Uproszczony model rozkładu pierśnic jednowiekowych niepielęgnowanych drzewostanów sosnowych (Pinus sylvestris L.)

Although modelling of the diameter at the breast height (DBH) distributions has long history, theoretical discrete distributions have not so far been used for this purpose. In this study we use measurements covering 25 years (six inventories) without silvicultural influence on 14 even−aged Scots pine (Pinus sylvestris L.) stands to develop the DBH distribution models. Analysed stands are located in Murowana Goślina Forest Experimental Station (W Poland). The objective of the study was to elaborate the most simplified model that applies stand variables easy to assess and uncomplicated theoretical distribution. We employed two−parameter Gamma Poisson (GP) distribution and compared it to Weibull (W) and Sb Johnson (SbJ) ones. When maximum likelihood estimation (MLE) was used, GP gave similar results to W and both were slightly worse than SbJ. We found that both DBH standard deviation and stand density have substantial impact for model bias when above distributions used. Stepwise regression analysis was used for obtaining linear equations for parameter prediction of GP distribution. Then, GP model was simplified by removing standard deviation of DBH (SDD) from equation for overdispersion parameter. Results showed slight increase in mean of error values (i.e. modified Reynolds e index and root mean square error) for simplified model (SGP) compared with those for model including SDD, but differences in means were insignificant. Minimal and mean DBH represent enough variability of diameter distribution to obtain appropriate model based on Gamma Poisson distribution. Error was only 5% greater from four−parameter SbJ (MLE) distribution with similar range: 8.2−28.8% against 5.1−25.5% for SGP and SbJ respectively. The presented model can be used in many branches of forestry for more accurate calculation of stand level variables, when additional allometric equations employed, for instance assimilation apparatus volume or below− and aboveground biomass.