Nested inference of pairwise interactions from strain frequency data across settings and context-dependent mutual invasibilities

How does coexistence of multiple species or pathogen strains arise in a system? What do coexistence patterns in time and space reveal about the epidemiology, ecology and evolution of such systems? Species abundance patterns often defy fully mechanistic explanations, especially when compositional variation and relative taxa abundances differ across settings. To link such variation to deterministic biological processes in a cause-and-effect fashion requires modeling frameworks that are general in spirit, simple enough to understand and implement, and easily-applicable to multi-site data and their environmental gradients. Here, we propose a method to study variation in serotype frequencies of Streptococcus pneumoniae bacteria across different geographic endemic settings. We use the framework of replicator dynamics, derived for a multi-strain SIS model with co-colonization, to extract from 5 countries data fundamental parameters of inter-strain interactions, based on pairwise invasion fitnesses and their context-dependence. We integrate serotype frequency distributions and serotype identities (SAD + identities) collected from cross-sectional epidemiological surveys in Denmark, Nepal, Iran, Brazil and Mozambique. The snapshot observations are modelled under the same nested framework, by which we present a rationale for mechanistically linking and fitting multi-strain distributions across sites. Besides yielding an effective numerical estimation for more than 70% of the 92 x 92 (α_ij) in the pneumococcus serotype interaction matrix, this study offers a new proof-of-concept in the inference of random multi-species interactions. We show that in pneumococcus the vast majority of standardized interaction coefficients in co-colonization are concentrated near zero, with a few serotype pairs displaying extreme deviations from the mean. This statistical pattern confirms that the co-colonization coefficients in pneumococcus display a random probability distribution governed by a limited set of parameters, which are slightly modulated in each epidemiological context to shape coexistence. We also discuss key assumptions that must be carefully balanced in the estimation procedure. Our study paves the way for a deeper qualitative and quantitative understanding of the high-dimensional interaction landscape in multi-strain co-colonization systems.