Analysis of distribution of root length density of apple trees on different dwarfing rootstocks

This paper considers statistical analyses for comparing the distribution of root length density (RLD) of apple trees under different rootstocks and tr ee spacing. The source data included RLD values (cm cm(-3)) measured by soi l coring the root systems of eight trees in each of two seasons. We formula ted a regression model which assumed the RLD dropped exponentially with soi l depth, and this relationship varied with the radial distance from the tre e. The model fitted to the log transformed mean data described the RLD dist ribution well. Young trees (5-year-old) of M.26 (semidwarf) and MM.106 (sem i-vigourous) had a higher mean RLD and showed a more layered vertical distr ibution, compared with trees of the dwarf Mark rootstock. Differences among rootstocks were not evident in older (9-year-old) trees. In general, young root systems were more bowl shaped, whereas older trees had a higher RLD f urther away from the tree trunk. RLD is a positive and continuous variable except for the possibility of an excess of exact zeros. A generalized linea r model with a Poisson-gamma type distribution allows modelling of individu al RLD data with zeros contributing to parameter estimation. It does not, h owever, provide simplicity of biological interpretation. In this paper we p resent a model that assumes the realization of RLD data is due to a Bernoul li and an exponential process. The fitting of the Bernoulli-exponential mod el by maximum likelihood is illustrated, and further generalization suggest ed. (C) 1999 Annals of Botany Company.