Exploring the relative importance of biotic and abiotic factors that alter the self-thinning rule: Insights from individual-based modelling and machine-learning

The generality and variability of the self-thinning rule in plant populations have been intensively debated in the past decades. Recent studies on self-thinning focus on understanding how the variability arises and are dedicated to a broader theory, with different biotic and abiotic factors suggested to explain the variability of the self-thinning line. However, the relative role and importance of different factors in altering the self-thinning line are still unclear. Using a generic individual-based model which simultaneously implements different modes (symmetric versus asymmetric) of both competition and facilitation among individual plants, we explored the variability of the self-thinning line in simulated plant populations. We employed a machine learning approach (Random Forests) to evaluate the potential effect and importance of seven biotic and abiotic factors (i.e. mode of competition, mode of facilitation, abiotic stress level, initial density, initial spatial distribution pattern, threshold of death and method used for fitting self-thinning lines) on simulated self-thinning lines. Simulations of the individual-based model demonstrated a significant variation in self-thinning lines. Our Random Forests models were able to explain and predict more than 98% of the variation in both the slope and intercept of the self-thinning line. These models identified mode of competition as being the most important factor that alters both the slope and intercept of the self-thinning line. For the variation of slope, other factors were much less important than competition. Most of the factors were more important in altering the intercept rather than the slope of self-thinning line. Changes of the slope and intercept in response to different factors indicated their divergent roles and partial effects on self-thinning mechanisms. Our study demonstrates that different biotic and abiotic factors have distinct effects and importance in altering the self-thinning rule, implying context dependent outcomes and consequences. We highlight that individual-based models and machine learning approaches are powerful tools to evaluate driving factors and to understand hidden mechanisms underlying complex patterns. The joint application of the two powerful tools will help to extend the framework of self-thinning and foster other research in ecology.