Nonlinear versus linearised model on stand density model fitting and stand density index calculation: analysis of coefficients estimation via simulation

The stand density index,one of the most important metrics for managing site occupancy,is generally calculated from empirical data by means of a coefficient derived from the“self-thinning rule”or stand density model.I undertook an exploratory analysis of model fitting based on simulated data.I discuss the use of the logarithmic transformation(i.e.,linearisation)of the relationship between the total number of trees per hectare(N)and the quadratic mean diameter of the stand(QMD).I compare the classic method used by Reineke(J Agric Res 46:627–638,1933),i.e.,linear OLS model fitting after logarithmic transformation of data,with the“pure”powerlaw model,which represents the native mathematical structure of this relationship.I evaluated the results according to the correlation between N and QMD.Linear OLS and nonlinear fitting agreed in the estimation of coefficients only for highly correlated(between-1 and-0.85)or poorly correlated([-0.39)datasets.At average correlation values(i.e.,between-0.75 and-0.4),it is probable that for practical applications,the differences were relevant,especially concerning the key coefficient for Reineke’s stand density index calculation.This introduced a non-negligible bias in SDI calculation.The linearised log–log model always estimated a lower slope term than did the exponent of the nonlinear function except at the extremes of the correlation range.While the logarithmic transformation is mathematically correct and always equivalent to a nonlinear model in case of prediction of the dependent variable,the difference detected in my studies between the two methods(i.e.,coefficient estimation)was directly related to the correlation between N and QMD in each simulated/disturbed dataset.In general,given the power law as the“natural”structure of the N versus QMD relationship,the nonlinear model is preferred,with a logarithmic transformation used only in the case of violation of parametric assumptions(e.g.data distributed non-normally).

Douglas-fir climate sensitivity at two contrasting sites along the southern limit of the European planting range

Douglas-fir(Pseudotsuga menziesii(Mirb.)Franco)is an important exotic tree species that was planted across a large part of Europe during the last century.In both experimental trials and conventional forest plantations,the trees grow at a high rate and produce high-quality timber.The present study investigated climate-growth relationships of Douglas-fi r at two Italian sites that contrast in climate:a Mediterranean area in southern Italy(Mercurella site)and a cooler,moister site in the northern Apennines without summer aridity(Acquerino).The relationship between tree-ring chronologies and monthly climatic variables was evaluated by a moving average and correlation analysis.Results showed that the minimum temperature in February and in March play a key role for Douglas-fi r at both sites,with a positive eff ect on growth.At the northern site,it is also highly sensitive to late summer temperatures(negative correlation)and spring–summer precipitation(positive correlation).Growth rates in southern latitudes were high even in Europe and in the Mediterranean environment,with low sensitivity to climatic fl uctuation.On the basis of our results,further common garden experiments should test adaptation and the interaction between genetics and environment of second-or third-generation seeds from old stands across Europe such as done by the old International Union of Forest Research Organizations(IUFRO)or the European Douglasfi r Improvement Research Cooperative(EUDIREC)experimentation programmes.