Fig 1.
Schematic representation of the multi-species metacommunity and the temporal dynamics of the model.
We consider a metacommunity consisting of M distinct patches (represented by symbols) and supporting different species (represented by colours/shapes). We assume that each patch is populated by only one species (a coloured geometric shape in the picture). Species in the metacommunity can contain a beneficial gene in their genome, here schematically represented by a cross. The time evolution of the metacommunity is the result of a migration-selection dynamics across patches, and selective effects are associated to the presence-absence of beneficial genes. The spread of beneficial genes in the metacommunity is the result of HGT events between patches.
Fig 2.
In absence of HGT, an infinite-allele model provides a diversity-maintenance mechanism with an intrinsic time scale.
A. We consider a standard neutral model maintaining diversity. At each time step, corresponding to a basic migration-sweep time scale each patch can be swept neutrally by a new species, with an innovation event taking place with rate ν (per patch, per time step), or alternatively, its species can migrate and sweep, invading another patch (and sweeping neutrally), with a rate 1 − ν. Panel B shows diversity (S(t), defined as the total number of distinct species present in the metacommunity at a given time t) in a typical simulation. Diversity relaxes to a plateau, in agreement with (Eq 1). The parameters of the simulation are ν = 0.01 and M = 10 000. C. Comparison between Eq 1 (valid in the limit M ≫ 1 and ν ≪ 1) and simulated data for the equilibrium value of the diversity, plotted as a function of the innovation rate (ν). Simulations correspond to M = 10 000 and averages over 100 independent realizations. For each simulated value of ν the distribution of diversity S is shown as a box plot (blue line: mean value, box: inter-quartile range, fences: max and min values) D. Characterization of the equilibration time scale for the average trajectories of the diversity. The plot shows diversity (scaled by its equilibrium value) vs time, scaled by the common equilibration time scale N/ν. Simulations were performed over 100 independent realizations, for different values of the innovation rate ν (shown in the legend, coded by color and symbol). All the simulations were initialized with a metacommunity of a single species (S(t = 0) = 1).
Fig 3.
In presence of HGT only, and no diversity-maintenance mechanism, the fixation of a beneficial gene in the metacommunity can lead to a moderate loss of diversity.
A. A beneficial gene can spread across patches (i) via migration events (reducing diversity) or (ii) via HGT-sweep (maintaining diversity) The two processes take place at each time step, with rate pm (per patch, per time step) and ph (per patch, per time step) respectively. Here, we assume that no diversity-maintenance mechanism counteracts the diversity loss (this assumption will be relaxed later) B. Simulations of this model show a diversity (S(t)) loss from the initial value (Si) to a new stable value (Sf), corresponding to complete invasion of the beneficial gene. Each solid line is a realization, with initial condition of the simulations generated by the neutral model described in Fig 2 (M = 10000 and ν = 0.02), and with parameters ph = 0.2 and pm = 1 − ph. C-D. Comparison between analytical prediction (Eq 3) and simulated data for the sweep parameter Q = 〈Sf/Si〉 as a function of the ratio ph/pm (panel C, ν = 0.01), and of the innovation rate of the neutral model generating the initial diversity (panel D, ph = 0.1, pm = 0.9). Simulations performed with M = 10 000. The panels CD show the distribution of diversity S over 100 realizations as a box plot (blue line: mean value, box: inter-quartile range, fences: max and min values).
Fig 4.
Competition of gene-sweep and diversity-restoring dynamics affects the minimal and maximal observed diversity.
A. Spread of a beneficial gene over a metacommunity can compete with a diversity-restoring mechanism occurring with a rate ν. HGT-sweep and migration-sweep events take place with a joint rate 1 − ν and are realized by picking two random patches within the metacommunity. In innovations, new species will carry a beneficial gene with probability f0 equal to the fraction of populations (patches) within the metacommunity carrying the beneficial gene. Neutral migration-sweep events occur if both populations carry the beneficial gene, or neither of them does. If the first of the two populations carries the beneficial gene and the second does not, a (selective) migration-sweep event occurs with probability pm (and a total rate (1 − ν)pm) while an HGT-sweep event occurs with probability ph (and a total rate (1 − ν)ph), see Fig 3. B. The dynamics of diversity after the emergence of a beneficial gene is characterized by two time scales: (i) the time until the beneficial gene reaches fixation (τfix), during which the diversity drops and (ii) an equilibration time (τeq), restoring its initial value. C. Minimum diversity quantified by the scaled sweep parameter Q/Q0, where Q = 〈Smin/S0〉, and Q0 is the sweep parameter (Fig 3). The distribution of Q/Q0 shown as a box plot shows an increasing trend with increasing innovation rate ν. D. If multiple beneficial genes emerge periodically after a time 1/ω, diversity shows an oscillatory dynamics. E. The maximum diversity (Smax, shown as a box plot) divided by the expected value under neutral biodiversity (S0), decreases after a critical value of the scaled parameter ω/ω0, where . Other model parameters: M = 10000, ph = 0.1, pm = 0.9. All rates are per patch, per time step unless otherwise specified.