Effectively tuning plant growth models with different spatial complexity: A statistical perspective

Abstract

Forest gap models (non-spatial, patch- and individual-based models) and size structure models (non-spatial stand models) rely on two assumptions: the mean field assumption (A-I) and the assumption that plants in one patch do not compete with plants in other patches (A-II). These assumptions lead to differences in plant size dynamics between these models and spatially explicit models (or observations of real forests). Therefore, to more accurately replicate dynamics, these models require model tuning by (1) adjusting model parameter values or (2) introducing a correction term into models. However, these model tuning methods have not been systematically and statistically investigated in models using different patch sizes.We used a simple spatially explicit model that simulated growth and competition processes, and rewrote it as patch models. The patch sizes of the patch models were set between 4 and 1500m2. First, we estimated the parameter values (the intrinsic growth rate, metabolic loss, competition coefficient, and competitive asymmetry) of these models that best reproduce plant size growth under competition using field data from a Sakhalin fir stand, and compared the parameter values among the models. Second, we introduced correction terms into the patch models and estimated the optimal correction term for reproducing plant size growth under competition using the field data.The estimated parameter values of the patch models for all patch sizes differed greatly from those of the spatially explicit models. Therefore, parameter values should not be shared between spatially explicit models and patch models. In addition, the parameter value sets for the models with small patches differed from those with large patches. This is because parameter values for small patches mainly improve biases of A-II, while those for large patches mainly improve biases of A-I. Therefore, parameter values should not be shared between patch models with small patches and with large patches.The estimated correction term in the patch models with large patches excluded the competitive effects of small and medium-sized plants on their neighbors, even though these effects exist in real stands. This exclusion can be ascribed to the discrepancy between their competition in real plant populations and A-I. Therefore, the competitive effects of small and medium-sized plants should not be included in patch models with large patches. Finally, the reproducibility of the models tuned with correction terms was higher than those with adjusted parameters.