title: The effect of competition and horizontal trait inheritance on invasion, fixation, and polymorphism.
abstract: Horizontal transfer (HT) of heritable information or 'traits' (carried by genetic elements, plasmids, endosymbionts, or culture) is widespread among living organisms. Yet current ecological and evolutionary theory addressing HT is scant. We present a modeling framework for the dynamics of two populations that compete for resources and horizontally exchange (transfer) an otherwise vertically inherited trait. Competition influences individual demographics, thereby affecting population size, which feeds back on the dynamics of transfer. This feedback is captured in a stochastic individual-based model, from which we derive a general model for the contact rate, with frequency-dependent (FD) and density-dependent (DD) rates as special cases. Taking a large-population limit on the stochastic individual-level model yields a deterministic Lotka-Volterra competition system with additional terms accounting for HT. The stability analysis of this system shows that HT can revert the direction of selection: HT can drive invasion of a deleterious trait, or prevent invasion of an advantageous trait. Due to HT, invasion does not necessarily imply fixation. Two trait values may coexist in a stable polymorphism even if their invasion fitnesses have opposite signs, or both are negative. Addressing the question of how the stochasticity of individual processes influences population fluctuations, we identify conditions on competition and mode of transfer (FD versus DD) under which the stochasticity of transfer events overwhelms demographic stochasticity. Assuming that one trait is initially rare, we derive invasion and fixation probabilities and time. In the case of costly plasmids, which are transfered unilaterally, invasion is always possible if the transfer rate is large enough; under DD and for intermediate values of the transfer rate, maintenance of the plasmid in a polymorphic population is possible. In conclusion, HT interacts with ecology (competition) in non-trivial ways. Our model provides a basis to model the influence of HT on evolutionary adaptation.
authors.affiliation: Univ. Lille, CNRS, UMR 8198 - Evo-Eco-Paleo, F-59000 Lille, France. Electronic address: sylvain.billiard@univ-lille1.fr.
authors.forename: Sylvain
authors.initials: S
authors.lastname: Billiard
authors.affiliation: CPHT, Ecole Polytechnique, CNRS, Université Paris-Saclay, route de Saclay, 91128 Palaiseau Cedex-France. Electronic address: collet@cpht.polytechnique.fr.
authors.forename: Pierre
authors.initials: P
authors.lastname: Collet
authors.affiliation: Eco-Evolution Mathématique, CNRS UMR 7625, Ecole Normale Supérieure, PSL Research University, 46 rue d'Ulm, 75230 Paris cedex 05, France; University of Arizona, Department of Ecology & Evolutionary Biology, Tucson AZ 85721, USA. Electronic address: ferriere@biologie.ens.fr.
authors.forename: Régis
authors.initials: R
authors.lastname: Ferrière
authors.affiliation: CMAP, Ecole Polytechnique, CNRS, Université Paris-Saclay, route de Saclay, 91128 Palaiseau Cedex-France.
authors.forename: Sylvie
authors.initials: S
authors.lastname: Méléard
authors.affiliation: Univ. Lille, CNRS, UMR 8524 - Laboratoire P. Painlevé, UFR de Mathématiques, F-59000 Lille, France. Electronic address: chi.tran@math.univ-lille1.fr.
authors.forename: Viet Chi
authors.initials: VC
authors.lastname: Tran
mesh_terms: D000222:Adaptation, Physiological / Q000235:genetics; D000465:Algorithms; D000818:Animals; D003163:Competitive Behavior; D017753:Ecosystem; D019143:Evolution, Molecular; D022761:Gene Transfer, Horizontal / Q000235:genetics*; D005828:Genetics, Population; D008957:Models, Genetic; D010641:Phenotype; D011110:Polymorphism, Genetic / Q000235:genetics*; D011156:Population Density; D011157:Population Dynamics; D011336:Probability; D013269:Stochastic Processes; D013997:Time Factors
keywords: Bacterial conjugation; Fixation probability; Horizontal gene transfer; Invasion; Mobile genetic elements; Plasmid; Stochastic individual-based models and their limits