Incorporating the soil environment and microbial community into plant competition theory.

Plants affect microbial communities and abiotic properties of nearby soils, which in turn influence plant growth and interspecific interaction, forming a plant-soil feedback (PSF). PSF is a key determinant influencing plant population dynamics, community structure, and ecosystem functions. Despite accumulating evidence for the importance of PSF and development of specific PSF models, different models are not yet fully integrated. Here, we review the theoretical progress in understanding PSF. When first proposed, PSF was integrated with various mathematical frameworks to discuss its influence on plant competition. Recent theoretical models have advanced PSF research at different levels of ecological organizations by considering multiple species, applying spatially explicit simulations to examine how local-scale predictions apply to larger scales, and assessing the effect of PSF on plant temporal dynamics over the course of succession. We then review two foundational models for microbial- and litter-mediated PSF. We present a theoretical framework to illustrate that although the two models are typically presented separately, their behavior can be understood together by invasibility analysis. We conclude with suggestions for future directions in PSF theoretical studies, which include specifically addressing microbial diversity to integrate litter- and microbial-mediated PSF, and apply PSF to general coexistence theory through a trait-based approach.