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            <title xml:lang="en">Towards a mathematical understanding of invasion resistance in multispecies communities</title>
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                <forename type="first">Erida</forename>
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            <funder>This study benefited from PESSOA grant no. 5666/44637YE awarded by Portuguese Foundation for Science and Technology (FCT) (to E.G. and S.M.) and cooperative agreement 2020-2001-230-Y20V7 by Le Studium, Loire Valley Institute of Advanced Studies (E.G.). E.G. acknowledges support also by CEECIND/03051/2018 and funding via FCT project 2022.03060.PTDC.</funder>
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            <idno type="stamp" n="UNIV-ORLEANS">Université d'Orléans</idno>
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                <term xml:lang="en">colonization resistance</term>
                <term xml:lang="en">microbial ecology</term>
                <term xml:lang="en">multispecies community</term>
                <term xml:lang="en">pairwise invasion fitness matrix</term>
                <term xml:lang="en">replicator equation</term>
                <term xml:lang="en">system invasibility</term>
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              <p>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.</p>
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