Biology subjects

Madec, S.

Publications and source records attributed to Madec, S..

10 recordsLinked to original sources

bioRxiv2026

How host contact network impacts N -strain SIS dynamics with coinfection via a global replicator equation

Dynamical processes on complex networks have a long history of study with increasing applications across many fields. While epidemics in heterogeneous networks have received much attention in terms of how connectivity patterns drive epidemic outbreaks, affect critical thresholds, timescales, final outbreak size and immunization efforts, less attention has been devoted to endemic multi-strain scenarios and questions of selection and coexistence dynamics. Here, we provide an SIS framework for multiple co-circulating strains and co-infection, which can be reduced to a replicator dynamics on a host contact network. Using the analytical tractability of the replicator formalism, we study how network heterogeneity affects multi-strain dynamics, and compare its effects relative to the homogeneous contact distribution, identifying key relevant metrics for comparison. In particular, the pairwise invasion fitness matrix comparison reveals that higher network heterogeneity acts to increase the speed of multi-strain dynamics and typically tends to have stabilizing effects that reduce the number of coexisting strains. While many aspects of the replicator dynamics remain complex to study, especially for high number of strains, the advantage of this model representation lies in the dimensional reduction of a huge system, enabling general, more direct and efficient numerical computations. Furthermore the explicit bottom-up constitution of crucial parameters yields biological and epidemiological insight for critical system transitions across macroscopic gradients and can be used to guide interventions.

biophysics↗

bioRxiv2025

Multi-strain SIS dynamics with coinfection across heterogeneous patches

We study a Susceptible-Infected-Susceptible (SIS) model with coinfection and multiple interacting strains where hosts move between a set of inter-connected patches. Under strain similarity and slow migration, we obtain a discrete model, following the corresponding continuous space model derived in (Le and Madec, 2023). In this model, the fast variables are total prevalence of susceptibles, single-infected and co-infected hosts in each patch (S, I, D). The slow variables are strain frequencies (z) in each patch. These local strain frequencies in each patch are governed by a replicator-like equation, where an additional contribution arises from migration, scaled explicitly by emergent patch heterogeneity. In our model, the strains can vary epidemiologically within- and between-patches along several traits, including transmission rates, clearance rates, priority effects and pairwise susceptibilities to coinfection; a complexity that totally defies straightforward prediction of their ecological outcome. However, harnessing the analytical advantage of this model reduction, we can investigate several key scenarios for the outcome of the coupled P-patch N-strain system. We focus on the global and local factors that promote or hinder coexistence, and on regimes that favour spatial segregation of strains, or ultimately competitive exclusion. The analytical tractability of this meta-population model, illustrated with several examples for N = 2 strains and 2-3 patches, makes it a useful framework for application to general multi-species co-colonization systems with migration across heterogeneous environments.

ecology↗

bioRxiv2024

Unpacking fitness differences between two invaders in a multispecies context

Ecosystems are constantly exposed to newcoming strains or species. Which newcomer will be able to invade a resident multi-species community depends on the invaders relative fitness. Classical fitness differences between two growing strains are measured using the exponential model. Here we complement this approach, developing a more explicit framework to quantify fitness differences between two co-invading strains, based on the replicator equation. By assuming that the resident species frequencies remain constant during the initial phase of invasion, we are able to determine the invasion fitness differential between the two strains, which drives growth rate differences post-invasion. We then apply our approach to a critical current global problem: invasion of the gut microbiota by antibiotic-resistant strains of the pathobiont Escherichia coli, using previously-published data. Our results underscore the context-dependent nature of fitness and demonstrate how species frequencies in a host environment can explicitly modulate the selection coefficient between two strains. This mechanistic framework can be augmented with machine-learning algorithms and multi-objective optimization to predict relative fitness in new environments, to steer selection, and design strategies to lower resistance levels in microbiomes.

ecology↗

bioRxiv2024

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

We propose a method to estimate pairwise strain interactions from population-level frequencies across different endemic settings. We apply the framework of replicator dynamics, derived from a multi-strain SIS model with co-colonization, to extract from 5 datasets the fundamental backbone of strain interactions. In our replicator, each pairwise invasion fitness explicitly arises from local environmental context and trait variations between strains. We adopt the simplest formulation for multi-strain coexistence, where context is encoded in basic reproduction number R0 and mean global susceptibility to co-colonization k, and trait variations ij capture pairwise deviations from k. We integrate Streptococcus pneumoniae serotype frequencies and serotype identities collected from 5 environments: epidemiological surveys in Denmark, Nepal, Iran, Brazil and Mozambique, and mechanistically link their distributions. Our results have twofold implications. First, we offer a new proof-of-concept in the inference of multi-species interactions based on cross-sectional data. We also discuss 2 key aspects of the method: the site ordering for sequential fitting, and stability constraints on the dynamics. Secondly, we effectively estimate at high-resolution more than 70% of the 92 x 92 pneumococcus serotype interaction matrix in co-colonization, allowing for further projections and hypotheses testing. We show that in these bacteria both within- and between- serotype interaction coefficients distribution emerge to be unimodal, their difference in mean broadly reflecting stability assumptions on serotype coexistence. This framework enables further model calibration to global data: cross-sectional across sites, or longitudinal in one site over time, - and should allow a more robust and integrated investigation of intervention effects in such biodiverse ecosystems.

ecology↗

bioRxiv2022

SegVeg: Segmenting RGB images into green and senescent vegetation by combining deep and shallow methods

The pixels segmentation of high resolution RGB images into background, green vegetation and senescent vegetation classes is a first step often required before estimating key traits of interest including the vegetation fraction, the green area index, or to characterize the sanitary state of the crop. We developed the SegVeg model for semantic segmentation of RGB images into the three classes of interest. It is based on a U-net model that separates the vegetation from the background. It was trained over a very large and diverse dataset. The vegetation pixels are then classified using a SVM shallow machine learning technique trained over pixels extracted from grids applied to images. The performances of the SegVeg model are then compared to a three classes U-net model trained using weak supervision over RGB images with predicted pixels by SegVeg as groundtruth masks. Results show that the SegVeg model allows to segment accurately the three classes, with however some confusion mainly between the background and the senescent vegetation, particularly over the dark and bright parts of the images. The U-net model achieves similar performances, with some slight degradation observed for the green vegetation: the SVM pixel-based approach provides more precise delineation of the green and senescent patches as compared to the convolutional nature of U-net. The use of the components of several color spaces allows to better classify the vegetation pixels into green and senescent ones. Finally, the models are used to predict the fraction of the three classes over the grids pixels or the whole images. Results show that the green fraction is very well estimated (R2=0.94) by the SegVeg model, while the senescent and background fractions show slightly degraded performances (R2=0.70 and 0.73, respectively). We made SegVeg publicly available as a ready-to-use script, as well as the entire dataset, rendering segmentation accessible to a broad audience by requiring neither manual annotation nor knowledge, or at least, offering a pre-trained model to more specific use.

plant biology↗

bioRxiv2021

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

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. We show that coinfection is not always a promoter of coexistence; instead, its effect to favour or prevent polymorphism is non-monotonic and depends on the type and level of phenotypic differentiation between strains. This framework offers a deeper analytical understanding of 2-strain competitive games in coinfection, with theoretical and practical applications in epidemiology, ecology and evolution.

ecology↗

bioRxiv2021

Towards a mathematical understanding of colonization resistance

Microbial community composition and dynamics are key to health and disease. Explaining the forces generating and shaping diversity in the microbial consortia making up our bodys defenses is a major aim of current research in microbiology. For this, tractable models are needed, that bridge the gap between observations of patterns and underlying mechanisms. While most microbial dynamics models are based on the Lotka-Volterra framework, we still do not have an analytic quantity for colonization resistance, by which a microbial systems fitness as a whole can be understood. Here, inspired by an epidemiological perspective, we propose a rather general modeling framework whereby colonization resistance can be clearly mathematically defined and studied. In our model, N similar species interact with each other through a co-colonization interaction network encompassing pairwise competition and cooperation, abstractly mirroring how organisms effectively modify their micro-scale environment in relation to others. This formulation relies on a generic notion of shared resources between members of a consortium, yielding explicit frequency-dependent dynamics among N species, in the form of a replicator equation, and offering a precise definition of colonization resistance. We demonstrate that colonization resistance arises and evolves naturally in a multispecies system as a collective quadratic term in a replicator equation, describing dynamic mean invasion fitness. Each pairwise invasion growth rate between two ecological partners, [Formula], is derived explicitly from species asymmetries and mean traits. This makes the systemic colonization resistance [Formula] also an emergent function of global mean-field parameters and trait variation architecture, weighted by the evolving relative abundances among species. In particular, if the underlying invasion fitness matrix {Lambda} displays species-specific invasiveness or invasibility structure, colonization resistance will be insensitive to mean micro-scale cooperation or competition. However, in general, colonization resistance depends on and may undergo critical transitions with changes in mean environment, e.g. cooperation and growth level in a community. We illustrate several key links between our proposed measure of colonization resistance and invader success, including sensitivity to timing, and to the intrinsic pairwise invasion architecture of the resident community. Our simulations reveal that symmetric and invader-driven mutual invasion among resident species tend to maximize systemic colonization resistance to outsiders, when compared to resident-driven, anti-symmetric, almost anti-symmetric and random {Lambda} structures. We contend this modeling approach is a powerful new avenue to study, test and validate interaction networks and invasion topologies in diverse microbial consortia, and quantify analytically their role in colonization resistance, system function, and invasibility.

microbiology↗

bioRxiv2020

The key to complexity in interacting systems with multiple strains

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 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 is small, whereas as 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.

ecology↗

bioRxiv2019

Co-colonization interactions drive explicit frequency-dependent dynamics among N types

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 susceptible-infected-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- co-colonizer 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(N2) 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 Fishers fundamental theorem and to conservative Lotka-Volterra systems.

ecology↗

bioRxiv2017

Leaf rolling in maize crops: from leaf scoring to canopy level measurements for phenotyping

Leaf rolling in maize crops is one of the main plant reactions to water stress that may be visually scored in the field. However, the leaf scoring did not reach the high-throughput desired by breeders for efficient phenotyping. This study investigates the relationship between leaf rolling score and the induced canopy structure changes that may be accessed by high-throughput remote sensing techniques.\n\nResults gathered over a field phenotyping platform run in 2015 and 2016 show that leaf starts to roll for the water stressed conditions around 9:00 and reaches its maximum around 15:00. Conversely, genotypes conducted under well watered conditions do not show any significant rolling during the same day. Leaf level rolling was very strongly correlated to canopy structure changes as described by the fraction of intercepted radiation fIPARWS derived from digital hemispherical photography. The changes in fIPARWS were stronly correlated (R2=0.86, n=50) to the leaf level rolling visual score. Further, a very good consistency of the genotype ranking of the fIPARWS changes during the day was found ({rho}=0.62). This study demonstrating the strong coordination between leaf level rolling and its impact on canopy structure changes poses the basis for new high-throughput remote sensing methods to quantify this water stress trait.\n\nHighlighThe diurnal dynamics of leaf rolling scored visually is strongly related to canopy structure changes that can be documented using Digital hemispherical photography. Consequences for high-throughput field phenotyping are discussed

plant biology↗