Aanpassing van groei- en aanwasformules van BACKMAN bij ontbreken van gegevens uit de eerste levensjaren
Authors: Goossens R. 
Published: July 2016

The  adjustment of the growth and increment formulas from BACKMAN in the case of  missing data for the first years of growth - In the  present paper, that starts with a critical evaluation of the method of  Thomasius, The parameters from the growth-formula of Backman (a, b) are  determined to work out the equalities (g), (h) and (i), by using the  incrementformula (c). When the parameters k0, k1 and k2 are known, they are  substituted in the equalities (d), (e) and (f), from which the parameters for  the growthformula can be recovered.     This method was tested on data for height (Yh) and diameter (Yd) of Populus euramericana cv Marilandica (2nd quality) from the  yieId tabIes of Wiedemann- Schöber. (Tab. I).     The results are summarized in table 3. In tables 2 and 4 the comparison is  made between the calculated results and the data for increment and growth  from the yield tables ofWiedemann-Schober.    It thus appears that a very good similarity exists between the given data  and the results obtained by use of the increment-formula. This is not the  case for the growth formula on account of inadmissible systematic errors.  These errors result from the indirect determination of the growth formula,  that, in fact, may not be used when data for the first years are unavailable.      To avoid these errors a 'grafic method' is developed by the author. This  method requires less arithmetic work to to test the asymptotic values. In  principle this method is based on the fact that in representing growth  progress in an axes system (absis t for time and ordinate y/J), all  coordinated points (t; y/J) will be situated on a straigh line, when the axes  are graduated respectively in a logaritmic and probability scale. This means,  practically, that the value of J has to be estimated till nearly all the  points are on a straight line. By adapting a line through these points, using  the terms (m) and (p), it becomes possible to determine c1 and c2, while (q)  gives the value for c0. On the other hand, when the parameters of the growth  formula are known, the parameters of the increment formula can be determined  by calculating (r), (s) and (v).     A comparison between data thus obtained and the data from table 1 is made  in table 6. By a similar procedure as was used for the evaluation by the  method of Thomasius, the author was able to clearly prove that a good  similarity exists between given and calculated data on growth and increment  for height and diameter of Populus euramericana cv Marilandica (Tab. 5 and 7).     In conclusion, a comparison is made between both methods (Thomasius/graphic  method) (tabIe 8) by determining for diameter and height, the average  deviation between the calculated and given values for increment (∆y') and  growth (∆y).     A t-test for P = 0,01 proves that no essential difference exists between  the precision of the increment formula, calculated according to either  method. This can not be said for the growth formula as the average errors,  for height and diameter are near zero, while these errors are respectively  4,6 m and 7,9 cm for the method of Thomasius.