BACKGROUND
production of wood biomass is a mandatory trait in any forest tree breeding program regardless of the final use be it pulp and paper, energy, construction or engineered wood products.
understanding the contribution of genetic and environmental factors as well as their interaction in tree growth and adaptation is a prerequisite for accelerating tree domestication to meet the increasing demand for wood  <cit> .
in this context, fast growing trees such as eucalyptus will play a major role, not only as wood supply, but also as a model system to decipher the determinism of growth.
indeed, eucalypts are cultivated worldwide on more than twenty million hectares and are the most planted hardwoods in the world  <cit> .
this genus comprises about  <dig> species  <cit>  distributed naturally over a wide range of pedoclimatic conditions.
within that diversity, a few species or inter-specific hybrids combining the adaptive capacities and fast growth rates of the parental species , are widely used in planted forest.
wood biomass formation is a dynamic process resulting from a wide array of physiological processes  <cit>  some of which  are dependent on environmental variations.
it is also a product of height and circumference growth, involving the activity of the shoot apical meristem  <cit>  and the vascular cambium  <cit> .
the dynamics of both primary and secondary growth have been extensively described and modelled up to the rotation age in many forest tree species  <cit>  with the main objectives of predicting biomass production and optimizing sylvicultural practices.
the first models corresponded to yield models and with the improved understanding of plant/tree physiological functioning and its interplay with climatic factors, process or mechanistic models were subsequently developed taking into account carbon allocation, nutrient and water availability, and climate effects  <cit> .
these models were often developed for a particular species  <cit>  without explicitly taking into account the genetic diversity within species, while a genetic effect of the response to environmental variation has been described in eucalyptus on different scales of growth analysis   <cit> .
the genetic determinism of tree growth and its trend over-time have been fairly well studied in most forest tree species of commercial interest  <cit> .
as regards time trends, the franklin model  <cit> , suggesting three phases in variance components for growth traits , was tested in different species  <cit> .
in short rotation species with rapid initial growth such as in eucalyptus, a more stable trend was usually observed up to the rotation age  <cit> .
similarly, the ratio between dominance and additive variances has been analysed over time, with a major share of additive variance in pinus taeda <cit>  and more balanced in eucalyptus <cit> .
age-age genetic correlations were found to be generally high between successive measurements and tended to decrease when the time lag increased i.e.
between juvenile and mature stages  <cit> .
overall, these studies reveal low to moderate heritability for growth traits, indicating a strong environmental effect on the determinism of growth.
more recent studies have tried to link genetic of growth response to environmental variation  <cit> .
in eucalyptus globulus, costa e silva et al.
<cit>  reported a genetic effect on radial growth in response to temperature, rainfall and solar radiation.
a similar result was presented by a more recent study showing a genetic effect for suceptibility to drought damage in e. globulus <cit> .
nevertheless, there is still a need to improve our understanding of genetic and environmental determinants of growth, through measurements covering intervals better connected with environmental variations.
an analysis of the genetic architecture of growth traits  can also provide a better understanding of the genetic basis of growth.
thus, over the past two decades, many studies have been undertaken to detect qtls controlling part of the phenotypic variation of wood biomass in forest trees such as pines  <cit> , poplar  <cit>  and eucalyptus  <cit> .
in eucalyptus, several genomic regions have been detected harbouring qtls with low to moderate effects on the phenotypic variation of growth traits  <cit> .
these studies, although carried out with a relatively small number of growth measurement time points revealed qtl instability over time  <cit> .
the functional mapping approach taking into account the growth trajectory in qtl analysis  <cit>  showed similar results with early and late qtls in poplar  <cit> .
however, rather few studies connecting the genetic architecture of growth traits and different environmental conditions have been carried out  <cit> .
in eucalyptus freeman et al.
<cit>  as well as teixeira et al.
<cit> , highlighted major qtl x environment interactions.
all these studies conducted on an inter-annual scale are consistent with the idea that growth is an integrative trait involving a large number of ecophysiological  <cit>  and molecular  <cit>  processes on which environmental conditions can act to determine the final genetic architecture of growth.
therefore, understanding the interplay between early growth and abiotic factors  and how environmental variations impact the genetics of growth is a key issue, especially as part of eucalyptus breeding programmes.
in this context, the objective of this study was to dissect the genetic basis of the growth trajectory and its interplay with seasonal variation in water availability.
to that end, one interspecific cross of eucalyptus urophylla x e. grandis was planted in three different field trials in the republic of congo where contrasting environmental conditions in term of water availability , were suitable for observing the effect of drought on growth.
we used two complementary types of growth trait: integrative traits  and responsive traits  in combination with climatic data to characterize growth response to changes in water availability and reveal its genetic component.
this comprehensive dissection of growth enabled us to characterize the genetic determinism of primary  and secondary  growth using conventional quantitative genetics and qtl detection approaches.
methods
plant material and field experiments
a full-sib family generated from a single controlled cross between eucalyptus urophylla  x e. grandis  was used in this study in three environmental settings corresponding to three field experiments.
the first two trials were planted using a single tree plot design with seedlings: in april  <dig> with  <dig> genotypes  and already used in previous qtl studies  <cit>  and in april  <dig>  with  <dig> genotypes .
the third trial was planted in november  <dig>  and corresponded to a clonal test with  <dig> genotypes in common with p <dig> replicated by rooted-cuttings with  <dig> copies per genotype.
the three trials were established in the republic of congo, in the pointe-noire region .
p <dig> and p <dig> were planted at a density of  <dig> trees/ha, whereas p <dig> was planted at  <dig> trees/ha.
to reduce border effects a triple border row was planted around all the plantations.
dna extractions for the full-sib progenies were carried out using dry leaves according to doyle and doyle  <cit> .
environmental characterization
the trials were planted on ferralic arenosols  at the kissoko forestry station .
this soil is considered to be poor due to a low water retention, a small cationic exchange capacity and a low organic matter content  <cit> .
the climate in the pointe-noire region corresponds to a tropical savanna climate  <cit>  characterized by a dry season from may to october with annual rainfall of about  <dig>  mm.
the high atmospheric humidity  and high temperature  display slight seasonal variations, at 2% and 3°c, respectively.
to compare the climate between trials and especially the length of dry period during the dry season, we used the de martonne aridity index .
idm was calculated monthly with the following formula  <cit> :
idm=12p/
where p is the total monthly rainfall and t the monthly mean temperature.
according to de martonne  <cit> , a threshold of idm = <dig> was chosen as an upper limit to define the dry season.
climatic data  were recorded at pointe-noire about 25 km from the field trials.
phenotypic traits
growth measurements
tree growth was assessed by measuring both cumulative height and circumference at  <dig>  m for each tree, at different ages.
p <dig> was measured at  <dig>   <dig>   <dig>   <dig> and 59 months old.
p <dig> was measured more frequently over time at  <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig> and 62 months old.
p <dig> was measured at  <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>   <dig>  and 60 months old.
the net growth increments between two time points were calculated using the following formulas:
traitn1−n2=traitn2−traitn <dig>
where trait n is the cumulative height or circumference at “n” months old.
growth modelling
we used the monomolecular growth equation to model height and circumference growth in trials p <dig>  p <dig> and p <dig>  the monomolecular growth equation is a particular case of the von bertalanffy-richards growth model  <cit>  which has been widely applied and compared for tree growth modelling  <cit> .
for fast growing trees like eucalypts, the monomolecular model is well adapted because of its concave shape with no inflection point  <cit> .
the equation is expressed in the following form:
lt=asym1−e−elrct‒c <dig>
where l is the cumulative growth at time t; asym is the maximum growth ; lrc is the logarithm of the growth constant and c <dig> is the theoretical age for which l is zero.
growth modelling was performed with r software  using the r package: nlme <cit> .
trees with a high proportion of missing data were removed, based on the duration and the phase  at which missing data occurred.
selected trees presented on average  <dig> ,  <dig>  and  <dig> % of growth curve that is missing for p <dig>  p <dig> and p <dig> respectively.
for each selected genotype, a nonlinear model  was fitted to obtain the above-mentioned growth curve parameters  for both height and circumference.
the model fitted the data well as illustrated for circumference in additional file  <dig>  moreover the pseudo r-squared calculated for all adjusted models were higher than  <dig> .
predicted values were also calculated for p <dig> for the same time points as in p <dig> .
broad-sense heritability of growth
broad-sense heritabilities were estimated using trial p <dig> which corresponded to a clonal test with  <dig> replicates of  <dig> full-sibs.
analyses were conducted using markov chain monte carlo methods implemented in the r mcmcglmm package  <cit> .
the following mixed effects model was used for each trait:
y=µ+rowi+colj+gk+ϵ
where y is the individual tree measurement, μ is the general mean, rowi is the fixed effect of the row, colj is the fixed effect of the column, g
k
is the random effect of the genotype ~no,σg <dig> and ϵ is the residual random effect ~no,σϵ <dig>  the intersection between individual tree coordinates in the trial  represented the spatial position of each tree.
broad-sense heritability for the full-sib family  was estimated for each trait using the following formula:
h2=σg2/σg2+σϵ <dig>
where σg <dig> is the genetic variance and σg2+σϵ <dig> is the phenotypic variance  <cit> .
molecular markers and linkage mapping
for each parental genotype  and each trial , a genetic map was constructed according to a two-way pseudo-test cross mapping strategy  <cit> .
for p <dig>  the two genetic linkage maps were constructed using rapd ssr, est, and sts markers genotyped on  <dig> individuals  <cit> .
for p <dig>  only rapd markers selected on the basis of their map position in the p <dig> linkage maps were used for genetic mapping with  <dig> individuals.
the set of common polymorphic markers genotyped in both p <dig> and p <dig>  enabled the unambiguous identification of homologous linkage groups  between the two parental maps of the same species.
in addition, the codominant markers used in p <dig>  enabled the identification of orthologous regions between e. urophylla and e. grandis <cit> .
joinmap® version  <dig>   <cit>  was used to perform the linkage analysis.
chi-squared tests were performed to test whether markers followed the expected mendelian segregation ratios.
distorted markers  were excluded from linkage analysis.
markers with more than 40% of missing data were also excluded.
for the four maps, markers were grouped into lgs at the independence logarithm-of-the-odds  score ≥  <dig> .
then, markers within linkage groups were ordered using the monte carlo maximum likelihood mapping algorithm  <cit> .
finally, mapping quality tools were used to classify markers leading to a poorer fit as accessory markers, located near the closest framework markers.
accessory markers with significant deviation from expected mendelian segregation  were indicated by * on the genetic maps.
genetic distances in centimorgan  were calculated with the kosambi mapping function  <cit> .
the lg nomenclature corresponds to that defined by brondani et al.
<cit> .
qtl analysis
qtl mapping
quantitative trait locus  analyses were performed with r software using the qtl package  <cit> .
we carried out simple and composite interval mapping using the multiple imputation method of sen and churchill  <cit>  with a step interval of 1 cm, a genotyping error rate of  <dig>  and  <dig> imputations per genotypes.
it has been shown that this imputation method performs better with missing genotypic data  <cit> .
the whole-genome significance thresholds for all traits were determined with  <dig>  permutations  <cit> .
qtls that met or exceeded 95th and 90th percentiles were assessed to be significant or suggestive, respectively.
confidence intervals for each qtl position were obtained using bayes credible intervals .
genetic maps and qtl positions were drawn using mapchart  <cit> .
detection of qtl x environment interaction
for each parent, we were able to test the qtl x environment interaction  using markers common to both trials , and for growth traits at five different ages  based on measurements for p <dig> and predicted values at the same ages for p <dig>  gcp were also used for both trials.
to test the qtl x e, an analysis of variance  was carried out according to the following model:
y=µ+trial+marker+trial×marker+ϵ
where y is the individual tree measurement, μ is the general mean, trail is the fixed effect of the trial , marker is the fixed effect of the closest marker associated with a qtl detected by cim, trail × marker is the interaction between the two fixed effects and ϵ is the residual random effect ~no,σϵ <dig>
RESULTS
climatic conditions
the de martonne index  was calculated monthly during the growth period of p <dig> and p <dig> .
idm mainly reflected seasonal changes in water availability because the mean temperature remained very stable across seasons with only 3°c of amplitude.
the two curves exhibited different patterns at the beginning of the plantation , then evolved in parallel before separating again after 45 months.
the timing and the intensity of the dry periods  were different between the two trials.
indeed, p <dig> exhibited longer dry periods than p <dig> , amounting to four supplementary months of drought over the study period.
using the dry periods defined by idm, specific growth increments were determined for p <dig> only, because measurement points were lacking for p <dig>
trend in phenotypic variation and correlation
the mean trajectories for cumulative growth, height  and circumference , were slightly different between the three trials .
mean cir values were significantly smaller in p <dig>  whereas final ht values at 60 months old were higher , probably due to a higher tree density in p <dig>  these differences were reduced between p <dig> and p <dig>  two trials planted at the same period  and with the same tree density.
the mean trajectory of growth increments, estimated from p <dig> , showed a global decrease over the 60 months after planting, with two periods of lower growth rates that occurred during the second and third dry periods .
these two periods flanked a growth rate peak at 21 months that occurred during the second rainy season.
the pattern of phenotypic variations for cumulative growth  was very similar between trials.
indeed the variance increased gradually over time and the coefficient of phenotypic variation  for ht remained rather stable .
the same tendency was observed for cir.
the cvp of growth increments for p <dig> and p <dig> were more variable compared to cumulative growth, as exemplified by cvp values for ht_inc ranging from  <dig>  to  <dig>  for p <dig> and from  <dig>  to  <dig>  for p <dig>  a similar range of values was observed for cir_inc.
given the large number of measurements in p <dig>  we were able to characterize the evolution of cvp over time for ht_inc and cir_inc.
two growth rate peaks cvp were observed during the second and the third dry periods , corresponding to a lower growth increment on average.
these results suggest that growth rate differences between genotypes were enhanced during these two dry periods.
this hypothesis was supported by the analysis of pearson correlations between height or radial increments and idm calculated at both trial and tree levels using data from p <dig> .
at trial level , positive correlations were found for both early  and late  growth, indicating a strong effect of rainfall on growth.
for both levels, early growth was found to be more responsive  than late growth, although fewer data were available at the later stage, which could have affected the estimation of correlation coefficients.
the tree level reflected the phenotypic plasticity of each genotype in response to water availability .
at tree level, correlations between idm and circumference increments were higher than those with height increments .
these differences were particularly apparent during early growth with 95% of trees having a coefficient of correlation over  <dig> , including 81% of trees with a significant correlation .
this suggests that secondary growth was more prone to changes in water availability than primary growth, especially at the juvenile stage.
dm
pearson’s coefficients of correlation were calculated for early  and late  growth at trial and tree levels.
the analysis of phenotypic correlations between cumulative growth  revealed strong correlations  over time in each trial.
as expected, the age–age correlations for both cumulative growth traits  were highly positive and stable over time, and comparable between the three trials .
for ht and cir, the correlations between current age and final growth increased dramatically over the two first years to reach at least  <dig>  at two years old .
high correlations were also found between asym and the final growth.
more interestingly, pearson correlation coefficients for growth increments were variable over time.
moreover, correlations for ht_inc and cir_inc displayed roughly opposite patterns during early growth .
as illustrated for p <dig> in figure  <dig>  correlations for ht_inc dropped from high and significant levels  to non-significant levels revealing contrasting behaviour between genotypes in their response to the environment between the beginning of the second dry period and the 34th month.
conversely, correlations for cir_inc became significant during the same period revealing a similar response between genotypes.
trend in the genetic control of growth traits
broad-sense heritabilities  were estimated for cumulative growth traits, growth increment, and the gcp based on the data from p <dig>  for all traits, h <dig> values were small to medium.
although standard errors associated with h <dig> were high , we observed a regular increase in heritability with time for cumulative growth: ht , cir  .
the heritabilities for the asym parameter  were only slightly higher than those obtained for final ht and cir, which is consistent with the strong correlation between these pairs of traits.
h <dig> for growth increments were more heterogeneous than h <dig> for cumulative traits , even though the variation ranges were similar .
given the standard error around h <dig>  only differences between cumulative and incremental growth for ht  were found to be significant between the two types of trait, while no significant differences for cir were observed.
h <dig> for ht_inc and cir_inc had nearly an opposite pattern from  <dig> to 35 months, then their patterns became more similar.
the lowest heritabilities for ht and cir clearly corresponded to the coefficient of variation peak occurring during the third dry season  and suggest a greater environmental effect at that period.
linkage mapping
the linkage analysis was performed for the p <dig> and p <dig> trials separately.
table  <dig> summarizes the characteristics of each genetic map.
for p <dig>   <dig> co-dominant markers mapped by gion et al.
enabled the identification of orthologous regions between e. urophylla and e. grandis parents.
these regions covered a total of 989 cm for e. urophylla and 847 cm e. grandis, amounting respectively to 66% and 67% of the total map length.
the macro-colinearity of common markers between parental maps was well conserved except for  <dig> small inversions in lgs  <dig>   <dig> and  <dig> .
for p <dig>  the two parental maps were constructed in this study, using a total of  <dig> rapd markers for e. urophylla and  <dig> rapds for e. grandis.
a total of  <dig> and  <dig> framework markers were positioned in  <dig>  and  <dig> linkage groups  for e. urophylla and e. grandis parents respectively.
the two maps provided a resolution of one marker every  <dig>  cm  and  <dig>  cm  for a total map length of  <dig>  cm  and  <dig>  cm .
e. urophylla
and
e. grandis
in both the p <dig> and p <dig> trials
e. urophylla
e. grandis
lg linkage group.
among the framework markers,  <dig> markers for the female map and  <dig> markers for the male map were common between p <dig> and p <dig> maps.
these “bridge markers” enabled the identification  <dig> homologous regions for the e. urophylla parent covering 73%  and 90%  of total map length.
for e. grandis,  <dig> homologous regions were identified, covering of 79%  and 89%  of the total map length.
as expected, the order between markers was well conserved between p <dig> and p97: 89% and 93% of the common markers presented the same order for the e. urophylla and the e. grandis maps, respectively.
the four genetic maps with links between bridge markers revealing homologous and orthologous regions are represented in additional file  <dig>
genetic architecture of growth traits
qtl detection in p93
a total of  <dig> qtls were detected for the female parent  and  <dig> for the male parent  at the genome-wide type i error rate of 10% .
71% of the qtls remained significant at the 5% genome-wide error rate.
these qtls were associated with  <dig> and  <dig> different traits for e. urophylla and e. grandis respectively; representing  <dig> and  <dig> different regions distributed over  <dig> different linkage groups for each parental map.
for the e. urophylla parent, the variance explained by all the detected qtls associated with one trait ranged from  <dig> %  to  <dig> %  with an average of  <dig> % .
for the male parent, this proportion of variance ranged from  <dig> %  to  <dig> %  with an average of  <dig> % .
qtls for e. urophylla were located on lg <dig>  lg <dig>  lg <dig>  lg <dig> and lg <dig> with two hotspots  gathering 16% and 47% of the total number of qtls respectively.
qtls for e. grandis were located on lg <dig>  lg <dig>  lg <dig>  lg <dig> and lg <dig> with two hotspots  gathering 22% and 33% of the total number of qtls, respectively.
the distribution of qtls between the two parents was different, of the seven lgs with qtls only two  were common to both parents.
two specific qtls were found for the growth curve parameter on the e. urophylla map on lg <dig> .
no qtl for gcp were found on the e. grandis map.
qtl detection in p97
unlike p <dig>  fewer qtls were detected for the female parent  than for the male parent  at the genome-wide type i error rate of 10%, while 74% of the qtls remained significant at 5%.
these qtls associated with  <dig> and  <dig> different traits, represented  <dig> and  <dig> different regions distributed on  <dig> and  <dig> different lgs for e. urophylla and e. grandis, respectively .
for e. urophylla, the variance explained by all the detected qtls associated with one trait ranged from  <dig> %  to  <dig> %  with an average of  <dig> % .
this proportion of variance ranged from  <dig> %  to 17%  with an average of  <dig> %  for the male parent .
qtls for e. urophylla were located on lg <dig>  lg <dig>  lg <dig>  lg <dig>  lg <dig> and lg <dig> with three hotspots  gathering 12%, 34% and 16% of the total number of qtls, respectively.
qtls for e. grandis were located on lg <dig>  lg <dig>  lg <dig>  lg <dig>  lg <dig>  lg <dig> and lg <dig> with three hotspots  gathering 6%, 6% and 60% of the total number of qtls, respectively.
all lgs with qtls were common to both parents except for lg <dig>  for which no qtl was detected in e. urophylla.
one specific qtl region was found for the gcp located on the e. grandis map on lg <dig> .
the other gcp qtls co-located with qtls for different traits.
qtls for growth increment were located on more lgs than qtls for cumulative growth .
the range of phenotypic variance explained by qtls was similar between cumulative growth and growth increment.
for both parents more significant qtls  were found for growth increments.
these genomic regions were located on lg <dig>  lg <dig> and lg <dig> for e. urophylla and on lg <dig>  lg <dig> and lg <dig> for e. grandis.
in addition to these specific qtls for growth increments, one qtl region for e. urophylla on lg <dig> was found to be associated with early cumulative growth only .
more interestingly, all qtls for late cumulative growth for both parents co-localized with qtls for early growth increments, as illustrated for e. urophylla on lg <dig> at 47 cm and for e. grandis on lg <dig> at 0/10 cm and on lg <dig> at 22/42 cm .
moreover, a co-localization with a qtl for the asym_c parameter was found for two of these qtls  suggesting that the genetic architecture of growth response  at the early stage affected the genetic architecture of cumulative growth at the adult stage.
additionally, on lg <dig>  a qtl for the correlation coefficient between growth increment and idm was found  for e. grandis .
this qtl co-located with the hotspot on lg <dig> for e. grandis.
for this qtl region, genotypes with a higher growth were also the more responsive .
qtl comparison across trials
trials p <dig> and p <dig> were compared using the growth traits , gcps, as well as specific predicted values .
proportionally to the number of traits, fewer qtl were detected for e. urophylla in p <dig> compared to p <dig>  the proportion of qtls detected for late growth traits  was higher than for early growth traits for e. grandis in both trials and was equivalent for e. urophylla in both trials.
this may reflect the higher heritability of late growth traits compared with early growth as shown for the same family with p <dig>  considering p <dig> and p <dig>  qtls were detected on all lgs except on lg <dig> and lg <dig>  however, for lg <dig> and lg <dig>  qtls were detected in p <dig> only.
qtls for gcp were found on three maps .
they were mainly located in growth trait qtl-hotspots except for e. urophylla on lg <dig> and lg <dig> in p <dig> and lg <dig> in p <dig>  qtls for predicted values were all detected at the same location as other qtls for growth.
thus, qtls for predicted values described well the genetic architecture of growth for p <dig> allowing the comparison with p <dig>
co-locating qtls between p <dig> and p <dig> were found on lg <dig> and  <dig> for the e. grandis parent only, involving strong overlapping of confidence intervals.
these two co-localizations involved hotspots of one of two trials but represented few of all the detected qtls.
indeed a jaccard index  was calculated between the two trials  for e. grandis .
this difference in the genetic architecture of growth traits between p <dig> and p <dig> suggested a strong qtl x environment interaction  that was tested using the predicted values obtained for p <dig> based on growth curve modelling.
thus, using closest markers already associated with qtls, a two way analysis of variance was conducted to test qtl x e interaction for growth traits at ages  <dig>   <dig>   <dig>   <dig> and 59 months for p <dig> and predicted values at the same ages for p <dig>  gcp were also used for both trials .
we found that most of tested markers revealed a significant interaction with the environment  for both parents, e. urophylla 60% and 80%, e. grandis 40% and 90% for p <dig> and p <dig> respectively.
for both trials, qtl x e was more significant for e. grandis than for e. urophylla.
discussion
incremental growth at the early stage is related to water availability and determines biomass production at rotation age
we combined the measurement of growth on a sub-annual scale with a monthly characterisation of climate variation using an aridity index , and first showed that seasonal changes in water availability affected secondary and primary growth at the early stage of tree development.
indeed, idm was found to be strongly correlated with radial growth increment before two years old, while it was less related to growth after two years.
besides, the correlation at early stage was more significant for radial growth  than for vertical growth , indicating that processes underlying secondary growth are more prone to environmental variation than those involved in primary growth.
other studies have already reported a relationship between apical or radial incremental growth and rainfall on different time scales  in different species  <cit> .
in this study, we showed that the first two years corresponded to the highest biomass productivity period, during which 60% of the final height and 65% of final circumference was reached, representing a biomass productivity of 20-27 m <dig> ha- <dig> year- <dig>  therefore, the early growing period constitutes a key period with a strong impact on final growth, as illustrated by the high correlations values between each measurement point and the final growth at 60 months old.
in tropical eucalypt plantations, it was found that the maximum growth rate occurred around two years, followed by a decline in production after canopy closure  <cit> .
therefore, our results suggest that climatic conditions underlying the aridity index  have a strong impact on early growth response and consequently determine biomass production at rotation age.
early growth response to water availability is genetically variable
the small sample size  used to calculate h <dig> limited the accuracy of the estimation.
however, the comparison of time trends in h <dig> between cumulative and incremental growths highlighted contrasting patterns over time which was significant only for ht.
indeed, cumulative growth displayed an asymptotic increase up to rotation age, contrary to incremental growth which showed high temporal heterogeneity.
for eucalyptus grown in congo, h <dig> for cumulative growth calculated using a wider genetic background were found to range from  <dig>  to  <dig>   <cit>  and to stabilize after two or three years.
the same trend in h <dig> for cumulative growth was found in eucalyptus in other environments  <cit> .
interestingly, this stabilization of cumulative growth heritabilities occurred at the same time as the decline in wood biomass productivity  <cit> , with a decrease in or stabilization of the g x e interaction  <cit> .
it could thus be suggested that the integrative nature of cumulative growth at a mature stage aggregates past genetic responses to environmental variations.
the heterogeneity of h <dig> for incremental growth observed for both height and radial growth suggests a variation in the impact of environmental conditions on growth response.
the slowest values of incremental growth heritability were observed during the third dry period.
in pinus pinaster, such heterogeneous trends in h <dig> have been shown for yearly incremental growths  <cit>  and the variability described was significantly linked to environmental effects .
on a lower scale, parisi  <cit>  also reported a heterogeneous pattern for narrow and broad-sense heritabilities for incremental height growth in pinus taeda.
in addition to the contrast between cumulative and incremental growth, h <dig> patterns for growth increment revealed opposite patterns during the 25th and 35th months between primary and secondary growth responses.
costa and durel  <cit>  also reported a clear difference between primary and secondary growth increments and suggested more stable genetic control for secondary growth response.
between-tree variation in this early growth response, depicted by the distribution of phenotypic correlations between growth increments and idm during early growth, suggested a genetic effect as a major component in this response.
other studies have already suggested a genetic effect in response to water availability.
drew et al.
<cit>  observed such contrasting behaviour in response to climatic variations  between different eucalyptus hybrids i.e.
an e. grandis x e. urophylla susceptible to drought with intermittent growth, and a less susceptible e. grandis x e. camaldulensis maintaining a continuous growth.
similar results were found between e. alba and e. urophylla x e. grandis in congo  <cit> , associated with a significant genotype x environment interaction for traits related to height growth and carbon isotope discrimination .
these genetic differences in environmental susceptibility were also suggested by bouvet et al.
<cit>  comparing different eucalyptus clones.
interestingly, in the present study, we found a qtl for the correlation between idm and radial growth increment, suggesting that early growth response to water availability is indeed genetically controlled.
the genetic architecture of final growth is driven by the early growth response to the environment
given the high macro-synteny and colinearity between eucalyptus genomes, we were able to compare the position of the mapped qtls to that detected in other studies in different genotypes of the same species or different species.
this comparison enabled us to identify two lgs where growth qtls were frequently detected  <cit> .
as already mentioned by thumma et al.
<cit> , and supported by our result, lg <dig> was found to contain qtls for height and radial growth in different eucalyptus species  <cit>  as well as qtls for foliar chemicals  <cit> .
to a lesser extent, lg <dig>  which was associated with both incremental and cumulative growth in our study, was also associated with growth-qtls in three other studies  <cit> , as well as qtls for rooting ability  <cit>  and qtls for resistance to biotic stresses  <cit> .
in addition to these two main lgs, and in agreement with the oligogenic model, i.e.
few genes with large effects detected as qtls and many genes with small effects controlled quantitative traits  <cit> , qtls were found to be distributed across the other nine chromosomes  <cit> .
in this study, a similarity index revealed that most of the growth qtls were not shared between two experimental trials showing different environmental trajectories .
the statistical power of qtl detection and of estimated effects is directly related to sample size, so called beavis effect  <cit> .
therefore qtls with intermediate or small effects are likely to be not detected with a small sample size .
thus one cannot rule out the fact that qtl instability between p <dig> and p <dig> is the result of a rather low sample size:  <dig> and  <dig> genotypes for p <dig> and p <dig>  respectively.
this lack of qtl stability could also reveal true biological effect, i.e.
a genotypic sensitivity to environmental conditions, as supported by the significant qtl x e interaction found in both parents, and more particularly in e. grandis.
interestingly, the two studied species display contrasting adaptability to congolese conditions with e. urophylla better adapted than e. grandis <cit> .
the instability of growth-qtls between trials also contrasted with the qtl stability found for other traits measured on the same offspring .
this difference in sensitivity to environmental variations is generally used to explain the greater pev and larger number of wood property qtls in comparison to growth related traits  <cit> .
it has been found that growth-qtls often presented a higher level of interaction with the environment  <cit>  than wood property-qtls  <cit> .
the temporal analysis of qtl detection showed the presence of early stage, intermediate and late qtls.
among these three patterns of qtl expression, a large proportion of qtls associated with cumulative growth exhibited early or intermediate patterns: 50%  and 75%  for e. urophylla and 75%  and 33%  for e. grandis.
these three qtl patterns were also reported by emebiri et al.
<cit>  on three-year-old pines.
this instability over time is frequently reported in forest tree literature in relation to low heritabilities associated with growth.
in e. globulus, a study also reported a lack of qtl stability over time for diameter at breast height between two and six years  <cit> .
in the same species, bundock et al.
<cit>  found partial qtl stability for stem diameter with the same location of lod peaks between the diameter at two and six years old.
along the same lines, thumma et al.
<cit>  also reported relatively low stability for growth qtls  over time  in one family.
in our study, partial stability was found on lg <dig>  and lg <dig> .
moreover, stable qtls after two or three years old were found on lg <dig> , lg <dig>  and lg <dig> .
qtl stability over the years has also been reported in gymnosperms  <cit>  but their measurements were limited to the young stage  and did not therefore reflect the genetic architecture of the whole growth trajectory.
to our knowledge, our study provides the most comprehensive view of the global instability of growth genetic architecture in a forest tree species thanks to a detailed analysis of the temporal and environmental dynamics of growth over the whole rotation period.
indeed, the fine scale characterization of both growth  and the environment  enabled a precise qtl dissection from early to late growth.
in the literature, growth increments are mostly calculated on a yearly basis.
consequently, differences in genetic determinism between cumulative and incremental are less noticeable  <cit> .
in our study, the wider variety of growth responses captured by short incremental data was instrumental to characterizing the genetic architecture of growth and depicting its temporal plasticity.
more remarkably, thanks to the fine characterization of growth, we found that all qtls detected at the mature stage for cumulative growth, co-localized with qtls for early growth increment on both parents .
this result, which goes far beyond a simple age-age correlation analysis, suggests a partly common genetic determinism between early growth response to environmental variation and final growth.
the qtl for the correlation with idm detected on lg <dig> in e. grandis, as well as the pattern of lod scores for qtls detected for mature growth on p <dig> , corroborate this assumption.
to sum up, our study shows that the variability of growth plasticity observed at the young stage partly determined the pattern of cumulative growth genetic architecture at rotation age.
CONCLUSIONS
this study showed differences at phenotypic and genetic levels  between cumulative and incremental growth, for both primary and secondary growth in a fast growing tree species.
growth increments  were found to be highly responsive to climatic variations  over the two first years, contrary to cumulative growth.
however, qtl analysis showed a common genetic basis between early growth increments and final growth.
moreover, strong instability was found in growth-qtls between the two trials, which was also supported by the analysis of qtl x e. these results suggest that early growth responses  to soil water availability partially shape the genetic determinism of late growth and thus growth trajectories.
specific genomic regions were also found for growth increments and growth curve parameters, showing the merits of a combined approach with sequential  and global  growth traits to dissect its genetic determinism.
our results highlight the importance of considering growth as a compound trait for a better understanding of its genetic bases, and suggest to combine selection on early and cumulative growth to improve the ability of trees to produce wood biomass in an optimal way.
competing interests
the authors have no competing interests to declare.
authors’ contributions
fs: dna extraction and genotyping.
jmb, pv: field trial management.
jb: growth modelling, linkage analysis, qtl mapping.
jb, jmg, cp, jmb: manuscript preparation.
jmg: funding and overall supervision.
all authors read and approved the final manuscript.
supplementary material
additional file 1
growth trajectories of four individuals  randomly selected from the full-sib progenies of each trial.
the circumference growth trajectories were fitted by the monomolecular model .
the mean growth curve for all individuals is represented with a blue line.
click here for file
additional file 2
mean trajectory for cumulative height and circumference for the three trials, p <dig>  p <dig> and p <dig>  the thick coloured bars along the x-axis represent dry periods  for each trial .
click here for file
additional file 3
summary of phenotypic data for each trial, p <dig>  p <dig> and p <dig>  traits, number of values, minimum , maximum , mean, standard deviation  and coefficient of phenotypic variation .
click here for file
additional file 4
evolution over time of the cvp for cumulative and incremental growth for p <dig> and p <dig>  the thick grey bars along the x-axis represent dry periods .
cumulative growth is in dashed lines and incremental growth is in solid lines.
height is in blue with circles, circumference is in orange with triangles.
click here for file
additional file 5
matrix of pearson correlation coefficients.
for all traits: cumulative growth, growth increment, growth curve parameters and predicted values for p <dig> , p <dig>  and p <dig> .
only significant correlation values  are displayed.
click here for file
additional file 6
phenotypic correlations between final growth and current growth for the three trials.
cumulative growth is in dashed lines and incremental growth is in solid lines.
height is in blue with circles, circumference is in orange with triangles.
vertical grey bars indicate the dry periods.
click here for file
additional file 7
broad sense heritabilities  with confidence interval  for growth related traits.
click here for file
additional file 8
genetic maps of
e. urophylla
and
e. grandis
for p <dig> and p <dig>  the lg nomenclature corresponds to the one defined by brondani et al.
<cit> .
distances between markers are indicated in centimorgans  by a scale on the left side.
common markers between parental maps for p <dig> and p <dig> are in bold.
orthologous regions between the p <dig> and p <dig> maps are shown in red  or orange  hatching.
common markers between the two parents of p <dig> are in bold and grey, orthologous regions are represented by a grey bar segment.
accessory markers are positioned near the closest framework marker with the distance in brackets.
qtls are represented by boxes extended by lines representing 95% bayes credible intervals.
if multiple qtls of the same trait type for different ages co-localize, only one qtl is represented with the largest interval and  indicates if one or more qtls were significant at 5% whole-genome level.
accessory markers with an  were distorted .
traits have been explained in the text.
click here for file
additional file 9
qtls detected in p <dig> by composite interval mapping in
e. urophylla
and
e. grandis.
the trait, the number of genotype used for analysis , the linkage group , the position, the lod value , the percentage of variance explained by the qtl  and the difference between the two qtl allele effects  are indicated.
click here for file
additional file 10
qtls detected in p <dig> by composite interval mapping in
e. urophylla
and
e. grandis.
the trait, the number of genotype used for analysis , the linkage group , the position, the lod value , the percentage of variance explained by the qtl  and the difference between the two qtl allele effects  are indicated.
click here for file
additional file 11
analysis of variance for markers associated with a qtl in p <dig>  or p <dig> .
similar measurement ages or predicted values were used to analyse the two trials.
* p <  <dig> , ** p <  <dig> , *** p <  <dig> .
click here for file
additional file 12
evolution of lod scores at hotspot locations on
e. urophylla
and
e. grandis
for p <dig>  height is in blue with a circle, circumference is in orange with a triangle.
the purple zone contains qtls which are significant at the 10% genome-wide level, above are the qtls significant at the 5% genome wide level.
vertical grey bars indicate the dry periods .
click here for file
acknowledgements
the authors would like to thank the technicians at crdpi  for trial establishment and follow-up.
the authors acknowledge two anonymous reviewers for their constructive comments and suggestions on the manuscript.
this study was supported by grants from feder .
jb received a phd fellowship from the bios department of cirad .

 production of wood biomass is a mandatory trait in any forest tree breeding program regardless of the final use be it pulp and paper, energy, construction or engineered wood products. understanding the contribution of genetic and environmental factors as well as their interaction in tree growth and adaptation is a prerequisite for accelerating tree domestication to meet the increasing demand for wood. in this context, fast growing trees such as eucalyptus will play a major role, not only as wood supply, but also as a model system to decipher the determinism of growth. indeed, eucalypts are cultivated worldwide on more than twenty million hectares and are the most planted hardwoods in the world. this genus comprises about species distributed naturally over a wide range of pedoclimatic conditions. within that diversity, a few species or inter-specific hybrids combining the adaptive capacities and fast growth rates of the parental species, are widely used in planted forest. wood biomass formation is a dynamic process resulting from a wide array of physiological processes some of which are dependent on environmental variations. it is also a product of height and circumference growth, involving the activity of the shoot apical meristem and the vascular cambium. the dynamics of both primary and secondary growth have been extensively described and modelled up to the rotation age in many forest tree species with the main objectives of predicting biomass production and optimizing sylvicultural practices. the first models corresponded to yield models and with the improved understanding of plant/tree physiological functioning and its interplay with climatic factors, process or mechanistic models were subsequently developed taking into account carbon allocation, nutrient and water availability, and climate effects. these models were often developed for a particular species without explicitly taking into account the genetic diversity within species, while a genetic effect of the response to environmental variation has been described in eucalyptus on different scales of growth analysis. the genetic determinism of tree growth and its trend over-time have been fairly well studied in most forest tree species of commercial interest. as regards time trends, the franklin model, suggesting three phases in variance components for growth traits, was tested in different species. in short rotation species with rapid initial growth such as in eucalyptus, a more stable trend was usually observed up to the rotation age. similarly, the ratio between dominance and additive variances has been analysed over time, with a major share of additive variance in pinus taeda and more balanced in eucalyptus. age-age genetic correlations were found to be generally high between successive measurements and tended to decrease when the time lag increased i.e. between juvenile and mature stages. overall, these studies reveal low to moderate heritability for growth traits, indicating a strong environmental effect on the determinism of growth. more recent studies have tried to link genetic of growth response to environmental variation. in eucalyptus globulus, costa e silva et al. reported a genetic effect on radial growth in response to temperature, rainfall and solar radiation. a similar result was presented by a more recent study showing a genetic effect for suceptibility to drought damage in e. globulus. nevertheless, there is still a need to improve our understanding of genetic and environmental determinants of growth, through measurements covering intervals better connected with environmental variations. an analysis of the genetic architecture of growth traits can also provide a better understanding of the genetic basis of growth. thus, over the past two decades, many studies have been undertaken to detect qtls controlling part of the phenotypic variation of wood biomass in forest trees such as pines, poplar and eucalyptus. in eucalyptus, several genomic regions have been detected harbouring qtls with low to moderate effects on the phenotypic variation of growth traits. these studies, although carried out with a relatively small number of growth measurement time points revealed qtl instability over time. the functional mapping approach taking into account the growth trajectory in qtl analysis showed similar results with early and late qtls in poplar. however, rather few studies connecting the genetic architecture of growth traits and different environmental conditions have been carried out. in eucalyptus freeman et al. as well as teixeira et al., highlighted major qtl x environment interactions. all these studies conducted on an inter-annual scale are consistent with the idea that growth is an integrative trait involving a large number of ecophysiological and molecular processes on which environmental conditions can act to determine the final genetic architecture of growth. therefore, understanding the interplay between early growth and abiotic factors and how environmental variations impact the genetics of growth is a key issue, especially as part of eucalyptus breeding programmes. in this context, the objective of this study was to dissect the genetic basis of the growth trajectory and its interplay with seasonal variation in water availability. to that end, one interspecific cross of eucalyptus urophylla x e. grandis was planted in three different field trials in the republic of congo where contrasting environmental conditions in term of water availability, were suitable for observing the effect of drought on growth. we used two complementary types of growth trait: integrative traits and responsive traits in combination with climatic data to characterize growth response to changes in water availability and reveal its genetic component. this comprehensive dissection of growth enabled us to characterize the genetic determinism of primary and secondary growth using conventional quantitative genetics and qtl detection approaches. methods plant material and field experiments a full-sib family generated from a single controlled cross between eucalyptus urophylla x e. grandis was used in this study in three environmental settings corresponding to three field experiments. the first two trials were planted using a single tree plot design with seedlings: in april with genotypes and already used in previous qtl studies and in april with genotypes. the third trial was planted in november and corresponded to a clonal test with genotypes in common with p replicated by rooted-cuttings with copies per genotype. the three trials were established in the republic of congo, in the pointe-noire region. p and p were planted at a density of trees/ha, whereas p was planted at trees/ha. to reduce border effects a triple border row was planted around all the plantations. dna extractions for the full-sib progenies were carried out using dry leaves according to doyle and doyle. environmental characterization the trials were planted on ferralic arenosols at the kissoko forestry station. this soil is considered to be poor due to a low water retention, a small cationic exchange capacity and a low organic matter content. the climate in the pointe-noire region corresponds to a tropical savanna climate characterized by a dry season from may to october with annual rainfall of about  mm. the high atmospheric humidity and high temperature display slight seasonal variations, at 2% and 3°c, respectively. to compare the climate between trials and especially the length of dry period during the dry season, we used the de martonne aridity index. idm was calculated monthly with the following formula: idm=12p/ where p is the total monthly rainfall and t the monthly mean temperature. according to de martonne, a threshold of idm = was chosen as an upper limit to define the dry season. climatic data were recorded at pointe-noire about 25 km from the field trials. phenotypic traits growth measurements tree growth was assessed by measuring both cumulative height and circumference at  m for each tree, at different ages. p was measured at and 59 months old. p was measured more frequently over time at and 62 months old. p was measured at and 60 months old. the net growth increments between two time points were calculated using the following formulas: traitn1−n2=traitn2−traitn where trait n is the cumulative height or circumference at “n” months old. growth modelling we used the monomolecular growth equation to model height and circumference growth in trials p p and p the monomolecular growth equation is a particular case of the von bertalanffy-richards growth model which has been widely applied and compared for tree growth modelling. for fast growing trees like eucalypts, the monomolecular model is well adapted because of its concave shape with no inflection point. the equation is expressed in the following form: lt=asym1−e−elrct‒c where l is the cumulative growth at time t; asym is the maximum growth; lrc is the logarithm of the growth constant and c is the theoretical age for which l is zero. growth modelling was performed with r software using the r package: nlme. trees with a high proportion of missing data were removed, based on the duration and the phase at which missing data occurred. selected trees presented on average, and % of growth curve that is missing for p p and p respectively. for each selected genotype, a nonlinear model was fitted to obtain the above-mentioned growth curve parameters for both height and circumference. the model fitted the data well as illustrated for circumference in additional file moreover the pseudo r-squared calculated for all adjusted models were higher than. predicted values were also calculated for p for the same time points as in p. broad-sense heritability of growth broad-sense heritabilities were estimated using trial p which corresponded to a clonal test with replicates of full-sibs. analyses were conducted using markov chain monte carlo methods implemented in the r mcmcglmm package. the following mixed effects model was used for each trait: y=µ+rowi+colj+gk+ϵ where y is the individual tree measurement, μ is the general mean, rowi is the fixed effect of the row, colj is the fixed effect of the column, g k is the random effect of the genotype ~no,σg and ϵ is the residual random effect ~no,σϵ the intersection between individual tree coordinates in the trial represented the spatial position of each tree. broad-sense heritability for the full-sib family was estimated for each trait using the following formula: h2=σg2/σg2+σϵ where σg is the genetic variance and σg2+σϵ is the phenotypic variance. molecular markers and linkage mapping for each parental genotype and each trial, a genetic map was constructed according to a two-way pseudo-test cross mapping strategy. for p the two genetic linkage maps were constructed using rapd ssr, est, and sts markers genotyped on individuals. for p only rapd markers selected on the basis of their map position in the p linkage maps were used for genetic mapping with individuals. the set of common polymorphic markers genotyped in both p and p enabled the unambiguous identification of homologous linkage groups between the two parental maps of the same species. in addition, the codominant markers used in p enabled the identification of orthologous regions between e. urophylla and e. grandis. joinmap® version was used to perform the linkage analysis. chi-squared tests were performed to test whether markers followed the expected mendelian segregation ratios. distorted markers were excluded from linkage analysis. markers with more than 40% of missing data were also excluded. for the four maps, markers were grouped into lgs at the independence logarithm-of-the-odds score ≥ . then, markers within linkage groups were ordered using the monte carlo maximum likelihood mapping algorithm. finally, mapping quality tools were used to classify markers leading to a poorer fit as accessory markers, located near the closest framework markers. accessory markers with significant deviation from expected mendelian segregation were indicated by * on the genetic maps. genetic distances in centimorgan were calculated with the kosambi mapping function. the lg nomenclature corresponds to that defined by brondani et al.. qtl analysis qtl mapping quantitative trait locus analyses were performed with r software using the qtl package. we carried out simple and composite interval mapping using the multiple imputation method of sen and churchill with a step interval of 1 cm, a genotyping error rate of and imputations per genotypes. it has been shown that this imputation method performs better with missing genotypic data. the whole-genome significance thresholds for all traits were determined with permutations. qtls that met or exceeded 95th and 90th percentiles were assessed to be significant or suggestive, respectively. confidence intervals for each qtl position were obtained using bayes credible intervals. genetic maps and qtl positions were drawn using mapchart. detection of qtl x environment interaction for each parent, we were able to test the qtl x environment interaction using markers common to both trials, and for growth traits at five different ages based on measurements for p and predicted values at the same ages for p gcp were also used for both trials. to test the qtl x e, an analysis of variance was carried out according to the following model: y=µ+trial+marker+trial×marker+ϵ where y is the individual tree measurement, μ is the general mean, trail is the fixed effect of the trial, marker is the fixed effect of the closest marker associated with a qtl detected by cim, trail × marker is the interaction between the two fixed effects and ϵ is the residual random effect ~no,σϵ  climatic conditions the de martonne index was calculated monthly during the growth period of p and p. idm mainly reflected seasonal changes in water availability because the mean temperature remained very stable across seasons with only 3°c of amplitude. the two curves exhibited different patterns at the beginning of the plantation, then evolved in parallel before separating again after 45 months. the timing and the intensity of the dry periods were different between the two trials. indeed, p exhibited longer dry periods than p, amounting to four supplementary months of drought over the study period. using the dry periods defined by idm, specific growth increments were determined for p only, because measurement points were lacking for p trend in phenotypic variation and correlation the mean trajectories for cumulative growth, height and circumference, were slightly different between the three trials. mean cir values were significantly smaller in p whereas final ht values at 60 months old were higher, probably due to a higher tree density in p these differences were reduced between p and p two trials planted at the same period and with the same tree density. the mean trajectory of growth increments, estimated from p, showed a global decrease over the 60 months after planting, with two periods of lower growth rates that occurred during the second and third dry periods. these two periods flanked a growth rate peak at 21 months that occurred during the second rainy season. the pattern of phenotypic variations for cumulative growth was very similar between trials. indeed the variance increased gradually over time and the coefficient of phenotypic variation for ht remained rather stable. the same tendency was observed for cir. the cvp of growth increments for p and p were more variable compared to cumulative growth, as exemplified by cvp values for ht_inc ranging from to for p and from to for p a similar range of values was observed for cir_inc. given the large number of measurements in p we were able to characterize the evolution of cvp over time for ht_inc and cir_inc. two growth rate peaks cvp were observed during the second and the third dry periods, corresponding to a lower growth increment on average. these results suggest that growth rate differences between genotypes were enhanced during these two dry periods. this hypothesis was supported by the analysis of pearson correlations between height or radial increments and idm calculated at both trial and tree levels using data from p. at trial level, positive correlations were found for both early and late growth, indicating a strong effect of rainfall on growth. for both levels, early growth was found to be more responsive than late growth, although fewer data were available at the later stage, which could have affected the estimation of correlation coefficients. the tree level reflected the phenotypic plasticity of each genotype in response to water availability. at tree level, correlations between idm and circumference increments were higher than those with height increments. these differences were particularly apparent during early growth with 95% of trees having a coefficient of correlation over, including 81% of trees with a significant correlation. this suggests that secondary growth was more prone to changes in water availability than primary growth, especially at the juvenile stage. dm pearson’s coefficients of correlation were calculated for early and late growth at trial and tree levels. the analysis of phenotypic correlations between cumulative growth revealed strong correlations over time in each trial. as expected, the age–age correlations for both cumulative growth traits were highly positive and stable over time, and comparable between the three trials. for ht and cir, the correlations between current age and final growth increased dramatically over the two first years to reach at least at two years old. high correlations were also found between asym and the final growth. more interestingly, pearson correlation coefficients for growth increments were variable over time. moreover, correlations for ht_inc and cir_inc displayed roughly opposite patterns during early growth. as illustrated for p in figure  correlations for ht_inc dropped from high and significant levels to non-significant levels revealing contrasting behaviour between genotypes in their response to the environment between the beginning of the second dry period and the 34th month. conversely, correlations for cir_inc became significant during the same period revealing a similar response between genotypes. trend in the genetic control of growth traits broad-sense heritabilities were estimated for cumulative growth traits, growth increment, and the gcp based on the data from p for all traits, h values were small to medium. although standard errors associated with h were high, we observed a regular increase in heritability with time for cumulative growth: ht, cir. the heritabilities for the asym parameter were only slightly higher than those obtained for final ht and cir, which is consistent with the strong correlation between these pairs of traits. h for growth increments were more heterogeneous than h for cumulative traits, even though the variation ranges were similar. given the standard error around h only differences between cumulative and incremental growth for ht were found to be significant between the two types of trait, while no significant differences for cir were observed. h for ht_inc and cir_inc had nearly an opposite pattern from to 35 months, then their patterns became more similar. the lowest heritabilities for ht and cir clearly corresponded to the coefficient of variation peak occurring during the third dry season and suggest a greater environmental effect at that period. linkage mapping the linkage analysis was performed for the p and p trials separately. table  summarizes the characteristics of each genetic map. for p co-dominant markers mapped by gion et al. enabled the identification of orthologous regions between e. urophylla and e. grandis parents. these regions covered a total of 989 cm for e. urophylla and 847 cm e. grandis, amounting respectively to 66% and 67% of the total map length. the macro-colinearity of common markers between parental maps was well conserved except for small inversions in lgs and. for p the two parental maps were constructed in this study, using a total of rapd markers for e. urophylla and rapds for e. grandis. a total of and framework markers were positioned in and linkage groups for e. urophylla and e. grandis parents respectively. the two maps provided a resolution of one marker every  cm and  cm for a total map length of  cm and  cm. e. urophylla and e. grandis in both the p and p trials e. urophylla e. grandis lg linkage group. among the framework markers, markers for the female map and markers for the male map were common between p and p maps. these “bridge markers” enabled the identification homologous regions for the e. urophylla parent covering 73% and 90% of total map length. for e. grandis, homologous regions were identified, covering of 79% and 89% of the total map length. as expected, the order between markers was well conserved between p and p97: 89% and 93% of the common markers presented the same order for the e. urophylla and the e. grandis maps, respectively. the four genetic maps with links between bridge markers revealing homologous and orthologous regions are represented in additional file genetic architecture of growth traits qtl detection in p93 a total of qtls were detected for the female parent and for the male parent at the genome-wide type i error rate of 10%. 71% of the qtls remained significant at the 5% genome-wide error rate. these qtls were associated with and different traits for e. urophylla and e. grandis respectively; representing and different regions distributed over different linkage groups for each parental map. for the e. urophylla parent, the variance explained by all the detected qtls associated with one trait ranged from % to % with an average of %. for the male parent, this proportion of variance ranged from % to % with an average of %. qtls for e. urophylla were located on lg lg lg lg and lg with two hotspots gathering 16% and 47% of the total number of qtls respectively. qtls for e. grandis were located on lg lg lg lg and lg with two hotspots gathering 22% and 33% of the total number of qtls, respectively. the distribution of qtls between the two parents was different, of the seven lgs with qtls only two were common to both parents. two specific qtls were found for the growth curve parameter on the e. urophylla map on lg. no qtl for gcp were found on the e. grandis map. qtl detection in p97 unlike p fewer qtls were detected for the female parent than for the male parent at the genome-wide type i error rate of 10%, while 74% of the qtls remained significant at 5%. these qtls associated with and different traits, represented and different regions distributed on and different lgs for e. urophylla and e. grandis, respectively. for e. urophylla, the variance explained by all the detected qtls associated with one trait ranged from % to % with an average of %. this proportion of variance ranged from % to 17% with an average of % for the male parent. qtls for e. urophylla were located on lg lg lg lg lg and lg with three hotspots gathering 12%, 34% and 16% of the total number of qtls, respectively. qtls for e. grandis were located on lg lg lg lg lg lg and lg with three hotspots gathering 6%, 6% and 60% of the total number of qtls, respectively. all lgs with qtls were common to both parents except for lg for which no qtl was detected in e. urophylla. one specific qtl region was found for the gcp located on the e. grandis map on lg. the other gcp qtls co-located with qtls for different traits. qtls for growth increment were located on more lgs than qtls for cumulative growth. the range of phenotypic variance explained by qtls was similar between cumulative growth and growth increment. for both parents more significant qtls were found for growth increments. these genomic regions were located on lg lg and lg for e. urophylla and on lg lg and lg for e. grandis. in addition to these specific qtls for growth increments, one qtl region for e. urophylla on lg was found to be associated with early cumulative growth only. more interestingly, all qtls for late cumulative growth for both parents co-localized with qtls for early growth increments, as illustrated for e. urophylla on lg at 47 cm and for e. grandis on lg at 0/10 cm and on lg at 22/42 cm. moreover, a co-localization with a qtl for the asym_c parameter was found for two of these qtls suggesting that the genetic architecture of growth response at the early stage affected the genetic architecture of cumulative growth at the adult stage. additionally, on lg a qtl for the correlation coefficient between growth increment and idm was found for e. grandis. this qtl co-located with the hotspot on lg for e. grandis. for this qtl region, genotypes with a higher growth were also the more responsive. qtl comparison across trials trials p and p were compared using the growth traits, gcps, as well as specific predicted values. proportionally to the number of traits, fewer qtl were detected for e. urophylla in p compared to p the proportion of qtls detected for late growth traits was higher than for early growth traits for e. grandis in both trials and was equivalent for e. urophylla in both trials. this may reflect the higher heritability of late growth traits compared with early growth as shown for the same family with p considering p and p qtls were detected on all lgs except on lg and lg however, for lg and lg qtls were detected in p only. qtls for gcp were found on three maps. they were mainly located in growth trait qtl-hotspots except for e. urophylla on lg and lg in p and lg in p qtls for predicted values were all detected at the same location as other qtls for growth. thus, qtls for predicted values described well the genetic architecture of growth for p allowing the comparison with p co-locating qtls between p and p were found on lg and for the e. grandis parent only, involving strong overlapping of confidence intervals. these two co-localizations involved hotspots of one of two trials but represented few of all the detected qtls. indeed a jaccard index was calculated between the two trials for e. grandis. this difference in the genetic architecture of growth traits between p and p suggested a strong qtl x environment interaction that was tested using the predicted values obtained for p based on growth curve modelling. thus, using closest markers already associated with qtls, a two way analysis of variance was conducted to test qtl x e interaction for growth traits at ages and 59 months for p and predicted values at the same ages for p gcp were also used for both trials. we found that most of tested markers revealed a significant interaction with the environment for both parents, e. urophylla 60% and 80%, e. grandis 40% and 90% for p and p respectively. for both trials, qtl x e was more significant for e. grandis than for e. urophylla. discussion incremental growth at the early stage is related to water availability and determines biomass production at rotation age we combined the measurement of growth on a sub-annual scale with a monthly characterisation of climate variation using an aridity index, and first showed that seasonal changes in water availability affected secondary and primary growth at the early stage of tree development. indeed, idm was found to be strongly correlated with radial growth increment before two years old, while it was less related to growth after two years. besides, the correlation at early stage was more significant for radial growth than for vertical growth, indicating that processes underlying secondary growth are more prone to environmental variation than those involved in primary growth. other studies have already reported a relationship between apical or radial incremental growth and rainfall on different time scales in different species. in this study, we showed that the first two years corresponded to the highest biomass productivity period, during which 60% of the final height and 65% of final circumference was reached, representing a biomass productivity of 20-27 m ha- year- therefore, the early growing period constitutes a key period with a strong impact on final growth, as illustrated by the high correlations values between each measurement point and the final growth at 60 months old. in tropical eucalypt plantations, it was found that the maximum growth rate occurred around two years, followed by a decline in production after canopy closure. therefore, our results suggest that climatic conditions underlying the aridity index have a strong impact on early growth response and consequently determine biomass production at rotation age. early growth response to water availability is genetically variable the small sample size used to calculate h limited the accuracy of the estimation. however, the comparison of time trends in h between cumulative and incremental growths highlighted contrasting patterns over time which was significant only for ht. indeed, cumulative growth displayed an asymptotic increase up to rotation age, contrary to incremental growth which showed high temporal heterogeneity. for eucalyptus grown in congo, h for cumulative growth calculated using a wider genetic background were found to range from to and to stabilize after two or three years. the same trend in h for cumulative growth was found in eucalyptus in other environments. interestingly, this stabilization of cumulative growth heritabilities occurred at the same time as the decline in wood biomass productivity, with a decrease in or stabilization of the g x e interaction. it could thus be suggested that the integrative nature of cumulative growth at a mature stage aggregates past genetic responses to environmental variations. the heterogeneity of h for incremental growth observed for both height and radial growth suggests a variation in the impact of environmental conditions on growth response. the slowest values of incremental growth heritability were observed during the third dry period. in pinus pinaster, such heterogeneous trends in h have been shown for yearly incremental growths and the variability described was significantly linked to environmental effects. on a lower scale, parisi also reported a heterogeneous pattern for narrow and broad-sense heritabilities for incremental height growth in pinus taeda. in addition to the contrast between cumulative and incremental growth, h patterns for growth increment revealed opposite patterns during the 25th and 35th months between primary and secondary growth responses. costa and durel also reported a clear difference between primary and secondary growth increments and suggested more stable genetic control for secondary growth response. between-tree variation in this early growth response, depicted by the distribution of phenotypic correlations between growth increments and idm during early growth, suggested a genetic effect as a major component in this response. other studies have already suggested a genetic effect in response to water availability. drew et al. observed such contrasting behaviour in response to climatic variations between different eucalyptus hybrids i.e. an e. grandis x e. urophylla susceptible to drought with intermittent growth, and a less susceptible e. grandis x e. camaldulensis maintaining a continuous growth. similar results were found between e. alba and e. urophylla x e. grandis in congo, associated with a significant genotype x environment interaction for traits related to height growth and carbon isotope discrimination. these genetic differences in environmental susceptibility were also suggested by bouvet et al. comparing different eucalyptus clones. interestingly, in the present study, we found a qtl for the correlation between idm and radial growth increment, suggesting that early growth response to water availability is indeed genetically controlled. the genetic architecture of final growth is driven by the early growth response to the environment given the high macro-synteny and colinearity between eucalyptus genomes, we were able to compare the position of the mapped qtls to that detected in other studies in different genotypes of the same species or different species. this comparison enabled us to identify two lgs where growth qtls were frequently detected. as already mentioned by thumma et al., and supported by our result, lg was found to contain qtls for height and radial growth in different eucalyptus species as well as qtls for foliar chemicals. to a lesser extent, lg which was associated with both incremental and cumulative growth in our study, was also associated with growth-qtls in three other studies, as well as qtls for rooting ability and qtls for resistance to biotic stresses. in addition to these two main lgs, and in agreement with the oligogenic model, i.e. few genes with large effects detected as qtls and many genes with small effects controlled quantitative traits, qtls were found to be distributed across the other nine chromosomes. in this study, a similarity index revealed that most of the growth qtls were not shared between two experimental trials showing different environmental trajectories. the statistical power of qtl detection and of estimated effects is directly related to sample size, so called beavis effect. therefore qtls with intermediate or small effects are likely to be not detected with a small sample size. thus one cannot rule out the fact that qtl instability between p and p is the result of a rather low sample size: and genotypes for p and p respectively. this lack of qtl stability could also reveal true biological effect, i.e. a genotypic sensitivity to environmental conditions, as supported by the significant qtl x e interaction found in both parents, and more particularly in e. grandis. interestingly, the two studied species display contrasting adaptability to congolese conditions with e. urophylla better adapted than e. grandis. the instability of growth-qtls between trials also contrasted with the qtl stability found for other traits measured on the same offspring. this difference in sensitivity to environmental variations is generally used to explain the greater pev and larger number of wood property qtls in comparison to growth related traits. it has been found that growth-qtls often presented a higher level of interaction with the environment than wood property-qtls. the temporal analysis of qtl detection showed the presence of early stage, intermediate and late qtls. among these three patterns of qtl expression, a large proportion of qtls associated with cumulative growth exhibited early or intermediate patterns: 50% and 75% for e. urophylla and 75% and 33% for e. grandis. these three qtl patterns were also reported by emebiri et al. on three-year-old pines. this instability over time is frequently reported in forest tree literature in relation to low heritabilities associated with growth. in e. globulus, a study also reported a lack of qtl stability over time for diameter at breast height between two and six years. in the same species, bundock et al. found partial qtl stability for stem diameter with the same location of lod peaks between the diameter at two and six years old. along the same lines, thumma et al. also reported relatively low stability for growth qtls over time in one family. in our study, partial stability was found on lg and lg. moreover, stable qtls after two or three years old were found on lg, lg and lg. qtl stability over the years has also been reported in gymnosperms but their measurements were limited to the young stage and did not therefore reflect the genetic architecture of the whole growth trajectory. to our knowledge, our study provides the most comprehensive view of the global instability of growth genetic architecture in a forest tree species thanks to a detailed analysis of the temporal and environmental dynamics of growth over the whole rotation period. indeed, the fine scale characterization of both growth and the environment enabled a precise qtl dissection from early to late growth. in the literature, growth increments are mostly calculated on a yearly basis. consequently, differences in genetic determinism between cumulative and incremental are less noticeable. in our study, the wider variety of growth responses captured by short incremental data was instrumental to characterizing the genetic architecture of growth and depicting its temporal plasticity. more remarkably, thanks to the fine characterization of growth, we found that all qtls detected at the mature stage for cumulative growth, co-localized with qtls for early growth increment on both parents. this result, which goes far beyond a simple age-age correlation analysis, suggests a partly common genetic determinism between early growth response to environmental variation and final growth. the qtl for the correlation with idm detected on lg in e. grandis, as well as the pattern of lod scores for qtls detected for mature growth on p, corroborate this assumption. to sum up, our study shows that the variability of growth plasticity observed at the young stage partly determined the pattern of cumulative growth genetic architecture at rotation age.  this study showed differences at phenotypic and genetic levels between cumulative and incremental growth, for both primary and secondary growth in a fast growing tree species. growth increments were found to be highly responsive to climatic variations over the two first years, contrary to cumulative growth. however, qtl analysis showed a common genetic basis between early growth increments and final growth. moreover, strong instability was found in growth-qtls between the two trials, which was also supported by the analysis of qtl x e. these results suggest that early growth responses to soil water availability partially shape the genetic determinism of late growth and thus growth trajectories. specific genomic regions were also found for growth increments and growth curve parameters, showing the merits of a combined approach with sequential and global growth traits to dissect its genetic determinism. our results highlight the importance of considering growth as a compound trait for a better understanding of its genetic bases, and suggest to combine selection on early and cumulative growth to improve the ability of trees to produce wood biomass in an optimal way. competing interests the authors have no competing interests to declare. authors’ contributions fs: dna extraction and genotyping. jmb, pv: field trial management. jb: growth modelling, linkage analysis, qtl mapping. jb, jmg, cp, jmb: manuscript preparation. jmg: funding and overall supervision. all authors read and approved the final manuscript. supplementary material additional file 1 growth trajectories of four individuals randomly selected from the full-sib progenies of each trial. the circumference growth trajectories were fitted by the monomolecular model. the mean growth curve for all individuals is represented with a blue line. click here for file additional file 2 mean trajectory for cumulative height and circumference for the three trials, p p and p the thick coloured bars along the x-axis represent dry periods for each trial. click here for file additional file 3 summary of phenotypic data for each trial, p p and p traits, number of values, minimum, maximum, mean, standard deviation and coefficient of phenotypic variation. click here for file additional file 4 evolution over time of the cvp for cumulative and incremental growth for p and p the thick grey bars along the x-axis represent dry periods. cumulative growth is in dashed lines and incremental growth is in solid lines. height is in blue with circles, circumference is in orange with triangles. click here for file additional file 5 matrix of pearson correlation coefficients. for all traits: cumulative growth, growth increment, growth curve parameters and predicted values for p, p and p. only significant correlation values are displayed. click here for file additional file 6 phenotypic correlations between final growth and current growth for the three trials. cumulative growth is in dashed lines and incremental growth is in solid lines. height is in blue with circles, circumference is in orange with triangles. vertical grey bars indicate the dry periods. click here for file additional file 7 broad sense heritabilities with confidence interval for growth related traits. click here for file additional file 8 genetic maps of e. urophylla and e. grandis for p and p the lg nomenclature corresponds to the one defined by brondani et al.. distances between markers are indicated in centimorgans by a scale on the left side. common markers between parental maps for p and p are in bold. orthologous regions between the p and p maps are shown in red or orange hatching. common markers between the two parents of p are in bold and grey, orthologous regions are represented by a grey bar segment. accessory markers are positioned near the closest framework marker with the distance in brackets. qtls are represented by boxes extended by lines representing 95% bayes credible intervals. if multiple qtls of the same trait type for different ages co-localize, only one qtl is represented with the largest interval and indicates if one or more qtls were significant at 5% whole-genome level. accessory markers with an were distorted. traits have been explained in the text. click here for file additional file 9 qtls detected in p by composite interval mapping in e. urophylla and e. grandis. the trait, the number of genotype used for analysis, the linkage group, the position, the lod value, the percentage of variance explained by the qtl and the difference between the two qtl allele effects are indicated. click here for file additional file 10 qtls detected in p by composite interval mapping in e. urophylla and e. grandis. the trait, the number of genotype used for analysis, the linkage group, the position, the lod value, the percentage of variance explained by the qtl and the difference between the two qtl allele effects are indicated. click here for file additional file 11 analysis of variance for markers associated with a qtl in p or p. similar measurement ages or predicted values were used to analyse the two trials. * p < , ** p < , *** p < . click here for file additional file 12 evolution of lod scores at hotspot locations on e. urophylla and e. grandis for p height is in blue with a circle, circumference is in orange with a triangle. the purple zone contains qtls which are significant at the 10% genome-wide level, above are the qtls significant at the 5% genome wide level. vertical grey bars indicate the dry periods. click here for file acknowledgements the authors would like to thank the technicians at crdpi for trial establishment and follow-up. the authors acknowledge two anonymous reviewers for their constructive comments and suggestions on the manuscript. this study was supported by grants from feder. jb received a phd fellowship from the bios department of cirad.
the correlation between growth increments and an aridity index revealed that growth before two years old was more responsive to changes in water availability than late growth for both height and circumference. the genetic basis of growth traits has been widely studied in forest trees. quantitative trait locus studies have highlighted the presence of both stable and unstable genomic regions accounting for biomass production with respect to tree age and genetic background, but results remain scarce regarding the interplay between qtls and the environment. these results suggest that early growth responses to water availability determine the genetic architecture of total growth at the mature stage and highlight the importance of considering growth as a composite trait for a better understanding of its genetic bases. within the trials, qtl analysis revealed collocations between primary and secondary growth qtls as well as between early growth increments and final growth qtls. heritabilities for incremental growth were more heterogeneous over time even if ranges of variation were similar. in this study, our main objective was to dissect the genetic architecture of the growth trajectory with emphasis on genotype x environment interaction by measuring primary and secondary growth covering intervals connected with environmental variations. we found a regular increase in heritability with time for cumulative growth for both height and circumference. between trials, few common qtls were detected highlighting a strong environmental effect on the genetic architecture of growth, validated by significant qtl x e interactions. three different trials with the same family of eucalyptus urophylla x e. grandis hybrids were planted in the republic of congo, corresponding to two qtl mapping experiments and one clonal test.
 the genetic basis of growth traits has been widely studied in forest trees. quantitative trait locus studies have highlighted the presence of both stable and unstable genomic regions accounting for biomass production with respect to tree age and genetic background, but results remain scarce regarding the interplay between qtls and the environment. in this study, our main objective was to dissect the genetic architecture of the growth trajectory with emphasis on genotype x environment interaction by measuring primary and secondary growth covering intervals connected with environmental variations.  three different trials with the same family of eucalyptus urophylla x e. grandis hybrids were planted in the republic of congo, corresponding to two qtl mapping experiments and one clonal test. height and radial growths were monitored at regular intervals from the seedling stage to five years old. the correlation between growth increments and an aridity index revealed that growth before two years old was more responsive to changes in water availability than late growth for both height and circumference. we found a regular increase in heritability with time for cumulative growth for both height and circumference. heritabilities for incremental growth were more heterogeneous over time even if ranges of variation were similar. within the trials, qtl analysis revealed collocations between primary and secondary growth qtls as well as between early growth increments and final growth qtls. between trials, few common qtls were detected highlighting a strong environmental effect on the genetic architecture of growth, validated by significant qtl x e interactions.  these results suggest that early growth responses to water availability determine the genetic architecture of total growth at the mature stage and highlight the importance of considering growth as a composite trait for a better understanding of its genetic bases. growthgrowth modellingplasticityqtl x e interactionheritabilityeucalyptus 