Nonlinear effect of dispersal rate on spatial synchrony of predator-prey cycles.

Spatially-separated populations often exhibit positively correlated fluctuations in abundance and other population variables, a phenomenon known as spatial synchrony. Generation and maintenance of synchrony requires forces that rapidly restore synchrony in the face of desynchronizing forces such as demographic and environmental stochasticity. One such force is dispersal, which couples local populations together, thereby synchronizing them. Theory predicts that average spatial synchrony can be a nonlinear function of dispersal rate, but the form of the dispersal rate-synchrony relationship has never been quantified for any system. Theory also predicts that in the presence of demographic and environmental stochasticity, realized levels of synchrony can exhibit high variability around the average, so that ecologically-identical metapopulations might exhibit very different levels of synchrony. We quantified the dispersal rate-synchrony relationship using a model system of protist predator-prey cycles in pairs of laboratory microcosms linked by different rates of dispersal. Paired predator-prey cycles initially were anti-synchronous, and were subject to demographic stochasticity and spatially-uncorrelated temperature fluctuations, challenging the ability of dispersal to rapidly synchronize them. Mean synchrony of prey cycles was a nonlinear, saturating function of dispersal rate. Even extremely low rates of dispersal (<0.4% per prey generation) were capable of rapidly bringing initially anti-synchronous cycles into synchrony. Consistent with theory, ecologically-identical replicates exhibited very different levels of prey synchrony, especially at low to intermediate dispersal rates. Our results suggest that even the very low rates of dispersal observed in many natural systems are sufficient to generate and maintain synchrony of cyclic population dynamics, at least when environments are not too spatially heterogeneous

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

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

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