Towards a mathematical understanding of colonization resistance in multispecies microbial communities

Gjini, Erida; Madec, Sten

doi:10.1101/2021.01.17.426995

“…Data accessibility. Data and codes related to this study can be found on the Dryad Digital Repository: https://doi.org/ 10.5061/dryad.0k6djhb60 [65].…”

Section: Discussionmentioning

confidence: 99%

Towards a mathematical understanding of invasion resistance in multispecies communities

Gjini,

Madec

2023

R. Soc. open sci.

2

0

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Multispecies community composition and dynamics are key to health and disease across biological systems, a prominent example being microbial ecosystems. Explaining the forces that govern diversity and resilience in the microbial consortia making up our body’s defences remains a challenge. In this, theoretical models are crucial, to bridge the gap between species dynamics and underlying mechanisms and to develop analytic insight. Here we propose a replicator equation framework to model multispecies dynamics where an explicit notion of invasion resistance of a system emerges and can be studied explicitly. For illustration, we derive the conceptual link between such replicator equation and N microbial species’ growth and interaction traits, stemming from micro-scale environmental modification. Within this replicator framework, mean invasion fitness arises, evolves dynamically, and may undergo critical predictable shifts with global environmental changes. This mathematical approach clarifies the key role of this resident system trait for invader success, and highlights interaction principles among N species that optimize their collective resistance to invasion. We propose this model based on the replicator equation as a powerful new avenue to study, test and validate mechanisms of invasion resistance and colonization in multispecies microbial ecosystems and beyond.

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“…When there is just variation in co-colonization coefficients k ij , we recover the model and the Θ in (Madec and Gjini, 2020). Further, recall in (Madec and Gjini, 2020) the term z T Λz is denoted as Q and referred to as mean invasibility of the system, also revisited in terms of colonization resistance (Gjini and Madec, 2021b). In the 2-strain system, more explicitly we have:…”

Section: Parametermentioning

confidence: 99%

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

Le

¹

,

Madec

²

,

Gjini

³

2022

Journal of Theoretical Biology

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A general theory for competitive dynamics among many strains at the epidemiological level is required to understand polymorphisms in virulence, transmissibility, antibiotic resistance and other biological traits of infectious agents. Mathematical coinfection models have addressed specific systems, focusing on the criteria leading to stable coexistence or competitive exclusion, however, due to their complexity and nonlinearity, analytical solutions in coinfection models remain rare. Here we study a 2-strain SIS compartmental model with co-infection/co-colonization, incorporating multiple fitness dimensions under the same framework: variation in transmissibility, duration of carriage, pairwise susceptibilities to coinfection, coinfection duration, and transmission priority effects from mixed coinfection. Taking advantage of a singular perturbation approach, under the assumption of strain similarity, we expose how strain dynamics on a slow timescale are explicitly governed by a replicator equation which encapsulates all traits and their interplay. This allows us to predict explicitly not only the final epidemiological outcome of a given 2-player competition, but moreover, their entire frequency dynamics as a direct function of their relative variation and of strain-transcending global parameters. Based on mutual invasion fitnesses, we analyze and report rigorous results on transition phenomena in the 2-strain system, strongly mediated via coinfection prevalence. This framework offers a deeper analytical understanding of 2-strain competitive games in coinfection, with applications to virulence, interventions, antibiotic resistance, and social evolution theory.

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“…When there is just variation in co-colonization coefficients k ij , we recover the model and the Θ in (Madec and Gjini, 2020). Further, recall in (Madec and Gjini, 2020) the term z T Λz is denoted as Q and referred to as mean invasibility of the system, also revisited in terms of colonization resistance (Gjini and Madec, 2021b). In the 2-strain system, more explicitly we have: Q = z T Λz = (λ 2 1 + λ 1 2 )z 1 z 2 , and this quantity is positive only in the case of coexistence between two strains.…”

Section: Parametermentioning

confidence: 99%

“…When there is just variation in co-infection susceptibility coefficients k ij , we recover the model and the Θ in (Madec and Gjini, 2020). Further, recall in (Madec and Gjini, 2020) the term z T Λz is denoted as Q and referred to as mean invasibility of the system, capturing resistance of the system to invasion by outsiders (Gjini and Madec, 2021b). In the 2-strain system, more explicitly we have:…”

Section: Pairwise Invasion Fitness and Replicator Dynamics Via Timescale Separationmentioning

confidence: 99%

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

Tmt

¹

,

Madec

²

,

Gjini³

2021

Preprint

Self Cite

1

0

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A general theory for competitive dynamics among many strains at the epidemiological level is required to understand polymorphisms in virulence, transmissibility, antibiotic resistance and other biological traits of infectious agents. Mathematical coinfection models have addressed specific systems, focusing on the criteria leading to stable coexistence or competitive exclusion, however, due to their complexity and nonlinearity, analytical solutions in coinfection models remain rare. Here we study a 2-strain SIS compartmental model with co-infection/co-colonization, incorporating multiple fitness dimensions under the same framework: variation in transmissibility, duration of carriage, pairwise susceptibilities to coinfection, coinfection duration, and transmission priority effects from mixed coinfection. Taking advantage of a singular perturbation approach, under the assumption of strain similarity, we expose how strain dynamics on a slow timescale are explicitly governed by a replicator equation which encapsulates all traits and their interplay. This allows us to predict explicitly not only the final epidemiological outcome of a given 2-player competition, but moreover, their entire frequency dynamics as a direct function of their relative variation and of strain-transcending global parameters. Based on mutual invasion fitnesses, we analyze and report rigorous results on transition phenomena in the 2-strain system, strongly mediated via coinfection prevalence. This framework offers a deeper analytical understanding of 2-strain competitive games in coinfection, with applications to virulence, interventions, antibiotic resistance, and social evolution theory.

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Towards a mathematical understanding of colonization resistance in multispecies microbial communities

Cited by 3 publications

References 71 publications

Towards a mathematical understanding of invasion resistance in multispecies communities

Towards a mathematical understanding of invasion resistance in multispecies communities

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

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

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