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At least 19 recordsLinked to original sources
PubMed1998

[Wing shape and developmental temperature in two Drosophila species: different wing regions exhibit different reaction norms].

Reaction norms of different parts of the wing in relation to developmental temperature were analyzed in Drosophila melanogaster and D. simulans using polynomial adjustments. Six rearing temperatures that encompass the whole physiologically possible range of these species were used. Different morphometric traits of the wing were shown to have different shapes of reaction norms. In particular, traits belonging to the posterior wing compartment and to the edge of the wing had various reaction norm shapes, which differed from that of the total wing length. Temperatures of maximum values (TMVs) of most traits were higher in D. melanogaster than in D. simulans. In general, reaction norm shapes in D. simulans were more varied. The results are discussed in relation to thermal adaptation of the species studied.

Adaptation, Physiological↗
PubMed2006

Bayesian analysis of the linear reaction norm model with unknown covariates.

The reaction norm model is becoming a popular approach for the analysis of genotype x environment interactions. In a classical reaction norm model, the expression of a genotype in different environments is described as a linear function (a reaction norm) of an environmental gradient or value. An environmental value is typically defined as the mean performance of all genotypes in the environment, which is usually unknown. One approximation is to estimate the mean phenotypic performance in each environment and then treat these estimates as known covariates in the model. However, a more satisfactory alternative is to infer environmental values simultaneously with the other parameters of the model. This study describes a method and its Bayesian Markov Chain Monte Carlo implementation that makes this possible. Frequentist properties of the proposed method are tested in a simulation study. Estimates of parameters of interest agree well with the true values. Further, inferences about genetic parameters from the proposed method are similar to those derived from a reaction norm model using true environmental values. On the other hand, using phenotypic means as proxies for environmental values results in poor inferences.

Bayes Theorem↗
PubMed2002

Measuring probabilistic reaction norms for age and size at maturation.

We present a new probabilistic concept of reaction norms for age and size at maturation that is applicable when observations are carried out at discrete time intervals. This approach can also be used to estimate reaction norms for age and size at metamorphosis or at other ontogenetic transitions. Such estimations are critical for understanding phenotypic plasticity and life-history changes in variable environments, assessing genetic changes in the presence of phenotypic plasticity, and calibrating size- and age-structured population models. We show that previous approaches to this problem, based on regressing size against age at maturation, give results that are systematically biased when compared to the probabilistic reaction norms. The bias can be substantial and is likely to lead to qualitatively incorrect conclusions; it is caused by failing to account for the probabilistic nature of the maturation process. We explain why, instead, robust estimations of maturation reaction norms should be based on logistic regression or on other statistical models that treat the probability of maturing as a dependent variable. We demonstrate the utility of our approach with two examples. First, the analysis of data generated for a known reaction norm highlights some crucial limitations of previous approaches. Second, application to the northeast arctic cod (Gadus morhua) illustrates how our approach can be used to shed new light on existing real-world data.

Age Factors↗
PubMed2005

Natural selection and genetic variation for reproductive reaction norms in a wild bird population.

Many morphological and life-history traits show phenotypic plasticity that can be described by reaction norms, but few studies have attempted individual-level analyses of reaction norms in the wild. We analyzed variation in individual reaction norms between laying date and three climatic variables (local temperature, local rainfall, and North Atlantic Oscillation) of 1126 female collared flycatchers (Ficedula albicollis) with a restricted maximum likehood linear mixed model approach using random-effect best linear unbiased predictor estimates for the elevation (i.e., expected laying date in the average environment) and slope (i.e., adjustment in laying date as a function of environment) of females' reaction norms. Variation in laying date was best explained by local temperature, and individual females differed in both the elevation and the slope of their laying date-temperature reaction norms. As revealed by animal model analyses, there was weak evidence for additive genetic variance of elevation (h2 +/- SE = 0.09 +/- 0.09), whereas there was no evidence for heritability of slope (h2 +/- SE = 0.00 +/- 0.01). Selection analysis, using a female's lifetime production of fledglings or recruits as an estimate of her fitness, revealed significant selection for a lower phenotypic value and breeding value for elevation (i.e., earlier laying date at the average temperature). There was selection for steeper phenotypic values of slope (i.e., greater plasticity in the adjustment of laying date to temperature), but no significant selection on the breeding values of slope. Although these results suggest that phenotypic laying date is influenced by additive genetic factors, as well as by an interaction with the environment, selection on plasticity would not produce an evolutionary response.

Animals↗
PubMed2006

Caloric restriction increases longevity substantially only when the reaction norm is steep.

Evolutionary theory leads to the general expectation that dietary restriction will often result in increased survival probabilities, and thus increased lifespan. The reaction norm is a basic tool of evolutionary analysis that quantifies the relationship between environmental parameters and functional characters, including reproduction and longevity. In rodents, the reaction norm connecting adult longevity to caloric intake is fairly steep; small changes in intake lead to large changes in longevity. If this strong quantitative relationship were evolutionarily conserved among all mammals, then the prospects for a substantial increase in human lifespan from caloric restriction would be very good. In theory, however, reaction norms are expected to evolve for fitness related characters such as reproduction and survival. It has been shown experimentally in Drosophila that dietary reaction norms readily evolve in the laboratory, suggesting that they can do so among mammals as well, particularly over the millions of years since contemporary rodents and primates last shared a common ancestor. Our previous work crudely estimates that the dietary reaction norms of rodents and humans have diverged substantially, with a very flat dietary reaction norm for human longevity. These general principles and our specific results suggest that the benefits from human caloric restriction would be minor.

Adaptation, Physiological↗
PubMed2001

Reaction norms with bifurcations shaped by evolution.

Two versions of a model for the evolution of seasonal polyphenism investigate the evolution of reaction norm bifurcation and branching. The first version is without a specific submodel for morphological development and the second has an explicit developmental map. Version 1 is evolutionarily relatively unconstrained: (i) reaction norms are specified by matrices containing the probabilities of occurrence of environment-phenotype combinations, (ii) all conceivable reaction norm matrices are reachable through a sequence of mutations, and (iii) small as well as large mutational effects occur. This version is used to find the evolutionarily stable strategy favoured by the population ecology that is characterized by stabilizing viability selection with a cyclically fluctuating selection optimum. When the strength of selection is large and when the lag between initiation of development and selection on mature phenotype is not a multiple of half the period of the environmental cycle, a branching reaction norm evolves. In the second model version, branching reaction norms occur for certain parameter combinations of the developmental submodel, but the evolution of this pattern is often constrained. The evolutionary trajectory becomes trapped in a local selective optimum for the parameters of the developmental system. Substantial developmental noise evolves, but mutations that produce a selectively advantageous branching pattern do not occur from there.

Animals↗
PubMed1997

Evolutionary changes of nonlinear reaction norms according to thermal adaptation: a comparison of two Drosophila species.

While the adaptive significance of discontinuous reaction norms is generally accepted, the evolutionary interpretation of continuous response curves remains speculative, and the occurrence of internal constraints is often suggested as an explanation of experimental observations. In Drosophila melanogaster, various morphometrical traits exhibit convex reaction norms to growth temperature, with a maximum value within the developmental thermal range. We compared a cold-adapted species (D. subobscura) with a mid thermal range at 16 degrees C, to the warm-adapted D. melanogaster (mid thermal range at 22 degrees C) for three different morphometrical traits: wing and thorax length in both sexes and ovariole number in females. Maximum value temperatures were ordered in the same way for the three traits in both species: ovariole number > thorax length > wing length. Significant differences were also observed between the two species for the curvature parameter of the quadratic adjustment. The major observation was a significant lateral shift in the reaction norms: maximum values were observed at much lower temperatures in the cold-adapted species than in the warm-adapted one. The parallelism between mid thermal range variation and the position of the maximum value strongly suggests an adaptive displacement of the response curves. Natural selection may thus act not only on trait mean values but also on phenotypic plasticity and on the shape of reaction norms.

Animals↗
PubMed2004

Quantitative genetics of continuous reaction norms: thermal sensitivity of caterpillar growth rates.

A continuous reaction norm or performance curve represents a phenotypic trait of an individual or genotype in which the trait value may vary with some continuous environmental variable. We explore patterns of genetic variation in thermal performance curves of short-term caterpillar growth rate in a population of Pieris rapae. We compare multivariate methods, which treat performance at each test temperature as a distinct trait, with function-valued methods that treat a performance curve as a continuous function. Mean growth rate increased with increasing temperatures from 8 to 35 degrees C, was highest at 35 degrees C, and declined at 40 degrees C. There was substantial and significant variation among full-sib families in their thermal performance curves. Estimates of broad-sense genetic variances and covariances showed that genetic variance in growth rate increased more than 30-fold from low (8-11 degrees C) to high (35-40 degrees C) temperatures, even after differences in mean growth rate across temperatures were removed. Growth rate at 35 and 40 degrees C was negatively correlated genetically, suggesting a genetic trade-off in growth rate at these temperatures; this trade-off may represent either a generalist-specialist trade-off and/or variation in the optimal temperature for growth. The estimated genetic variance-covariance function (G function), the function-valued analog of the variance-covariance matrix (G matrix), was quite bumpy compared with the estimated G matrix; and results of principal component analyses of the G function were difficult to interpret. The use of orthogonal polynomials as the basis functions in current function-valued estimation methods may generate artifacts when the true G function has prominent local features, such as strong negative covariances at nearby temperatures (e.g. at 35 and 40 degrees C); this may be a particular issue for thermal performance curves and other highly nonlinear reaction norms.

Analysis of Variance↗
PubMed1998

Reaction norm functions and QTL-environment interactions for flowering time in Arabidopsis thaliana.

Many plant traits are phenotypically plastic in response to resource levels that vary continuously among environments. To be able to predict phenotypes in new environments, it is useful to model reaction norms as functions, rather than as a collection of discrete character states. Flowering date and rosette leaf number were measured in 100 recombinant inbred lines of Arabidopsis thaliana, grown on a gradient of light intensity. The results show that there is genetic variation among the recombinant inbred lines for parameters of the reaction norm functions. Genetic variances for leaf number and flowering date are highest under low light conditions. Underlying quantitative trait loci (QTLs) affecting the shape of the reaction norm functions were mapped by modifying Haley & Knott (1992) regressions to include polynomial effects of the environment. Quantitative trait loci of large effect were generally insensitive to the resource gradient. Seven QTLs affecting flowering date and eight QTLs for rosette leaf number were identified, of which only two had significant effects on the linear and quadratic components of the reaction norm function. These results suggest that the genotype-environment interactions for flowering time are controlled by many minor genes, whose effects are below the detection limit in most mapping experiments.

Arabidopsis↗
PubMed2006

Relating environmental variation to selection on reaction norms: an experimental test.

Theoretical models predict that selection on reaction norms should depend on the relative frequency of environmental states experienced by a population. We report a laboratory experimental test of this prediction for thermal performance curves of larval growth rate in Pieris rapae in relation to their thermal environment. We measured short-term relative growth rate (RGR) for each individual at a series of five temperatures, and then we assigned individuals randomly to warm or cool selection treatments, which differ in the frequency distributions of environmental temperatures. Selection gradient analyses of two independent experiments demonstrated significant positive selection for increasing RGR, primarily through its effects on survival to adulthood and on development rate. In both the warm and cool selection treatments, the magnitude of directional selection on RGR was consistently greater at lower (suboptimal) temperatures than at higher temperatures; differences in selection between the treatments did not match model predictions. The temporal order and duration of environmental conditions may affect patterns of selection on thermal performance curves and other continuous reaction norms, complicating the connections between variation in environment, phenotype, and fitness.

Animals↗
PubMed1999

Growth temperature and reaction norms of morphometrical traits in a tropical drosophilid: Zaprionus indianus.

Ten isofemale lines of Zaprionus indianus were analysed to study the reaction norms of five morphometrical traits (wing and thorax length, body weight, sternopleural bristle and ovariole number) in relation to growth temperature. All these traits exhibited nonlinear concave reaction norms and were characterized by the coordinates of their maximum: MV (maximum value), and TMV (temperature of maximum value). Wing/thorax ratio, which is related to flight capacity, was also calculated and exhibited a monotonically decreasing reaction norm. Intraclass correlations were on average quite low, with no significant differences between traits, temperature or sex; a highly significant trait-temperature interaction was, however, observed. Sex dimorphism was very low in Zaprionus, contrasting with data previously obtained in other species. MVs among lines were positively correlated for the three size-related traits, whereas sternopleural bristle and ovariole number were genetically independent. TMVs were different between the traits, but higher than in D. melanogaster and other cold-adapted species, in agreement with the hypothesis that the norm shape evolves according to species thermal adaptation. MVs and TMVs were never correlated, indicating that mean values and plasticity are genetically independent. Some positive correlations were observed among TMVs of different traits, suggesting that the same genetic system might regulate plasticity of different traits.

Animals↗
PubMed1989

A quantitative genetic model for growth, shape, reaction norms, and other infinite-dimensional characters.

Infinite-dimensional characters are those in which the phenotype of an individual is described by a function, rather than by a finite set of measurements. Examples include growth trajectories, morphological shapes, and norms of reaction. Methods are presented here that allow individual phenotypes, population means, and patterns of variance and covariance to be quantified for infinite-dimensional characters. A quantitative-genetic model is developed, and the recursion equation for the evolution of the population mean phenotype of an infinite-dimensional character is derived. The infinite-dimensional method offers three advantages over conventional finite-dimensional methods when applied to this kind of trait: (1) it describes the trait at all points rather than at a finite number of landmarks, (2) it eliminates errors in predicting the evolutionary response to selection made by conventional methods because they neglect the effects of selection on some parts of the trait, and (3) it estimates parameters of interest more efficiently.

Analysis of Variance↗
PubMed2006

The genetic basis of thermal reaction norm evolution in lab and natural phage populations.

Two major goals of laboratory evolution experiments are to integrate from genotype to phenotype to fitness, and to understand the genetic basis of adaptation in natural populations. Here we demonstrate that both goals are possible by re-examining the outcome of a previous laboratory evolution experiment in which the bacteriophage G4 was adapted to high temperatures. We quantified the evolutionary changes in the thermal reaction norms--the curves that describe the effect of temperature on the growth rate of the phages--and decomposed the changes into modes of biological interest. Our analysis indicated that changes in optimal temperature accounted for almost half of the evolutionary changes in thermal reaction norm shape, and made the largest contribution toward adaptation at high temperatures. Genome sequencing allowed us to associate reaction norm shape changes with particular nucleotide mutations, and several of the identified mutations were found to be polymorphic in natural populations. Growth rate measures of natural phage that differed at a site that contributed substantially to adaptation in the lab indicated that this mutation also underlies thermal reaction norm shape variation in nature. In combination, our results suggest that laboratory evolution experiments may successfully predict the genetic bases of evolutionary responses to temperature in nature. The implications of this work for viral evolution arise from the fact that shifts in the thermal optimum are characterized by tradeoffs in performance between high and low temperatures. Optimum shifts, if characteristic of viral adaptation to novel temperatures, would ensure the success of vaccine development strategies that adapt viruses to low temperatures in an attempt to reduce virulence at higher (body) temperatures.

Base Sequence↗
PubMedDate not supplied

Developmental constraints on an adaptive plasticity: reaction norms of pigmentation in adult segments of Drosophila melanogaster.

Variation of dark pigmentation according to developmental temperature was investigated in two geographic populations (France and India) with the isofemale line technique (20 lines for each population). The response curves called the reaction norms, were established in females for seven different segments: the mesothorax and abdomen segments 2-7 (Abd 2-7). In all cases the response curves were non-linear and had to be described either by a quadratic convex polynomial for thorax and Abd 2-5, or by a cubic polynomial for Abd 6 and 7. Among abdomen segments, increasing antero-posterior gradients were observed for several traits, including average pigmentation, overall phenotypic plasticity, the temperature of minimum pigmentation, and the curvature parameter of quadratic norms. Genetic correlations between abdomen segments were high when adjacent segments were considered, but became nil when more distant segments were correlated, suggesting that different pigmentation genes are expressed in the anterior and the posterior part of the abdomen. Characteristic values of reaction norms provided information either on trait value (i.e., the extension of pigmentation) or on plasticity. Correlations between plasticity and pigmentation were generally low and non-significant, suggesting their genetic independence. The overall darker pigmentation which is observed at low temperatures is assumed to be an adaptive plasticity. However, the differences which are evidenced among segments reveal strong interactions with developmental genes. These interactions are less likely to be a consequence of natural selection and are better interpreted as developmental constraints. The reaction norms analysis reveals the complexity of these interactions and should help, in the future, in the identification of the responsible thermosensitive genes.

Adaptation, Physiological↗
PubMed2005

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.

Animals↗
PubMedDate not supplied

Response to mass selection when the genotype by environment interaction is modelled as a linear reaction norm.

A breeding goal accounting for the effects of genotype by environment interaction (G x E) has to define not only traits but also the environment in which those traits are to be improved. The aim of this study was to predict the selection response in the coefficients of a linear reaction norm, and response in average phenotypic value in any environment, when mass selection is applied to a trait where G x E is modelled as a linear reaction norm. The optimum environment in which to test the selection candidates for a given breeding objective was derived. Optimisation of the selection environment can be used as a means to either maximise genetic progress in a certain response environment, to keep the change in environmental sensitivity at a desired rate, or to reduce the proportion of animals performing below an acceptance level. The results showed that the optimum selection environment is not always equal to the environment in which the response is to be realised, but depends on the degree of G x E (determined by the ratio of variances in slope and level of a linear reaction norm), the correlation between level and slope, and the heritability of the trait.

Animals↗
PubMed1996

Reaction norms of Arabidopsis IV. Relationships between plasticity and fitness.

The study of the association between fitness and reaction norms is of primary importance given the hypothesized role for phenotypic plasticity in shaping evolutionary patterns: in microevolution, as one of mechanism for maintaining genetic variation, and in macroevolution, as a means of generating phenotypic novelties. In a glasshouse experiment, we investigated variation in reaction norms to nutrient availability in populations of Arabidopsis thaliana, and the relationship between this variation and reproductive fitness. We found evidence for across-treatment directional selection on the means for leaf number, flowering time, plant height, branching and growth rate; across-treatment stabilizing selection was detected for growth rate; and across-treatment disruptive selection was significant for leaf number. We also uncovered selection on the plasticity of some traits: directional for the plasticity of branching, and stabilizing for the plasticity of both branching and growth rate. When the two environments were considered separately, directional selection for height was detected under low nutrients; under high nutrients, we found evidence for directional selection on leaf number and height, and for disruptive selection on flowering time. The genetic correlation between a trait's expression in one environment and its expression in the alternate environment was positive and highly significant only for flowering time and growth rate. A principle components analysis revealed possible constraints on future selection responses, because of correlations among character means and among character plasticities.

Analysis of Variance↗
PubMed2006

Does size matter most? The effect of growth history on probabilistic reaction norm for salmon maturation.

Body size is widely believed to affect the occurrence of sexual maturation. Recent studies have used changes in the age-specific body size at which the probability of maturing is 50%, a feature of probabilistic reaction norms, to quantify purported evolution of life histories. However, body size results from a combination of growth rates during successive developmental stages. Therefore, to understand the evolution of the maturation schedule, it is necessary to comprehend the relationships among body size, growth history, and maturation schedule. We examined the relationships among body size, previous growth history, and maturation probability in chum salmon (Oncorhynchus keta). In this study, previous growth history was estimated from yearly specific growth increments that provide information describing body size. Previous growth history was found to be more closely linked to maturation probability than body size. The most recent growth condition was the most important factor affecting whether a fish matured during the subsequent breeding season. Because individuals of similar body size and same age can have different growth histories, the relationship between body size and maturation probability could be plastically modified by growth history. This may violate an assumption required to infer evolution, namely that size-related maturation trends in probabilistic reaction norms are immune to growth history.

Animals↗