Abstract
Pairwise models are commonly used to describe many-species communities. In these models, an individual receives additive fitness effects from pairwise interactions with each species in the community ('additivity assumption'). All pairwise interactions are typically represented by a single equation where parameters reflect signs and strengths of fitness effects ('universality assumption'). Here, we show that a single equation fails to qualitatively capture diverse pairwise microbial interactions. We build mechanistic reference models for two microbial species engaging in commonly-found chemical-mediated interactions, and attempt to derive pairwise models. Different equations are appropriate depending on whether a mediator is consumable or reusable, whether an interaction is mediated by one or more mediators, and sometimes even on quantitative details of the community (e.g. relative fitness of the two species, initial conditions). Our results, combined with potential violation of the additivity assumption in many-species communities, suggest that pairwise modeling will often fail to predict microbial dynamics.