Juha Lappi, Timo Pukkala. (2020). Analyzing ingrowth using zero-inflated negative binomial models. Silva Fennica vol. 54 no. 4 article id 10370. https://doi.org/10.14214/sf.10370

Keywords: regeneration; continuous cover forestry; count data; generalized linear model; overdispersion; right-censoring

Highlights: Models were developed to describe ingrowth in national forest inventory data; The data were more dispersed than Poisson data and included many zeros; Fixed-effects models had larger zero-inflation probability and overdispersion parameter than mixed-effect models; Mixed-effects models had larger likelihood than fixed-effects models but provided biased predictions; Prediction of right-censored ingrowth may be useful owing to large overdispersion.

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Ingrowth 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 fixed-effects 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 sub-xeric 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 m² 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.

Lappi, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: juha.lappi.sjk@gmail.com
Pukkala, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland E-mail: timo.pukkala@uef.fi

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