TY - JOUR
T1 - The effect of competition and horizontal trait inheritance on invasion, fixation, and polymorphism
AU - Billiard, Sylvain
AU - Collet, Pierre
AU - Ferrière, Régis
AU - Méléard, Sylvie
AU - Tran, Viet Chi
N1 - Funding Information:
S.B., S.M. and V.C.T. have been supported by the ANR MANEGE ( ANR-09-BLAN-0215 ), the Chair “Modélisation Mathématique et Biodiversité” of Veolia Environnement-Ecole Polytechnique-Museum National d'Histoire Naturelle-Fondation X. V.C.T. also acknowledges support from Labex CEMPI (ANR-11-LABX-0007-01) and has been invited by the University of Arizona. R.F. acknowledges support from the Pépinière Interdisciplinaire CNRS-PSL “Eco-Evo-Devo” and the Partner University Fund.
Publisher Copyright:
© 2016 Elsevier Ltd
PY - 2016/12/21
Y1 - 2016/12/21
N2 - 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.
AB - 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.
KW - Bacterial conjugation
KW - Fixation probability
KW - Horizontal gene transfer
KW - Invasion
KW - Mobile genetic elements
KW - Plasmid
KW - Stochastic individual-based models and their limits
UR - http://www.scopus.com/inward/record.url?scp=84992025914&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84992025914&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2016.10.003
DO - 10.1016/j.jtbi.2016.10.003
M3 - Article
C2 - 27742260
AN - SCOPUS:84992025914
VL - 411
SP - 48
EP - 58
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
ER -