Asymmetry as a predictor of growth, fecundity and

survival

AbstractMeasures of developmental stability such as fluctuating asymmetry have beenassumed to predict individual performance because asymmetry reflects an inability tocope with stressful situations, and because asymmetry hampers locomotion.However, the magnitude of this relationship between important fitness components(growth, fecundity, survival) and asymmetry has never been assessed. Based on aliterature survey, estimates of the correlation between asymmetry and the three fitnesscomponents are presented. Pearson's correlation coefficients weighted for sample sizebetween asymmetry and growth, fecundity, and survival, respectively, were ±0.15,±0.35, and ±0.25, respectively, with all three coefficients being highly significant. Allthree relationships were extremely robust given very large fail-safe numbers. Theresults were independent of whether studies or species were used as units of analysis.Hence asymmetry is a robust predictor of performance in fitness domains such asgrowth, fecundity, and survival, although only accounting for 2.1%, 12.3%, and6.0% of the variance. This may be of importance for studies of sexual selection, butalso for ecological and conservation biological studies, where the performance ofindividuals or groups of individuals are assessed.

KeywordsDevelopmental stability, fecundity, fluctuating asymmetry, growth, meta-analysis,survival, viability.

Ecology Letters (1999) 2 : 149±156

I N T R O D U C T I O N

Currently, there is an increasing interest in the use ofvarious measures of developmental instability to under-stand a wide range of ecological and evolutionaryproblems, and also questions in fields such as humanand veterinary medicine, conservation, and animal welfare(see reviews in Mùller & Swaddle 1997; Thornhill &Mùller 1997). The main reason for this interest stems fromthe hypothesis that measures of developmental instabilitymay provide reliable information about the ability ofindividuals and populations to cope with their environ-ment given their genetic set-up. Recent reviews suggestthat estimates of developmental instability such asfluctuating asymmetry reliably predict success in realmsof natural and sexual selection (reviews in Mùller &Swaddle 1997; Mùller & Thornhill 1998). However, weknow very little about how general such relationships maybe. For example, recent reviews only reported resultsfrom a few studies (Clarke 1995a, four studies; Clarke1995b, six studies; Markow 1995, four studies). A recent

meta-analysis of fluctuating asymmetry and fitness byLeung & Forbes (1996) found an overall very weakaverage effect. This conclusion may partly be due toinclusion of such indirect studies as those investigatingthe relationship between size and asymmetry of secondarysexual characters and studies of the relationship betweenasymmetry and heterozygosity. Furthermore, Leung &Forbes (1996) only included a minority of the studies ofthe present analysis, simply because most studies haveonly been published very recently. Mùller (1997) provideda vote-counting summary of the literature, suggesting thatmost studies found results in the predicted direction of anegative relationship between asymmetry and measures offitness, although the magnitude of the effect was notdetermined because of lack of sufficient data. Recently,Clarke (1998) has suggested that the conclusion by Mùller(1997) was not warranted, although this was not sub-stantiated by a quantitative assessment of the literature.

If simple phenotypic measures such as fluctuatingasymmetry of morphology were related to performance,this would have important implications for ecological and

#1999 Blackwell Science Ltd/CNRS

Anders Pape Mùller

Laboratoire d'Ecologie, CNRS

URA 258, Universite Pierre et

Marie Curie, BaÃt. A, 7eÁme eÂtage,

7 quai St. Bernard, Case 237,

F-75252 Paris Cedex 05, France.

E-mail:

amoller@hall.snv.jussieu.fr

Ecology Letters, (1999) 2 : 149±156

R E P O R T

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evolutionary studies. In particular, we could use measuresof fluctuating asymmetry as a covariate in studies wherewe were testing the effects of a treatment, such as densityor levels of parasitism, on performance. Similarly, wecould investigate the effects of experimental treatments onthe development of asymmetry for growing individuals,or the change in asymmetry for organisms with repeateddevelopment of paired characters such as plants, birds,and mammals.

The main aim of this paper was to provide an estimateof the relationship between asymmetry and performancein three important fitness domains (growth, fecundity,and survival). This was done by assessing the averagemagnitude of these relationships, and also the robustnessof the associations. The three fitness components werechosen because they are closely related to lifetimereproductive success. Individuals that are able to growfaster would enter the stage of reproduction earlier, withthe assumption that there are advantages associated withearly reproduction (reviews in Roff 1992; Stearns 1992).Similarly, individuals that produce more offspring andsurvive for longer are assumed to have greater lifetimereproductive success, as shown in general to be the case(Clutton-Brock 1988; Newton 1989). Obviously, thesecomponents will be subject to some stabilising selection assuggested by life history theory (reviews in Roff 1992;Stearns 1992).

The relationship between asymmetry and performancewas quantified using meta-analysis, which is a class ofstatistical techniques that allows quantitative assessmentof a body of literature (Hedges & Olkin 1985; Rosenthal1991; Cooper & Hedges 1994). Ecological reviews aretraditionally based on a narrative summary, but thisapproach is potentially misleading because effects ofparticular studies may be nonsignificant either because oflow statistical power, or because of true, weak effects.Any literature is likely to be biased to some extent (Csadaet al. 1996; Silvertown & McConway 1997), although thisproblem cannot readily be addressed, since we can neverknow all the studies available. However, we can obtain ameasure of the robustness of a finding by calculating thenumber of null results needed to nullify a recorded effectin the published literature (Rosenthal 1991). This so-calledfail-safe number provides a quantitative measure of thereliability of a finding. Rosenthal (1991; p. 106) suggeststhat a fail-safe number that is larger than five times thenumber of published studies plus 10 will indicate that aneffect is robust. The present analysis presents a generalassessment of the magnitude of the relationship betweenasymmetry and the three fitness components, but also anassessment of the robustness of these relationships.Furthermore, the effects of a number of potentiallyconfounding factors are investigated and discussed.

M A T E R I A L A N D M E T H O D S

Data on viability and asymmetry were obtained by anextensive search of the literature and by correspondencewith researchers in the field. Growth was defined asgrowth rates or duration of growth. Fecundity was definedas clutch size or seasonal reproductive success. Survivalwas defined as probability of survival or differences inphenotype between survivors and nonsurvivors. Ifestimates controlled for potentially confounding variables,such estimates were preferred for the present analysis overuncorrected estimates. Experimental studies were includedwhere changes in fecundity were associated with experi-mental changes in asymmetry. Although such asymmetrycannot be directed stated to reflect developmental instabil-ity, the perceptive mechanisms associated with discrimina-tion against asymmetry must have been maintained by theability to distinguish between individuals differing in theirlevel of individual fluctuating asymmetry. This type ofstudy is limited to a single (Swaddle 1996), and theconclusions remain unaltered by exclusion of this study.Studies based on variation among individuals within apopulation were distinguished from studies based onvariation among populations, although the latter com-prised only three studies in total. Studies that tested fordirectional asymmetry and anti-symmetry, and did not findthese kinds of asymmetry, were distinguished from studieswithout such tests. This distinction was made because wecannot be sure that studies without such tests representfluctuating asymmetry. The entire data set is provided inthe supplementary material given on the Blackwell Sciencejournal website (http://www.blackwell-science.com/ele).

Meta-analyses are problematic, if null results tend not tobe published (Hunter & Schmidt 1990). There are a numberof methods available for testing for reporting or publicationbiases (Light & Pillemer 1984; Vandenbroucke 1988; Berlinet al. 1989; Dear & Begg 1992; Hedges 1992; Thompson1993; Mengersen et al. 1995). Most of these methods requirerelatively large data sets. However, a simple prediction isthat a plot of effect size in relation to log-transformedsample size should give rise to a funnel shape around the``true'' effect size. The reason is that variance in effect sizeshould be higher for small sample studies than for largesample studies, and that observed effect sizes should benormally distributed around this effect with no trend inrelation to sample size (Light & Pillemer 1984; Vanden-broucke 1988). Obviously, we can never know how manyunpublished studies of negative results are available, but thisproblem can be addressed by calculating the fail-safenumber of publications (Rosenthal 1991).

The measure of effect size used was Pearson'scorrelation coefficient. If the original sources did notprovide a correlation coefficient, the statistics were trans-

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formed into a correlation coefficient using the formulaefor transformation given by Rosenthal (1991, Table 16.1).If more than a single estimate was reported, the z-trans-formed effect size weighted by sample size was used as theoverall estimate (Rosenthal 1991). Most studies reportedparametric statistics, but some studies based on nonpara-metric correlation coefficients were used directly as ameasure of effect size, although such coefficients provideless powerful tests of a relationship than parametricPearson correlation coefficients. In cases where onlyprobabilities were reported, these were transformed intoPearson's correlation coefficients using the standardtransformation (Sokal & Rohlf 1995). Pearson correlationcoefficients were subsequently transformed by means ofFisher's transformation to z values on which subsequentanalyses were performed. This measure of effect size wasadjusted for sample size using N ± 3 as an adjustmentfactor (Rosenthal 1991; pp. 27±28), based on theassumption that a larger sample size should provide amore reliable estimate of the unknown, true relationship.

An overall effect using mean effect size adjusted forsample size after z transformation was calculated usingthe equation:

Mean weighted zr=S[(Nj ± 3)zrj ]/S(Nj ± 3)

where zrj is the z-transformed effect size for analysis unit j.The mean weighted zr values were tested against the nullhypothesis of no effect by examining the significance oftheir associated r 's. This was done by back-transformingthe mean weighted effect size to a correlation coefficientand testing the significance of this coefficient given thetotal sample size (Rosenthal 1991). The analyses wererepeated using studies and species as units of analysis.Species-specific values were mean z-transformed correla-tion coefficients weighted by sample size.

An estimate of heterogeneity in effect sizes amongsamples was subsequently calculated using the formulaprovided by Rosenthal (1991; pp. 73±74):

w2=S(Nj ± 3)(zrj ± mean zr)2,

which has a w2-distribution with K ± 1 degrees of freedom,where K is the number of analysis units.

The fail-safe number of studies, X, needed to nullify aneffect was calculated, following Rosenthal (1991; p. 104), as:

X=(Szj)2/2.706 ± K

where zj= zrj H(Nj ± 3) and K is the number of anal-ysis units.

It was tested whether verification of absence ofsignificant directional asymmetry and anti-symmetry wasassociated with a systematic change in effect size using aplanned contrast test (Rosenthal 1991; pp. 79±84). Thestatistical significance of the difference in two groups of ris obtained from a z (the standard normal deviate),calculated as:

Slj zr /[HS(lj2/wj)],

where lj is the contrast weight determined by ahypothesis of the analysis unit (samples, species), chosenso that the sum of j equals zero. 1/Nj is the weightingfactor, where Nj is the number of samples in each of the jcategories. wj is the inverse of the variance of the effectsize for the analysis unit.

R E S U L T S

The average relationship between asymmetry and thethree fitness components is given in Table 1. The averageweighted effect size for all three components is statisticallyhighly significant, which implies that there is evidence fora general relationship. The magnitude of the effect whenstudies are used as units of analysis is smallest for growthwith a mean weighted r=±0.15, implying that 2.1% ofthe variance in growth is explained by asymmetry, inter-mediate for survival with a mean weighted r=±0.25,implying that 6.0% of the variance in survival is explainedby asymmetry, and highest for fecundity with a meanweighted r=±0.35, explaining 12.3% of the variance.These conclusions were almost identical if species wereused as units of analysis (Table 1).

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Asymmetry and fitness 151

Weighted effect size No. of Heterogeneity Fail-safeFitness component (95% CI) studies test number

StudiesGrowth ±0.146 (±0.096, ±0.196)*** 11 27.46** 168Fecundity ±0.350 (±0.316, ±0.384)*** 21 597.28*** 2707Survival ±0.248 (±0.226, ±0.267)*** 29 216.86*** 4626

SpeciesGrowth ±0.156 (±0.106, ±0.206)*** 10 25.03** 150Fecundity ±0.340 (±0.306, ±0.374)*** 14 557.56*** 1813Survival ±0.244 (±0.224, ±0.264)*** 23 209.78*** 3765

**P 5 0.01, ***P 5 0.001

Table 1 Weighted mean effect sizesbetween fitness components and asym-metry (and the 95% CI), number ofstudies, results of heterogeneity tests,and fail-safe numbers for studies andspecies as units of analysis based oncalculations using data in the sup-plementary material given on theBlackwell Science journal website(http://www.blackwell-science.com/ele).

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Three studies were based on analysis of variationbetween populations (two studies for growth, none forfecundity, one study for survival), but the generalconclusions did not depend on the level of analysisbecause weighted effect sizes were almost identical afterexclusion of these studies.

Planned contrasts between studies where tests fordirectional asymmetry and anti-symmetry had beenperformed or not performed revealed a highly significantdifference for fecundity [z=8.30, weighted r (studieswith tests)=±0.324, N=16, weighted r (studies withouttests)=±0.411, N=5] and survival [z=16.29, weightedr (studies with tests)=±0.254, N=23, weighted r (studieswithout tests)=±0.156, N=6], but not for growth(z=1.18, N.S.).

Potential bias was tested for in the effect size measuresby determining whether plots of effect sizes againstsample size were funnel shaped (Light & Pillemer 1984;Vandenbroucke 1988), with no change in mean effect sizewith sample size. The sample size of studies of growthrate was very small, so the analyses were restricted tofecundity and survival. The variance in transformedz values for small sample sizes below the median wasnot larger than the variance for large sample sizes forfecundity studies (15.196 vs. 6.298, respectively, F-test,F=2.41, d.f.=10,10, P 5 0.10). The relationshipbetween transformed z values and log-transformed samplesize was not statistically significant (linear regression:F=1.71, d.f.= 1,19, P=0.21). The power of both thesetests, however, is low due to the low sample size. Forsurvival the variance for studies with a sample size belowthe median was significantly larger than the variance forstudies with large sample sizes (10.097 vs. 1.665,respectively, F-test, F=6.06, d.f.=14,13, P 5 0.01).The relationship between transformed z scores and log-transformed sample size was statistically significant (linearregression: F=6.14, d.f.=1,27, P=0.02, r=0.43),indicating that the results may have been biased forstudies based on small samples.

All three mean effect sizes demonstrated highlysignificant heterogeneity among studies and species(Table 1), implying that one or more moderator variablesinfluenced the correlations. When more studies becomeavailable, it will be possible to start investigating suchexplanatory variables.

The robustness of the average weighted effect sizes canbe calculated from the fail-safe number, which representsthe number of unknown additional studies that would beneeded to eliminate an overall effect's significance at the5% level when those studies showed an average null result(Rosenthal 1991; p. 104). All three estimates of the fail-safe number if studies are used as units of analysis are veryhigh, ranging from 168 for growth, to 2707 for fecundity,

and to 4626 for survival. These values exceed by far theaccepted threshold for considering a result to be robust,which has been suggested to be five times the number ofstudies included in an analysis plus 10 (Rosenthal 1991; p.106), i.e. 65 for growth, 115 for fecundity, and 155 forsurvival. Similar conclusions were reached if species wereused as the unit of analysis.

D I S C U S S I O N

The present study provides estimates of the magnitudeand the robustness of the relationship between asymmetryand three important components of fitness (growth rate,fecundity, and survivorship) in a wide variety oforganisms ranging from plants to humans. The threemean correlation coefficients were relatively small andaccounted only for 2.1% of the variance in growth, 12.3%of the variance in fecundity, and 6.0% of the variance insurvival. However, no other general phenotypic measureis currently known to be a better general predictor ofthese fitness components. It is not certain that thereported relationships are not caused by covariation witha third variable. However, effects based on partialcorrelation coefficients were used whenever possible.Furthermore, experimental studies such as those of Mùller(1992, 1993) demonstrate that fecundity is affected directlyby variation in asymmetry. Most studies (45 of 61) testedfor directional asymmetry and anti-symmetry and did notreport such asymmetry. Hence, it seems likely that moststudies were based on measures of developmentalinstability. Planned contrast tests demonstrated significantdifferences in effect size between studies with and studieswithout such tests for fecundity and survival (weightedeffect being stronger for studies with tests in the case ofsurvival, but weaker for studies with tests in the case offecundity), although the estimates are not biased in aparticular direction. It should also be kept in mind thatstudies without tests might still demonstrate the featuresof fluctuating asymmetry. All three relationships were of astatistically small to intermediate magnitude (Cohen1988), with the estimated effect sizes being extremelyrobust. The effect size estimates are bound to beinfluenced by a number of factors such as measurementerror, a number of potentially confounding variables, andbiological variables. Therefore, the estimated effects arehighly likely to be under-estimates since only experimentalstudies will be able to control for potentially confoundingvariables. Finally, fluctuating asymmetry is a poorestimate of underlying developmental instability, andeffect sizes for the relationship between asymmetriescorrected for the repeatability of estimates and fitness willbe considerably larger than the uncorrected values (VanDongen 1998; Whitlock 1998).

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The distributions of effect sizes were funnel shapedwith no indication of changes in effect size with samplesize for fecundity. However, there was a slight decrease ineffect size with increasing sample size for studies ofsurvival. Although such dependence on sample size can beinterpreted as evidence of publication or reporting bias,an alternative explanation is that scientists with a goodknowledge of the approximate effect, e.g. from a pilotstudy, may deliberately use a small sample in a particularexperiment. Second, experiments tend to use manipula-tions that give rise to greater variance than the naturalvariance, and since experiments generally are small forlogistic reasons, experiments will tend to have moreextreme values for small sample sizes than observationalstudies with a similar sample size. Furthermore, scientistsmay increase sample size when recording a small effectsize in a pilot study to ensure a sufficiently high power formaking reasonable conclusions. Anyway, the problem oflarge effect sizes for small sample sizes is controlled in themeta-analysis by the use of effect sizes adjusted for samplesize in all the analyses of the present paper.

The ecological implications of the present findings arepotentially large. First, the reliability of predictions basedon correlation coefficients in the range ±0.15 to ±0.35 isfar from great. However, these coefficients can potentiallybe improved by using asymmetry in multiple rather than asingle character as a measure of developmental instability(Mùller & Swaddle 1997) (only few studies in the presentreview were based on composite indices of asymmetry), orby using plasticity in asymmetry developed underdifferent environmental conditions as a measure ofdevelopmental instability (Shykoff & Mùller 1998).Repeated measures of developmental performance canreadily be obtained in organisms that moult regularly ordevelop leaves in successive seasons. Second, ecologistsworking on individual or even population based researchoften need to be able to make a priori predictions of theperformance of their study subjects. Asymmetry may beexactly such as measure because measurements can bemade nondestructively in many organisms, such as mostvertebrates and plants. Rather than assessing performanceof all experimental subjects on an average basis,considerable amounts of information can be gained interms of understanding mechanisms behind patterns ofselection if success can be related to individual phenotype.Third, if asymmetry generally is associated with perfor-mance in important fitness domains such as growth,fecundity, and survival, this has important implicationsfor studies of conservation biology. Asymmetric indivi-duals would be predicted to perform poorly in popula-tions in danger of extinction, and populations consistingof more asymmetric individuals would be predicted toperform less well than populations with symmetric

individuals. Although differences in performance betweenpopulations may be due to habitat differences, such afinding would also provide important information forconservation purposes.

The evolutionary implications of the present study aremany. First, sexual selection is often associated withasymmetry, with symmetric individuals enjoying im-proved mating success (Mùller & Thornhill 1998), andthis effect is greater than that for size of the samecharacters (Thornhill & Mùller 1998). Such strongpreferences for symmetry seems much more readilyunderstandable with the relationships between asymmetryand growth, fecundity, and survival shown in the presentstudy. Choosy females preferring symmetric males willgain an advantage because such males survive longer,which may give rise to direct benefits in species wheremales participate in parental care, but choosy females mayalso be able to gain indirect fitness benefits if the ability toresist environmentally caused stress has a genetic basis.There is some evidence that measures of developmentalinstability are heritable, although the magnitude of thisheritability only may be in the order of 0.05±0.10 (Mùller& Thornhill 1997; associated comments). On an evolu-tionary time scale, the very intense selection pressuresassociated with asymmetry may provide females withconsiderable benefits even with small heritabilities. Theheritability of fitness itself is certainly less than 0.10(review in Burt 1995), although this is still an importantfactor in sexual selection (Mùller & Alatalo 1998).Second, if there are relatively strong associations betweenasymmetry and fitness components, this has importantimplications for which individuals are contributing tofuture generations. For example, it is possible thatsymmetric individuals of a threatened species in need ofconservation will contribute relatively more to futuregenerations than more asymmetric individuals. Third, ifasymmetry to some extent is a predictor of fitness comp-onents such as growth, fecundity, survival, and matingsuccess, and if such components display heritable varia-tion, then this may have practical implications for animaland plant breeding programs, where performance is oftenmeasured in terms of growth, fecundity, and survival.

In conclusion, asymmetry and other measures ofmorphological irregularity is generally negatively corre-lated with fitness components, as demonstrated by thisstudy and that of Mùller & Thornhill (1998) for sexualselection. Obviously, assessment of the relationshipbetween asymmetry and various fitness components doesnot constitute a test for the relationship with fitness per se.However, given the strongly positive correlations be-tween lifetime reproductive success and fecundity and, inparticular, survival (Clutton-Brock 1988; Newton 1989),this is not a serious objection.

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A C K N O W L E D G E M E N T S

R. Thornhill and three anonymous referees kindlyprovided constructive criticism. My research was sup-ported by an ATIPE BLANCHE from CNRS.

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Scutt, D., Manning, J.T., Whitehouse, G.H. & Leinster, S.J.(1998). Breast asymmetry and a predisposition to breast cancerin healthy women. Manuscript.

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Wauters, L.A., Dhondt, A.A., Knothe, H. & Parkin, D.T.(1996). Fluctuating asymmetry and body size as indicators ofstress in red squirrel populations in woodland fragments. J.Appl. Ecol., 33, 735±740.

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Editor, L. KellerManuscript received 6 November 1998First decision made 30 November 1998Manuscript accepted 12 January 1999

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156 A.P. Mùller

B I O S K E T C H

A.P. Mùller works on the ecological and evolutionary causesand consequences of developmental instability.

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