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J. evol. Biol. 7: l-12 (1994) lOlO-061X/94/010001L12$ 0 1994 BirkhHuser 1.50+0.20/O Verlag, Base1 Mini-review A general model of the relation and genetic response P. H. van Tienderen’,2 between phenotypic selection and G. de Jong3 ‘Netherlands Institute of Ecology, Centre for Terrestrial Ecology, Department of Plant Population Biology, P.O. Box 40, 6666 ZG Heteren, The Netherlands ‘Department of Genetics, Agricultural University Wageningen 3Department of Plant Ecology and Evolutionary Biology, University of Utrecht Key words: Quantitative genetics; selection; heritability; trade-offs; birds. Abstract The phenotypic view of selection assumes that genetic responses can be predicted from selective forces and heritability - or in the classical quantitative genetic equation: R = h2S. However, data on selection in bird populations show that often no selection response is found, despite consistent selective forces on phenotypes and significant heritable variation. Such discrepancies may arise due to the assumption that selection only acts on observed phenotypes. We derive a general selection equation that takes into account the possibility that some relevant (internal or external) traits are not measured. This equation shows that the classic equation applies if selection directly acts on the measured, phenotypic traits. This is not the case when, for instance, there are unknown internal genetic trade-offs, or unknown common environmental factors affecting both trait and fitness. In such cases, any relationship between phenotypic selection and genetic response is possible. Fortunately, the classical model can be tested by comparing phenotypic and genetic covariances between traits and fitness; an indication that important internal or external traits are missing can thus be obtained. Such an analysis was indeed found in the literature; for selection on fledging weight in Great Tits it yielded valuable extra information. Introduction Genetic changes in a population can be predicted by tracing the flow of genes from one generation to the next. Robertson’s secondary theorem of natural 2 van Tienderen and de Jong selection states this more precisely: ‘the change in any character produced by a selection process is equal to the additive genetic covariance between fitness and the character itself’ (Robertson, 1968; Crow and Nagylaki, 1976). When selection is due to differences in viability, the covariance between trait and relative fitness is simply the difference in mean breeding value before and after selection. More generally, this covariance sums up the additive effects of the genes affecting the trait, taking into account their expected frequencies in the next generation (i.e. weighted by relative fitness). The secondary theorem lacks an explicit reference to selection at the phenotypic level, and follows a ‘genetic approach’. However, natural selection is often seen as the result of (i) heritable phenotypic variation and (ii) consistent fitness differences between phenotypes (Endler, 1986). This ‘phenotypic approach’ is summarized in the familiar quantitative genetic formula R = h2S, with R the response to selection, h2 the heritability and S the selection differential (Falconer, 198 I), or in its multivariate form R = GP- ‘S in which R and S are now vectors of responses and selection differentials, and G and P genetic and environmental covariance matrices, respectively (Lande, 1982). The phenotypic approach suggests that selection can be adequately described by combining measurements of selection on phenotypic traits, and estimates of heritabilities and genetic correlations. The empirical appeal is evident: field studies can measure selective forces on phenotypes, phenotypic optimization models can be used to derive optimal strategies, and the population should show a response in the predicted direction, towards a peak in the fitness landscape, provided that there is adequate genetic variation. Problems with this phenotypic approach have been detected in numerous studies of selection in bird populations (Boyce and Perrins, 1987: Rockwell, Findlay and Cooke, 1987; Gibbs, 1988; Price, Kirkpatrick and Arnold, 1988; Price and Liou, 1989; Alatalo, Gustafsson and Lundberg, 1990; Cooke et al., 1990). Unlike many other organisms birds allow an integrated analysis of selection and genetic variation in natural populations. These papers reported directional selection and significant heritabilities, without any indication of a selection response. Apparently, the observed phenotypic correlation between trait and fitness was not accompanied by a genetic correlation between trait and fitness (unless the selection response was exactly counterbalanced by changes in conditions over time, cf. Cooke et al., 1990). Plausible hypotheses concerning the absence of selection response were given. For instance, Price and Liou (1989) argued that apparent selection on clutch size was in fact due to a correlation between the non-heritable nutritional state and clutch size; Alatalo, Gustafsson and Lundberg (1990) argued that selection was acting on the environmental component of tarsus length rather than on the phenotype. In more general terms, there are two reasons why the phenotypic approach may be too simple. Firstly, expectations are based on a model with specific assumptions about the genetics underlying quantitative traits, concerning number of loci, allelic effects, polygenic mutation rates, pleiotropy and epistasis. Our knowledge of the actual genetics of quantitative traits is very limited (Barton and Turelli, 1989) genetic details may matter (Turelli, 1988) and simple expectations may be wrong. Here we focus on an entirely different complicating factor, the fact that we observe only a subset of the traits under selection. The purpose of this paper is to show how Phenotypic selection and genetic response 3 the relationship between observed selection forces and genetic responses is affected by lack of information. We derive a general equation for the relationship between apparent selection and genetic response. A general framework for selection A morphological or behavioural trait is affected by a complex network of genes and their products, interacting with the ambient environmental conditions (Endler and McLellan, 1988; Wade and Kalisz, 1990; Rausher, 1992) (Fig. 1). A functional explanation can often be given for the relationship between the external phenotype and fitness. For instance, the optimal timing of breeding in Great Tits depends on the peak in caterpillar density when rearing the chicks (Perrins, 1991). This might be called ‘external selection’, as selection depends on conditions in the external environment. ‘Internal selection’ on the genes, mechanisms and ‘intermediate structures’ (Stearns, 1981) that underlie the external phenotype may also affect the outcome of selection. For example, genes that cause early breeding may have effects on fitness other than those mediated by the breeding data and its effect on the Fig. 1. Example of a simple network of traits: genes affect internal traits, that affect external traits (e.g. morphology, behaviour) and/or fitness components (e.g. viability, fecundity). Arrows indicate translations from one level to the next, that may be affected by environmental factors E (no arrows drawn for clarity here). At each level there may be variation within the population. The subset of observed traits is given by thick boxes. It is usually impossible to cover all relevant traits and pathways. For instance, gene G3 affects internal trait 13, hence traits 22, 23 and fitness component W3. Consequently, the observed correlation between 22 and fitness is due to (i) external selection on the phenotype (path Z2-W2-W) and (ii) genes such as G3 that affect both 22 (path G3-13-22) and, but independently, W (path G3-13-23.W3 or C3-13-W3). 4 van Tienderen and de Jong clutch, e.g. due to an internal metabolic cost of breeding early. The external and internal selective forces may also interact. Females that breed early in the season may be confronted with low temperatures and limited food supplies; this in turn may result in relatively high metabolic costs of laying the clutch. In contrast, a female that starts early because she lives in a warmer habitat with an earlier food supply may not pay extra costs for earliness. Therefore the relationship between earliness and fitness may critically depend on whether earliness is due to genetic or to environmental factors. Environmental effects on the phenotype are not easy to discern, and measuring all relevant (especially internal) traits may not be possible at all. Simplifying assumptions have to be made. One possible simplification is that the relationship between the external phenotype and fitness is independent of the factors causing phenotypic variation. However, this is not a fortunate choice: there are inevitably genes that affect (i) the phenotype of a focal trait and hence fitness and (ii) fitness(-components) by independent pathways (Fig. 1). Such genes have independent pleiotropic effects on trait and fitness, and cause a correlation between trait and fitness that is not tied to the functional relationship between fitness and focal trait (Price and Langen, 1992). Similarly, environmental factors may affect both phenotype and fitness independently (Rausher, 1992). This situation applies to the explanation given for selection on clutch size and breeding data (Price, Kirkpatrick and Arnold, 1988; Price and Liou, 1989): if nutritional state is not heritable, but affects both the trait and component(s) of fitness, an apparent selection differential can be shown to persist at equilibrium (i.e. without a genetic response). The observed phenotypic correlation may not be due to a direct causal relationship between phenotype and fitness. If we focus on selection on a single trait, we can simplify the complex network of Fig. 1 to six relations (Fig. 2): the phenotype as affected by (1) genetic, (2) environmental, and (3) other factors, and the relations between (4) phenotype and fitness (i.e. external selection), (5) the genes that affect both the focal trait and - independently from the focal trait - fitness, and (6) environmental factors that affect both trait and, independently, fitness. Whenever Fig. 2. Possible relationships between a focal trait (Z), its genetic (G) and environmental (E) component, and fitness (IV). The standard model assumes that only relationships t-4 exist: selection on phenotypes, and variation in phenotypes partly determined by additive genetic variation. Arrows 5 and 6 exist when genes or environmental factors affect fitness not only via the phenotype Z, but also by independent pathways. Phenotypic selection and genetic response 5 genes or environmental factors affect fitness in other ways than mediated by the focal trait (5 or 6) the standard model will not be applicable. For instance, for artificial selection it is well-known that the selection response cannot be adequately predicted if there is additional selection on a genetically correlated trait (e.g. Lerner and Dempster, 195 1; Falconer, 198 1). Natural selection can only be adequately described if all the relevant traits and constraints among traits are taken into account (Lande and Arnold, 1983; Burger, 1986; Arnold, 1992). It seems important to safeguard ourselves against situations in which this is uncertain. Model specifications For simplicity, the model focuses on one trait only. The approach allows derivation of more complex formulae for selection on multiple traits, but if only part of the complex system of traits is observed similar problems are expected. We assume that fitness may not only be related to the phenotype per se, but also, and independently, to the underlying genetic and environmental components of variation. These relations are quantified as partial regression coefficients of fitness on phenotype, on breeding value and on environmental deviation, respectively. The regression of fitness on phenotype, b,+, measures the direct causal effects of the phenotype on fitness, i.e. regardless of the genetic and environmental background of the phenotype. The partial regression of fitness on genotypic value, bwlc, measures residual effects on fitness of the genes affecting the focal trait that are not attributable to a causal link between trait and fitness (cf. Fig. 2). Similarly, bWJE measures the effects on fitness of those environmental factors that influence one or more fitness components through other pathways than via the focal trait. Once these regression coefficients are defined, further derivation is straightforward if we assume that the multivariate distribution of breeding values and environmental deviations is Gaussian, and that the regression of offspring phenotypes on the mid-parental breeding values is linear (for conditions implicit to these assumptions see Turelli, 1988; Nagylaki, 1992). When we compare the final equation of Table 1 with R = h2S we see that the equation for the selection response is much more complex; the selection response can be in an opposite direction to that of the selection differential, for instance, leading to a negative realized heritability (R/S). It appears that the classical model is valid for conditions common to artificial selection, but perhaps uncommon in natural selection. In artificial selection, the ‘fitness’ of an individual (or group of individuals) is assigned on the basis of their phenotype. For instance, if the phenotype is less than a certain threshold value, the individual is excluded from the selection lines. In this case the partial regression coefficients on genotype and on environmental deviation are absent, and the realized heritability reduces to Cov,,/l/,, with Cov,, = V, + Cov,,. Furthermore, in plant or animal breeding, genotypes are usually randomized over environments, so that environmental and genetic values are not correlated (Cov,, = 0). The covariance between genotype and phenotype Cov,, is then equal to the genetic variance V,, and consequently the realizable heritability equals the ratio additive van Tienderen and de Jong 6 Table 1. The phenotype Z is written as the sum of an additive genetic component (G) or breeding value, an environmental component (E), and an error term (e) that, for instance, can be due to non-additive genetic effects or developmental noise. More complex models can be made in a similar fashion. Tbe model is defined as follows: Model Z=G+E+& GEE Additive Genetic, Environmental and srror component W Relative fitness v, VG vE Phenotypic, Genetic, Environmental and error varianees v, CovzG Cov, Cove, Corresponding eovarianees (all covariances with error component assumed absent) h/z Partial regression coefficient of relative fitness OK) on Z, G and E, bwlc hvla holding the other components constant s = cov, Selection differential R = Cov, Expected Selection Response Define a vector of covsrianees x = (Cov, regression coefficients $ = (bwlz bw,, Cov, bw,dT. COV,,)~, and a vector of partial Assume a multivariate gaussisn distribution for Z and its components G, E and E, with A tbe varianee/covariance matrix of Z, G and E. Using the definition of the multiple regression coefficients we get: $ = A-’ x or & = A b. Expanding the first two elements of x in full, we get: covGW = covZG hflZ+ vG hVjG+ CovGEblE covzw = v, hVlZ+ covZG bVIG+ covZE hVfE and after rearranging R covZG hVlZ + vG bVlG + covGE bwlE vz hVlZ + CovZG hlG + covZE b.'JE = S genetic to phenotypic variance. For artificial selection the secondary theorem and h2S are equivalent, since Cov,,/Cov,, = V,/Vz = h2. For natural the prediction selection the equation may not reduce to a simpler form, due to (i) non-random distribution of genotypes over environments, e.g. if some form of habitat choice is present (Cov,, # 0), (ii) direct selection on unmeasured, internal traits that are genetically correlated (bWIG # 0), or (iii) environmental factors that affect both the phenotype and fitness (bWIE # 0). Phenotypic selection Complications and genetic response for the classical approach Genotype-Environment Covariance Genotype-environment covariance can arise due to non-random distribution of genotypes over environments (Falconer, 1981). It leads to a covariance term in the selection equation that can inflate or attenuate the selection response (Tab. 1). In general, negative covariances reduce, and positive covariances increase the selection response. When individuals with high breeding values do not have above average phenotypic values due to a negative genotype-environment covariance that nullifies the genetic covariance (Cov,, = V, + Cov,, = 0), no selection response is expected at all. If the covariance is strongly negative, the selection response can be opposite in direction to the selection differential. Selection on unmeasured, genetically correlated traits In Fig. 3, we assumed external directional selection for higher phenotypic values. In addition, we assumed a genetic link between focal trait and fitness that was not mediated by the phenotype, e.g. due to a genetic correlation with a second, unmeasured trait under selection (b wlc # 0). This may be the result of an internal cost: genes that result in a higher phenotype may also cause a reduction in a component of fitness. Without this link, the classical model applies and R = h2S Fig. 3. The effects of independent selection on the genetic component of variation. The scale for phenotypic variation is taken as b‘= = 1. External selection of the phenotype is taken as constant, with the partial selection differential due to selection on the phenotype bwlz = 1, the narrow-sense heritability hZ = 0.5, and no selection on the environmental component of variation, b,lE = 0. 8 van Tienderen and de Jong (Fig. 3, on the ordinate). If selection on the genetic component is positive, i.e. in the same direction as selection at the phenotypic level, the response is faster than predicted, and the realized heritability R/S is higher than the narrow-sense heritability Vc /V, (in this case 0.5) for the trait. If selection on the genetic component is in an opposite direction, the selection response is slower. At some point a response is absent, the realized heritability has dropped to zero, while directional selection is still observed. The population is in equilibrium, and selection at the phenotypic level is offset by selection on the genetic component of variation. For instance, genes that cause earlier egg-laying may also have negative pleiotropic effects on the survival of the adult (b,+ > 0); in contrast, environmental factors causing early breeding (e.g. microclimate) may not have such negative effects. The pleiotropic effects may then counteract possible benefits of earlier breeding due to a better synchronization with food availability when rearing the chicks (bWlz < 0). If selection on the genetic component is even more negative (e.g. due to stronger selection on the correlated trait) a positive selection differential coincides with a negative response. Finally, for very negative values of selection against large genotypic values, the selection differential is absent, but a negative selection response is expected. The external selection for higher phenotypic values is then completely masked by the internal selection for lower genetic trait values. Environmental factors afleeting phenotype and$tness Effects on an environmental correlation due to environmental factors that affect both the focal phenotype and fitness (via other pathways) are shown in Fig. 4. In this example, the external selection on the phenotype was assumed to be constant, and the genetic covariance between trait and fitness was fixed. Thus, the environmental correlation between trait and fitness (b + # 0) affects the selection differential but not the genetic response. In the absence of such a correlation, on the ordinate of the graph, the standard model applies. If the environmental correlation works in the same direction as the phenotypic selection, the selection differential and hence the prediction h2S is increased. If the environmental correlation works in the opposite direction, the selection differential is reduced, eventually to negative values. These examples show several things. Firstly, the absence of a selection response despite selection differentials and heritable variation, as observed in the bird examples, may have several causes. However, problems with the phenotypic approach are not restricted to this situation. There can also be no phenotypic selection, but a genetic response, without a change in environment between generations. Or the selection response can be in the opposite direction than that expected. These discrepancies are due to a lack of knowledge of the interplay of environments and genes on the one hand, and phenotypes and fitness on the other. Any relationship between observed phenotypic selection and selection response is possible. Phenotypic selection and genetic 9 response Fig. 4. The effects of spurious correlations between environmental factors that determine trait value and fitness. The scale for phenotypic variation is taken as V z = 1. External selection on the phenotype is assumed constant, with the partial selection differential due to selection on the phenotype b,lz = 1, the narrow-sense heritability hZ = 0.2, and no selection at the genotypic level other than that mediated by the phenotype, !I,,, = 0. Tests to estimate different expectations for selection response The genetic and environmental components of variation are not directly observable. Additive genetic covariances between trait and fitness can be estimated from data on relatives such as parent-offspring combinations, or sib-families. This assumes that the additive genetic component can be estimated from the covariance between relatives; obviously, complications arise when the covariances between relatives are also affected by non-genetic factors (e.g. maternal effects, or a common environment) (Falconer, 1981). Assuming that the additive genetic covariances are measured correctly, they can be compared with a predicted response from phenotypic selection differential and heritability (Rausher, 1992). Van Noordwijk (1988) performed such a regression analysis for selection of fledging weight in Great Tits, using survival in the first three months after fledging as a component of fitness. Regression was calculated not only for the focal trait of the chick but also for the mean of its parents (Tab. 2). Parent-offspring regressions of fledging weight gave estimates of heritabilities in the period under study, so that independent estimates of S, h2 and the additive genetic covariance between (mid)parental trait and offspring survival were obtained. The latter measured the expected genetic response in the focal trait due to selection in the life-cycle stage studied. The results suggested that the selection on the phenotype was not associated with selection on genes (Tab. 2). On average, the heritability was 0.35, a higher survival rate of larger chicks resulted in a positive selection differential of 0.4g, hence an expected genetic 10 van Tienderen and de Jong Table 2. Selection on nestling weight of Great Tits during three months after fledging. Data reproduced from Van Noordwijk (1988). Comparison of mean nestling weight of h2 hzS parents, and survival of their offspring Average nestling s weight (g) cov, CW 1975 16.38 0.24 0.38 0.09 0.00 1976 16.90 0.68 0.47 0.32 0.03 1977 17.55 0.16 0.26 0.04 0.06 1978 17.06 0.53 0.29 0.15 0.05 0.40 0.35 0.14 0.03 ML?ZUl response of 0.14g. However, the covariance between the survival of the young and the average weight of the parent was only 0.03. Van Noordwijk concluded that the observed phenotypic selection was not translated into a genetic response. A similar analysis could be employed for sib-data, by estimating genetic covariances between traits and fitness (components), and comparing these to the expectation from h2 and selection differentials. Selection due to differential survival in the succeeding winter was also studied. There appeared to be no discrepancy (Van Noordwijk, 1988). Discussion Lande and Arnold (1983) warned that predictions from (multivariate) selection models were inadequate if selection acted on an unmeasured, correlated trait. Of course, one cannot know if such traits exist, or know when to stop measuring more traits. However, one can check whether selection is adequately described by the selective forces, heritabilities and genetic covariances of the set of traits that one is measuring. In fact the approach is identical to using the multivariate selection equation R = GP-~‘S = Gb (Lande, 1982), but with fitness as one of the traits in the analysis, rather than an external entity; in this way, both fundamental theorems resurface (Van Tienderen, 1989). The partial regression of fitness on fitness equals one, that of fitness on other traits equals zero: the response in fitness itself becomes equal to the additive genetic variance in fitness, the response in an arbitrary trait becomes equal to the additive genetic covariance between trait and fitness, i.e. Fisher’s first and secondary fundamental theorems. These derivations are based on quantitative genetic models with many assumptions about the actual genetics involved (Nagylaki, 1992). Although the details may differ, we believe that the complexity of the relation between selection on the external phenotype and at the Phenotypic selection and genetic 11 response genetic level causes fundamental problems. An important suggestion is to measure the genetic variances and covariances of traits and fitness or components of fitness directly. Absence of a selection response can have several causes. Obviously, without additive genetic variation there cannot be a response. Secondly, selection on the phenotype may be in one direction (say for earlier breeding), while selection on the genetic component of variation is in an opposite direction (for later breeding). For instance, internal genetic tradeoffs may counterbalance external selection on the phenotype. Thirdly, if the observed selection differential is solely due to a correlation between fitness and the environmental component of the phenotype, no selection response is expected unless there is genotype-environment covariance (e.g. genetically above-average individuals occupy territories that are above average both in environmental effects on the focal trait and in fitness). Finally, individuals with high breeding values may have average phenotypic values (Cov,, = 0) due to a negative genotype-environment covariance. Of course, more complex, hybrid situations may also occur. The current analysis is not only relevant to situations in which a selection response is absent. Any selective force we observe in nature is the result of causal relations between external phenotype and fitness, and indirect correlations due to pleiotropic effects of genes or spurious environmental correlations. It appears that a study of natural selection needs to assess these possibilities, and empiricists may want to take them into account. Unfortunately, observing phenotypic selection on a trait, and estimating heritabilities and genetic covariances may not be sufficient to understand how selection changes a population. The real challenge, should discrepancies be found, comes with detection of the responsible external or internal mechanisms. Acknowledgements We would like to thank A. J. van Noordwijk, comments on previous drafts. T. Price, J. M. Tinbergen and J. A. Shykoff for valuable References Alatalo, R. V., L. Gustafsson and A. Lundberg. 1990. Phenotypic selection on heritable size traits: environmental variance and genetic response. Amer. Natur. 135: 4644471. Arnold, S. 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