Describing size-related mortality and size distribution by nonparametric estimation and model selection using the Akaike Bayesian Information Criterion

When we calculate mortality along a gradient such as size, dividing into size classes and calculating rates for every class often involves a trade-off: fine class intervals produce fluctuating rates along the gradient, whereas broad ones may miss some trends within an interval. The same trade-off occurs when we want to illustrate size distribution by a histogram. This paper introduces nonparametric methods, published in a statistical journal, into forest ecology, in which the fine-class strategy is used in an extreme way: (1) a smoothly changing pattern is approximated by a fine step function, (2) the goodness-of-fit to the data and the smoothness along the gradient are formulated as a weighting sum within a Bayesian framework, (3) the Akaike Bayesian Information Criterion (ABIC) selects the weighting system that most appropriately balances the two demands, and (4) the values of the step function are optimized by the maximum likelihood method. The nonparametric estimates enable us to represent various patterns visually and, unlike parametric modeling, calculations do not demand the determination of a functional form. Mortality and size distribution analyses were conducted on 12-year forest tree monitoring data from a 4 ha permanent plot in an old-growth warm–temperate evergreen broad-leaved forest in Japan. From trees of 11 evergreen species with a diameter at breast height (DBH) greater than 5 cm, we found three types of trend with increasing DBH: decreasing, ladle-shaped and constant mortality. These patterns reflect variations in life history particular to each species.