Intransitivity in plant-soil feedbacks is rare but is associated with multispecies coexistence

Although plant-soil feedback (PSF) is being recognized as an important driver of plant recruitment, our understanding of its role in species coexistence in natural communities remains limited by the scarcity of experimental studies on multispecies assemblages. Here, we experimentally estimated PSFs affecting seedling recruitment in 10 co-occurring Mediterranean woody species. We estimated weak but significant species-specific feedback. Pairwise PSFs impose similarly strong fitness differences and stabilizing-destabilizing forces, most often impeding species coexistence. Moreover, a model of community dynamics driven exclusively by PSFs suggests that few species would coexist stably, the largest assemblage with no more than six species. Thus, PSFs alone do not suffice to explain coexistence in the studied community. A topological analysis of all subcommunities in the interaction network shows that full intransitivity (with all species involved in an intransitive loop) would be rare but it would lead to species coexistence through either stable or cyclic dynamics.

Autocatalytic networks in biology: structural theory and algorithms

Self-sustaining autocatalytic networks play a central role in living systems, from metabolism at the origin of life, simple RNA networks and the modern cell, to ecology and cognition. A collectively autocatalytic network that can be sustained from an ambient food set is also referred to more formally as a 'reflexively autocatalytic food-generated' (RAF) set. In this paper, we first investigate a simplified setting for studying RAFs, which is nevertheless relevant to real biochemistry and which allows an exact mathematical analysis based on graph-theoretic concepts. This, in turn, allows for the development of efficient (polynomial-time) algorithms for questions that are computationally intractable (NP-hard) in the general RAF setting. We then show how this simplified setting for RAF systems leads naturally to a more general notion of RAFs that are 'generative' (they can be built up from simpler RAFs) and for which efficient algorithms carry over to this more general setting. Finally, we show how classical RAF theory can be extended to deal with ensembles of catalysts as well as the assignment of rates to reactions according to which catalysts (or combinations of catalysts) are available.