Modeling ingrowth for empirical forest prediction systems

Abstract Accurate and representative prediction of ingrowth is essential for modeling forest development. Besides the number of ingrowth trees, the basic tree attributes diameter and species are also important. In this study, these three characteristics were modeled based on data from the Swiss National Forest Inventory (NFI). The study covered large gradients of stand conditions and climate variables, making the models suitable to predict ingrowth under climate change. As the number of ingrowth trees per plot included more zeros than is expected for a Poisson distribution, we used three alternative probability distributions: zero-inflated Poisson distribution (ZIP), negative binomial distribution (NB) and zero-inflated negative binomial distribution (ZINB). Models with each of the three variants were fitted with and without random effects, resulting in six different model types. Model selection was performed backward using the BIC criterion. Of the final models, ZIP showed the best predictions of independently observed number of ingrowth trees. Our results indicate that the number of ingrowth trees strongly depended on the development stage of forests and on stand basal area, while temperature and precipitation, nitrogen deposition and water holding capacity each had a lower but still significant and plausible effect. The Weibull function was used to describe the probability distribution of the diameter of ingrowth trees and parameters were estimated using the Likelihood approach. The diameter of ingrowth trees was larger where there was a better site index and decreased with increasing stand density. Further, twelve species groups of ingrowth trees were fitted with a multinomial regression approach and showed clear dependence on climate: the probability of spruce and larch ingrowth clearly decreased with increasing temperature, whilst all other tree species profited from warmer conditions. The probability of fir, beech and ash ingrowth increased with increasing basal area, demonstrating the relevance of shade tolerance. The most important variable for predicting the species of ingrowth was the leading tree species group in a plot.