Analyzing ingrowth using zero-inflated negative binomial models

yIngrowth is an important element of stand dynamics in several silvicultural systems, especially in continuous cover forestry. Earlier predictive models for ingrowth in Finnish forests are few and not based on up-to-date statistical methods. Ingrowth is here defined as the number of trees over 1.3 m entering a plot. This study developed new ingrowth models for Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies (L.) H. Karst.) and birch (Betula pendula Roth and B. pubescens Ehrh.) using data from the permanent sample plots of the Finnish national forest inventory. The data were over-dispersed compared to a Poisson process and had many zeros. Therefore, a zero-inflated negative binomial model was used. The total and species-specific stand basal areas, temperature sum and fertility class were used as predictors in the ingrowth models. Both fixedeffects and mixed-effects models were fitted. The mixed-effects model versions included random plot effects. The mixed-effects models had larger likelihoods but provided biased predictions. Also censored prediction was considered where only a certain maximum number of ingrowth trees were accepted for a plot. The models predicted most pine ingrowth in pine-dominated stands on subxeric and xeric sites where stand basal area was low. The predicted amount of spruce ingrowth was maximized when the basal area of spruce was 13 m(2) ha(-1). Increasing temperature sum increased spruce ingrowth. Predicted birch ingrowth decreased with increasing stand basal area and towards low fertility classes. An admixture of pine increased the predicted amount of spruce ingrowth.