known with certainty, indicating that covariance between G and the directional selection gradient beta is usually small enough in magnitude that it introduces only a small bias in estimates of the net selection gradient. Our results also show, however, that the contemporary G-matrix only serves as a rough guide to G. The most promising approach for the estimation of G is probably through comparative phylogenetic analysis. Overall, our results show that directional selection actually can increase stability of the G-matrix and that retrospective analysis of selection is inherently feasible. One major remaining challenge is to gain a sufficient understanding of the G-matrix to allow the confident estimation of G.     

Relationships between genotype x environment interaction and genetic correlation of the same trait measured in different environments

Summary Relationships between genotype x environment interaction and genetic correlation of the same trait measured in different fixed environments are derived by comparing the variance-covariance structures of observations between a one-way multiple-trait linear model and a two-way single-trait mixed linear model. In the latter model, heterogeneity of interaction variances among environments and non-zero covariances among interactions are assumed, in addition to the heterogeneity of error variances and non-zero covariances between genetic-group effects and interactions that were accommodated in earlier work. The results are applicable to more than two environments and to unbalanced data. This paper is a generalization and a correction of earlier works.