Sap flow as a function of variables within nested scales: ordinary least squares vs. spatial regression models

Abstract

Understanding scale-dependent influential drivers of sap flow variability can help managers and policymakers to allocate resources within a particular scale to improve forest health and resiliency against water-stress stimuli such as drought and insects, e.g. bark beetle infestations. We defined a daily measure of sap flow as a function of variables within nested scales of landscape, stand, and tree, using ordinary least squares (OLS), spatial lag and error regression models. Model covariates were elevation, latitude (Y-coordinate), longitude (X-coordinate), neighborhood tree density, tree diameter at breast height, and bark temperature for 40-surveyed Norway spruce ( Picea abies ) in the Czech Republic, Central Europe. Trees were spatially distributed within 19-established subplots across five plots, with distances ranging 2–9 km, at which variations in soil water potential and temperature were limited. The daily measure of sap flow within the regional scale allowed us to avoid the temporal and spatial variability of climate effects on sap flow. A relatively flat terrain across subplots also allowed us to control the effects of slope, aspect, and topography-related solar incidence angle on sap flow. Sap flow was strongly spatially autocorrelated, so OLS models failed to take spatial autocorrelation into account unless to some extent, depending on the spatial distribution of samples, by including latitude and/or longitude in the models. Among spatial regression models, spatial error models performed better than lag models, allowing to capture the effects of unmeasured independent variables. Sap flow variability for the most part (∼70%) was explained by the landscape-level variable of elevation followed by the stand-level variable of tree density, and the remaining part by variables related to tree characteristics; a nested down-scaling function, defined and visualized for the first time. Therefore, thinning forest stands and future plantations with optimum distances, based on the elevation gradients, may be required to counterbalance the allocation of resources, e.g. water, nutrients, and light, among trees, leading to enhance forest health and resiliency against water-stress stimuli.

Keywords

• ecological modeling
• parametric models
• spatial autocorrelation
• forest ecology and management
• tree physiology
• tree density