Fitting the Truncated Bivariate Normal Distribution to the Relationship between Diameter and Length of Current-Year Shoots in Betula Platyphylla in Hokkaido, Northern Japan

We fitted a truncated bivariate normal distribution to the relationship between diameter and length of current-year shoots in Betula platyphylla saplings, and examined the effects of light intensity at the branch tip and branch height on the relationship. We measured shoot length, diameter at the shoot base, light intensity at the branch tip, and branch height for all shoots on 49 sampled saplings. The relationship between shoot diameter and shoot length was almost linear with a positive intercept. The truncated bivariate normal distribution could describe the relationship of shoot diameter and shoot length none of which was an independent variable. The result of model fitting revealed that, given a shoot length, shoot diameter was larger for shoots that were located in higher positions in crowns and captured more light.