A slow-fast dynamic decomposition links neutral and non-neutral coexistence in interacting multi-strain pathogens

2019

Preprint

Self Cite

Multi-type spreading processes are ubiquitous in ecology, epidemiology and social systems, but remain hard to model mathematically and to understand on a fundamental level. Here, we describe and study a multi-type susceptibleinfected-susceptible (SIS) model that allows for up to two co-infections of a host. Fitness differences between N infectious agents are mediated through altered susceptibilities to secondary infections that depend on colonizer-cocolonizer interactions. By assuming small differences between such pairwise traits (and other infection parameters equal), we derive a model reduction framework using separation of timescales. This 'quasi-neutrality' in strain space yields a fast timescale where all types behave as neutral, and a slow timescale where non-neutral dynamics take place.On the slow timescale, N equations govern strain frequencies and accurately approximate the dynamics of the full system with O(N 2 ) variables. We show that this model reduction coincides with a special case of the replicator equation, which, in our system, emerges in terms of the pairwise invasion fitnesses among strains. This framework allows to build the multi-type community dynamics bottom-up from only pairwise outcomes between constituent members.We find that mean fitness of the multi-strain system, changing with individual frequencies, acts equally upon each type, and is a key indicator of system resistance to invasion. Besides efficient computation and complexity reduction, these results open new perspectives into high-dimensional community ecology, detection of species interactions, and evolution of biodiversity, with applications to other multi-type biological contests. By uncovering the link between an epidemiological system and the replicator equation, we also show our co-infection model relates to Fisher's fundamental theorem and to conservative Lotka-Volterra systems.Many factors have been shown to be important for ecological biodiversity. These include inter-vs. intra-species 2 interactions (Tilman, 1987), population size (Taylor et al., 2004), number and functional links with resources (Armstrong and McGehee, 1976), and movement in space (Nowak and May, 1992). Diversity of an ecosystem is closely 4 related to its stability, resilience to perturbations and productivity (Hooper et al., 2005). Co-colonization processes appear in many diverse ecological communities, from plant and marine ecosystems to infectious diseases: two species 6 encountering and coexisting together in a unit of space or resource. Interactions between resident and co-colonizer entities upon encounter may exhibit asymmetries, randomness, and special structures, and may range from facilitation 8 to competition. Although special cases for low dimensionality seem to be tractable analytically, the entangled network that arises between N interacting entities in co-colonization, and its consequences for multi-type dynamics over short 42 play. These studies have also considered very low system size (N = 2), and either only cooperative or only compe...

Section: Neutral Systemsupporting

confidence: 84%

Section: Derivation Details For the Slow-fast Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

PredictingN-strain coexistence from co-colonization interactions: epidemiology meets ecology and the replicator equation

2019

Preprint

Self Cite

“…This model has been described in detail elsewhere (Gjini and Madec, 2017) for the case of N = 2. The model allows for each strain to interact differently with other strains upon co-colonization, altering the suceptibility of an already-colonized host to incoming strains.…”

Section: N-strain Sis Model With Co-colonizationmentioning

confidence: 99%

The key to complexity in interacting systems with multiple strains

2020

Preprint

Self Cite

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.

The ratio of single to co‐colonization is key to complexity in interacting systems with multiple strains

2021

Ecology and Evolution

Self Cite

The high number and diversity of microbial strains circulating in host populations have motivated extensive research on the mechanisms that maintain biodiversity. However, much of this work focuses on strain‐specific and cross‐immunity interactions. Another less explored mode of pairwise interaction is via altered susceptibilities to co‐colonization in hosts already colonized by one strain. Diversity in such interaction coefficients enables 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 endemic systems remain poorly understood. In a recent study (Madec & Gjini, Bulletin of Mathematical Biology , 82), we obtained an analytic representation for N ‐type coexistence in an SIS epidemiological model with co‐colonization. We mapped multi‐strain dynamics to a replicator equation using timescale separation. Here, we examine what drives coexistence regimes in such co‐colonization system. We find the ratio of single to co‐colonization, µ , critically determines the type of equilibrium and number of coexisting strains, and 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, requires balancing between higher mean competition in favorable environments, and higher cooperation in harsher environments, and is consistent with the stress gradient hypothesis. Multi‐strain coexistence tends to steady‐state attractors for small µ , whereas as µ increases, dynamics tend to more complex attractors. Following strain frequencies, evolutionary dynamics in the system also display contrasting patterns with µ , interpolating between multi‐stable and fluctuating selection for cooperation and mean invasion fitness, in the two extremes. This co‐colonization framework could be applied more generally, to study invariant principles in collective coexistence, and to quantify how critical shifts in community dynamics get potentiated by mean‐field and environmental gradients.