The relative weight of ontogeny, topology and climate in the architectural development of three North American conifers

Abstract Knowledge of plant architecture allows retrospective study of plant development, hence provides powerful tools, through modelling and simulation, to link this development with environmental constraints, and then predict its response to global change. The present study aims to determine some of the main endogenous and exogenous variables driving the architectural development of three North American conifers. We measured architectural traits retrospectively on the trunk, branches and twigs of whole tree crowns for each species: annual shoot length (ASL), needle length, branching patterns and reproduction organs (male and female). We fitted a partial least square (PLS) regression to explain each architectural trait with respect to topological, ontogenic and climatic variables. Results showed a significant weight of these three groups of variables for previous and current year, corresponding, respectively, to organogenesis and elongation. Topological and ontogenic variables had the greatest weight in models. Particularly, all architectural traits were strongly correlated with ASL. We highlighted a negative architectural response of two species to higher than average temperatures, whereas the third one took advantage of these higher temperatures to some degree. Tree architectural development weekly but significantly improved with higher precipitation. Our study underlines the strong weight of topology and ontogeny in tree growth patterns at twig and branch scales. The correlation between ASL and other tree architectural traits should be integrated into architectural development models. Climate variables are secondary in importance at the twig scale. However, interannual climate variations influence all axis categories and branching orders and therefore significantly impact crown development as a whole. This latter impact may increase with climate change, especially as climate affects architectural traits over at least 2 years, through organogenesis and elongation.


Appendix 1 -Method to compute the branch relative vigour index
For each species and for each branching order, log(ASL) was linearly correlated with branch Age (Fig. 5). Table a1 displays the parameters of linear models. Then we computed for each AS an index for its length, considering its position in a normal distribution with the mean dependant on the age and given by the linear regression, and the standard deviation (SD) corresponding to the standard deviation of the residuals of the linear model. For example, the indices of annual shoots which length are equal to the mean minus 2*SD, the mean and the mean plus 2*SD are respectively 0.05, 0.5 and 0.95. The vigour index of an axis is computed as the average of the indices of all its ASs. Thus the most vigorous the axis relatively to its branching order, the highest its mean index.
Tab a1 Parameters of linear models for log(ASL) vs Age fitted by species and branching order. Sd resid Column reports the standard deviation of the residuals. The p-value (P) for intercept (Int) and Age coefficient (coef) was always below 1*10 -3 . We used 1999-2013 daily data (minimum temperature, mean temperature, maximal temperature and total rainfall) from L'Etape weather station for Parc des grands jardins and 1999-2013 daily data (same variables) from Chénéville weather station for Réserve Papineau. Environmental variables should have an impact on architecture, our hypothesis is that the environmental conditions occurring during organogenesis and elongation will shape the architecture. For studied species organogenesis occurs the year before the elongation. Thus, we calculated for each year between 2000 and 2013 the following variables (appear in bold the variable aliases):  TNn: absolute minimum temperature in °C  TN: minimum temperature (mean of minimum temperatures) in °C  TM: mean temperature (mean of mean temperatures) in °C  TX: maximum temperature (mean of maximum temperatures) in °C  TXx: absolute maximum temperature in °C  R: total rainfall in mm  DD: degree-day in °C These variables were computed for three time spans: seasonally(Wint for January to march, Sprg for April to June, Sumr for July to September and Aut for October to December), monthly (01 for January, 02 for February, etc.) and a bimonthly (01a for the first half of January, 01b for the second half of January, 02a for the first half of February, etc.), the current year of elongation (year n = Curr) and the previous year (year n-1 = Prev). Variable aliases are then composed of three parts: climatic parameter first, then after a dot the period of the year and finally the year. TM.06.Curr stands for the mean temperature in June of the year n and R.Sprg.Prev stands for the total rainfall between April and June of year n-1. We also calculated DD.x as the degree-day with the basis ( ∈ [0, 20]) in °C, for the actual and the previous year. Then DD.10.Curr stands for the degree-day with basis 10°C for the year n, whereas DD.01.Prev stands for the degree-day with basis 1°C for the year n-1.

Appendix 3 -PLS analysis protocol
The PLS algorithm operated as follow:  For each architectural variable we performed six analyses: for all analyses we used as predictors the topological variables, autocorrelation (value of the previous annual shoot), and annual shoot length (except for ASL itself), then we added in turn seasonal climatic variables (with or without degree-day), monthly climatic variables (with or without degree-day) and bimonthly climatic variables (with or without degree-day).  We started each analysis by a PLS regression with all variables, with 6 axis.
We performed a linear PLS regression for log(ASL) log(NL) and Lg♂ (the last one only for twigs with male cones), and a logistic regression for P♂ (binomial), N ram, N cone, Polyc, int ram, and whorl ram. Each analysis then iterates the following steps: o For each axis, if all variables are significant, the model is accepted, o For each axis, if some variables are non-significant, they are removed and PLS regression is performed again  At the end, the model with the highest Q² is selected.

Appendix 4 -Parameters for all PLS models
Tables a4-BS, -EWP and -JP give the significant variables of PLS models for black spruce, Jack pine and Eastern white pine respectively. ASL, NL and Lg male models correspond to linear PLS regression, whereas N male, int ram, whorl ram, N ram, N cone and Polyc correspond to logistic PLS regression. For logistic regression, each table first displays the classes used (lower│upper limit). Ontogenic (Ont, in white lines), topological (Topo, light grey italic) and climate (clim, darker grey bold) variables are sorted together by decreasing VIP absolute value, thus by relative weight in the model. Local variables (loc, in white lines) are sorted separately below the previous ones, by decreasing VIP as well.
The relative role of top and low crown branches (or middle and low branches for Eastern white pine) was analysed separately for relevant PLS models, those with at least 6 branches showing a significant weight in the model: number of male cones, inter-whorl branching and number of cone by AS for black spruce, probability of male cones, number of cones per AS and polycyclism for Eastern white pine, annual shoot length for Jack pine. The corresponding table is added on the right of the main VIP table, along with the result of the comparison, displaying the method (variance analysis or Wilcoxon test) and the probability of the difference. Branches are sorted by signed VIP (the sign of variable coefficient was added to its VIP) highlighting the relative role of branch position in the crown in these models (top = blue lines in bold, low = orange lines).