phenotypic plasticity of growth trajectory and ontogenic allometry

Phenotypic Plasticity of Growth Trajectory and Ontogenic Allometry inResponse to Density for Eucalyptus Hybrid Clones and Families

JEAN-MARC BOUVET1,*, PHILIPPE VIGNERON1 and AUBIN SAYA2

1Cirad—Forest Department—Research Unit 39 ‘‘Diversity and Breeding of Forest Tree Species’’ TA 10C,

Campus International de Baillarguet, 34398 Montpellier Cedex, France and 2Research Unit on Plantation

Productivity UR2PI, BP 1291, Pointe-Noire, Republic of Congo

Received: 11 April 2005 Returned for revision: 10 May 2005 Accepted: 2 June 2005 Published electronically: 25 July 2005

� Background and Aims Response to density is a crucial aspect of the ecology of trees in forests and plantations. Fewstudies have investigated the genetics of plasticity in response to density for growth traits such as height andcircumference through development.� Methods Two experiments were carried out in the field, the first with full-sib families of Eucalyptus urophylla ·E. grandis hybrids, and the second with clones of E. tereticornis · E. grandis hybrids planted across a rangeof densities (625, 1111 and 2500 trees ha�1). Height, circumference and stem taper were measuredthrough development in both experiments. Variance components were estimated and a repeated measureapproach for plasticity and three different methods were used to compare the variance–covariance matrix acrossdensities.� Key Results Genetic variance was significantly different from zero but the density · genotype interaction wassignificant only for clone experiments at the adult stage. Significant plasticity for three traits in both experiments wasfound. In the clone experiments, a significant clone · time · density interaction was found, suggesting that plasticityfor growth and stem form is under genetic control. In both experiments, density did not affect environmentalcorrelation, which remained high throughout tree development. The impact of density on genetic correlation wasmarked in the clone experiment, with a reduced value at lower density, but was not observed in the family trial. Thedifferences between clones and family are mainly explained by the distribution of genetic variation within andamong genotypes.� Conclusions The results suggest that plasticity for growth traits and form of tropical Eucalyptus species is undergenetic control and that the environment changes genetic co-variation through ontogeny. The findings confirm that atree population with a narrow genetic basis (represented by clones) is sensitive to a changing environment, whereasa population with a broader genetic basis (full-sib family here) exhibits a more stable reaction.

Key words: Height, circumference, growth trajectory, allometry, density, phenotypic plasticity, variance components,correlation, Eucalyptus, hybrid, clones, full-sib family.

INTRODUCTION

Environmentally induced phenotypic change, phenotypicplasticity, has been recognized as an important strategyfor plants to maximize or maintain fitness in variablebiotic and abiotic environments (e.g. Via and Lande,1995; Schlichting and Pigliucci, 1998; Wright andMcConnaughay, 2002). In an organism, phenotypic plastic-ity generally concerns different traits that can be related byan allometric relationship which varies through develop-ment (e.g. Archibald and Bond, 2003; Bonser and Aarssen,2003). Although these issues have been addressed in severalplant species (Schlichting and Pigliucci, 1998; Preston andAckerly, 2004), very few studies exist for tree species,especially those addressing the genetic basis of phenotypicplasticity and ontogenic allometry.

Being long-lived organisms, trees experience fluctuationsin their competitive neighbourhood both spatially andthrough development (Coomes and Grubb, 1998; Alvesand Santos, 2002; Martinez and Lopez-Portillo, 2003).Competition due to increased density is among the mostcrucial factors that influence growth and trait expression in

both natural forest tree stands (Archibald and Bond, 2003)and in forestry plantations (Evert, 1971; Bouvet et al.,2003). Higher tree density translates into a reduction oflight, water and nutrient resources which, in turn, canhave manifold phenotypic effects on an individual. Densitygenerally reduces tree circumference and to a certain extenttree height (e.g. Dhote 1997). Higher density also affectsoverall plant vigour through reduction in canopy size, andfruit production, both fitness-related traits (Archibald andBond, 2003). In the most widely planted forestry species,including pine (Kusnandar et al., 1998), temperate eucalyp-tus (Wei and Borralho, 1998) and tropical eucalyptushybrids (Bouvet and Vigneron, 1995), it has been recog-nized that genetic and environmental variances change withage. Our temporal understanding of the genetic variation oftraits through development comes primarily from modelsthat compare the magnitude of variances of growth traitsat different stages of stand development (Balocchi et al.,1993), but very few studies have taken a developmentalreaction norm perspective to examine trait variation acrosschanging environments (Brouard and John, 1999; Bouvetet al., 2003). Here, the impact of inter-plant spacing on theplasticity of growth trajectories and on ontogenic allometryis analysed from a genetic point of view.* For correspondence. E-mail [email protected]

Annals of Botany 96: 811–821, 2005

doi:10.1093/aob/mci231, available online at www.aob.oxfordjournals.org

ª The Author 2005. Published by Oxford University Press on behalf of the Annals of Botany Company. All rights reserved.

For Permissions, please email: [email protected] from https://academic.oup.com/aob/article-abstract/96/5/811/180417by gueston 11 April 2018

Tropical Eucalyptus and their hybrids are among thespecies most used in plantations. Because of their economicvalue, species of the genus Eucalyptus have been the subjectof many research programmes in genetics and silviculture(e.g. Vigneron and Bouvet, 2000; Henson and Smith, 2004;McRae et al., 2004). In addition, the rapid growth, shortperiod until reproductive maturation (adult size is reachedafter 5–7 years), and their ability to be cloned easily facili-tate their use in forest genetic experiments. Numerousstudies have demonstrated significant additive genetic com-ponents in growth traits through development (Bouvet,1995; Bouvet and Vigneron, 1996) and have shownthat several quantitative trait loci (QTL) explain variation(Verhaegen et al., 1997; Gion, 2001), but no studies haveaddressed the genetic basis of ontogenic plasticity.

In this study, based on two experiments including clonesand full-sib families of eucalyptus hybrids, several specificquestions are asked: (1) Is there genetic variation for plas-ticity of growth trajectory for height, stem circumference,and allometry between those two traits across tree densities?(2) Is there variation through ontogeny for the genetic andenvironmental correlations between height and stem cir-cumference with changing tree densities? (3) Are there dif-ferences in patterns of plasticity between two sets of hybridpopulations (one population of clones and the other offamilies)? The experiments were conducted with two popu-lations that differ in their within-genotype variation (nogenetic variation within each clone, high within-familyvariation). Although these hybrid populations have a singleparent species in common, it is possible to gain some insightinto whether the population with a broader genetic diversityexhibits a more stable reaction to changing environments.

MATERIALS AND METHODS

Study organisms and experimental design

Data were obtained from two field trials established in theRepublic of Congo at the experimental research centre —Unite de Recherche sur les Plantations Industrielles duCongo (04�450S, 12�000E, 50m a.s.l.). The climate is tropi-cal humid with a mean annual temperature of 24 �C and amean annual rainfall of 1200mm. The dry season lasts fromMay to October. The first experiment, R91-1, used a set of12 hybrid clones of Eucalyptus tereticornis · Eucalyptusgrandis planted in 1992 at three densities 2m · 2m(2500 trees ha�1), 3m · 3m (1111 trees ha�1) and 4m ·4m (625 trees ha�1). The 12 clones were originally selectedfrom a naturalized hybrid population from the Republicof Congo. The E. tereticornis parent trees represent theprogeny of a single tree introduced to the Congo in the1960s. Thus, the 12 clones were likely to be closely related,but there is not enough information to determine kinshipcoefficients. The experiment used a split-plot design, den-sity as the main effect and clone as the secondary effect.Rectangular plots of 30 trees were replicated across threeblocks. To minimize the impact of competition betweenplots, a buffer zone of one row of trees was planted betweenblocks and only the 12 inner trees of the 30 were measured.

The second experiment, R95-10, used a set of 16 hybridfamilies of Eucalyptus urophylla · Eucalyptus grandis. Thehybrid families were created by controlled pollinations in amating design that included 16 unrelated parents for eachspecies. The experiment was planted in 1995 at the samethree densities 2m · 2m (2500 trees ha�1), 3m · 3m(1111 trees ha�1) and 4m · 4m (625 trees ha�1). Theexperiment was a split-plot design with three blocks,with density as the main effect and family the secondaryeffect. Each square plot was composed of 36 trees. The totalnumber of trees per family was 324. To minimize the impactof competition between plots, in each plot only the 16 innertrees were measured.

Circumference at breast height (C) and total height (H)were measured at several points during ontogeny. For theclone experiment, measurements were done monthlybetween months 9 and 24, biannually during the juvenileand the mature phase which spanned from 24 to 74 months.In the family experiment, measurements were done bian-nually from 7 to 39 months and yearly thereafter. Allometrywas assessed by examining the form of the stem, which wasquantified from the relative rate of change in stem diameterwith increasing tree height (hereafter called the stem taper).Stem taper (DM) was estimated using the formula DM =C/(H – 1�3), cm m�1 (developed in forestry science; Larson,1963). Mortality was assessed at the time of each measure-ment. The percent mortality was calculated within each plotas the ratio of dead individuals to the total number of plantedindividuals.

There are two non-independent interpretations that can bemade when contrasting the two experiments. First, thehybrids of the two experiments share one parent species,but the other two parent species are different. Thereforedifferences between the experiments could be attributedto differences in genetic background of the species thatare not shared. Second, since the hybrids share one-halfof their genetic background, it could be assumed that theobserved differences in variance trends with age areexplained by the different distributions of genetic variationbetween and within the two designs (family and clones).

In experiment R91-1, as the clones were selected from ahybrid population, the variance among clones is an estima-tion of the total genetic variance including additive, domi-nance, and epistatic effects. The within-clone varianceestimates the variance due to environmental effects. Thisis a classical application of the quantitative genetic model(Gallais, 1991). On the other hand, in experiment R95-10, the variance among families is an estimate of halfof the additive genetic variance and a quarter of thedominance variance and some percentage of epistatic vari-ance. The within-family variance includes both genetic andenvironmental variance (Gallais, 1991; Falconer andMacKay, 1996).

Data analyses

Analysis of interaction (model 1). The analysis ofplasticity through development was first examined throughclassical analysis of variance in SAS version 8, GLMprocedure (SAS Institute, 1988). In order to fulfil the

812 Bouvet et al. — Developmental Reaction Norms to Tree Density

Downloaded from https://academic.oup.com/aob/article-abstract/96/5/811/180417by gueston 11 April 2018

assumptions of ANOVA, height and circumference werelog transformed. In models testing the interaction of prin-cipal factors, the residual variances are assumed to be ident-ical for all spacings, and Bartlett’s test was used to verifyhomogeneity of variances (Snedecor and Cochran, 1989).At each age, the GLM procedure tested the density, geno-type, the block and the genotype · density interactioneffects. All terms were tested with the appropriate errorvariance. Density, block and family or clone effects weretested over the density by family or clone interaction. Thedensity by genotype interaction was tested over the fullmodel error term. Although the sample size is limited forboth clone and family experiments (12 and 16 genotypes,respectively), a random model considering the clone andfamily effects as random and the interaction with density asrandom was used.

Repeated measure analysis of variance (model 2).Plasticity through development was analysed throughrepeated measure analyses of variance in SAS version 8,GLM procedure (SAS Institute, 1988) following the meth-odologies of Pigliucci et al. (1997). The model includedtime (indicating growth in traits over time), block (indicat-ing micro-environmental variation among blocks), familyor clone (indicating genetic variation), time · density inter-action (indicating plasticity in the growth trajectory), time ·family or clone (indicating genetic variation in growthtrajectory) and time · density · family or clone interaction(indicating genetic variation for plasticity of growth)over time.

All terms were tested with the appropriate error variance;density, block and family or clone effects were tested overthe density by family or clone interaction. The density bygenotype interaction was tested over the full model errorterm. The multivariate Wilk’s l test was used to account forthe reduction in the number of degrees of freedom due to thenon-independence of the variance–covariance matrices ofthe time intervals. Wilk’s l is a conservative test and appro-priate for unbalanced designs, which is the case in bothexperiments.

Estimation of variance–covariance matrix within eachdensity (model 3). Covariance matrices between height andcircumference were estimated utilizing standard quantita-tive genetics techniques (Falconer and MacKay, 1996).Analyses were conducted separately for each experiment.For each density, the mixed model used included block(fixed effect to account for micro-environmental variation),family or clone (a random effect with variance of s2

g andmean 0), and the interaction between family or clone andblock (random effect with variance of s2

b·g and mean 0).Genetic and residual variance and co-variance componentsbetween height (H) and circumference (C) were calculatedusing the SAS GLM procedure (MANOVA option) and theType III sums of squares (SAS Institute, 1988). The varianceand covariance components were estimated by equating theexpected mean square (calculated by the random option) tothe mean square given by type III of analysis of variance(Becker, 1984). The correlation coefficients between H andcircumference C were calculated using the estimates ofvariance and covariance given by the mixed model. Two

correlation coefficients of correlation can be estimated,s(H, C) being the covariance between traits H and C, s2

ðHÞand s2

ðCÞ being the variance of height and circumference.The genetic correlation coefficient can be calculatedusing: rg = sg(H,C)/sg(H) · sg(C). The residual within-popu-lation coefficients of correlation rr = sr(H,C)/sr(H) · sr(C) areinterpreted differently for the two experiments. The residualcorrelation coefficient estimates environmental correlationfor the clone experiment and estimates a part of both geneticand environmental correlation for the family experiment (seealso Gallais, 1991).

Comparison of variance–covariance and correlation matrix

There have been several attempts to compare the covari-ance matrix or correlation matrix of populations in variableenvironments. Roff (2002) suggested that using comple-mentary methods to examine covariance matrices is themost appropriate methodology. Here three approacheswere used, two based on correlation coefficients and onebased on the covariance matrix.

Comparisons of correlation coefficients: method 1. First,the two correlations were examined to see if they havedifferent strengths (Papoulis, 1990). The null hypothesisfor this test is that both samples show the same correlationstrength, i.e. rg1 = rg2. The test requires the assumption thatthe values of both members of both pairs of samples con-form to a normal bivariate distribution. To approximate anormal distribution, the correlation coefficients are trans-formed using the Fisher z-transformation (Sokal and Rholf,1969). The z statistic is used to determine the level of sig-nificance. The first method is the least sensitive of all thetests used.

Comparisons of correlation coefficients: method 2. Thecorrelation coefficients were compared by using ajackknife approach (e.g. Knapp et al., 1989; Roff, 1997).A t statistic is constructed where rg is the genetic correlationfor the ith population (i = 1, 2), ni is the number of pseudo-values generated in the jackknife procedure for the ith popu-lation and Si is the estimated standard deviation ofthe pseudovalues. In the cases of experiments R91-1 andR95-10, ni is the number of families (16) and clones (12).The comparison of coefficient is done using the t-statisticformula:

t =rg1 � rg2

� �ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n1 � 1ð ÞS21+ n2 � 1ð ÞS2

2

n1 + n2 � 2

� �n1 + n2

n1n2

� �r

This is a usual formulation for t-statistics and its signifi-cance is tested with appropriate tables.

Comparisons of variance–covariance: method 3. Themethod developed by Roff (2002) is based on boththe jackknife procedure and multivariate analysis of vari-ance (MANOVA), following a log transformation to mini-mize scaling effects. In each experiment the geneticvariance–covariance matrix is estimated after deleting inturn one genetic unit, a clone in R91-1 or a family in

Bouvet et al. — Developmental Reaction Norms to Tree Density 813


R95-10, and the pseudovalues of the matrix are calculatedaccording to the jackknife procedure. These estimates arethen used as data points in MANOVA to compare experi-mental tree densities. MANOVA has the advantage oftaking into account the correlation between the varianceand the co-variance.

RESULTS

Impact of density on mortality, growth and form

The two trials were differently affected by mortality, withgreater overall mortality in the family experiment (Table 1).In the clone experiment R91-1, a low percentage of deadtrees across all three densities was found (Table 1), althoughthere was a slight (but non-significant) increase in percent-age with increasing age and density. In the family experi-ment R95-10, the mortality was fairly high, especially at thefinal measurement for both the 625 trees ha�1 and 2500 treesha�1 densities (Table 1). The increase in mortality over timewas greater for the family than the clone experiment.Mortality in the family experiment was mainly due totermite-generated damage during the first 18 months, andis not family- or treatment-specific.

Tropical eucalyptus species generally exhibit rapidgrowth during the first 2 or 3 years and then the growthrate progressively declines (Bouvet, 1991). This pattern(illustrated in Figs 1 and 2) was observed in both experi-ments. By later life stages there is evidence of strongcompetition, demonstrated by a significant reduction in cir-cumference and height as experimental density increases(Table 2). Tree height decreased by <30% from 625 to2500 tree ha�1, while circumference decreased by 46%.The coefficient of variation increased markedly withincreased density for height and circumference.

Stem taper decreased with age, with most reductionoccurring before 3 years of age, suggesting that, architec-turally, trees changed from a conical to a more cylindricalform (Fig. 3). Density also affected stem taper, as treeshaving a more cylindrical form were in the higher densitytreatments (Table 2). The coefficient of variation for thistrait did not vary strongly among density treatments yetthe magnitude was reduced in comparison to height andcircumference (Table 2).

Variation of growth trajectory and stem taper

A significant density effect was apparent from the resultsof ANOVA model 1 (see Appendix I), which included den-sity, clone or family, and the density · clone (or family)interaction effects, for each of the three traits. Clone andfamily variance were significantly different from zero andthe density · genotype interaction effect was significant forheight and circumference at some ages and for stem taperacross all ages only for the clone experiment.

Table 3 presents the developmental reaction norms usinganalysis of variance with repeated measurement (model 2).Examination of the results shows that time was a highlysignificant effect for all three traits, which demonstrates theincrease in size and change in architectural form with age. Asignificant time · density interaction was also found whichindicates an overall plasticity for growth, represented byincreases in height and circumference, and for stem taperover time. Also a highly significant time · genotype

TABLE 1. Trends in mortality (%) with age (months) in theclone and family experiments, for each density (625, 1111 and

2500 trees ha�1)

Clone trial: R91-1 Family trial: R95-10

Trees ha�1 Trees ha�1

Months 625 1111 2500 Months 625 1111 2500

12 1.6 2.3 3.4 11 5.4 3.4 7.524 1.6 2.3 3.5 20 9.7 4.6 9.448 2.1 2.5 3.9 39 11.0 5.1 10.474 2.1 2.5 3.9 59 12.0 6.2 11.3

Percentages are cumulative. 2500 trees ha−1

1111 trees ha−1

625 trees ha−1

0

5

10

15

20

25

Hei

ght (

m)

0

10

20

30

40

50

60

0 20 40 60 80Age (months)

Cir

cum

fere

nce

(cm

)

A

B

F I G . 1. Growth curves for height (A) and circumference (B) of arepresentative sample of four genotypes planted in the three densities in

the clone experiment R91-1.



interaction was found which suggests variation amongclones (Figs 1 and 3A) or families (Figs 2 and 3B) intheir growth trajectories and stem taper. The three-wayinteraction time · genotype · density was significant forthe clone experiment (R91-1), indicating plasticity ofgrowth that differed among clones (genetic variation forplasticity of growth). This pattern was not found for thefamily experiment (R95-10) but was marginally significantfor circumference (P = 0�007). In the case of the cloneexperiment the latter result suggests that some clones ini-tially grew rapidly but ceased their growth early in lowdensity, whereas the same clones initially grew more slowlyand grew for a longer period in high density (see Fig. 1).

Genetic and environmental co-variation betweenheight and circumference over time

Although sample size was small in both experiments, thephenotypic correlation between height and circumferencewas significantly different from zero. Using a power anal-ysis (Kendall and Stuart, 1963) to calculate which truecorrelation produces an 80% chance of being distinguishedfrom zero, a one-sided test of a sample of 16 or 12 with a0�05 significance level was used: r = 0�607 for the familytest and r = 0�689 were found—values which were smallerthan those obtained in both experiments (results not shown).

For both experiments, the within-genotype coefficient ofcorrelation was high (rr > 0�9) and was not affected bydensity or age (Figs 4A and 5A). The between-clone orfamily genetic correlation coefficient, however, exhibiteddifferent patterns of variation with age and density (Figs 4Band 5B).

In the clone experiment (Fig. 4B), the between-clonecoefficient of correlation remained constant and close to 1for 2500 trees ha�1 but decreased slowly for 625 trees ha�1

from age 20 months (rg = 0�9) up to 74 months (rg = 0�57).For 1111 trees ha�1 it dropped markedly from age 10 (rg =0�9) up to 30 months (rg = 0�12) and then increased to aplateau at 50 months (rg = 0�70). Comparison of the coef-ficients using the method described by Papoulis (1990)(method 1 above) revealed significant stage-specific differ-ences (Table 4), but the jackknife method (Knapp et al.,1989; method 2) and MANOVA (Roff, 2002; method 3) didnot uncover any significant density effects (illustrated inTable 5).

In the family experiment R95-10, the between-familycoefficient of correlations was slightly affected by density(Fig. 5B), and no significant differences among densitieswere observed with any of the three methods. However, theoverall patterns of variation with age were different fromthat of the clone experiment. The three coefficients of gen-etic correlation were reduced between 12 and 24 months(rg = 0�90 and rg = 0�50, respectively) and then increased tofluctuate around rg = 0�7.

DISCUSSION

Experiments that examine genetic variation and phenotypicplasticity in trees are often limited in replication or

F I G . 2. Growth curves for height (A) and circumference (B) of arepresentative sample of four genotypes according to the three densities

in the family experiment R95-10.

TABLE 2. Impact of density (trees ha�1) on height (m),circumference (cm) and stem taper (cm/m) means andcoefficients of variation for the clone (at 74 months) and family

experiments (at 59 months)

Height Circumference Stem taper

Density Mean CV Mean CV Mean CV

Clone experiment 625 21.2 7 48.9 14 2.45 101111 18.2 14 38 22 2.24 112500 14.6 24 26.2 30 1.96 9

Family experiment 625 21.6 19 51.0 22 2.51 121111 19.6 22 41.6 25 2.27 122500 16.6 28 30.6 33 2.00 15



restricted to early seedling stages (Bonser and Aarsen, 1994;Chen and Klinka, 1998; Spinnler et al., 2003). However,understanding developmental reaction norms in the field canlead to novel insights into the patterns of growth for long-lived perennial taxa. Experimentally manipulating theeffects of density in a silviculture setting allows the effectof tree density to be isolated while minimizing other envi-ronmental variation present in natural forest systems (Chenand Klinka, 1998). For the study two crosses of Eucalyptusin the field at multiple life stages were chosen to examine

how patterns of plasticity vary with density and howpatterns of plasticity change over time.

The present strategy based on field experiment led to theanalysis of a small sample. The sample size effect on errorsin the parameter estimates have been considered by numer-ous authors in genetic experiments (Sales and Hill, 1976).The precision of variance components is reduced whensample size is small. The error is higher when consideringthe coefficient of correlation because three parameters arerequired for the calculation. To reduce the effect of small

F I G . 3. Change in stem taper with age and density using four clones (A) and four families (B) as representative examples of observed patterns.

TABLE 3. Repeated measure analysis of variance for the experiments R91-1 clone experiment and R95-10 family experiment andthe three traits (model 2)


Source of variation Wilk’s l F Wilk’s l F Wilk’s l F

Clone experimentTime 0.001 3817.2 0.003 1369.1 5 · 10�4 2319.0Time · density 0.0001 46.83 0.0006 27.47 9 · 10�4 43.82Time · clone 6 · 10�6 2.89 8 · 10�6 3.5 8 · 10�7 5.95Time · density · clone 0.002 2.22 0.004 2.19 5 · 10�6 1.71

Family experimentTime 0.002 3989.4 0.0043 2264.9 0.006 1440.5Time · density 0.008 24.7 0.0038 38.19 0.044 9.46Time · family 0.0001 4.05 0.0004 2.85 0.0004 2.73Time · density · family 0.083 1.09 0.072 1.16 0.077 1.12

Multivariate test of no effect for each source of variation.Bold font indicates P < 0�0001.



sample size in the experiments, the clones and families wereselected to represent the entire variation of their respectivepopulation. In addition, the number of individual trees usedto calculate the effect was high: 108 and 36 per density foreach family and clone, respectively. Although there is nooptimal design from which to draw general conclusions,the results constitute a first step towards understandingphenotypic plasticity with increased competition in afield experiment.

Plasticity in growth trajectory and allometry

The impact of density on plant size characters is oftensize-asymmetric, i.e. slightly larger individuals receivemore resources than smaller trees, and such size inequalitiesincrease with density (Evert, 1971; Pierik et al., 2004).Higher densities also increase the phenotypic variation, con-firming the size asymmetry hypothesis, a pattern which hasbeen observed in other tree species such as Douglas fir(Campbell et al., 1986; Dreyfus 1990). In the case of thetwo hybrids of Eucalyptus, in the poor soil conditions of thefield trials, the impact of closer spacing is dramatic in that itstrongly reduces circumference, height and consequentlythe growth trajectories.

Previous results have shown that height was higher inclose spacing during the first months (Bouvet, 1997), whichcan be explained by the morphological response of plants tothe presence of neighbours with enhanced shoot elongation,the so-called shade-avoidance response (Pierik et al.,2004). The rapid growth leads to strong competition

00·10·20·30·40·50·60·70·80·9

1

Cor

rela

tion

betw

een

H a

nd C

2500 trees ha−1 1111 trees ha−1 625 trees ha−1

A

R91-1within clone correlation

00·10·20·30·40·50·60·70·80·9

1

0 10 20 30 40 50 60 70 80Age (months)

Cor

rela

tion

betw

een

H a

nd C

B

R91-1between clone correlation

F I G . 4. Trends in patterns of correlation between height and circumferenceat the three densities for the clone experiment R91-1: (A) within-clone

correlations and (B) between-clone correlations.

00·10·20·30·40·50·60·70·80·9

1

Cor

rela

tion

betw

een

H a

nd C

2500 trees ha−1

1111 trees ha−1

625 trees ha−1

00·10·20·30·40·50·60·70·80·9

1

0 10 20 30 40 50 60 70Age (months)

Cor

rela

tion

betw

een

H a

nd C

A

B

R95-10within family correlation

R95-10between family correlation

F I G . 5. Trends in patterns of correlation between height and circumferenceat the three densities for the family experiment R95-10: (A) within-family

correlations and (B) between-family correlations.

TABLE 5. Parameters associated with MANOVA examiningthe influence of the three densities of the variance–covariancematrix (G matrix) and with ANOVA examining the influenceof the three densities of the genetic coefficient of correlation in

the clone experiment R91-1

Age (months) Wilk’s l F d.f. Prob > F

Comparison of coefficient of correlation ANOVA (method 2)30 – 0.46 2, 27 0.6374 – 0.54 2, 27 0.59

Comparison of G matrix with MANOVA (method 3)30 0.82 0.86 6, 50 0.5374 0.64 2.08 6, 50 0.07

TABLE 4. Test of comparison of the genetic correlationcoefficients (method 1) estimated at each age in each density

giving the probability associated with the test

Clone experimentR91-1

Age (months)

12 24 30 36 48 62 74

Density compared625/1111 n.s. n.s. n.s. n.s. n.s. n.s. n.s.625/2500 n.s. n.s. n.s. n.s. 0.062 0.037 0.0472500/1111 n.s. n.s. 0.030 n.s. 0.046 0.078 0.095

n.s., non-significant at 10% level.



affecting circumference but also height in later life stages.In temperate species, Parde and Bouchon (1988) havedemonstrated that density reduces the growth in circumfer-ence but does not affect the height. However, here we con-firm the pattern that others have observed in tropicalEucalyptus in which density influences both height andcircumference (Patinot-Valera and Kageyama, 1995;Brouard and John, 1999).

The impact of tree density on the allometric relationshiphas demonstrated that species adapt to crowding in differentways, e.g. greater elongation of branches for Abies com-pared with Picea (Takahashi, 1996), more flexibility inrelative allocation of energy in growth for rainforest species(Alves and Santos, 2002). However, the impact of densityon allometric relationships through ontogeny for treespecies remains poorly documented, especially usingcontrolled experimental approaches (Saint-Andre et al.,2005). The relationship between height and circumference,the stem taper, was found to decrease with age and withclose spacing. This result has been explained by variousauthors (Larson, 1963; Bouillet and Lefevre, 1996). Ithas been observed that in open-grown trees with long vig-orous crowns, stem taper continues down the branch-freebole. In lower density, the size of the crown is proportion-ally greater than in closer density where natural pruningeliminates under shaded branches; as the crown baserecedes and the clear boles elongates with increasing treeage and stand closure, the stem become more cylindricalbecause photosynthates are regularly distributed and theincrement in basal area is constant along the bole.

Genetic control of ontogenic plasticity in eucalyptus

Genetic variation for plastic responses of different traitshas been widely observed for different non-perennial plantspecies (Schlichting and Pigliucci, 1998). Pigliucci andSchlichting (1995) and Pigliucci (1997) suggested thatinclusion of ontogenic data in plasticity studies will broadenour understanding of how phenotypes evolve in response toselection. Although genetic variation for growth trajectoryhas been demonstrated for several tree species (Namkoogand Conckle, 1976; Bouvet, 1991; Danjon, 1994), as far asis known, few studies have examined the genetic basis ofontogenic plasticity for growth and form in trees, except inPopulus (Wu, 1997; Wu and Stettler, 1998).

Here, high genetic variation among clones and amongfamilies for growth trajectory and stem form was observed.Although this result was based on a limited number ofgenotypes (12 clones and 16 families), other studies oneucalyptus hybrid populations introduced in the Congo,using a significant sample, have shown high genetic varia-tion within these two hybrid species (Bouvet and Vigneron,1996). These results demonstrate that these populationsmaintain significant quantitative genetic variation thatcould be used for breeding programmes. In the clone experi-ment R91-1, a significant time · clone · density interactioneffect was observed, implying that the plasticity of growthtrajectory for height, circumference and ontogenic allome-try (stem taper) has a genetic component. The interactionwas not significant for the other experiment (R95-10) which

used a family rather than a clonal structure. Two explana-tions are proposed to examine the different results of thesetwo experiments.

The first explanation relates to the fact that clones aregenerally more unstable when the environment changes.Broader within-family genetic variation allows a morestable response of the genotype to a changing environment.These results have often been observed in plants, the higherthe within-genotype (clone, family) variation, the smallerthe genotype · environment interaction (Gallais, 1991).Although the time · family · density interaction was notsignificant for the three traits, it should be stressed that theprobability was close to the threshold of significance forcircumference (F = 1�16, P = 0�0862), whereas for heightF = 1�09 and P = 0�217. This point can be explained bygreater sensitivity of circumference to competition andconfirms previous results showing that height is less sensi-tive to density.

The second explanation could be related to the higherpreponderance of epistatic effects involved in between-clone compared with between-family genetic variance.Several authors have suggested that epistatic mechanismscould explain genetic plasticity. Pigliucci (2003) has sug-gested that regulatory elements could play an important rolein the genetics of development. Blows and Sokolowski(1995) have demonstrated that expression of non-additivegenetic variation is increased at both extremes of the envi-ronmental range. In a Populus clone study, Wu (1997) sug-gested that the genetic difference in response to differentenvironments might be mainly due to epistasis betweenregulatory loci for plasticity and loci for trait means. Asepistatic effects are preponderant in the ‘genetic variancebetween clones’ compared with the ‘genetic variancebetween families’ (Gallais, 1991), genetic control of plas-ticity could be greater in clone populations.

Impact of density on ontogenic allometry

Ontogenic allometry was analysed through the relation-ship of stem taper with age but also through the genetic andenvironmental correlations between height and circum-ference. According to several authors (e.g. Parson, 1987;Bennington and McGraw, 1996) both phenotypic and gen-etic variation are enhanced under stressful conditions butfew studies have investigated the impact of density on envi-ronmental and genetic correlations in plants. Examples inrice (Kawano and Hara, 1995) and in an annual plantTagetes patula (Weiner and Thomas, 1992) have shownthat with increasing density the number of significantphenotypic correlations between traits increases and thatthe allometric relationships between height and diameterchange with higher density. For tree species, the geneticbasis of ontogenic allometry has rarely been investigated.Poplar is one exception. Wu and Stettler (1998) demon-strated higher genetic correlation between crown andgrowth traits in a less favourable environment, but theirstudy follow-up was only 2 years. In the present study,the genetic and environmental correlations were analysedfrom juvenile up to adult size and cast new light on the



genetic and environmental basis of the relationship betweentraits in a changing environment.

The within-genotype correlation was positive and variedlittle with the density and age of the stand (Figs 4A and 5A).In the case of clones, the origin of within-clone variationand co-variation is purely environmental because geneticvariation does not exist among ramets. The high environ-mental correlation means that changes in the environmentare likely to influence the genetics underlying circumfer-ence and height in similar ways. The present finding isconsistent with data on other forest trees where favourablesituations lead to a simultaneous increase of height andcircumference (Bouvet, 1995). In the case of the familyexperiment, a similar result is observed, although within-family variance and co-variance are composed of geneticand environmental variance. This is explained by thegreater magnitude of environmental variance comparedwith genetic variance, a result which is generally observedin forest trees and especially in eucalyptus (Bouvetet al., 2003).

The genetic correlations between circumference andheight were positive in both experiments. This positivegenetic co-variation is consistent with experiments onother tree species (Zobel and Talbert, 1984) and especiallyin eucalyptus (Bouvet, 1995). Most of these investigationshave concluded that height and circumference are likely tobe governed by similar genes and that pleiotropy could bean explanatory factor for these relationships. Studies ofmolecular genetics have demonstrated that the same setof QTL explains a part of genetic variation in height andcircumference (Verhaegen et al., 1997; Gion, 2001). Thisresult, which has been observed for other species (Wu et al.,2003), suggests the maintenance of integration withinmodule, i.e. between functionally related traits in plants(Murren, 2002; Preston and Ackerly, 2003), and agreeswith quantitative genetic models suggesting that selectionfavours positive correlation between functionally relatedtraits (Hartl and Clark, 1997).

The trend in genetic correlation with density presentsdifferent patterns in the clone and family experiments(Figs 4B and 5B). This difference can be explained bymultiple factors (sampling, species) but, as for genetic con-trol of plasticity, the distribution of genetic effects betweenand within each genotype (family vs. clone) is also anexplanatory factor. With respect to the clone experiment,which represents phenotypic expression of individual trees,these results suggest that genetic control of ontogenydepends on environmental conditions. Although the geneticmechanisms behind plasticity of trait correlation are poorlyelucidated (Murren and Kover, 2004), one hypothesis is thatregulatory genes with environmentally dependent expres-sion might explain variation in genetic correlation in chang-ing environments. Epistatic variance within geneticvariance between clones (Gallais, 1991) might explainthe marked impact of density on genetic correlation.

The variation in genetic correlation with age can be inter-preted for both clone and family experiments, as if thegenetic control of height and circumference is progressivelydissociated during establishment of the competition phase,and then, once competition is established, the correlated

genetic control of the two traits is re-established. Onegene action model can be proposed to explain this obser-vation. During the progressive competition phase, genescontrolling height growth are very active because a rapidheight growth facilitates light capture. When trees reach acritical height which threatens their stability, genes control-ling circumference growth act to ensure they remain stable.Another complementary explanation of the variation in gen-etic correlation with age is age-related changes in genescontrolling growth. Genes involved in height and circum-ference may change during tree development thus changingthe co-variation between those traits. This assumption issupported by data on QTL of height and circumferencein some eucalyptus experiments. With the same hybrid asin experiment R95-10, Gion (2001) has shown that the QTLof height and circumference change between 14 and 59months. More research is needed to clarify the molecularbasis of ontogenic allometry in the tropical eucalyptus andthe impact of a changing environment. A first step would beto apply to this population the statistical model for QTLanalysis developed by Wu et al. (2003).

Summary and conclusion

Although the present results are based on a small sample,thus affecting the precision of variance components andthe power of the experiment, they suggest that tropicalEucalyptus species tested in the present study are plasticfor growth traits and form and present a genetic system ableto respond to a changing environment. The present cloneand family experiments demonstrate that competition due toclose spacing induces different patterns for the environmen-tal and genetic correlations, suggesting that a simple pheno-typic approach is not the most appropriate way to analysethe functional basis of plasticity and allometry. The presentresults also suggest that the environment changes thegenetic expression of growth trait co-variation throughontogeny, which is a new result in forest trees whichmust be confirmed by further research. The present findingconfirms that a tree population with a narrow genetic basis(represented by clones in the experiments) is sensitive to achanging environment, whereas a population with a broadergenetic basis (full-sib family here) exhibits a more stablereaction.

ACKNOWLEDGEMENTS

We are grateful to URPPI (Unite de Recherche sur le Pro-ductivite des Plantations Industrielles) of the Republic ofCongo in Pointe Noire, especially to the monitoring team,for providing valuable assistance and data collection inthese two experiments. We are grateful to Courtney Murrenfor his valuable comments which greatly improved thismanuscript.

LITERATURE CITED

Alves LF, Santos FAM. 2002. Tree allometry and crown shape of four treespecies in Atlantic rain forest, south-east Brazil. Journal of TropicalEcology 18: 245–260.



Archibald S, Bond WJ. 2003. Growing tall vs. growing wide: treearchitecture and allometry of Acacia karroo in forest, savanna, andarid environments. Oikos 102: 3–14.

Balocchi CE, Bridgwater FE, Zobel BJ, Jahromi S. 1993. Age trends ingenetic parameters for tree height in a nonselected population ofloblolly pine. Forest Science 39: 231–251.

BeckerWA. 1984. Manual of quantitative genetics, 4th edn. Pullman,WA:Academic Enterprises.

Bennington CC, McGraw JB. 1996. Environment-dependence ofquantitative genetic parameter in Impatiens pallida. Evolution 50:1083–1097.

Blows MW, Sokolowski MB. 1995. The expression of additive andnonadditive genetic variation under stress. Genetics 140: 1149–1159.

Bonser SP, Aarssen LW. 2003.Allometry and development in herbaceousplants: functional responsesofmeristemallocation to light andnutrientavailability. American Journal of Botany 90: 404–412.

Bouillet JP, LefevreM. 1996. Influence des eclaircies sur la forme du troncde Pinus kesiya. Bois et Forets des Tropiques 248: 17–30.

Bouvet J-M. 1991. Analyse des tests clonaux d’Eucalyptus hybrides.Reflexions sur la methodologie de selection. MSc Thesis, InstitutNational Agronomique Paris.

Bouvet J-M. 1995. Evolution de la variabilite avec l’age et correlationjuvenile-adulte dans des populations d’Eucalyptus. PhD Thesis,INAPG, Paris.

Bouvet J-M. 1997. Effect of spacing on juvenile growth and variability ofeucalyptus clones. Canadian Journal of Forestry Research, 27:174–179.

Bouvet J-M, Vigneron PH. 1995.Age trends in variances and heritabilitiesin Eucalyptus factorial mating designs. Silvae Genetica 44: 206–216.

Bouvet J-M, Vigneron PH. 1996. Variance structure in Eucalyptus hybridpopulations. Silvae Genetica 45: 171–177.

Bouvet J-M, Vigneron PH, Saya A, Gouma R. 2003. Trends in variancesand heritabilities with age for growth traits in eucalyptus spacingexperiments. Silvae Genetica 52: 121–132.

BrouardJS, JohnS.1999.Tree spacingaffects clonal ranking inEucalyptusgrandis·E. urophylla hybrids. Journal of Sustainable Forestry10: 13–23.

CampbellRK,EcholsRM,StonecypherRW.1986.Genetic variances andinteraction in 9-year-old Douglas fir grown at narrow spacings. SilvaeGenetica 35: 24–31.

Chen HYH, Klinka K. 1998. Survival, growth, and allometry of plantedLarix occidentalis seedlings in relation to light availability. ForestEcology and Management 106: 169–179.

Coomes DA, Grubb PJ. 1998. A comparison of 12 tree species ofAmazonian caatinga using growth rates in gaps and understorey,and allometric relationships. Functional Ecology 12: 426–435.

DanjonF. 1994.Heritabilities and genetic correlations for estimated growthcurve parameters in maritime pine. Theoretical and Applied Genetics89: 911–921.

Dhote JF. 1997. Effets des eclaircies sur le diametre dominant dans desfutaies regulieres de hetre ou de chene sessile. Revue ForestiereFrancaise XLIX – 6.

Dreyfus PH. 1990. Interaction genotype-densite et competition dans undispositif clinal d’epicea commun. Annales des Sciences Forestieres47: 1–16.

EvertF. 1971.Spacing studies a review. In Information report FMR-X-37ofthe Forest Management Institute. Canadian Forestry Services,Department of the Environment.

Falconer DS, Mackay TFC. 1996. Introduction to quantitative genetics,Harlow: Longman Science and Technology.

Gallais A. 1991. Theorie de la selection en amelioration des plantes. Paris:Editions Masson.

Gion J-M. 2001. Etude de l’architecture genetique de caracteresquantitatifs chez l’Eucaltyptus: des marqueurs anaonymes aux genescandidats. PhD Thesis, Universite de Montpellier.

Hartl DL, Clark AG. 1997. Principles of population genetics, 3rd edn.Sunderland, MA: Sinauer Associates.

Henson M, Smith H. 2004. Borrowed technologies: adaptation of familyforestry for Eucalypts in NSW, Australia. In: Borralho NMG,Pereira JS, Marques C, Coutinho J, Madeira M, Tome M, eds.Eucalyptus in a changing world. Proceedings of the IUFROConference, Aveiro, 11–15 October 2004, RAIZ, InstitutoInvestigacao da Floresta e Papel, Portugal.

Kawano S, Hara T. 1995. Optimal balance between propagule output,propagule size, and cost of propagule production in plants with specialreference to its evolutionary—ecological implications. Plant SpeciesBiology 10: 119–125.

KendallMG, Stuart A. 1963. The advanced theory of statistics. NewYork,NY: Harner Publishing Co.

Knapp SJ, Bridges WC Jr, Yang M-H. 1989. Non parametric confidenceinterval estimators for heritability and expected selection response.Genetics 121: 891–898.

KusnandarD,GalweyNW,HertzlerGL,ButcherTB.1998.Age trends invariances and heritabilities for diameter and height in maritimepine (Pinus pinaster Ait.) in Western Australia. Silvae Genetica 47:136–141.

Larson PR. 1963. Stem form development of forest trees. Forest ScienceMonograph 5: 1–31.

McRae T, Pilbeam D, Powell M, Dutkowski G, Joyce K, Tier B. 2004.Genetic evaluation in Eucalypt breeding programs. In:BorralhoNMG,Pereira JS, Marques C, Coutinho J, Madeira M, Tome M, eds. Euca-lyptus in a changing world. Proceedings of the IUFRO Conference,Aveiro, 11–15October 2004, RAIZ, Instituto Investigacao da Florestae Papel, Portugal.

Martinez AJ, Lopez-Portillo J. 2003. Allometry of Prosopis glandulosavar. torreyana along a topographic gradient in the Chihuahuan desert.Journal of Vegetation Science 14: 111–120.

Murren CJ. 2002. Phenotypic integration in plants. Plant Species Biology17: 89–99.

Murren CJ, Kover PK. 2004. QTL mapping, a first step toward anunderstanding of molecular genetic mechanisms behind phenotypiccomplexity/integration In: Pigliucci M, Preston K, eds.Phenotypic integration. New York, NY: Oxford University Press,195–211.

Namkoong G, Conkle MT. 1976. Time trends in genetic control of heightgrowth in ponderosa pine. Forest Science 22: 2–12.

Papoulis A. 1990. Probability and statistics. Englewood Cliffs, NJ:Prentice Hall.

Parde J, Bouchon J. 1988. Dendrometrie, 2nd edn. Nancy: ENGREF.Parson PA. 1987. Evolutionary rates under environmental stress. Evolution

Theory 21: 311–347.Patinot-Valera F, Kageyama PY. 1995. Parametros geneticos y

espaciamieto en progenie de Eucalyptus saligna Smith. ResearchPaper IPEF, Piracicaba 48/49: 61–76.

Pierik R, Voesenek LACJ, de Kroon H, Visser EJW. 2004.Density-induced plant size reduction and size inequalities inethylene-sensing and ethylene-insensitive tobacco. Plant Biology6: 201–205.

Pigliucci M. 1997. Ontogenetic phenotypic plasticity during thereproductive phase in Arabidopsis thaliana (Brassicaceae). AmericanJournal of Botany 84: 887–895.

Pigliucci M, Schlichting CD. 1995. Ontogenic reaction norms in Lobeliasiphilitica (Lobeliaceae): response to shading. Ecology 76:2134–2144.

Pigliucci M, DiIorio P, Schlichting CD. 1997. Phenotypic plasticity ofgrowth trajectories in two species of Lobelia in response to nutrientavailability. Journal of Ecology 85: 265–276.

Pigliucci M, Pollard H, Cruzan M. 2003. Comparative studies ofevolutionary responses to light environments in Arabidopsis.American Naturalist 161: 68–82.

PrestonKA,AckerlyDD. 2003.Hydraulic architecture and the evolution ofshoot allometry in contrasting climates. American Journal of Botany90: 1502–1512.

RoffD. 1997.Evolutionary quantitative genetics. NewYork, NY:Chapmanand Hall.

Roff D. 2002. Comparing G matrices: a MANOVA approach. Evolution56: 1286–1291.

Sales J, HillWG. 1976. Effect of sampling errors on efficiency of selectionindices. 1. Use of information from relatives for single traitimprovement. Animal Production 22: 1–17.

Saint-Andre L, M’Bou TA, Mabiala A, Mouvondy W, Jourdan C,Roupsard O, et al. 2005. Age-related equations for above- andbelow-ground biomass of a Eucalyptus hybrid in Congo. ForestEcology and Management 205: 199–214.

SAS Institute 1988. SAS/STAT user’s guide, release 6�03 edition. Cary,NC:SAS Institute Inc.



Schlichting CD, PigliucciM. 1998. Phenotypic evolution: a reaction normperspective. Sunderland, MA: Sinauer Associates.

Snedecor W, Cochran GC. 1989. Statistical methods, 8th edn. Ames, IA:Iowa State University Press.

Sokal RR, Rohlf FJ. 1995. Biometry—the principles and practices ofstatistics in biological research. San Francisco, CA: W.H. Freemanand Co.

Spinnler D, Egli P, Komer CH. 2003. Provenance effects andallometry in beech and spruce under elevated CO2 and nitrogenon two different forest soils. Basic and Applied Ecology 4:467–478.

Takahashi K. 1996. Plastic response of crown architecture to crowding inunderstorey trees of two co-dominating conifers. Annals of Botany77: 159–164.

VerhaegenD, PlomionC,Gion J-M, PoitelM,Costa P,KremerA. 1997.Quantitative trait dissection analysis in Eucalyptus using RAPDmarkers. 1. Detection of QTL in interspecific hybrid progeny, stabilityof QTL expression across different ages. Theoretical and AppliedGenetics 95: 597–608.

Via S, LandeR. 1995.Genotype–environment interaction and the evolutionof phenotypic plasticity. Evolution 39: 505–522.

Vigneron P, Bouvet JM. 2000. Eucalyptus. In: Charrier A, Jacquot M,Nicolas, D, eds. Collection repere du cirad. Update. Tropical plantbreeding. Enfields, NH: Science Publisher.

WeiX,BorralhoNMG.1998.Genetic control ofgrowth traitsofEucalyptusurophylla S.T. Blake in South East China. Silvae Genetica 47:158–164.

Weiner J, Thomas SC. 1992. Competition and allometry in three speciesof annual plants. Ecology 73: 648–656.

Wright SD, McConnaughay KDM. 2002. Interpreting phenotypicplasticity: the importance of ontogeny. Plant Species Biology 17:119–131.

Wu RL. 1997. Genetic control of macro- and micro-environmentalsensitivities in Populus. Theoretical and Applied Genetics 94:104–114.

WuR, Stettler RF. 1998.Quantitative genetics of growth and developmentin Populus. III. Phenotypic plasticity of crown structure and function.Heredity 81: 299–310.

Wu RL, Ma CX, Lou YX, Casella G. 2003. Molecular dissection ofallometry, ontogeny, and plasticity: a genomic view of developmentalbiology. Bioscience 53: 1041–1047.

Zobel B, Talbert J. 1984. Applied forest tree improvement. New York,NY: John Wiley and Sons.

APPENDIX

Probability value associated with the Fisher test of the analysisof variance testing the density (D), the genotype (G) (family orclone), and the density · genotype interaction (D · G), for the

clone and family experiments (model 1)

Age(months)


D G D · G D G D · G D G D · G

Clone experiment R91-112 0.003 10�4 0.05 10�4 10�4 0.27 10�4 10�4 0.0024 10�4 10�4 0.30 10�4 10�4 0.25 10�4 10�4 0.0148 10�4 10�4 0.11 10�4 10�4 0.02 10�4 10�4 0.0074 10�4 10�4 0.002 10�4 10�4 0.003 10�4 10�4 0.00

Family experiment R95-1011 0.58 10�4 0.95 10�4 10�4 0.96 10�4 10�4 0.4020 10�4 10�4 0.78 10�4 10�4 0.95 10�4 10�4 0.3539 10�4 10�4 0.72 10�4 10�4 0.84 10�4 10�4 0.3759 10�4 10�4 0.89 10�4 10�4 0.89 10�4 10�4 0.68



phenotypic plasticity of growth trajectory and ontogenic allometry

Documents