ORIGINAL ARTICLE

doi:10.1111/j.1558-5646.2012.01777.x

EVOLUTION OF STATIC ALLOMETRIES:ADAPTIVE CHANGE IN ALLOMETRIC SLOPESOF EYE SPAN IN STALK-EYED FLIESKjetil L. Voje1,2 and Thomas F. Hansen1

1Department of Biology, Centre for Ecological and Evolutionary Synthesis, University of Oslo, Oslo, Norway2E-mail: k.l.voje@bio.uio.no

Received December 18, 2011

Accepted July 25, 2012

Data Archived: Dryad doi:10.5061/dryad.h6q26

Julian Huxley showed that within-species (static) allometric (power-law) relations can arise from proportional growth regulation

with the exponent in the power law equaling the factor of proportionality. Allometric exponents may therefore be hard to

change and act as constraints on the independent evolution of traits. In apparent contradiction to this, many empirical studies

have concluded that static allometries are evolvable. Many of these studies have been based, however, on a broad definition of

allometry that includes any monotonic shape change with size, and do not falsify the hypothesis of constrained narrow-sense

allometry. Here, we present the first phylogenetic comparative study of narrow-sense allometric exponents based on a reanalysis

of data on eye span and body size in stalk-eyed flies (Diopsidae). Consistent with a role in sexual selection, we found strong

evidence that male slopes were tracking “optima” based on sexual dimorphism and relative male trait size. This tracking was

slow, however, with estimated times of 2–3 million years for adaptation to exceed ancestral influence on the trait. Our results are

therefore consistent with adaptive evolution on million-year time scales, but cannot rule out that static allometry may act as a

constraint on eye-span adaptation at shorter time scales.

KEY WORDS: Allometry, evolutionary constraints, morphology, phylogenetic comparative method, phylogenetic inertia, sexual

selection.

Morphological traits often scale with a power of each other amongindividuals at the same developmental stage (Huxley 1932; Gould1966a). An early interpretation of such static morphological al-lometries was that they resulted from a constant proportionalityof growth between the traits under study (e.g., Huxley 1932).Allometric exponents were therefore viewed as characters withlow evolvability and as potential constraints on the independentevolution of traits (e.g., Huxley 1932; Rensch 1959; Gould andLewontin 1979; Lande 1979, 1985; Cheverud 1982; Gould 1989,2002). A more recent interpretation is that static allometries canbe understood as reaction norms, reflecting resource allocationsto traits across a range of possible final body sizes (e.g., Emlenand Nijhout 2000; Bonduriansky and Day 2003; Kodric-Brown

et al. 2006). In both interpretations, the allometric exponent re-flects a developmental constraint that may or may not ensure afunctional relation between traits and overall body size.

Over the last decades, the allometric-constraint hypothesishas been challenged by the argument that allometric exponentsshould be evolutionary labile like most quantitative traits (e.g.,Eberhard and Gutierrez 1991; Emlen and Nijhout 2000). Indeed,many researchers have argued or assumed that the slopes of staticallometries are determined by selection on traits and size (Petrie1988; Green 1992; Eberhard et al. 1998; Bernstein and Bernstein2002; Hosken et al. 2005; Kodric-Brown et al. 2006; Eberhard2009). It has been claimed that allometric slopes vary consider-ably among populations and closely related taxa, hinting at rapid

1C⃝ 2012 The Author(s).Evolution

K. L. VOJE AND T. F. HANSEN

evolution of allometric relationships (Emlen and Nijhout 2000;Shingleton et al. 2007; Frankino et al. 2009). Artificial selectionexperiments changing linear scaling relationships between traitson an arithmetic scale have also been used as arguments for highevolvability of allometric parameters (e.g., Weber 1990, 1992;Wilkinson 1993; Frankino et al. 2005, 2007, 2009).

Many recent studies of short- or long-term evolution of mor-phological allometries have, however, relied on a broader defi-nition of allometry compared to how the concept was originallyconceived. Instead of defining allometry as the study of pro-portional changes between traits (censu Huxley 1932; Huxleyand Tessier 1936; Gould 1966a; von Bertalanffy 1969; Cheverud1982; Lande 1985; Eberhard 2009) much recent literature use itto refer to any linear or nonlinear scaling relationship on nonlog-transformed traits (e.g., Emlen 1996; Emlen and Nijhout 2000;Baker and Wilkinson 2001; Moczek and Nijhout 2003; Frank-ino et al. 2005, 2007). In effect, this broad-sense allometry canbe used to refer to practically any monotonic change in shapewith size (see, e.g., review in Frankino et al. 2009). In contrast,Huxley’s narrow-sense allometry entails the very specific powerlaw relation Y = aXb, between a trait Y and body size X, which thenyields the standard linear allometric equation log(Y) = log(a) +blog(X), where b is the allometric slope. It is the derivation ofthis power law from simple growth laws (e.g., Huxley 1924,1932; Savageau 1979; Lande 1985; Stevens 2009) that justifies theallometry-as-constraint hypothesis, just as the interest in powerlaws in physiology, life-history theory, and other fields is mo-tivated by specific models (e.g., Schmid-Nielsen 1984; Charnov1993; Kozlowski and Weiner 1997; West et al. 1997; Frank 2009).The hypothesis that allometric relations constitute a constraint onevolutionary change must therefore refer to narrow-sense allome-try to have general explanatory power. Scale transformations cancompletely change the meaning of the fitted model and linearregressions on arithmetic and proportional scales are not test-ing the same hypothesis. When Weber (1990, 1992), Wilkinson(1993), Emlen and Nijhout (2000), Baker and Wilkinson (2001),Frankino et al. (2005, 2007), Okada and Miyatake (2009), andothers are reporting on selection responses or evolutionarychanges in (broad-sense) allometry, they are studying shape evolu-tion, but they are not estimating the theoretically relevant param-eters for testing the allometric-constraint hypothesis of Huxleyand Gould (Houle et al. 2011).

Consequently, little information about the evolution and evo-lutionary potential of narrow-sense allometry has been assembled.For example, Egset et al. (2012) seems to be the first experimentalselection study that has specifically selected on and measured theresponse in narrow-sense static allometric slopes; they found noresponse over three generations of selection on a tail-fin allome-try in guppy despite a robust response in the allometric intercept.Furthermore, although many studies have documented species

differences in static allometric slopes (e.g., Simmon and Tomkins1996; Tomkins and Simmons 1996; Kawano 2004, 2006; Hoskenet al. 2005), there are yet no phylogenetic comparative studies thatassess the tempo and mode of evolution in narrow-sense static ordevelopmental allometries.

For this reason, we re-analyze data presented by Baker andWilkinson (2001) on the evolution of eye span in relation to bodysize in Diopsid stalk-eyed flies to specifically test hypothesesabout the evolution of the narrow-sense allometric exponent. Theoriginal study investigated the evolution of the within-speciesarithmetric slope of eye span on body length in relation to sex-ual dimorphism. Our analysis differs from Baker and Wilkinson(2001) in two important ways. First, we study the slope of log eyespan on log body size, which corresponds to Huxley’s allometricmodel. Hence, we test a hypothesis that was not tested in the orig-inal study. Second, to test the hypothesis that allometric slopesevolve adaptively in relation to strength of sexual selection, weuse a phylogenetic comparative method specifically designed foradaptive evolution (Hansen 1997; Butler and King 2004; Hansenet al. 2008) in place of the independent-contrasts method used byBaker and Wilkinson (2001).

It has been argued that sexual selection in general favors theevolution of positive allometries (Petrie 1988; Green 1992, 2000;Simmons and Tomkins 1996, see Fairbairn 1997; Bonduriansky2007; Eberhard 2009 for review and critical discussion of thishypothesis). The effects of selection on growth rates are poorlyunderstood, however, and the theoretical basis of claims to theeffect that directional sexual selection should favor steeper al-lometries has been questioned (Bonduriansky and Day 2003).The lack of a general theory does not invalidate the empirical hy-pothesis however, and Bonduriansky and Day (2003) also showedthat steeper static allometries may evolve if there is a trade-off inresources between the trait and size, and the selection gradient onthe trait is increasing faster with size than the selection gradient onsize itself. This may fit with condition-dependent sexual selection.Here, we test the hypothesis that intra- and intersexual selectionon eye span is selecting indirectly for steep static allometric slopesin species in which eye span is the main character determiningmale reproductive success. Species in the Diopsidae family areeither sexually mono- or dimorphic in eyestalk length (Baker andWilkinson 2001). In dimorphic species, eye span is used in male–male competition for access to females (e.g., Burkhardt and de laMotte 1983, 1985; Panhuis and Wilkinson 1999). Strong femalepreferences for males with large eye spans have also been docu-mented for dimorphic species (Burkhardt and de la Motte 1988;Wilkinson et al. 1998; Hingle et al. 2001; Cotton et al. 2006),whereas such preferences have not been found in monomorphicspecies (Wilkinson et al. 1998).

Given the current consensus of evolvable static allometriesand the strong sexual selection pressure favoring males with large

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eye span in dimorphic Diopsids, one could predict rapid adapta-tion of eye-span allometries to different levels of sexual selection.We test this in two ways by using sexual dimorphism and relativetrait size as proxies for the influence of sexual selection. In addi-tion to the cross-species dataset, we also analyze a dataset of sevenhighly sexually dimorphic populations of the species Cyrtodiopsisdalmanni from Swallow et al. (2005). We also test Gould’s idea(1966a,b) that species with extreme body size would evolve shal-low allometries to avoid potentially maladaptive consequencesof extrapolating an allometric relation. Further, the Diopsidae isthe only group of hypercephalic flies in which females also pos-sess prominent head projections (Baker and Wilkinson 2001).Wilkinson (1993) demonstrated that females exhibit a correlatedresponse to selection on male eye span in C. dalmanni, suggest-ing that males and females share some genetic mechanisms in-fluencing eyestalk morphology. We therefore test whether femaleeye-span allometries evolve as a correlated response to changesin male allometries.

Material and MethodsDATA

Measurements of eye span and body length in 30 species of stalk-eyed flies used in the comparative analyses come from Baker andWilkinson (2001). Data on eye span and body length in sevenpopulations of C. dalmanni come from Swallow et al. (2005). Alldata (morphological and sequence data) were kindly provided byG. S. Wilkinson, R. H. Baker, and J. G. Swallow (pers. comm.).Eye span was measured across the outer edge of each eye andbody length was measured from the front of the head to the endof the wing. Baker and Wilkinson (2001) and Swallow et al.(2005) provide more information on how the measurements wereperformed.

PHYLOGENETIC RELATIONSHIP

Comparative analyses require phylogenies with branching pointsreflecting the timing of speciation events. Data from three mito-chondrial genes (cytochrome oxidase II, 12S ribosomal RNA, and16S ribosomal RNA) and three nuclear genes (elongation factor-1a, wingless, and white) are available for all 30 species fromwhich we have morphological data (Baker et al. 2001). Frag-ments of all six genes were compiled together and we constructedan alignment consisting of 3287 base pars.

Bayesian inference analysis was performed with MrBayesversion 3.1.2 (Huelsenbeck and Ronquist 2001). A general time-reversible model with invariable sites and a gamma distribution(GTR + I + !) fitted the sequences best according to the infor-mation criteria AICc, AIC, and BIC in jModeltest version 0.1.1(Posada 2008). We set the priors to match this model, but we didnot fix any of the parameters. Two independent analyses were

run simultaneously, each starting from different random trees.Each search was run with four Markov chains for 10,000,000generations and trees were sampled every 10,000 generation. Wediscarded the first 2,750,000 generations as burn-in. Plots show-ing generation versus the log likelihood were inspected to ensurethe two independent analyses had reached stationarity before theend of the burn-in.

The Bayesian inference tree is shown in Figure 1. The cladesupport (posterior probabilities) is generally high (mean 0.97), butthe tree includes one polytomy, which includes the only Chaeto-diopsis specimen. Paraphyly is common at the genus level andSphyracephala and Diopsis are the only monophyletic genera.

Dating phylogenetic trees is challenging. Stalk-eyed diop-sid flies occurred in North America and Europe during the LateEocene and Oligocene (Grimaldi and Engel 2005). The fossilstalk-eyed fly Prosphyracephala succini (Loew), often found em-bedded in Bitterfeld amber (Kotrba 2004; Rossi et al. 2005), hasbeen placed as a sistergroup to the Diopsinae, which includesall species in our study, except Teloglabrus entabenensis (Kotrba2004). The age of Bitterfeld amber has been debated, but re-cent studies have argued that it is independent of the older andbetter known Baltic amber with a suggested absolute age of 25.3–23.8 million years (e.g., Dunlop and Mitov 2009 and referencestherein). A rough estimate of the minimal length of our phylo-genetic tree is therefore 25 million years, but a much older rootcannot be excluded.

ESTIMATING STATIC ALLOMETRY

Static allometric relationships were estimated using the linearversion of the allometric equation log(Y) = log(a) + blog(X)using ordinary least-squares regression. We did not correct formeasurement error, because information was not available. Wecentered all body-size data for each population on the populationmean before estimating the allometries to control for the inher-ent negative correlation between slope and intercept (White andGould 1965; Gould 1966a, Egset et al. 2011). Centering the de-pendent variable before the analysis changes only the estimate ofthe intercept. Confidence intervals for regression parameters werecalculated using the MBESS package in R.

The best regression model for estimating allometric param-eters has been a subject of debate, and major axis and especiallyreduced major axis regression is often used in place of ordinaryregression. Unfortunately, neither of these alternative regressionsaccount for true biological variation around the regression, andwill typically give wrong results when such variation exists (Kellyand Price 2004; Hansen and Bartoszek 2012). Furthermore, thereduced major axis estimate of the regression slope is simply theratio between the SDs of the two traits, and does not even con-tain the covariance between traits. This means that any change ofvariance in the traits will be interpreted as changes in the slope,

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Figure 1. Bayesian inference of the phylogeny of the species included in the study, based on fragments of three mitochondrial genes andthree nuclear genes (see text for more information). Priors were set to match a GTR+I+! model. All branching points have a posteriorprobability of 1.00, except for the ones with values indicated and the polytomy. The scale bar on the lower left side represents onechange per 10 nucleotide positions. Gray boxes indicate sexual dimorphism in slope. The phylogeny (including branch lengths) has beendeposited in Dryad.

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regardless of whether the change is due to changes in the slopeitself or to changes in biological or other sources of residual varia-tion. For this reason, the finding of changes in reduced major axisslopes in the experimental selection study of Tobler & Nijhout(2010) does not imply a change in static allometry (Egset et al.2012). Accordingly, we base all our analyses and arguments onstandard regression methods.

COMPARATIVE APPROACH

The adaptation-inertia model (Hansen 1997; Butler and King2004; Hansen et al. 2008; Labra et al. 2009) was fitted with Rversion 2.8.1 (R Development Core Team) using the SLOUCH1.2 program. In SLOUCH, the evolution of the trait is modeledas an Ornstein–Uhlenbeck process, which can be represented bythe stochastic differential equation:

dy = −α(y − θ)dt + σdW,

where dy is the change in the trait, y, (e.g., male eye-span allomet-ric slope) over a time step dt, α is a parameter measuring the rate ofadaptation toward a primary optimum, θ, and σdW is a white-noiseprocess having independent, normally distributed random changeswith mean zero and variance σ2. The Ornstein–Uhlenbeck pro-cess includes both a deterministic tendency to evolve toward aprimary optimal state (sensu Hansen 1997), as well as a stochas-tic component, which can be interpreted as evolutionary changesdue to secondary noise generated by unmeasured selective forces,genetic drift, etc. The primary optimum, θ, is a linear function of arandomly changing predictor variable (sexual size dimorphism inour case). The predictor variable only influences the trait throughits influence on the primary optimum. The predictor variable itselfis only observed on the tips of the phylogeny, and its evolutionthrough the phylogeny is modeled as a Brownian-motion process(see Hansen et al. 2008 for details). The method uses generalizedleast squares for estimation of the regression parameters (i.e., theinfluence of the predictor on the primary optimum) and maximumlikelihood for estimation of α and σ2 in an iterative procedure.

The method returns an estimate of the regression of the pri-mary optimum on the predictor variables that can be interpretedas the optimal adaptive relationship free of ancestral influence.Unless adaptation is instantaneous, this “optimal regression” willbe steeper than the usual “evolutionary regression”, which alsoreflect maladaptation due to phylogenetic inertia. We report bothof these regressions, as their ratio (the “phylogenetic correctionfactor,” ρ) can be used to judge the influence of constraint onadaptation. The relative effects of phylogenetic inertia (resistanceof adaptation) and adaptation can also be described as a half-life,t1/2 = ln(2)/α, defined as the mean predicted time it takes for aspecies to evolve halfway toward a new optimum (Hansen 1997).If the half-life is short relative to branch lengths on the phylogeny,

then adaptation is quick and past history has little influence. Themethod also assesses the stochastic variance, σ2, in the evolution-ary process, but returns it as an estimate of vy = σ2/2α, whichis the expected residual variance when adaptation and secondarychanges have come to a stochastic equilibrium.

A phylogenetic effect can arise for two reasons. It can be dueto phylogenetic inertia (slowness of adaptation) or it can be due toa phylogenetic effect in the environment to which the species areadapting. It is essential that it is only phylogenetic inertia and notgeneral phylogenetic effects that are corrected for in the analysis(Hansen and Orzack 2005; Labra et al. 2009; Revell 2010). Inour model, this is done by estimating phylogenetic inertia as thehalf-life in a model including a predictor variable (the adaptiveeffect). The overall phylogenetic effects we report are half-livesobtained from models without predictor variables (i.e., with onlyan intercept). The difference between these half-lives can tellus whether the phylogenetic effects are due to inertia or to theenvironment (see Labra et al. 2009).

Observation or measurement errors may reduce the accu-racy of regression (Fuller 1987; Buonaccorsi 2010). We includedestimation variance in the individual species parameters as ob-servation variance in both predictor and response variables in theSLOUCH analysis. As both predictor and response variables insome of our analyses are derived from measures of eye span, wealso estimated and included observation covariance between thevariables. Because sample sizes differed by more than one orderof magnitude between species, we averaged the sample varianceacross species (assuming the sampling distributions of the dif-ferent species are the same) and then estimated the estimationvariances of the individual species means by dividing with thesample size of each species (Hansen and Bartoszek 2012). Weused a bootstrap procedure to estimate the observation variancesof the eye-span ratios as well as the observation covariances be-tween the variables. Data on male and female eye span were ran-domly sampled with replacement to create 10,000 pseudoreplicatedatasets for each species from which the variance and covarianceswere calculated. We also quantified the bias in all regressions dueto observation error by calculating a phylogenetically correctedreliability ratio K (Hansen and Bartoszek 2012), but with oneexception this bias was very small.

MODELING PREDICTOR VARIABLES

Our test of the hypothesis that static allometries are formed bysexual selection requires a measure of the relative importanceof sexual selection in the species. Unfortunately, there are nodirect measures of sexual selection available for most species.Here, we used two different proxy measures: One based on sexualdimorphism and one based on relative development of the maletrait. The use of sexual dimorphism to measure influence of sexualselection has a long history (e.g., Andersson 1994), and there

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has been debate about the best approach (Lovich and Gibbon1992; Smith 1999; Fairbairn 2007). Here, we used the differencebetween log male and log female eye span. We also tested thearithmetic ratio of the male and female eye span, which gavesimilar results (as expected, because the two are the same to afirst approximation). We chose to present results from the logdifference because it explained slightly more variation and hadslightly higher AIC value. Our relative-trait-size measure was thedifference between log male eye span and log male body length.Again, we also ran the analyses for the arithmetic ratio and gotqualitatively similar results with slightly worse fit.

Note that the SLOUCH model assumes that the predictorvariables have a longer phylogenetic half-life than the modelresiduals (Hansen et al. 2008). This is well supported for logrelative eye span, but for sexual dimorphism the half-life wassimilar to the model residuals, and this may explain the somewhatworse fit to this predictor.

To test Gould’s hypothesis of shallower allometries in specieswith large trait values, we used mean male body size on an arith-metic scale as a predictor variable. To test for a correlated responsein female allometries to changes in male allometries, we used fe-male allometric slope as a response variable and male allometricslope as predictor variable. Because the correlated-evolution hy-pothesis suggests a direct and not a delayed response as in thecase of adaptation, we set the phylogenetic correction factor to 1such that the optimal and evolutionary regression are forced to bethe same (see Hansen and Bartoszek 2012 for discussion). Notethat this analysis still allows for phylogenetic correlations in theresiduals. Finally, we studied the evolutionary allometry by re-gressing log mean eye span on log mean body size across species.This was also done both with a direct and a delayed response cor-responding either correlated or adaptive evolution (both allowingphylogenetic correlations in the residuals).

A concern with many of these analyses is that the responseand predictor variables partially derive from the same data. Thisintroduces a circularity that may create spurious relationships.We do not think this a problem with the analyses we present.First, note that there is no direct statistical correlation betweenthe allometric slope and the size of the trait, because there is nocorrelation between the slope and the intercept of a regressionwhen the intercept is taken at the mean of the predictor variable.A second issue is that correlated estimation error in the slopeand the predictor variables may give a spurious correlation in thecomparative analysis. We dealt with this by explicitly modelingthe estimation variances and covariances as measurement error inthe comparative analysis. This problem was also minor, becausethe estimation covariances were always rather small. Third, it isof course possible that static allometry may coevolve with maleand female trait or body sizes for reasons other than direct sex-ual selection, but this is not an issue that derives from circularity

in the data, and we explore some such alternatives by evaluat-ing the influence of trait and body size on the static allometry.We decided, however, to not present analyses of the relation ofeye span itself to sexual dimorphism or relative trait develop-ment, as such regressions would be highly vulnerable to spuriouscorrelations.

ResultsDOES STATIC ALLOMETRY VARY?

Mean body length, mean eye span, and eye-span allometric slopesand intercepts for both sexes in the 30 species are given in Table 1.Within-species regressions of log eye span on log body size showstrong fit for both males and females in all species: r2-valuesrange from 60% to 98% for males (mean = 87%, median = 89%)and 49% to 96% for females (mean = 85%, median = 89%). Pair-wise comparisons of male allometric slopes show that 267 of 435comparisons are different from each other on a 95% confidencelevel. Diasemopsis longipedunculata has the steepest slope (2.69)and is different from all the other 29 species (Fig. 2). In contrast,only 94 of 435 female pair-wise slope comparisons are differentfrom each other on a 95% confidence level. Males and females hadstatistically different allometric slopes in 18 species and differentintercepts (mean trait sizes) in 26 species.

Data for seven populations of C. dalmanni are given inTable 2. Also here, regressions of eye span on body size showstrong fit with r2-values ranging from 92% to 96% for males(mean = median = 94%) and 86% to 97% for females (mean =92%, median = 94%). All populations are sexual dimorphic ineye span after controlling for body size. Neither males nor femalesdiffer in slopes among populations on a 95% confidence level withthe exception of the Brastagi population (Fig. 3). Brastagi malesare unique in having a steeper slope than males in all the otherpopulations. Also the allometric slope in Brastagi females is sig-nificantly steeper than the female slopes in four other populations.

IS STATIC ALLOMETRY PHYLOGENETICALLY

STRUCTURED?

Both male and female static allometric slopes showed indicationsof phylogenetic effects (Fig. 4; Table 3a), meaning that more re-lated species have more similar static allometries. The maximum-likelihood estimate of the half-life for male allometric slope wast1/2 = 22% of tree height (two-unit support region = 0–199%),whereas for female allometric slope it was t1/2 = 61% of treeheight (two-unit support region = 16%–∞). Assuming a totaltree height of 25 million years, the best estimates correspond to5.5 and 15.25 million years to lose half the ancestral influence formales and females, respectively. The wide support regions showthat these estimates are highly uncertain, and the evidence for astronger effect in females than males is only a tentative indication.

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Table 1. Morphometric measurements of 30 species of stalk-eyed flies. Morphometric measurements of body length (BL) and eye span(ES) in millimeters, allometric slope and intercept are the least-squares regression of log eye span as function of log body size (N = samplesize).

Males

Mean BL in mm Mean ES in mm

Species N Mean SD Mean SD Slope±SE Intercept±SE r2 (%)

1 Eurydiopsis argentifera1 6 9.481 0.373 6.530 0.240 0.875±0.160 0.815±0.003 85.262 Diopsis apicalis1 31 7.384 0.481 8.184 0.952 1.730±0.136 0.910±0.004 84.273 Chaetodiopsis meigenii2 40 7.359 0.556 7.421 1.171 2.025±0.104 0.865±0.003 90.724 Diasemopsis sp. W2 21 7.286 0.681 7.287 1.132 1.688±0.097 0.857±0.004 93.785 Diopsis fumipennis1 25 7.090 0.487 6.857 0.621 1.276±0.082 0.834±0.002 90.916 Diasemopsis longipedunculata2 75 7.086 0.696 8.171 2.185 2.691±0.076 0.896±0.003 94.547 Diasemopsis hirsuta2 67 7.062 0.475 7.147 1.055 2.148±0.094 0.849±0.003 88.668 Cyrtodiopsis quinqueguttata 102 6.974 0.512 4.255 0.379 1.157±0.044 0.631±0.001 89.709 Diasemopsis elongata2 30 6.917 0.770 7.865 1.869 2.156±0.064 0.883±0.003 97.53

10 Diasemopsis silvatica2 82 6.811 0.388 7.182 0.933 2.252±0.082 0.852±0.002 90.3111 Diasemopsis aethiopica1 104 6.607 0.542 6.277 0.944 1.735±0.062 0.793±0.002 88.2912 Diasemopsis conjuncta2 65 6.508 0.565 5.670 0.841 1.639±0.074 0.749±0.003 88.3313 Diasemopsis dubia2 128 6.386 0.357 6.836 0.718 1.763±0.085 0.832±0.002 77.2314 Cyrtodiopsis whitei2 86 6.367 0.981 7.965 2.164 1.844±0.045 0.880±0.003 95.4415 Diasemopsis obstans2 124 6.329 0.418 6.395 0.934 2.216±0.063 0.801±0.002 90.8816 Teleopsis breviscopium2 57 6.322 0.629 10.985 2.182 1.722±0.175 1.033±0.008 63.0217 Diasemopsis nebulosa2 66 6.249 0.457 6.011 0.863 1.926±0.078 0.774±0.003 90.3218 Cyrtodiopsis dalmanni2 92 6.226 0.728 7.509 1.752 1.946±0.061 0.864±0.003 91.9119 Teloglabrus entabenensis1 18 5.928 0.377 1.167 0.090 1.194±0.083 0.066±0.002 92.4320 Diopsis gnu1 7 5.698 0.317 4.481 0.230 0.894±0.124 0.651±0.003 89.5021 Diasemopsis fasciata2 63 5.596 0.462 5.747 0.862 1.829±0.067 0.754±0.002 92.2222 Sphyracephala munroi 45 5.293 0.281 2.856 0.222 1.326±0.118 0.454±0.003 74.1123 Diasemopsis signata1 65 5.003 0.414 4.000 0.465 1.356±0.059 0.599±0.002 89.0924 Teleopsis quadriguttata 29 4.978 0.522 3.329 0.384 1.082±0.053 0.519±0.002 93.7725 Teleopsis rubicunda2 88 4.920 0.547 4.966 1.035 1.679±0.075 0.686±0.004 85.2326 Sphyracephala brevicornis1 32 4.868 0.422 1.831 0.141 0.825±0.064 0.362±0.006 84.1327 Diasemopsis albifacies 63 4.768 0.333 3.398 0.352 1.415±0.070 0.529±0.002 86.6428 Trichodiopsis minuta2 41 4.652 0.362 4.028 0.590 1.813±0.108 0.600±0.004 87.6429 Sphyracephala beccarii2 99 4.501 0.144 2.052 0.100 1.201±0.099 0.312±0.001 60.0730 Sphyracephala bipunctipennis2 23 4.012 0.353 2.341 0.419 1.944±0.155 0.261±0.002 87.65

Mean 59.13 6.155 0.488 5.625 0.861 1.645 0.697 87.12Median 63.00 6.326 0.469 6.144 0.852 1.726 0.783 89.30Mean sexually dimorphic species 61.38 6.323 0.512 5.930 0.947 1.704 0.720 87.53Mean sexually monomorphic species 50.17 5.483 0.389 4.405 0.516 1.408 0.605 85.49

Continued.

These phylogenetic effects in static allometries are weakerthan the phylogenetic effects in the traits themselves. Analyses ofboth log eyestalk length and log body size gave half-life valuesmany times the total tree length, indicating that the traits them-selves evolve as if by Brownian motion. This probably reflectsmore bounded evolution of the allometric slopes, which tends toremove the relationship with phylogeny.

DOES STATIC ALLOMETRY ADAPT TO PATTERNS OF

SEXUAL SELECTION?

We found clear evidence for adaptation of male static allometry toour two proxies for sexual selection (Table 3a, Fig. 5). Sexual di-morphism in eye span explained more than 40% of the variation instatic slopes, and relative eye span explained more than 60%. Inboth cases, the relationship was positive with the slope of the

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Table 1. Continued.

Females

Mean BL in mm Mean ES in mm

Species N Mean SD Mean SD Slope±SE Intercept±SE r2 (%)

1 Eurydiopsis argentifera1 9 9.903 0.351 6.756 0.236 0.874±0.174 0.829±0.003 75.212 Diopsis apicalis1 31 7.549 0.523 7.080 0.680 1.297±0.105 0.848±0.003 83.523 Chaetodiopsis meigenii2 27 7.567 0.531 6.403 0.547 1.110±0.111 0.805±0.003 79.374 Diasemopsis sp. W2 22 7.391 0.653 6.014 0.656 1.221±0.053 0.776±0.002 96.235 Diopsis fumipennis1 21 7.152 0.591 5.952 0.551 1.048±0.093 0.773±0.003 86.206 Diasemopsis longipedunculata2 50 7.305 0.707 5.986 0.761 1.299±0.045 0.773±0.002 94.507 Diasemopsis hirsuta2 67 7.343 0.554 6.431 0.709 1.450±0.061 0.805±0.002 89.548 Cyrtodiopsis quinqueguttata 57 7.149 0.455 4.283 0.375 1.127±0.065 0.636±0.002 84.089 Diasemopsis elongata2 29 7.370 0.812 6.191 0.928 1.403±0.054 0.786±0.003 95.99

10 Diasemopsis silvatica2 112 6.772 0.489 5.277 0.480 1.210±0.037 0.720±0.001 90.6911 Diasemopsis aethiopica1 93 6.658 0.553 5.501 0.750 1.557±0.060 0.736±0.002 87.7912 Diasemopsis conjuncta2 65 6.333 0.601 4.714 0.566 1.215±0.052 0.670±0.002 89.6113 Diasemopsis dubia2 107 6.532 0.400 5.145 0.422 1.268±0.054 0.710±0.001 83.9114 Cyrtodiopsis whitei2 86 5.548 0.663 4.671 0.765 1.324±0.030 0.665±0.002 95.9015 Diasemopsis obstans2 107 6.397 0.369 4.862 0.427 1.373±0.068 0.685±0.002 79.1816 Teleopsis breviscopium2 30 6.382 0.416 6.092 0.463 0.992±0.119 0.783±0.003 70.4017 Diasemopsis nebulosa2 66 6.598 0.583 5.159 0.608 1.312±0.045 0.709±0.002 92.8918 Cyrtodiopsis dalmanni2 91 5.854 0.611 5.211 0.725 1.286±0.037 0.713±0.002 93.1219 Teloglabrus entabenensis1 12 6.368 0.348 1.223 0.081 1.055±0.195 0.086±0.005 72.0920 Diopsis gnu1 6 6.065 0.401 4.712 0.435 1.380±0.130 0.671±0.004 95.7421 Diasemopsis fasciata2 63 5.864 0.553 4.885 0.637 1.316±0.058 0.685±0.002 89.3322 Sphyracephala munroi 14 5.960 0.262 2.884 0.147 1.054±0.148 0.459±0.003 79.3523 Diasemopsis signata1 63 5.425 0.463 4.145 0.446 1.206±0.054 0.615±0.002 88.8224 Teleopsis quadriguttata 18 5.211 0.544 3.368 0.354 0.996±0.064 0.525±0.003 93.4425 Teleopsis rubicunda2 51 5.445 0.516 4.650 0.612 1.343±0.052 0.665±0.002 93.1126 Sphyracephala brevicornis1 33 5.277 0.410 1.927 0.133 0.834±0.054 0.322±0.006 87.9427 Diasemopsis albifacies 67 5.150 0.388 3.439 0.321 1.198±0.047 0.534±0.002 90.7628 Trichodiopsis minuta2 34 4.890 0.415 3.643 0.398 1.242±0.066 0.559±0.003 91.3629 Sphyracephala beccarii2 110 4.971 0.159 2.097 0.075 0.813±0.072 0.321±0.001 53.6630 Sphyracephala bipunctipennis2 22 4.516 0.318 2.106 0.170 0.836±0.182 0.284±0.002 49.00

Mean 52.10 6.365 0.488 4.694 0.482 1.188 0.638 85.09Median 50.50 6.375 0.502 4.874 0.471 1.218 0.685 89.08Mean sexually dimorphic species 53.00 6.505 0.503 4.829 0.504 1.201 0.650 85.43Mean sexually monomorphic species 48.50 5.805 0.429 4.151 0.395 1.136 0.590 83.72

1Only intercept differs between the sexes at the 95% confidence level (t-test).2Slope and intercept are different between the sexes at the 95% confidence level (t-test).

optimal regression being 5.13 ± 1.07 on log (male eyespan/female eye span) and 0.68 ± 0.09 on log (male eye span/malebody size). The former number means that a 10% increase in maleeye span relative to female eye span would lead to about a 0.5increase in the (optimal) male static allometric slope. The secondnumber means that a 10% increase of male eye span relative tomale body length would give about a 0.07 increase in the (opti-mal) static allometric slope. These changes would probably notbe instantaneous, however, as the best estimates of the phyloge-

netic half-lives for these two models were 13% and 10% of treeheight, respectively, corresponding to 3.25 and 2.50 million years(Table 3a). This is less than the phylogenetic effect of 5.5 millionyears, which indicates that some, but not all, of the phylogeneticeffect in static allometry is due to phylogenetic inertia with therest an indirect effect of a phylogenetic signal in the predictorvariables. We caution, however, that the half-life estimates areuncertain and even instantaneous adaptation (t1/2 = 0) is includedin the support region.

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Figure 2. Male (gray broken lines) and female (black lines) static allometric slopes of log eye span on log body size. Error bars indicate95% confidence interval. Species are plotted as a decreasing function of mean body size. Number refers to species as they are listed inTable 1. Eighteen of 30 species are sexually dimorphic in slopes given a 95% confidence level.

Table 2. Morphometric measurements of seven populations of Cyrtodiopsis dalmanni. Morphometric measurements of body length(BL) and eye span (ES) in millimeters, allometric slope and intercept are the least-squares regression of log eye span as function of logbody size (N = sample size).

Mean BL in mm Mean ES in mm

Cyrtodiopsis dalmanni Sex N Mean SD Mean SD Slope±SE Intercept±SE r2 (%)

1 Brastagi, Sumatra1 F 38 6.760 0.730 6.050 0.910 1.400±0.040 1.002±0.006 96.57M 27 7.290 1.020 10.590 3.390 2.310±0.100 0.777±0.002 95.14

2 Belalong, Borneo1 F 14 5.950 0.720 5.190 0.710 1.110±0.110 0.880±0.004 90.22M 19 6.700 0.590 7.670 1.160 1.670±0.110 0.711±0.006 93.25

3 Cameron-Langat, F 118 5.880 0.720 5.220 0.800 1.200±0.030 0.854±0.002 93.67Malaysia1 M 149 6.680 0.740 8.740 1.580 1.940±0.030 0.713±0.002 95.65

4 Bogor, Java1 F 39 6.390 0.610 5.620 0.630 1.160±0.050 0.867±0.002 94.52M 74 6.500 0.740 7.530 1.540 1.780±0.040 0.747±0.002 95.69

5 Bt. Lawang, Sumatra1 F 49 6.030 0.740 5.230 0.750 1.150±0.040 0.849±0.003 94.97M 73 6.370 0.680 7.220 1.540 1.970±0.060 0.714±0.002 94.44

6 Soraya, Sumatra1 F 43 5.690 0.600 5.070 0.690 1.230±0.080 0.004±0.087 85.65M 24 6.110 0.710 7.080 1.590 1.690±0.110 0.701±0.004 91.61

7 Gombak, Malaysia1 F 89 5.740 0.640 5.070 0.670 1.150±0.040 0.834±0.002 91.31M 90 6.090 0.630 6.950 1.290 1.780±0.050 0.701±0.002 93.92

Mean F 55.71 6.063 0.680 5.350 0.737 1.200 0.756 92.42Median F 43.00 5.950 0.720 5.220 0.710 1.160 0.854 93.67Mean M 65.14 6.534 0.730 7.969 1.727 1.877 0.723 94.24Median M 73.00 6.500 0.710 7.530 1.540 1.780 0.713 94.44

1Slope and intercept are different between the sexes at the 95% confidence level (t-test).

EVOLUTION 2012 9

K. L. VOJE AND T. F. HANSEN1.

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Figure 3. Male (gray broken lines) and female (black lines) staticallometric slopes of log eye span on log body size from seven pop-ulations of Cyrtodiopsis dalmanni. Error bars indicate 95% confi-dence interval. Species are plotted as a decreasing function ofmean body size. Number refers to species as they are listed inTable 2. All populations are sexually dimorphic in slopes on a 95%confidence level.

Using log eye span and log body size as predictor variablesexplained much less of the variation in slopes than our proxyvariables above (Table 3a). This supports sexual dimorphism ineye span and relative eye span as the best predictors of speciesdifferences in static allometry, which is what the sexual selectionhypothesis predicts. Furthermore, sexual dimorphism and relativeeye span retain a strong effect when the logs of trait and body sizeare included as covariates in a multiple regression (Table 3a).

RELATIONSHIP BETWEEN BODY SIZE AND

ALLOMETRIC SLOPE

We found no support for Gould’s hypothesis that static allometriesshould be more shallow in large-bodied species to avoid extremetrait expression. In fact, the estimated optimal relation betweenstatic allometry and mean body size was not negative, but positivewith a slope of 0.17 ± 0.10 (0.38 ± 0.22 when corrected for biasdue to measurement error). This model, explaining 8.5% of thevariance, is marginally better than a model with no effect of bodysize according to AICc (Table 3b). The corresponding optimalregression in the females explained less than 1% of the variance,gave a slope of about 0, and was not supported by AICc.

EVOLUTION OF THE FEMALE ALLOMETRIC SLOPE

There was little evidence for strong correlated evolution betweenmale and female allometric slopes. A direct (no-delay) regressionof log female slope on log male slope returned a coefficient of 0.14± 0.25, and explained only 14% of the variation (Table 3c). Thephylogenetic half-life was 40% of tree height (support region =0–∞), slightly weaker than the phylogenetic effect.

Figure 4. Support surface for phylogenetic half-life, t1/2, in unitsof tree length (total tree length = 1) and stochastic equilibriumvariance, vy , in a model including only an intercept and no predic-tor variables for allometric slopes of males (A) and females (B). Themaximum-likelihood estimates of the half-lives are 0.22 and 0.61for male and female allometric slope, respectively. The flat partsof the diagrams represent parameter combinations that are morethan two support (log-likelihood) units worse than the best esti-mate. For all estimated parameter values for these two models,see Table 3a.

THE EVOLUTIONARY ALLOMETRY

The evolutionary allometry is the log–log regression of mean eyespan on mean body length across species. We did this based onboth an adaptation model with a delay in the approach to an opti-mal relation, and on a direct-effect model with an assumed imme-diate response of eye span to changes in body size. For males, bothmodels explained about 50% of the variance in log eye span, andthe direct-effect model showed slightly better fit (Table 3d). Forfemales, the direct-effect model was much better than the adap-tation model. The estimated allometric exponents in the directeffect models were 1.68 ± 0.52 for the males and 1.29 ± 0.30 forfemales, which are both almost exactly equal to the average staticallometries (Table 1). This result is consistent with the evolution-ary allometry being a result of constrained evolution along static

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Table 3a. Phylogenetic comparative analyses of the evolution of static allometry.For each model, we show the maximum-likelihood estimates of phylogenetic half-life, t1/2, in units of tree length (total tree length = 1) with its two-unit support

region, the stationary variance, vy , and GLS estimates of the intercept and slope of the optimal regression with standard errors (SE). We also show estimated

slopes corrected for bias due to measurement error (BCS). Model fit is described with a phylogenetically corrected r2, and the log likelihood (logL) and AICc of

the model. Lower AICc scores indicate a better model. When a “–” is entered for the predictor variable, only an intercept is included in the model. In this cases,

the phylogenetic half-life is a measure of the overall phylogenetic effect on the response variable.

Response variable Predictor variable t1/2 (supp. region) vy Intercept+SE Slope±SE BCS r2 (%) logL AICc

Male slope – 0.22 (0–1.99) 0.24 1.52 ± 0.14 – – – −17.1 41.2log(male eye span/

female eye span)– 0.11 (0–0.57) 0.01 0.06 ± 0.02 – – – 36.7 −66.4

Male slope log(male eye span/female eye span)

0.13 (0–0.72) 0.08 1.33 ± 0.11 5.13±1.07 5.14 42.81 −8.8 27.2

log(male eye span/male body length)

– 5.3 (0.28–∞) 4.67 −1.87 ± 0.36 – – – −25.1 57.1

Male slope log(male eye span/male body length)

0.10 (0–0.33) 0.05 2.52 ± 0.13 0.68±0.09 0.68 63.66 −2.1 13.7

Male slope Male log body size 0.24 (0–1.99) 0.23 0.27 ± 0.52 1.66±1.10 1.66 7.05 −16.0 41.7Male slope Male log eye span 0.30 (0–1.26) 0.17 0.38 ± 0.23 2.17±0.61 2.17 29.48 −11.9 33.5Multiple regressionsMale slope – 0.17 (0–0.90) 0.09 1.03 ± 0.24 43.52 −8.8 30.0

log(male eye span/female eye span)

4.32±1.61 4.31

log male eye span 0.59±0.59 0.59Male slope – 0.06 (0–0.27) 0.04 2.88 ± 0.35 65.81 −1.4 15.3

log(male eye span/male body length)

0.73±0.13 0.73

log male eye span −0.52±0.38 −0.52

b. Relationship between body size and allometric slope.

Response variable Predictor variable t1/2 (supp. region) vy Intercept±SE Slope±SE BCS r2 (%) logL AICc

Male slope – 0.22 (0—1.99) 0.24 1.52±0.14 – – – −17.1 41.2Male slope Mean male body size 0.27 (0–∞) 0.21 0.52±0.37 0.17±0.10 0.38 8.45 −15.6 40.7Female slope – 0.61 (0.16–∞) 0.06 1.09±0.08 – – – 12.1 −17.2Female slope Mean absolute body

size0.48 (0.11–∞) 0.05 0.90±0.16 0.03±0.06 0.08 0.97 12.2 −14.9

c. Evolution of female allometric slope.

Response variable Predictor variable t1/2 (supp. region) vy Intercept±SE Slope±SE BCS r2 (%) logL AICc

Female slope – 0.61 (0.16–∞) 0.06 1.09±0.08 – – – 12.1 −17.2Female slope (Direct effect of)

male slope0.40 (0–∞) 0.04 0.90±0.44 0.14±0.25 – 13.92 14.2 −18.9

d. Evolutionary allometries of eye span.

Response variable Predictor variable t1/2 (supp. region) vy Intercept±SE Slope±SE BCS r2 (%) logL AICc

log male eye span – 7.19 (0.35–∞) 0.55 0.46±0.11 – – – 11.3 −15.6log female eye span – 10.0 + (0.97–∞) 0.26 0.45±0.07 – – – 23.7 −40.5log male eye span log male body length 3.84 (2.41–5.93) 0.00 −12.72±0.28 17.23±4.95 17.25 45.46 22.2 −34.7log male eye span (Direct effect of) log

male body length5.00 (0.97–∞) 0.18 −0.78±0.41 1.68±0.52 – 53.28 22.7 −35.8

log female eye span log female body length 1.52 (0.28–5.61) 0.02 −2.49±0.13 3.98±1.11 3.98 29.85 29.3 −49.0log female eye span (Direct effect of) log

female body length10.0 + (1.15–∞) 0.12 −0.55±0.24 1.29±0.30 – 51.47 33.5 −57.4

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K. L. VOJE AND T. F. HANSEN

Figure 5. (A) Support surface for phylogenetic half-life (t1/2) andstochastic equilibrium variance (vy) in the analysis of phylogeneticinertia in male allometric slope using the log of the ratio of maleeye span on male body length as a predictor variable (best esti-mate: t1/2 = 0.10, vy = 0.05). (B) Phylogenetic regression of maleallometric slope on the log of the ratio of male eye span to malebody length. Both the evolutionary (dotted line, slope = 0.53) andthe optimal (solid line, slope = 0.68) regressions are shown. Theregressions explain 64% of the variation in allometric slope.

allometries. The alternative adaptation models had long half-livesand must be interpreted as consistent with trends toward pro-gressively steeper evolutionary allometries. Also the direct effectmodels had long half-lives indicating Brownian-motion-like evo-lution of the residual variation. Also the traits themselves evolvein a Brownian-motion-like pattern (Table 3d).

DiscussionDespite the interest in the evolvability of static allometries overthe last decades, little empirical information about the evolu-tion of narrow-sense allometric parameters has accumulated formorphological traits. This stems from a shift in the notion of

allometry from its original narrow-sense meaning as a power re-lationship (Huxley 1932) toward a broad-sense meaning as anychange in shape related to size (Mosimann 1970; Frankino et al.2009). There is nothing wrong with studying broad-sense allom-etry and shape evolution, but narrow-sense allometry was asso-ciated with theoretical ideas and models that do not transfer tobroad-sense allometry (Houle et al. 2011). As theoretical contextwas forgotten, students of allometry chose scales and models forstatistical rather than biological reasons. As a consequence, someof the specific hypotheses that relates to narrow-sense allometryremain substantially untested. In particular, the idea that narrow-sense allometric slopes are evolutionary constrained remains al-most untested for morphological traits and our study is the firstthat investigates the evolution of narrow-sense static allometricslopes using phylogenetic comparative methods.

Our main findings were that static allometric slopes indeedvaried considerably across the 30 species of stalk-eyed flies andthey did so in a way that is consistent with adaptation to sexual se-lection with our measures of sexual dimorphism and relative traitsize explaining, respectively, 43% and 64% of the among-speciesvariance in male eye-span static allometric slope. This adds tostudies cited in the introduction showing that static allometriesare evolvable on million-year time scales. Related species stillhave similar static allometries, however. If we assume that thebase of our phylogeny is approximately 25 million years back intime, the best estimate is that it takes 5.5 million years to lose halfthe ancestral effect in males. We caution that this parameter esti-mate has a wide support region and only unconstrained Brownianmotion can be definitely excluded (Fig. 4A).

Such phylogenetic effects can arise for two reasons (Hansenand Orzack 2005; Labra et al. 2009). If closely related specieshave similar niches, then adaptation to these will cause a nonran-dom distribution of trait values on the phylogeny. If phylogeneticeffects are generated in this way, they do not imply any constraintson the rate of adaptation. The other possible cause of phylogeneticeffects is a low rate of adaptation (phylogenetic inertia). Specifi-cally estimating phylogenetic inertia in the adaptive response ofstatic allometric slopes to sexual dimorphism and relative traitsize, we found half-life values around 3 million years. This is lessthan the phylogenetic effect of 5.5 million years and althoughthe difference may well be due to estimation error, it is consis-tent with the phylogenetic effect being a result of both adaptationand inertia, and that static allometries may therefore constrain theindependent evolution of eye span on time scales below a fewmillion years.

Million-year phylogenetic half-lives can be interpreted asslow adaptation. It is becoming clear, however, that adaptationand cumulative evolutionary change often take place on million-year time scales (Uyeda et al. 2011; Hansen 2012), and our staticallometries may be constrained, but not unusually constrained.

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EVOLUTION OF STATIC ALLOMETRIES

It would have been valuable with a direct comparison to ratesof adaptation in the trait intercept, but this would run into thecircularity problems discussed above.

Note that our adaptation models do not account for abouthalf the among-species variance in static allometric slopes. Thismay be partially due to our measures not fully capturing therelevant sexual selection on the trait, but it likely also reflectsother unmeasured factors of selection acting on allometry. Suchfactors may involve species differences in predicted costs of largeeye span (Swallow et al. 2000; Husak et al. 2011). It may alsoreflect alternative ways of achieving a large eye span. Worthingtonet al. (2012) have recently found a negative relationship betweenthe length of the eyestalks and the angle that they attach to the headwithin C. dalmanni. This shows that eye span is more complexthan the mere length of the eyestalks, and may also evolve byshape changes that have a different relations to body size thandoes stalk length.

If it takes several million years to get rid the majority of theancestral effect, we do not expect stalk-eyed flies with differentallometries to have diverged very recently. Our re-estimation ofthe allometric relationships in seven populations of C. dalmannifrom Swallow et al. (2005) shows that the Brastagi populationis the only population in which the male allometric slope differsfrom all the other monophyletic populations on a 95% confidencelevel. According to the phylogeny published by Swallow et al.(2005), the Brastagi population is the sister group to the rest ofthe six monophyletic populations in the study. The time of geneticdivergence between Brastagi and the other populations reportedin Swallow et al. (2005) is on average larger than the geneticdivergence times between the other populations. For example,based on the nuclear gene wingless, the mean genetic divergencebetween Brastagi and the other populations is 3.8 million years(calculated from Table 3 in Swallow et al. 2005), and the authorsconclude that their findings are consistent with old divergencetimes and very little gene flow since these populations startedto diverge. The difference in allometry between Brastagi and theother C. dalmanni populations may therefore have had sufficienttime to evolve without contradicting the results from our cross-species analysis.

THE RELATION BETWEEN SIZE AND SLOPE

Gould (1966a,b) proposed that natural selection could change theallometric slope so that large-sized animals have a smaller staticallometric slope compared to smaller-sized animals to avoid non-adaptive and absurd trait sizes in species with the larger individu-als. We found no support for Gould’s hypothesis. In fact there wasa weak positive, and not negative, relationship between male allo-metric slope and body size in the among-species dataset, whereasfemale slope and body size did not correlate at all. Our resultstherefore indicate that the observed differences in slopes between

species are not a solution to an allometrically size-imposed prob-lem in eyestalk length between species of different size.

A relationship between the allometric slope and overall sizecould be a mechanism for the evolution of altered allometricslopes as a side effect of body size evolution. This can be ruledout as a likely explanation of our results, because we got qualita-tively the same results using different proxies for sexual selection,both with and without controlling for the effect of body size oneye-span length. Another reasonable hypothesis is that the allome-tries could change as a side effect of direct selection on eye span.Although we found that eye-span evolution is somewhat con-strained by its allometric relation to body size, eye span is afterall the focal trait for sexual selection and is known to be understrong selection in many of the species (e.g., Wilkinson et al.1998; Panhuis and Wilkinson 1999; Hingle et al. 2001; Cottonet al. 2006). Indeed, male static allometric slopes were positivelyaffected by mean log eye span across species. However, the multi-ple regressions showed that it was our measures of sexual dimor-phism and relative trait size rather than the individual traits thatbest explained the evolution of static allometries, and althoughother selection pressures can not be ruled out, our results arevery consistent with a strong effect of sexual selection on staticallometry in eye span.

CONCLUSION: ALLOMETRY AND CONSTRAINT

Our analysis provides strong evidence that static allometric ex-ponents are evolvable on macroevolutionary time scales and thatspecies likely to have experienced stronger sexual selection haveevolved steeper static allometries. On one hand, this may indicatethat static allometries are not important as macroevolutionaryconstraints, but on the other, we have indications that the “adap-tive” changes take place on a million-year time scale, and wecannot exclude the possibility that static allometries constitutea significant constraint for trait evolution on microevolutionarytime scales. Although the lack of trait-independent measures ofsexual selection has precluded an analysis of sexual adaptationin the eyestalk itself, we did find that the estimated evolutionaryallometries are almost exactly equal to the median static allome-tries (1.68 vs. 1.73 for male slopes and 1.29 vs. 1.22 for femaleslopes). Combined with the fact that the direct-effect “constraint”model outperformed the adaptation model for eye-span evolution,this indicates that evolutionary changes in eye span and body sizehave tended to broadly follow along static allometries, as expectedif constraints were important. In contrast, we did not find supportfor the hypothesis that female eye span has evolved as a correlatedresponse to male eye span, as less than 14% of the among-speciesvariation in female eye span was explained by male eye span. Wethink this implies independent selection to maintain the stalks inmales and females, because it is unlikely that these will not be ge-netically correlated, and Wilkinson (1993) indeed demonstrated

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K. L. VOJE AND T. F. HANSEN

a correlated response in female eye span to artificial selection onmale eye span in C. dalmanni. Together, these results show thatselection and adaptation of eye span must be complex and gobeyond intrasexual selection on males.

ACKNOWLEDGMENTSWe would like to thank G. S. Wilkinson, R. H. Baker, and J. G. Swallowfor their kindness and willingness to share their data on stalk-eyed flies.We thank J. Pienaar for help with and development of the SLOUCHprogram. C. Pelabon and two anonymous reviewers provided helpful andinsightful comments on the manuscript and we thank members of theHansen and Pelabon Labs for discussions. The work was supported bygrant 196434/V40 from the Norwegian Research Council to ChristophePelabon at NTNU.

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