Copyright 0 1992 by the Genetics Society of America Comparing Evolvability and Variability of Quantitative Traits David Houle’ Department of Statistics, North Carolina State University, Raleigh, North Carolina27695, and Department of Ecology and Evolution, University of Chicago, Chicago, Illinois 60637 Manuscript received February 20, 1991 Accepted for publication September 12, 199 1 ABSTRACT There are two distinct reasons for making comparisons of genetic variation for quantitative characters. The first is to compare evolvabilities, or ability to respond to selection, and the second is to make inferences about the forces that maintain genetic variability. Measures of variation that are standardized by the trait mean, such as the additive genetic coefficient of variation, are appropriate for both purposes. Variation has usually been compared as narrow sense heritabilities, but this is almost always an inappropriate comparative measure of evolvability and variability. Coefficients of variation were calculated from 842 estimates of trait means,variances and heritabilities in the literature. Traits closely related to fitness have higher additive genetic and nongenetic variability by the coefficient of variation criterion than characters under weak selection. This is the reverse of the accepted conclusion based on comparisons of heritability. The low heritability of fitness components is best explained by their high residual variation. The high additive genetic and residual variability of fitness traits might be explained by the great number of genetic and environmental events they are affected by, or by a lack of stabilizing selection to reduce their phenotypic variance. Over one-third of the quantitative genetics papers reviewed did not report trait means or variances. Researchers should always report these statistics, so that measures of variation appropriate to a variety of situations may be calculated. VOLUTIONARY and ecological geneticists use single generation, and R is the response to selection E relative measures of genetic variation to gain in the following generation (FALCONER1989; TURELLI insight into two sorts of questions. First, we would and BARTON 1990). like to be able to predict the ability of a population to Heritability has been widely used to compare the respond to natural or artificial selection; this I will genetic variation of life history traits relative to traits term “evolvability.” Second, wewish to gain insight presumably subject to less strong selection (GUSTAFS- into the strength of the forces which maintain and SON 1986; ROFFand MOUSSEAU1987; MOUSSEAUand depletethe genetic variation on which evolvability ROFF 1987; FALCONER1989). The robust result of depends. For this, we need measures of the relative such comparisons is that life history traits have lower “variability” of traits. heritabilities. The conclusion drawn from such com- At the phenotypic level, we want to know about the parisons has typically been that life history traits in potential for evolutionof the mean phenotype. In the some absolute sense possess less genetic variation,and short term, this depends on the additive geneticvari- will evolve less readily than other traits. ance. An essential step in quantitative genetics is the In this paper I will show that trait means, rather partitioning of trait variance, Vp, into additive genetic than Vp are appropriate for standardizing geneticvar- variance, VA, and a remainder, V,, consisting of vari- iances for comparative purposes. To investigate some ance due to other genetic and environmental causes of the implications of mean-standardized comparative (FALCONER1989). Narrow-sense heritability, h2 = studies, I have reviewed over 200 quantitative genetic VA/Vp, is almost always used as a summary measureof studies of animal populations. When mean-standard- this partitioning. In part, this is because h2 plays an ized measures are compared, traits closely related to important role in determining the response to selec- fitness are more variable than morphological traits, tion as shown by the familiar equation the opposite conclusion to studies based on heritabil- ity. This has important implications for theoriesof the R = h2S, (1) maintenance of geneticvariation. Unfortunately, a very high proportion of quantitative genetic studies where S is the selection differential, the difference in report h2, but not trait means or variances. No sum- population mean before and after selection within a mary measure of variation, h2 or a mean-standardized ’ Address after March 1, 1992: Department of Biology, University of statistic, can substitute for basic statistics about astudy Oregon, Eugene, Oregon 97403. population. (;rnetics 130 195-204 (January, 1992) 196 D. Houle EVOLVABILITY A good measure of evolvability is the expected response to selection. Looking at Equation 1, it is I is related to the phenotypiccoefficient of variation, natural to interpreth2 as a sufficient descriptor of the CVP = lOO&/x. Application of Equation 1 yields a state of a population for comparing evolvabilities. It version of FISHER’S“fundamental theorem of natural fails to fulfill this purpose for two reasons. First, while selection (FISHER1930; PRICE1972; FALCONER1989): h‘ is a dimensionless quantity R is not. Since, for comparative purposes, we are most often interested Rw = vA/w. (8) in proportional, rather than absolute change (HAL- Standardizing this response to selection by the mean DANE 1949), the potentialresponse needs to be stand- yields an appropriate measure of the relative evolva- ardized. Onestraightforward way of doing so is using bility of fitness the population mean. Second, the selection differential S is not solely a function of the fitness function,but also contains informationabout the selected population.For ex- ample, in the case of truncation selection on a nor- At equilibrium, the predicted gains of Equation 8 mally distributed character, S = i6,where i is the would be offset by processes, such as mutation and “intensity” of selection, determined only by the pro- segregation, which restore both theoriginal mean and portion of the population selected for breeding (FAL- genetic variance. In this case ZA is also an appropriate indicator of the variability of fitness, as large values CONER 1989). For a given i, the higher the standard deviation of the selected population, the more the must be the result of powerful forces maintaining selected individuals may differ from the original pop- genetic variance. ulation mean. An appropriate mean-standardized pre- Equations 8 and 9 also hold for all multiplicative components of fitness (O’DONALD 1970; ARNOLDand dictor ofevolvability under truncation selection of WADE 1984), although forsuch characters the inter- unknown intensity is therefore pretation is complicated by the potential for correla- tions among them. Large values of ZA could also be the result of negative genetic correlationsamong Here, and throughout this paper, x represents the traits, which attenuate the effects of selection pre- population mean before selection. Ingeneral, for dicted for each character separately. Negative corre- fitness function W(X)and trait distribution F(X), lations are, however, not necessarily to be expected m (CHARLESWORTH 1990; HOULE 1991),and the empir- s = IT-’ J (X - Z)W(X)F(X)dX (3) ical evidence fortheir generality is weak (HOULE “m 1991). (KIMURAand CROW 1978) where A second case where h2 is a misleading indicator of evolvability is that of weak gaussian optimizing selec- w = lIW(X)F(X) dX, (4) tion the mean fitness of the population. If W(X) can be approximated as a polynomial of order n, S will be a function of the first n + 1 momentsof F(X).One must where u2is a parameter inversely proportional to the specify theform that selection will take before an strength of selection for the optimum 8. Assuming appropriate index of evolvability can be chosen. that X is normally distributed, In two important cases h2 is a particularly mislead- VP VAVP ing estimator of evolvability because S is a function of R=(O-X)-- vp+ u2 vp Vp. One such case is when X is fitness (W(X) = X), making (BULMER1980, p. 150).What data is available on the strength of stabilizing selection suggests thatfre- Jmm (X2 - XX)F(X) dX S= quently u2>> Vp for morphological characters (TUR- J-2XF(X) dX ELLI 1984), making the response to changes in 0 approximately independent of Vp.Then the standard- ized response to selection is Standardizing by the mean yields a quantity CROW (1 958) called the “opportunity forselection”: Com paring Genetic Variabilities Genetic Comparing 197 A good measure of the evolvability of the population h2, will decline to zero (CHARLESWORTH1987). How- in response to arbitrary changes in 0 is then VA/x. ever, fitness components do in general possess VA While (6 - x)/(Vp+ 0‘) is clearly important in deter- (ISTOCK1983; ROFFand MOUSSEAU1987; MOUSSEAU mining the actual response to selection, its future and ROFF1987), which is not too surprising given the value is not estimable and of no predictive value. variety of potentialperturbing forces (CHARLES- In both of these important cases, directional and WORTH 1987; MAYO, BURGERand LEACH1990). In weak stabilizing selection, a variance to mean ratio is the presence of additive genetic variance for fitness, the most appropriate measureof evolvability of a trait. the fundamental theorem makes no prediction about While IA and VA/xare distinct quantities, they are h2, as FISHERand others have made clear (FISHER correlated, as they share