The key to complexity in interacting systems with multiple strains - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2020

The key to complexity in interacting systems with multiple strains

Erida Gjini
  • Function : Author
  • PersonId : 985747
Sten Madec


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(N 2) 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 R 0 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.
Fichier principal
Vignette du fichier
Paper3_2020.pdf (3.09 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-02470047 , version 1 (07-02-2020)


  • HAL Id : hal-02470047 , version 1


Erida Gjini, Sten Madec. The key to complexity in interacting systems with multiple strains. 2020. ⟨hal-02470047⟩
76 View
45 Download


Gmail Facebook X LinkedIn More