Representative prey population dynamics.

<p>Red and blue lines in each panel give prey dynamics in two patches linked by dispersal, starting from day 20 when dispersal was initiated. (a-d) Failure to achieve synchrony with a dispersal rate of 0.125% per event, (c) slow achievement of synchrony with a dispersal rate of 5% per event, (d) rapid achievement of synchrony with a dispersal rate of 5% per event, (e) failure to achieve synchrony with dispersal rate of 2.5% per event, (f) rapid achievement of synchrony which was subsequently lost with dispersal rate of 2.5% per event, (g-h) rapid achievement of synchrony with a dispersal rate of (g) 9% or (h) 12.5% per event. Compare c-f to <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0079527#pone-0079527-g001" target="_blank">Figure 1</a>.</p

Prey synchrony vs. dispersal rate.

<p>Prey synchrony (<i>z</i>-transformed cross-correlation of log₁₀-transformed prey abundances) as a function of dispersal rate. Each open point gives results from one replicate pair of bottles. The solid curve is <i>y</i> = <i>ax</i>/(<i>b</i>+<i>x</i>) with estimated parameters (95% likelihood profile c.i.) of <i>a</i> = 0.59 (0.39, 1.25), <i>b</i> = 1.27 (0.14,8.50). The curve <i>y</i> = [<i>ax</i>/(<i>b</i>+<i>x</i>)][1+(1-<i>cx</i>)e^−<i>cx</i>] with estimated parameters (95% likelihood profile c.i.) of <i>a</i> = 0.59 (0.45, 1.26), <i>b</i> = 1.22 (0.45, 8.62), <i>c</i> = 14.66 (14.66, 44.64) is hidden by the solid curve. The dotted curve is a piecewise linear regression. The black diamond indicates the estimated location and 95% confidence interval for the discontinuity of the dotted curve. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0079527#pone.0079527-Hudson1" target="_blank">[34]</a> for review of the concept of profile confidence intervals.</p

Variation in realized synchrony due to demographic stochasticity.

<p>Simulated prey population dynamics in a two-patch Rosenzweig-MacArthur predator-model with demographic stochasticity <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0079527#pone.0079527-Yaari1" target="_blank">[33]</a>. In each panel, red and blue lines show prey dynamics in two patches linked by dispersal of prey and predators at the same per-capita rate. The four panels show four different realizations of the model, using the same parameter values and starting from the same, initially-antisynchronous state. Because the model is stochastic, different realizations can have very different behavior, including (a) slow achievement of synchrony (after ∼50 time units in this example), (b) rapid achievement of synchrony (after ∼12 time units) which is subsequently maintained, (c) failure to achieve synchrony during the simulated time period, and (d) achievement of synchrony (after ∼25 time units) which is subsequently lost. Dynamics were simulated using the SSA algorithm of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0079527#pone.0079527-Yaari1" target="_blank">[33]</a>, using the following parameter values: attack rate 0.01, handling time 3.0, predator per-capita mortality rate 0.5, predator conversion efficiency 0.4, prey intrinsic rate of increase 2.0 ( =  per-capita birth rate 3.0 - per-capita mortality rate 1.0), prey carrying capacity 1000, prey and predator per-capita dispersal rate 0.05.</p