Heredity 77 (1996) 453—460 Received 10 July 1995 Modelling phenotypic plasticity. II. Do genetic correlations matter? MASSIMO PIGLIUCCI Departments of Botany end of Ecology 8 Evolutionary Biology, University of Tennessee, Knoxville, TN 37996-1100, U.S.A. Predictionsof the evolutionary trajectory of reaction norms and interpretation of empirical results are usually based on two mathematically equivalent ways of partitioning phenotypic variance into its genetic, environmental, and interaction components: the genotype by environ- ment interaction estimated by means of an analysis of variance, or the interenvironment genetic correlation (i.e. the genetic correlation between the expressions of the same trait in two environments). Both these quantities are supposed to indicate the amount of genetic variability for plasticity in a natural population. I point out that not only are the qualitative predictions based on these statistical methods sometimes in conflict with each other, but that both may fail to predict rates of evolution and equilibria under some circumstances, because they ignore the details of the genetic machinery. It is shown that, ultimately, the only way to predict reliably the evolution of plasticity is actually to know its specific genetic basis and the genotypic constitution of the population, however inconvenient this may be from both theoret- ical and empirical standpoints. The discussion is framed in terms of a simple one-locus two-allele model that mimics the real case of the pennant/vestigial system describing plasticity of wing length to temperature in Drosophila melanogaster. Keywords:geneticcorrelations, genotype—environment interactions, phenotypic plasticity, population genetics, quantitative genetics. equivalent to quantitative genetic models (Charles- Introduction worth, 1990; Abrams et aL, 1993). All empirical Phenotypicplasticity is the ability of a genotype to studies of phenotypic plasticity quantify the genetic produce different phenotypes in different environ- variation for plastic responses in one of two ways. ments and it is a property of the norm of reaction of (1) The first method uses analyses of variance, that genotype (Woltereck, 1909; Schmalhausen, according to which the total phenotypic variance can 1949). Although very important for breeding experi- be accounted for by three major sources of varia- ments since the beginning of the century (Falconer, tion: genotype, environment, and genotype by 1990), in recent years phenotypic plasticity has environment interaction (e.g. Falconer, 1990). (2) increasingly been the focus of theoretical and The second method utilizes the concept of inter- empirical research in evolutionary biology (reviews environment genetic correlation, according to which in Bradshaw, 1965; Schlichting, 1986; Sultan, 1987; a very positive or very negative correlation between West-Eberhard, 1989; Schemer, 1993). the expression of the same traits in two environ- Theoretical models of the evolution of phenotypic ments implies strong constraints on the evolution of plasticity have been proposed mostly from within the plasticity, whereas a weak or near-zero correlation framework of quantitative genetics, i.e. they are corresponds to the greatest evolutionary degrees of statistical accounts of changes in mean phenotype freedom for the system (the concept was introduced caused by allelic substitutions at many loci, each by Falconer, 1952 and elaborated by Yamada, 1962; with small and additive effects (e.g. Via & Lande, it has been used in an evolutionary context by Via & 1985; Gillespie & Turelli, 1989; de Jong, 1990; Lande, 1985 and has been generalized to the multi- Gomulkiewicz & Kirkpatrick, 1992; Gavrilets & variate case by van Tienderen & Koelewijn, 1994 Schemer, 1993). Alternative approaches have made and de Jong, 1995). Both approaches ignore the use of optimization theory, but these are genetically details of the genetic machinery underlying plastic 1996 The Genetical Society of Great Britain. 453 454 M. F'IGLIUCCI responses. In the case of the analysis of variance, the More generally, several authors have recently genetics is simply considered as a 'black box': the pointed out the possibility that complex traits might goal is to achieve a statistical representation of the be under simple genetic and developmental control, population of interest, not to infer causal mechan- and that we might be placing too much emphasis on isms. Evolutionary quantitative genetics sets a more the (assumed) quantitative genetic basis of pheno- ambitious agenda: not only are we interested in types (e.g. Gottlieb, 1984; Orr & Coyne, 1992; describing the current genetic make-up of the popu- Kadereit, 1994). lation, but we want to infer how such make-up is Several levels of criticism have been raised likely to constrain future evolution of the popula- through the years to caution against the use of tion. Several empirical papers using either method genetic correlations as tools for estimating genetic draw conclusions about the amount of genetic varia- constraints in a population. These can be summa- tion for plasticity, and the possibility of evolutionary rized as follows. (1) Genetic correlations are, by changes given the current genetic variance—covar- definition, subject to change through evolutionary iance structure of the population(s) (e.g. Conner & time (Turelli, 1988). This is because rG values are Via, 1993; Andersson & Shaw, 1994), although reflections of the actual gene frequencies of the others find contradictions or difficulties in reconcil- population, which are bound to change during selec- ing the two approaches (e.g. Ebert et al., 1993; tion. Incidentally, this is the reason why quantitative Gebhardt & Stearns, 1993; Windig, 1994). genetic models of the evolution of plasticity assume A fundamental question that we need to ask when a very weak stabilizing selection on the across- evaluating empirical data on phenotypic plasticity environment phenotype. However, these simulations based on statistical models is: to what extent can we are typically carried out for thousands of generations ignore or simplify the details of the mechanistic basis (e.g. Via & Lande, 1985), a span of time during of phenotypes, and how does this affect our ability to which mutation pressure and drift would presumably interpret the past evolutionary history and predict the be sufficient to alter the genetic variances and covar- future one (Pigliucci, 1992)? In the following I will lances. (2) Genetic correlations are affected by present a series of simple scenariograms using which changes in the environment and by genotype by I will show how little we can infer about the evolu- environment interactions, and are therefore to be tion of phenotypic plasticity by means of statistical considered only local statistical estimators of popula- analyses (Lewontin, 1974) especially when major loci tion properties, not useful for broad evolutionary underlie such plasticity. I will therefore call both for predictions (Service & Rose, 1985; Clark, 1987; more cautious interpretations of analyses of variance Mazer & Schick, 1991; Stearns et at., 1991; Ebert et and genetic correlations in the absence of any know- al., 1993; Schlichting & Pigliucci, 1995). (3) Genetic ledge of the genetic control of plasticity, and for covariances and correlations can lead to misleading more studies of the actual genetics of phenotypic conclusions about constraints if the hierarchical plasticity. structure of genetic interactions that yield the observable correlation is ignored (Houle, 1991; Whatdo we know and what do we assume Gromko, 1995). The G matrix is a 'flat' representa- about the genetics of plasticity? tion of the correlation among characters, i.e. its entries are pairwise comparisons. If there is a hier- Veryfew empirical studies of phenotypic plasticity archical structure to the genetic architecture, i.e. if have addressed its actual genetic basis. One of the some traits are connected to others indirectly (as in classical examples is the pennant/vestigial system metabolic flux models), then the information determining wing length and its response to contained in the G matrix can be incomplete to say temperature in Drosophila melanogaster. The reac- the least, and could yield misleading predictions. (4) tion norms for this trait are fairly complex (figs 23 & Unlike classical genetic correlations, inter-environ- 24 in Schmalhausen, 1949). Yet the system is mental ones are actually determined by a mixture of governed by only one locus with two alleles. Other at least two different genetic effects (if we ignore apparently complex plastic phenotypes having a rela- linkage): changes in gene expression catalysed by tively simple genetic basis are wing dimorphism in environmentally influenced regulatory genes, and some insects (Tauber & Tauber, 1992; Roff & Fair- changes in the allelic sensitivity of the same gene bairn, 1993), phytochrome-controlled shade-avoid- products expressed in two different environments ance response in angiosperms (Schmitt & Wulff, (Schlichting & Pigliucci, 1993). Schlichting and 1993), and plasticity of flowering time to vernaliza- Pigliucci (1995) have argued that the confounding tion in Arabidopsis thaliana (Koornneef et at., 1991). effects of these two underlying sources of variation The Genetical Society of Great Britain, Heredity, 77, 453—460. PHENOTYPIC PLASTICITY AND GENETIC CORRELATIONS 455 can potentially generate any value for the genetic in environment 2. In these equations, p is the correlation