The key to complexity in interacting systems with multiple strains

Abstract

Ecological community structure, persistence and stability are shaped by multiple forces, acting on multiple scales. These include patterns of resource use and limitation, spatial heterogeneities, drift and migration. Pathogen strains co-circulating in a host population are a special type of an ecological community. They compete for colonization of susceptible hosts, and sometimes interact via altered susceptibilities to co-colonization. Diversity in such pairwise interaction traits enables the multiple strains to create dynamically their niches for growth and persistence, and ‘engineer’ their common environment. How such a network of interactions with others mediates collective coexistence remains puzzling analytically and computationally difficult to simulate. Furthermore, the gradients modulating stability-complexity regimes in such multi-player systems remain poorly understood. In a recent study, we presented an analytic framework for N-type coexistence in an SIS epidemiological system with co-colonization interactions. The multi-strain complexity was reduced from O(N2) dimensions of population structure to only N equations for strain frequency evolution on a long timescale. Here, we examine the key drivers of coexistence regimes in such a system. We find the ratio of single to co-colonization μ critically determines the type of equilibrium for multi-strain dynamics. This key quantity in the model encodes a trade-off between overall transmission intensity R0 and mean interaction coefficient in strain space k. Preserving a given coexistence regime, under fixed trait variation, can only be achieved from a balance between higher competition in favourable environments, and higher cooperation in harsher environments, consistent with the stress gradient hypothesis in ecology. Multi-strain coexistence regimes are more stable when μ is small, whereas as μ increases, dynamics tends to increase in complexity. There is an intermediate ratio that maximizes the existence and stability of a unique coexistence equilibrium between strains. This framework provides a foundation for linking invariant principles in collective coexistence across biological systems, and for understanding critical shifts in community dynamics, driven by simple and random pairwise interactions but potentiated by mean-field and environmental gradients.

Disentangling how multiple traits drive 2 strain frequencies in SIS dynamics with coinfection

“…By (3.1), taking R 0 → 1 + or k → 0 + , which implies µ → ∞, makes the nonlinear part tends to 0, which leads to the competitive exclusion. This remark coincides with the result about µ = 1 (R0−1)k in Gjini and Madec (2021a).…”

“…6.4 Dynamical transitions: from N = 2 to the N -strain network Throughout this study, we have shown explicitly and illustrated in detail how global parameters of the neutral model, embedded in the center of the dynamics, can shift qualitatively and quantitatively the net competitive outcome for any given pair of strains. Recall that the N = 2 system forms the basic unit in the full competitive network among an arbitrary number N of strains, and that qualitative shifts in each network 'edge', as a function of global parameters, can have far-reaching effects on the collective dynamics among multiple strains, even when strains differ just in co-colonization interactions (Gjini and Madec, 2021a). Having exposed further nonlinear gradient effects of µ, R 0 , k, γ, r in the more complete 2-strain system with variation along 5 fitness dimensions, opens the way towards deeper analysis of their higher-level effects on the N − strain dynamics and coexistence (Le et al, 2021).…”

Towards a mathematical understanding of colonization resistance in multispecies microbial communities

“…General structures of co-colonization interactions between N species yield coexistence scenarios of more complex nature than fixed points, including limit cycles and chaos [12]. Thus, depending on how frequency dynamics unfold, subject to intrinsic or extrinsic drivers, Q dynamics can be higher or lower, monotonic or oscillatory, and feed back on the system, in a fully analytically-explicit manner (Table 1).…”

“…It is precisely the analytical tractability of this model [21,12] that makes it easier to study global perturbation effects, and to interpolate across conditions (Table 1). Perturbations affecting global context, such as R 0 and k, directly change the mutual invasion fitnesses λ j i , and thus species dynamics.…”

“…In more diverse communities, perturbation effects are undoubtedly more complex. Among N species, a key modulator of coexistence regimes is the ratio of single-to co-colonization, µ [12], decreasing with R 0 and k. When µ → ∞, and all else fixed, the mutual invasibility network contains mostly competitive exclusion edges, which makes more species coexist, but in unstable and oscillatory fashion [12]. Thus, decreasing R 0 , leading possibly to a fluctuating Q, can make a given system more vulnerable to opportunistic invasion, particularly when Q is low or negative, even if transiently.…”