No. 1007

Title:

Matrix models using very fine size classes and their applications to population dynamics of tree species: Bayesian nonparametric estimation

Author(s):

ICHIRO K. Shimatani (The Institute of Statistical Mathematics), KUBOTA Yasuhiro (Kagoshima University), ARAKI Kiwako (Hokkaido University), AIKAWA Shin-ichi (Forestry and Forest Products Research Institute) and MANABE Tohru (Kitakyushu Museum and Institute of Natural History)

Key words:

ABIC, forest monitoring, mortality, smoothing, subcanopy

Abstract:

Matrix models have been widely used for investigating population dynamics of plant species. Under this method, we first divide individuals into groups and estimate transition probabilities per pair of groups. When a continuous variable such as plant size is used for grouping, we often suffer from a tradeoff; each group includes a small number of samples if class intervals are fine, while we may miss some changes within intervals if wide. This paper introduced a new matrix model in which we no longer have to divide individuals into arbitrarily determined size classes. The methodology is based on the Bayesian nonparametric binary regression. We first divide sizes into “very fine” intervals. For estimating transition probabilities in the model, we do not directly use observed transition rates, but we smooth neighboring observed rates and select the most adequate degree of smoothing by an information criterion called Akaike Bayesian Information Criterion (ABIC). Our approach was demonstrated to long-term forest monitoring data in an old-growth, warm-temperate evergreen forest, and we examined population dynamics of four subcanopy tree species. Smoothly changing transition probabilities in a large matrix visualized DBH-related growth and mortality patterns, and matrix analysis provided smoothly changing stable size distribution, reproductive values and elasticity along DBH. Our results contributed to clarifying characteristic life strategies of the subcanopy species and their interspecific variations.