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

Abstract

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 fineclass 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 warmtemperate 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.

Modelling irregular and multimodal tree diameter distributions by finite mixture models: an approach to stand structure characterisation

“…For this reason, DBH distribution models are used in ecology to simulate stand development (e.g. Pretzsch 1997Pretzsch , 2001Rubin et al 2006;Inoue et al 2008;Shimatani et al 2008). Moreover, DBH distribution models have become a useful tool in forest management and conservation (e.g.…”

Matrix models using fine size classes and their application to the population dynamics of tree species: Bayesian non‐parametric estimation

“…2007), and our models seemed to be valid for populations that (potentially) have U‐shaped mortality patterns. Previous studies (Shimatani et al . 2007) have shown a constant mortality pattern for Ca.…”

“…In general, size‐related mortality patterns can be divided into three classes: decreasing, constant and U‐shaped (Coomes et al . 2003; Shimatani et al . 2007), and our models seemed to be valid for populations that (potentially) have U‐shaped mortality patterns.…”

Diversity of patch structure in Central European forests: are tree diameter distributions in near‐natural multilayered Abies–Fagus stands heterogeneous?

“…The nonparametric functions are very flexible, and therefore the nonparametric methods can reveal various complex patterns (e.g., local extreme, stepped decreases/increases, changes in slopes and/or curvatures within a curve) (Shimatani et al 2008). These variations may not be fitted using a single function of the parametric modeling or the two-component mixture models.…”