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

Fox JW, Legault G, Legault G, Vasseur DA, Einarson JA - PLoS ONE (2013)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Sciences, University of Calgary, Calgary, Alberta, Canada.

ABSTRACT
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.

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Representative prey population dynamics.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 Figure 1.
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pone-0079527-g003: Representative prey population dynamics.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 Figure 1.

Mentions: While prey synchrony increased on average with increasing dispersal rate, there was substantial variation around this trend (Fig. 2). Replicates with the same dispersal rate often exhibited very different levels of synchrony. Figure 3 illustrates the population dynamics underpinning this variability. As intended, paired bottles invariably were anti-synchronous when dispersal began on day 20, with one prey population at high density and the other at low density. Subsequent dynamics clearly were cyclic in all bottles included in the analysis. However, the realized level of synchrony varied widely. Metapopulations that experienced very low dispersal rates (≤1% per event) rarely went into phase quickly and so never exhibited high prey synchrony (Fig. 3a,b). Conversely, metapopulations that experienced the highest dispersal rates (≥9% per event) typically went into phase quickly and so typically exhibited relatively high prey synchrony (Fig. 3g,h). At dispersal rates in between these extremes, prey cycles sometimes remained out of phase until late in the experiment (Fig. 3c), sometimes went into phase quickly (Fig. 3d), sometimes never went into phase at all (Fig. 3e), and sometimes went into phase quickly only to subsequently drift out of phase (Fig. 3f). This range of behavior closely resembles that produced by a spatial predator-prey model incorporating demographic stochasticity (compare Fig. 3c-f to Fig. 2).


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

Fox JW, Legault G, Legault G, Vasseur DA, Einarson JA - PLoS ONE (2013)

Representative prey population dynamics.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 Figure 1.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3823609&req=5

pone-0079527-g003: Representative prey population dynamics.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 Figure 1.
Mentions: While prey synchrony increased on average with increasing dispersal rate, there was substantial variation around this trend (Fig. 2). Replicates with the same dispersal rate often exhibited very different levels of synchrony. Figure 3 illustrates the population dynamics underpinning this variability. As intended, paired bottles invariably were anti-synchronous when dispersal began on day 20, with one prey population at high density and the other at low density. Subsequent dynamics clearly were cyclic in all bottles included in the analysis. However, the realized level of synchrony varied widely. Metapopulations that experienced very low dispersal rates (≤1% per event) rarely went into phase quickly and so never exhibited high prey synchrony (Fig. 3a,b). Conversely, metapopulations that experienced the highest dispersal rates (≥9% per event) typically went into phase quickly and so typically exhibited relatively high prey synchrony (Fig. 3g,h). At dispersal rates in between these extremes, prey cycles sometimes remained out of phase until late in the experiment (Fig. 3c), sometimes went into phase quickly (Fig. 3d), sometimes never went into phase at all (Fig. 3e), and sometimes went into phase quickly only to subsequently drift out of phase (Fig. 3f). This range of behavior closely resembles that produced by a spatial predator-prey model incorporating demographic stochasticity (compare Fig. 3c-f to Fig. 2).

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Sciences, University of Calgary, Calgary, Alberta, Canada.

ABSTRACT
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.

Show MeSH
Related in: MedlinePlus