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VARIATIONAL AND GENETIC PROPERTIES OF DEVELOPMENTALSTABILITY IN DALECHAMPIA SCANDENSAuthor(s): Christophe Pélabon, Thomas F. Hansen, Matthew L. Carlson, and W. Scott ArmbrusterSource: Evolution, 58(3):504-514. 2004.Published By: The Society for the Study of EvolutionDOI: 10.1554/03-439URL: http://www.bioone.org/doi/full/10.1554/03-439

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504

q 2004 The Society for the Study of Evolution. All rights reserved.

Evolution, 58(3), 2004, pp. 504–514

VARIATIONAL AND GENETIC PROPERTIES OF DEVELOPMENTAL STABILITY INDALECHAMPIA SCANDENS

CHRISTOPHE PELABON,1,2 THOMAS F. HANSEN,3 MATTHEW L. CARLSON,4 AND W. SCOTT ARMBRUSTER1,5

1Department of Biology, Norwegian University of Science and Technology, 7491 Trondheim, Norway2E-mail: christophe.pelabon@bio.ntnu.no

3Department of Biological Science, Florida State University, Tallahassee, Florida 323064Alaska Natural Heritage Program, Environment and Natural Resources Institute, University of Alaska, Anchorage, Alaska 99501

5Institute of Arctic Biology, University of Alaska, Fairbanks, Alaska 99775

Abstract. Because low developmental stability may compromise the precision with which adaptations can be reached,the variability and genetic basis of developmental stability are important evolutionary parameters. Developmentalstability is also an important clue to understanding how traits are regulated to achieve their phenotypic target value.However, developmental stability must be studied indirectly through proxy variables, such as fluctuating asymmetry,that are suggested to have noisy and often nonlinear relationships to the underlying variable of interest. In this paperwe first show that mean-standardized measures of variance and covariance in fluctuating asymmetry, unlike herita-bilities, repeatabilities, and correlations, are linearly related to corresponding measures of variation in underlyingdevelopmental stability. We then examine the variational properties of developmental stability in a population of theNeotropical vine, Dalechampia scandens (Euphorbiaceae). By studying fluctuating asymmetry in a large number offloral characters in both selfed and outcrossed individuals in a diallel design, we assemble strong evidence that bothadditive genetic and individual variation and covariation in developmental stability are virtually absent in this pop-ulation.

Key words. Dalechampia scandens, developmental stability, evolvability, fluctuating asymmetry, genetic variation,heritability, homozygosity.

Received July 23, 2003. Accepted October 14, 2003.

Adaptation of a biological trait is often equated with thefit of the population mean to a fitness optimum. However,this does not guarantee that the average individual is welladapted (Orzack and Sober 1994). In fact, the target of se-lection is not the population mean, but rather the adaptiveaccuracy, that is, the average closeness of individuals to thefitness optimum (Armbruster et al. 2004). The adaptive ac-curacy itself has two components: (1) the closeness of thetarget phenotype (i.e., the phenotype that would be reachedfrom a given genetic and environmental background withoutnoise of any kind; Nijhout and Davidowitz 2003) to the adap-tive optimum; and (2) the adaptive precision, the reliabilitywith which the individual is able to attain its target phenotypein the face of environmental and developmental disturbance.Because developmental noise may represent a substantial partof the total phenotypic variance, it can seriously hamper theprecision with which the target phenotype is reached andnegatively affect the accuracy of adaptation. This underscoresthe evolutionary relevance of developmental stability, theability of an individual to buffer disruptions of the devel-opmental trajectory and reduce developmental noise in a par-ticular environment (Palmer 1994).

Trait canalization, selection for increased developmentalprecision across variable genetic and environmental back-grounds, may also mask additive genetic variance and thusreduce the evolvability of characters (Gibson and Wagner2000). Ultimately, this may lead to reduced adaptive accu-racy, because target phenotypes are not able to evolve to newoptima. These observations reveal the importance of devel-oping a predictive theory for how developmental stabilityand other variational properties vary among characters, in-dividuals, and species. Toward such a theory, we need tounderstand the evolutionary potential of developmental sta-

bility itself. One important question is, then, what is the levelof additive genetic variation in developmental stability? Ad-dressing this question will help us to understand whetherdevelopmental stability is evolvable and what forces may beimportant in shaping its genetic architecture.

Fluctuating asymmetry (FA), subtle nondirectional depar-tures from perfect bilateral symmetry (Van Valen 1962), hasbeen widely used as a measure of developmental noise andto assess developmental stability (Palmer and Strobeck1986). Fluctuating asymmetry has the conceptual advantageof having a clear developmental optimum (perfect symme-try); because both sides of bilateral traits are expected to beinfluenced by the same genes and share the same macroen-vironment, deviations from perfect symmetry are thought toreflect microenvironmental disturbances and be negativelyrelated to developmental stability. It is, however, inherentlydifficult to assess the variational properties of developmentalstability, as variation in FA due to individual differences indevelopmental stability tend to be swamped by variation dueto developmental noise (Whitlock 1996, 1998; Houle 1997,2000; Van Dongen 1998; Fuller and Houle 2003).

The above limitation notwithstanding, evolvability of FA,and therefore of developmental stability, has been directlydemonstrated in the Australian blowfly (Lucilia cuprina;Clarke and McKenzie 1987; Davies et al. 1996). In this case,the initial increase in developmental noise, following a ge-netic modification caused by a pesticide-resistance gene, wasrapidly eliminated by selection. Recent reviews of the heri-tability of FA and developmental stability, however, haveshown conflicting results. Some authors have concluded thatadditive genetic components of FA and developmental sta-bility exist (Møller and Thornhill 1997; Polak and Starmer2001), whereas others remain skeptical (Houle 1997; Markow

505GENETICS OF DEVELOPMENTAL STABILITY

and Clarke 1997; Whitlock and Fowler 1997). In a meta-analysis using hierarchical modeling to take estimation ac-curacy into account, Van Dongen (2000) showed that theheritability of FA was extremely low on average. Severalauthors have argued that the heritability of FA stands in asigmoidal relationship to underlying genetic variation in de-velopmental stability (Whitlock 1996, 1998; Houle 1997,2000; Van Dongen 1998). This implies that small or moderateamounts of genetic variation in developmental stability aredifficult to detect and can remain hidden when measured asheritability.

In this paper, we first present theoretical observations onthe relationship between variation in developmental stabilityand variation in FA. Based on models by Whitlock (1996,1998) and Houle (1997, 2000), we show that mean-stan-dardized variances and covariances of FA map linearly tocorresponding mean-standardized measures of variation indevelopmental stability. We suggest that mean-standardizedvariances may thus be easier to interpret than heritabilities,repeatabilities, and correlations, which map nonlinearly ontounderlying variation. We then estimate the additive geneticvariance and evolvability of developmental stability of floraltraits of Dalechampia scandens (Euphorbiaceae), measuringFA on a large number of traits in both selfed and outcrossedindividuals. Variance components in FA were estimated us-ing a diallel design that is more powerful than regression-based methods (Fuller and Houle 2003).

THEORY

Here we present some simple theoretical relationships be-tween underlying developmental variation and organism-lev-el variational properties, such as FA. The aim of this sectionis to provide a background for interpretation of the experi-mental results presented below.

Model

Following Whitlock (1996, 1998) and Houle (1997, 2000),the right (R) and left (L) side of a bilateral trait can be mod-eled as

R 5 g 1 e 1 e and (1a)R

L 5 g 1 e 1 e , (1b)L

where g and e represent the genetic and environmental com-ponents of the trait common to both sides and eR and eL arethe developmental errors in each side. We assume that eachdevelopmental error is normally distributed with mean zeroand variance s2/2, such that

2R 2 L 5 e 2 e ; N(0, s ).R L (2)

From this it follows that

2FA 5 zR 2 Lz 5 ze 2 e z ; RN(0, s ),R L (3)

where RN is the normal distribution reflected around zero(i.e., a scaled x-distribution). The parameter s2 is a measureof developmental stability (called VN by Whitlock 1996).Conditional on a value of s, the expectation, variance, andcoefficient of variation for this distribution are

E[FA z s] 5 sÏ2/p , (4)

2Var[FA z s] 5 s (1 2 2/p), and (5)

CV[FA z s] 5 Ïp/2 2 1 ø 3/4, (6)

respectively. Note that the mean FA is proportional to s,whereas the variance in FA is proportional to s2. The FA isthus a direct measure of developmental stability on the s-scale; in the following, we will assume that developmentalstability is measured on a s-scale. The unconditional expec-tation, variance, and coefficient of variation are

E[FA] 5 E[E[FA z s]] 5 E[s]Ï2/p , (7)

Var[FA] 5 E[Var[FA z s]] 1 Var[E[FA z s]]

25 Var[s] 1 (1 2 2/p)E[s] , and (8)

2CV[FA] 5 Ï(p/2)CV[s] 1 p/2 2 1, (9)

respectively. Note that a CV[FA] larger than 3/4 indicatesindividual variation in susceptibility to developmental noise.Individual variation may also manifest itself as kurtosis inthe distribution of signed FA (Rowe et al. 1997; Gangestadand Thornhill 1999). The component of variation in FA thatis due to individual differences in degree of developmentalstability is Var[E[FAzs]] 5 (2/p)Var[s]. Van Dongen (1998)and Whitlock (1998) defined the hypothetical repeatability,R, as the proportion of variation in FA due to real differencesin developmental stability, that is:

Var[E[FA z s]] (2/p)Var[s]R 5 5 2Var[FA] Var[s] 1 (1 2 2/p)E[s]

2(2/p)CV[s]5 . (10)2CV[s] 1 1 2 2/p

Note that the repeatability links the phenotypic variationin FA to the phenotypic variation in underlying develop-mental stability as CV[s2] 5 RCV[FA]2. The variance insigned FA is

2 2Var[R 2 L] 5 E[s ] 5 Var[s] 1 E[s] . (11)

The variation in one side of the trait due to all sources ofdevelopmental stochasticity (including developmental noiseand developmental variation across individuals) is E[s2]/2.This is most efficiently estimated as half the variance of thesigned FA (e.g., Palmer 1994). The variance in developmen-tal stability, Var[s], can be estimated by obtaining two ofthe following: mean FA, variance in FA, or the variance insigned FA.

Genetic and Environmental Variation in DevelopmentalStability

The component of variation in FA due to additive geneticvariation in developmental stability is

Var [FA] 5 Var [E[FAzs]] 5 (2/p)Var [s].A A A (12)

Assuming only additive genetic variation, the heritability andthe coefficient of additive genetic variation of FA are

506 CHRISTOPHE PELABON ET AL.

FIG. 1. Relationship between CV[FA], R, CVA[FA] and CVA(s).This model includes no environmental variation. The hypotheticalrepeatability, R, is the proportion of variance in asymmetry due tothe real differences in developmental stability. In the case of noenvironmental variation in developmental stability, the repeatabilityequals the heritability.

2Var [FA] (2/p)CV [s]A A2 2h [FA] 5 5 5 Rh [s] (13)2Var[FA] CV[s] 1 1 2 2/pand

ÏVar [FA]ACV [FA] 5 5 CV [s]. (14)A AE[FA]

Thus, the additive genetic coefficient of variation of FAis identical to the additive genetic coefficient of variation indevelopmental stability, whereas the heritability of FA isnonlinearly related to heritability of developmental stabilityon the s-scale, because repeatability is itself a function ofvariation in developmental stability (eq. 10; Fig 1). Mean-standardized variances such as the CVA or IA (5 CVA

2) arethus theoretically preferable statistics for gauging the geneticvariance and evolutionary potential of developmental stabil-ity. We note, however, that the statistical problem of accu-rately estimating genetic variation in developmental stabilityis not thereby solved, as a low repeatability, or low signal-to-noise ratio, makes estimates of mean-standardized vari-ances very imprecise.

Furthermore, even very low heritabilities in FA are com-patible with high evolvabilities of developmental stability.Using IA as a measure of evolvability (Houle 1992; Hansenet al. 2003a), we find

2 2I [s] 5 I [FA] 5 h [FA]CV[FA] .A A (15)

This is derived by use of equation (14) and the definition ofheritability as the ratio of additive genetic and phenotypicvariances. Because CV[FA] has to equal or exceed

(eq. 9), the evolvabilities of FA and s must exceedÏp/2 2 1(p/2) 2 1 ø 0.57 times the heritability of FA. This meansthat even a heritability of 0.1 implies an evolvability in excessof 5%. The interpretation of the IA evolvability as a percentrefers to the expected percent response per generation in thetrait if exposed to a mean-standardized selection gradient ofslope one, which equals the strength of selection on relativefitness itself (for details see Hansen et al. 2003a). Thus, to

correctly assess the evolutionary potential of developmentalstability, it is preferable to evaluate evolvabilities directly inthe form of mean-standardized additive genetic variances.

We add the caveat that developmental stability is a com-plex property that can be expected to have many sources ofboth genetic and environmental variance. The complexity ofthe trait may lead to nonlinear interactions among the varioussources of variation (Klingenberg 2003). Epistasis and ge-notype 3 environment interactions may be expected, and theabove relationships, which are built on an additive model,are thus best seen as approximations that are most likely tobe valid when the variation in developmental stability is notlarge relative to the mean.

Covariance in Fluctuating Asymmetry

An important question regarding the genetic basis of de-velopmental stability is whether an organism-wide bufferingcapacity exists or, alternatively, whether developmental sta-bility is trait specific (Leamy 1993). If developmental sta-bility corresponds to an organism-wide property, sometimescalled an individual asymmetry parameter (Leamy 1993;Clarke 1998; Polak et al. 2003), some correlation of FAsamong traits of the same individual is expected. However,correlation among traits in FA may also result from a cor-relation in developmental noise, due, for example, to struc-tural relationships between traits (Klingenberg et al. 2001).

Consider two traits with fluctuating asymmetries FA1 andFA2, underlying developmental stabilities s1 and s2, respec-tively, and a developmental covariance s12.

We may write the covariance between the FAs of the twotraits as

Cov[FA , FA ] 5 E[Cov[FA , FA z s , s , s ]]1 2 1 2 1 2 12

1 Cov[E[FA z s ], E[FA z s ]]. (16)1 1 2 2

(This is analogous to the decomposition of variance in eq.8; for derivation of this equation in a different context seeHansen and Martins 1996.) From this, we see that the co-variance in FA can be divided into two components, whichwe may interpret as due to covariance in developmental noiseand covariance in developmental stability, respectively.

The component due to covariance in developmental sta-bility is the term

Cov[E[FA z s ], E[FA z s ]] 5 (2/p)Cov[s , s ],1 1 2 2 1 2 (17)

which we obtained by using equation (4). Thus, if the co-variance in developmental noise can be removed, there is adirect relationship of covariance in FA to covariance in de-velopmental stability. We can control for covariance due tocorrelated developmental noise by estimating the termE[Cov[FA1,FA2zs1, s2, s12]] in equation (16). There is nosimple analytical expression for this term, but it can easilybe computed numerically. In Figure 2, we describe this com-putation and show how the correlation in FA relates to thecorrelation in developmental noise (i.e., to r 5 s12/s1s2).

Provided there is no individual variation in directionalasymmetry (i.e., a constant difference between the left andthe right side), the covariance in signed FA can be taken asa direct estimator of the covariance in developmental noise,s12. Using this estimate with equations (16) and (17), we

507GENETICS OF DEVELOPMENTAL STABILITY

FIG. 2. Mapping of correlation in developmental noise to corre-lation in fluctuating asymmetry (FA). This is based on computationof the integral Cov[Abs[x], Abs[y]z s1, s2, s12] under the assumptionthat x and y follow a joint normal distribution with means zero,variances and , and covariance s12. If there is variation in2 2s s1 2these parameters, the population covariance is the expectation ofthis function over their distribution. The integration was computednumerically by use of Mathematica 4.0 (Wolfram 1999).

obtain an estimator of the covariance in developmental sta-bility as follows

pCov[s , s ] ø {Cov[FA , FA ]1 2 1 22

2 f(Cov[R 2 L , R 2 L ])}, (18)1 1 2 2

where f is the above-mentioned mapping from covariance indevelopmental noise to covariance in FA that is illustratedin Figure 2. This mapping is an approximation, as it is basedon the assumptions that there is no individual variation indirectional asymmetry or in the covariance of developmentalnoise (i.e., in s12).

Correlations in FA behave in a way that resembles theheritability. Using equations (4) and (8), the correlation inFA due to covariance in developmental stability is

Corr[E[FA z s ], E[FA z s ]]1 1 2 2

Corr[s , s ]1 25 .Ïp/2 1 (p/2 2 1)/CV[s ]Ïp/2 1 (p/2 2 1)/CV[s ]1 2

(19)

Thus, just like the heritability, the correlation stands in anonlinear relationship to the variance in developmental sta-bility. Therefore, the low correlation across traits and the lowheritability of FA may have a common mathematical basisin the nonlinear relationship with the underlying variation indevelopmental stability. It is therefore inherently difficult todetermine whether developmental stability is systemwide ortrait specific. Even if developmental stability is a completelysystemwide property, we will not expect to see strong cor-relations in FA across traits unless there is substantial com-ponent of individual variation in developmental stability. Wetherefore need to combine FA measures from many charactersto obtain more precise information on developmental stability(e.g., Zhivotovsky 1992; Leung et al. 2000). Note that thisis true whether we assume that there is global asymmetryparameter or whether we see the combination of measures asa meta-analysis that aims at estimating average developmen-tal stability of the organism.

MATERIALS AND METHODS

Study Organism

Dalechampia scandens is a Neotropical vine with unisexualflowers aggregated into bisexual, pseudanthial inflorescences,or blossoms (Webster and Webster 1972; Webster and Arm-bruster 1991). Each blossom typically contains 10 staminateflowers arranged in three groups of three flowers with anadditional central flower. Three pistillate flowers are presentunder (abaxial to) the staminate flowers. Associated with thestaminate subinflorescence is a gland composed of bractletsthat secrete resin (Armbruster 1984). Two large, showy in-volucral bracts subtend the pistillate flowers, staminate flow-er, and resin gland. Bees that collect the resin for nest con-struction pollinate the flowers. The blossoms of D. scandensare bilaterally symmetrical (Fig. 3; for detailed descriptionsof the blossom see also Webster and Webster 1972; Websterand Armbruster 1991). The area of the gland, which affectsthe production of resin reward, determines the subset of theresin-collecting bee fauna that will visit the blossoms. Incombination with the placement of anthers and stigma, thisdetermines which bees will be effective pollinators (Arm-bruster 1986, 1988, 1991).

Experimental Design and Rearing Conditions

We estimated the additive genetic variance in FA using adiallel analysis where 12 sets of five parental individuals werecrossed in complete 5 3 5 diallels, with both reciprocals andselfed offspring. The parental individuals used in this studywere derived from seeds collected near Tulum, Territorio deQuintana Roo, Mexico (208139N, 878269W) early in 1998.Seeds were collected and stored by maternal family. Severalseeds from each family were germinated in March–May 1998.At full flower (September–December 1998), these plants werecrossed. The experiment was conducted at the Departmentof Biology greenhouse, Norwegian University of Science andTechnology (Trondheim, Norway). Two individuals wereraised from each mating. Consequently, four full-sibs fromeach parental pair were present in the experimental popula-tion. Initial parents were not close relatives. Crossing meth-ods and rearing conditions are reported in more detail inHansen et al. (2003a). Plants were haphazardly repositionedin the greenhouse during the growth and measurement phases.Measurements were made between November 1999 and Sep-tember 2000.

Measurements and Definitions

Two observers made the measurements. In the first dataset(observer CP), a selection of traits (see Fig. 3, Table 1) wasmeasured on two different blossoms per plant (n 5 1042).Blossoms were collected haphazardly from each plant. Allmeasurements in this dataset were made using an opticalbinocular magnifier (Optivisor, Donegan Optical, KansasCity, MO; 53 and 103 magnification). In the second dataset(observer TFH), blossoms were dissected under a stereomi-croscope. This second set of measurements was performedto measure more detailed structures and was made on onlyone blossom per plant per type of cross (n 5 392). All mea-surements were made at 0.01-mm precision using digital cal-

508 CHRISTOPHE PELABON ET AL.

FIG. 3. Exploded view of the Dalechampia blossom displaying thedifferent traits measured (see Table 1 for definition).

TABLE 1. Definition of the traits measured on the blossoms ofDalechampia scandens (see Fig. 3 for a visual representation of thetraits). Gland-stigma distance is measured as the minimum distancebetween the tip of each stigma and the gland. For all traits signedFA was calculated as 100[ln(traitL) 2 ln(traitR)]. The FA is the2smvariance in FA due to measurement errors (see eq. 20–22). Mea-surement variances were estimated as follow: (FA) 5 Var(m1 22smm2), where m1 and m2 are the signed FAs calculated from the firstand second measurements on (n) repeated measures. Measurementerror for gland number could not be estimated due to the necessarydestructive dissection of the structure to count the number of brac-tlets forming the gland, but is probably near absent.

Trait N outcrossed N selfed s FA (n)2m

Upper bract length (UBL)Lower bract length (LBL)Gland-stigma distance (GSD)Gland width (GW)Gland height (GH)Gland depth (GD)

816816813816816288

224224223224224107

4.92 (54)3.00 (54)

26.78 (140)26.59 (97)19.06 (97)43.32 (54)

Style length (SL)Style width (SW)Gland number (GN)Gland area (GA)

287813287816

107223107224

6.15 (54)10.83 (118)

—43.06 (97)

ipers. Both observers performed repeated measures to assessmeasurement errors for each trait.

FA was measured on a set of traits showing bilateral sym-metry (Table 1, Fig. 3 for trait definitions). Following Clarke(1998), we measured FA on a log scale to allow direct com-parison of FA across traits and remove potential allometricrelationship between FA and trait size. Signed FA was es-timated as 100[ln(L) 2 ln(R)] and FA as 100zln(L) 2 ln(R)z.

Measurement Error and Bias Correction

Fluctuating asymmetry is inherently biased by measure-ment error (Palmer 1994; Whitlock 1996, 1998; Van Dongen1998). We can model this by adding an estimated measurementvariance to s2 in the above equations. Remember that the2smmeasurement variance in a unilateral trait is then /2. The2smconditional (on a value of s) mean and variance in FA become:

2 2E[FA z s] 5 Ï2/pÏs 1 s and (20)m

2 2Var[FA z s] 5 (s 1 s )(1 2 2/p). (21)m

Furthermore, the coefficient of variation is unaffected bymeasurement error, and a CV elevated above 3/4 cannot bedue to the effect of measurement error (provided it is nor-mally distributed). The mean and variance are, however, bi-ased. If the measurement error is known, a bias-correctedestimate of the mean FA can be obtained as

2 2FA 5 ÏFA 2 2s /p , (22)obs m

where FAobs is the observed FA. Similarly, the variation inFA due to measurement error is equal to (1 2 2/p), and2smthis term should be subtracted from the observed variance toobtain an unbiased estimate of the real variance. Measure-ment variances ( ) estimated from replicated measurements2smare given in Table 1. As explained above, we used these tocorrect our estimates of mean and variance in FA for bias.Repeatabilities and heritabilities can also be bias corrected

509GENETICS OF DEVELOPMENTAL STABILITY

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4.93

,1.

20)

18.9

629

.83

572.

8553

1.01

0.15

0.36

1.53

0.32

3.13

23.

826

17.6

4217

.668

0.82

50.

813

0.92

20.

797

0.10

30.

087

0.20

90.

065

0.73

30.

559

0.40

60.

017by adding this term to their denominators (Van Dongen 1998;

Whitlock 1998). These corrections are exact when there isno variation in developmental stability. If there is variationin s, the corrections becomes more complicated, but stillrelatively unimportant as long as sm is much smaller than s(not shown).

Statistical Analysis

Although we found some small differences in the level ofasymmetry measured by the two observers, there was no con-sistency in the direction of the differences (not shown). Mostanalyses in this study are based on the measurements fromthe first observer (CP) supplemented by the measurementsfrom the second observer (TFH) for the traits gland number(GN), gland depth (GD), and style length (SL).

The pedigree consisting of full-sibs, half-sibs, and someother types of relatives was analyzed statistically as describedin Lynch and Walsh (1998) with a mixed-model implementedinto PROC MIXED in SAS 6.12 by use of the TYPE 5 LINgeneral linear variance structure and restricted maximumlikelihood estimation of variance components (SAS Institute,Inc., Cary, NC; described in detail in Hansen et al. 2003a,b).We included an additive genetic effect in all analyses. In theanalyses involving FA for dataset 1, but not dataset 2, wealso included stage (i.e., one, two, or three staminate flowersopen) as a fixed effect and a random effect representing theindividual, as there were two blossoms from each individualin this set. Stage effects were always small and are not pre-sented.

FA measures are far from normally distributed and needto be transformed to make residuals comply with the as-sumptions of the mixed-model. The choice of transformationis not purely a statistical consideration, however. Fuller andHoule (2003) argued that Box-Cox transformation might ad-versely affect the estimation of the additive genetic variancein developmental stability, because it magnifies small errorsand compresses large differences in the right tail of the dis-tribution. However, large FA at the right end of the distri-bution may also result from major instead of minor distur-bances of developmental process such as physical injuries,and leaving the FA untransformed may give these an overlylarge effect on the outcome. For most of our traits a cube-root transformation appeared to give the best fit to a normaldistribution. However, because the square-root transforma-tion also gave very good fit and is much less extreme in itsmagnification of small errors, we chose this as a compromise,and square-root transformed all FA measures for the geneticanalysis. We verified that no result was qualitatively changedby use of square-root versus cube-root transformation.

RESULTS

Descriptive Statistics of Fluctuating Asymmetry

Descriptive statistics for FA in outcrossed and selfed in-dividuals are presented in Table 2. Directional asymmetrieswere extremely small, but sometimes statistically significant,except for gland-stigma distance (GSD), where the direc-tional asymmetry represented 3% of the mean trait size. Notealso that for the other directional asymmetries, the directions

510 CHRISTOPHE PELABON ET AL.

TA

BL

E3.

Gen

etic

com

pone

nts

offl

uctu

atin

gas

ymm

etry

(FA

;re

sult

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tic

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ysis

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).T

hem

odel

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udes

anad

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can

dan

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ct,

and

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enta

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age

asa

fixe

def

fect

.S

how

nar

ees

tim

ates

wit

hst

anda

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rors

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can

din

divi

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ance

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nts.

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yth

em

ean

effe

ctof

stag

e1

issh

own.

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illu

stra

tion

,w

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veal

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the

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nFA

;ad

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vege

neti

cva

riat

ion

scal

edw

ith

the

mea

n,I A

;he

rita

bili

ty,

h2;

and

tota

lph

enot

ypic

vari

atio

n,(n

otin

clud

ing

stag

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rian

ce),

all

onth

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ance

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sw

asco

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22

2s

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PS

SS

,ind

ina

sepa

rate

anal

ysis

,w

hich

also

incl

uded

anin

divi

dual

rand

omef

fect

and

afi

xed

stag

eef

fect

.T

hree

trai

ts(g

land

dept

h,gl

and

num

ber,

and

styl

ele

ngth

)w

ere

com

pute

dfr

omth

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alle

rda

tase

tan

ddo

not

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ude

ast

age

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one

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est

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tica

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sign

ifica

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1.93

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20.

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0.87

%

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002

0.02

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— —0.

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0.75

05.

264

2.99

2

were not consistent across observers (not shown). None ofthe distributions of signed FA showed significant skewness,but several showed some kurtosis.

The differences in FA between selfed and outcrossed in-dividuals were always small and inconsistent in directionacross traits (Table 2). Thus, there appears to be no effect ofhomozygosity on developmental stability in this population.This is expected from the mixed mating system of D. scan-dens, which is self-compatible (Armbruster 1988) with mostdeleterious recessive alleles likely having been purged. Theseresults should not be extrapolated to organisms with differentmating systems.

Genetic Variance in Fluctuating Asymmetry

Mean-scaled additive genetic variances (IA) and heritabil-ities (h2) of square-root-transformed FA (estimated from theoutcrossed dataset) were small and symmetrically distributedaround zero (six negative and four positive, Table 3). Theseestimates indicate that there were very low levels of additivegenetic variance in developmental stability. The same wastrue for family variances ( ) in the selfed dataset (four2sSSnegative—set to zero in a table 3—and six positive). Themaximum heritability, h2, of FA was 0.03. The IA evolva-bilities were generally low, but some approached the evolv-ability of the trait itself (Hansen et al. 2003a). Note also thatthe square-root transformation is likely to somewhat reducethe absolute value of IA. They were never statistically sig-nificant, however, and the low precision of these estimatesmeans that we expect to see this level of scatter around zero.

The individual variation in FA ( ) was as small and as2sindsymmetrically distributed around zero as was the genetic var-iance (Table 3). Thus, the FAs of the two blossoms on anindividual were not correlated (for all traits where two blos-soms per individual were measured: 20.046 , r , 0.040;all P . 0.30; n 5 510).

Components of Variance and Covariance in FluctuatingAsymmetry

The importance of developmental precision varied consid-erably from trait to trait: from 1% to 25% of the phenotypicvariation in the trait can be explained by lack of develop-mental precision (Fig. 4). Only a small proportion of varianceappears to be due to variation in degree of developmentalstability across individuals (Fig. 4; Table 4).

Covariances in FA were generally small. The decompo-sition into covariances due to developmental noise and de-velopmental stability revealed that covariances due to de-velopmental noise are practically zero for all trait combi-nations except in structurally related gland characters (Table4). Due to the rather small variances of developmental sta-bility for most traits, the estimates of covariance in devel-opmental stability are not very informative. Although someof the correlations in Table 4 are large, the covariances arein fact very close to zero (the variances are also very small).The absence of covariance in developmental stability is alsosuggested by the fact that some correlations were negative.Only the developmental stabilities of the gland characterswere all strongly positively correlated with each other. Be-cause these characters also showed the most variation in de-

511GENETICS OF DEVELOPMENTAL STABILITY

FIG. 4. Percentage of trait phenotypic variance (one side) ex-plained by developmental stochasticity (62 SE). This percentageis divided into two components, one due to developmental variance(light gray) and one due to variance in developmental stabilityacross individuals (dark gray). The developmental stochasticity isestimated as half the variance in signed FA. The standard errorsare based on the standard formula for the relative error of a varianceestimator, , where n is number of blossoms. The com-Ï2/(n 2 1)ponent due to variation in developmental stability is computed from(Var[R 2 L] 2 (p/2)E[FA]2)/2. For trait abbreviations, see Table 1.

TA

BL

E4.

Abo

veth

edi

agon

alar

eth

eco

rrel

atio

nin

fluc

tuat

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ry(F

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gned

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On

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onal

are

repo

rted

(lef

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pute

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reof

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ance

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ight

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cein

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ance

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tal

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ated

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/2)

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)22

(p/2

21)

].B

elow

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diag

onal

are

the

corr

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ions

inde

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pmen

tal

stab

ilit

y(C

orr[

s1,

s2])

.O

nly

outc

ross

edin

divi

dual

sw

ere

incl

uded

inth

isan

alys

is.

For

trai

tab

brev

iati

ons,

see

Tab

le1.

UB

LL

BL

GS

DG

WG

HG

DS

LS

WG

NG

A

UB

LL

BL

GS

DG

WG

H

14.1

5/0.

982

0.42

20.

012

0.03

20.

15

0.00

16.

08/0

.31

0.33

0.23

0.29

0.00

10.

002

71.6

9/1.

932

0.39

0.03

0.01

10.

001

0.00

182

.43/

6.02

0.52

0.00

10.

000

0.00

30.

010

66.6

5/14

.64

0.00

60.

010

0.01

50.

140.

074

0.01

80.

026

0.05

30.

011

0.00

1

0.00

00.

000

0.01

70.

000

0.00

2

0.00

10.

002

0.00

00.

280.

36

0.00

80.

001

0.00

30.

650.

59G

DS

LS

WG

N

0.86

0.61

0.13

20.

26

20.

610.

322

0.36

0.37

20.

912

1.15

0.19

20.

15

0.59

0.08

0.28

0.66

0.88

0.25

0.25

0.61

16.4

8/1.

430.

842

0.39

1.09

0.00

46.

20/0

.21

20.

540.

05

0.00

10.

022

12.0

2/1.

342

0.06

0.13

0.00

20.

004

221.

04/6

1.52

0.17

0.00

00.

000

0.57

GA

20.

200.

592

0.13

0.47

0.56

0.89

0.31

0.32

0.80

173.

81/1

3.62

velopmental stability (Fig. 4), joint control of developmentalstability is suggested. This is not surprising, as the glandcharacters are structurally related to each other. For example,variation in the position or number of bractlets in the glandcan simultaneously affect gland width, height, and depth.

DISCUSSION

Developmental instability can be a significant source ofadaptive imprecision. Figure 4 shows that as much as 25%of the phenotypic variation in adaptively important blossomtraits such as gland dimensions may be ascribed to a failureto reach the target phenotype. Similar values can be foundin other organisms (Lajus et al. 2003). Despite the obviousimportance of developmental imprecision in the Dalechampiablossoms, there appears to be little variation in developmentalstability itself across blossoms or individuals. In particular,there is no evidence for any additive genetic variation indevelopmental stability. This is consistent with similar resultsin several previous studies of the heritability of FA (forplants: Perfectti and Camacho 1999; Wilsey and Saloniemi1999; Andalo et al. 2000; Rao et al. 2002; for animals:Blanckenhorn et al. 1998; Woods et al. 1999; Bjorksten etal. 2000; Cadee 2000; Kruuk et al. 2003).

Several theoreticians have argued that we should not besurprised by such results, because genetic (or other) variationin FA will be almost impossible to detect (Whitlock 1996,1998; Houle 1997, 2000; Van Dongen 1998). For example,Houle (1997) argued that heritabilities of FA on the order of0.18, the median value found in the meta-analysis of Møllerand Thornhill (1997), were ‘‘implausible, if not impossible.’’Houle based his argument on a two-genotypes model in whichhe showed that the ratio between the two variances of de-velopmental stability, s2, must be .5 to produce heritabilities

512 CHRISTOPHE PELABON ET AL.

as high as this. He later extended this into a more realisticmodel, in which s2 was assumed to follow a gamma distri-bution, and reached the same conclusion (Houle 2000).

We question this theoretical position for two reasons. First,the question of what constitutes an implausibly high level ofvariation in developmental stability is a biological judgmentcall. A five-fold change in s2 translates into a -fold changeÏ5in s or in FA, which does not seem implausible. Second,even heritabilities of FA considerably smaller than 0.18, asfound in the careful meta-analysis of Van Dongen (2000),are compatible with high evolvability of developmental sta-bility. As seen from equation (15), even a heritability of FAof 0.04 is compatible with an IA evolvability in excess of2%, which is large enough to fuel a reasonable evolutionaryresponse (Hansen et al. 2003a).

Therefore, we regard the question of the evolvability ofdevelopmental stability as still open. Although it is almostimpossible to assess evolutionary potential through a con-sideration of the heritability of FA in a single trait, we suggestthat the question is accessible through the use of mean-stan-dardized variances and covariances of FA, which are moredirectly related to variation in developmental stability. Es-timation of these parameters is still very imprecise, and anassessment of genetic variation in developmental stabilityrequires either extremely large experiments or the simulta-neous assessment of FA in many traits.

Thus, although we cannot exclude a substantial evolva-bility of developmental stability in any of the individual traitswe studied, consideration of the 10 traits together shows thatthe best estimates of evolvability are centered on zero in bothselfed and outcrossed individuals. A similar result was foundwhen estimating genetic variance components of FA com-puted across two blossoms on each plant, for a total of 12size-corrected traits (not shown). This yielded seven positiveand five negative estimates in outcrossed individuals and fivepositive and seven negative estimates in selfed individuals.Also, the fact that the estimates of evolvability are not con-sistent across selfed and outcrossed offspring indicatesstrongly that the deviations from zero are due to estimationerror. Thus, we regard our results as a genuine demonstrationof extremely low evolvability in developmental stability.

It should be noted that our results comes from a populationthat has been previously shown to have rather low (althoughhighly statistically significant) levels of quantitative geneticvariation in the characters examined here (Hansen et al.2003a,b). Thus, we may not expect high levels of geneticvariation in developmental stability. Nevertheless, this is anexample of genetic variation in developmental stability beinglower than genetic variation in the morphological traits them-selves.

A genuine lack of additive genetic variation in develop-mental stability would be theoretically surprising. Devel-opmental stability is a complex character that would be ex-pected to have a large mutational target size (but see Mo-nedero et al. 1997). Furthermore, developmental stabilityevolves (Clarke and McKenzie 1987; Davies et al. 1996), andif not based on additive genetic variation, its evolvabilitymust be explained in other ways. Below, we consider somepossibilities based on canalization, epistasis, and genotype3 environment interaction.

Genetic canalization, the reduction of the effects of newmutations and segregating alleles on the phenotype, is a pre-dicted outcome of stabilizing selection on the trait (Wagneret al. 1997). A long history of selection for reduced devel-opmental noise may lower the expressed genetic variation indevelopmental stability under normal conditions (Rutherford2000). Hidden genetic variation may, however, be releasedfollowing the breakdown of the canalizing system (Wad-dington 1959; Levin 1970; Eshel and Matessi 1998; Ruth-erford 2000). Increased levels of FA may thus result fromdrastic genetic changes, such as after hybridization events(Graham 1992; but see Pelabon et al. 2004), or rapid adaptiveresponses to drastic environmental changes, such as the re-sponse to a novel pesticide in the Australian blowflies (Clarkeand McKenzie 1987; Davies et al. 1996).

Recent theoretical work on epistatic models suggests thatequilibria may exist in which additive genetic variation isabsent in mutation-selection balance (Hermisson et al. 2003).Surprisingly, this occurs when stabilizing selection on thetrait is relatively weak compared to the strength of epistasis.Trait symmetries are prime candidates for such equilibriabecause epistatic interactions are expected due to the complexfunctional architecture and stabilizing selection on the un-derlying genetic value is likely to be weak. If s is the strengthof stabilizing selection on a trait, the strength of the stabi-lizing selection on the underlying genotype will be sG 5 s/(1 1 2VE/s). Therefore, sG will strongly decrease with in-creasing effect of the environmental variance (VE) on thetrait. Because the relation of the selected phenotype to de-velopmental stability is inherently noisy and, as demonstratedby numerous studies, developmental stability is particularlysensitive to environmental disturbances, the strength of sta-bilizing selection on the underlying genetic basis should beweak. The epistatic variance could, however, be large in suchsituations. Leamy et al. (2002) and Leamy (2003) recentlyprovided evidence for epistatic genetic variance for FA incentroid size in the mandible of mice. The possibility of largeamounts of epistatic variance in FA needs further investi-gation.

Alternatively, because developmental noise often increasesunder stressful conditions (Parson 1990), it is possible thatdevelopmental stability captures (sensu Rowe and Houle1996) the genetic variability associated with stress resistance.In this case, individual variation in resistance to stress and,consequently, in developmental stability will only be ex-pressed in stressful environment. Both the genetic canali-zation and the stress-dependent-response hypotheses implythat the genetic basis of developmental stability should beanalyzed under situations sufficiently stressful to provokedrastic changes in the expression of the genetic informationand reveal the hidden genetic variation (but see Waddington1961; Woods et al. 1999; Andalo et al. 2000).

Through the use of unbiased measures of variance in de-velopmental stability on a large number of floral traits, wehave assembled strong evidence that levels of additive ge-netic variation in developmental stability are extremely lowin our study population. These results are consistent with theapparent absence of additive genetic variance in develop-mental stability observed in many previous studies, but they

513GENETICS OF DEVELOPMENTAL STABILITY

do not preclude the possibility of more subtle genetic effectsthrough, for example, epistatic interactions.

ACKNOWLEDGMENTS

We thank L. Antonsen, L. Dalen, and T. Berge for seedcollection in the field. Thanks to L. Antonsen, T. E. Brobakk,L. Dalen, M. Deveaud, G. Fyhn-Hanssen, T. Kjellsen, S.Lindmo, A. Moe, H. Myklebost, E. Sørmeland, and manyothers for greenhouse assistance. We thank M. Geber, C.Klingenberg, and several anonymous reviewers for their help-ful comments on the manuscript.

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