Citation: Viet, H.D.X.; Tymi ´ nska-Czaba ´ nska, L.; Socha, J. Modeling the Effect of Stand Characteristics on Oak Volume Increment in Poland Using Generalized Additive Models. Forests 2023, 14, 123. https://doi.org/ 10.3390/f14010123 Academic Editors: Huaqiang Du, Dengsheng Lu, Huaguo Huang, Mingshi Li and Yanjun Su Received: 15 December 2022 Revised: 3 January 2023 Accepted: 6 January 2023 Published: 10 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Article Modeling the Effect of Stand Characteristics on Oak Volume Increment in Poland Using Generalized Additive Models Hoang Duong Xo Viet 1,2, * , Luiza Tymi´ nska-Czaba ´ nska 1 and Jaroslaw Socha 1 1 Faculty of Forestry, University of Agriculture in Krakow, Al. 29 Listopada 46, 31-425 Krakow, Poland 2 Faculty of Forestry, University of Agriculture and Forestry, Hue University, Hue 530000, Vietnam * Correspondence: hdxviet@hueuni.edu.vn Abstract: Volume increment is one of the main concerns in forestry practice. The aim of our study was to examine the impact of factors influencing the periodic annual increment of oak. To meet our objective, we used measurement data from the national forest inventory in Poland from 2005 to 2019 for oak-dominated stands. Our study used data of 1464 sample plots with dominant oak species (Quercus sessilis Ehrh. ex Schur and Quercus robur L.) measured within the national forest inventory in Poland. We developed models explaining the dependence of the periodic annual volume increment on stand characteristics using the generalized additive model. The generalized additive model allows us to analyze each variable’s effect on the dependent variable, with all other variables fixed. We documented the effect of age, height, basal area, and relative spacing index (RSI) on the periodic annual volume increment (PAIv) of oaks in Poland. The PAIv of oaks decreased gradually as the tree aged. The dependence of the PAIv on stand density was shown through its relationship with the basal area and RSI. The developed model explained about 64.6% of the periodic annual volume increment variance. Keywords: periodic annual volume increment; GAM; stand density; basal area; RSI 1. Introduction The volume increment of stands is one of the most important indicators of forest dynamics. Knowledge of volume increment allows for forecasting and developing appro- priate forest management plans [1,2]. It is also vital in the context of determining biomass production and the potential for CO 2 sequestration by forest ecosystems [3–6]. Identifying how individual stand factors influence volume increment can be useful in forestry practice and is of growing importance in sustainable forest management. Essentially, increment describes the rate at which the tree or stand increases in weight or size over a given period of time [7]. The measurements on sample plots in national forest inventories (NFIs) can provide accurate and comprehensive information on the various components of the annual increment [8]. Instead of annual measurements, periodic surveys at n-year intervals are carried out; then, the recorded increment in height, diameter, and volume must be divided by n and is called the periodic annual increment [9]. The periodic annual increment is a more realistic indicator of a tree’s capacity (or a stand’s) to grow to a given age or size. The volume increment can be influenced by environmental factors and tree characteristics [7,10]. Toledo et al. [11] demonstrated that competition from neighboring trees is an essential biological factor limiting volume growth. Some studies have shown that stand volume increases with narrower plantation spacing. However, when a certain threshold is reached, the narrow plantation spacing can decrease the volume growth rate [12]. A study on Oriental beech (Fagus orientalis Lipsky) in Iran showed that stand volume at the beginning of the measurement period and tree diameter had the greatest impact on the variation in volume increment [13]. The influence of these on forest growth, productivity, and biodiversity can be important for sustainable forest management [14,15]. Forests 2023, 14, 123. https://doi.org/10.3390/f14010123 https://www.mdpi.com/journal/forests