LOCAL DISTURBANCE CYCLES AND THE MAINTENANCE OF HETEROGENEITY ACROSS SCALES IN MARINE METAPOPULATIONS

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1 Ecology, 88(3), 2007, pp Ó 2007 by the Ecological Society of America LOCAL DISTURBANCE CYCLES AND THE MAINTENANCE OF HETEROGENEITY ACROSS SCALES IN MARINE METAPOPULATIONS TARIK C. GOUHIER AND FRÉDE RIC GUICHARD 1 Department of Biology, McGill University, 1205 Doctor Penfield, Montre al, Que bec H3A 1B1 Canada Abstract. In marine systems, the occurrence and implications of disturbance recovery cycles have been revealed at the landscape level, but only in demographically open or closed systems where landscape-level dynamics are assumed to have no feedback effect on regional dynamics. We present a mussel metapopulation model to elucidate the role of landscape-level disturbance cycles for regional response of mussel populations to onshore productivity and larval transport. Landscape dynamics are generated through spatially explicit rules, and each landscape is connected to its neighbor through unidirectional larval dispersal. The role of landscape disturbance cycles in the regional system behavior is elucidated (1) in demographically open vs. demographically coupled systems, in relation to (2) onshore reproductive output and (3) the temporal scale of landscape disturbance dynamics. By controlling for spatial structure at the landscape and metapopulation levels, we first demonstrate the interaction between landscape and oceanographic connectivity. The temporal scale of disturbance cycles, as controlled by mussel colonization rate, plays a critical role in the regional behavior of the system. Indeed, fast disturbance cycles are responsible for regional synchrony in relation to onshore reproductive output. Slow disturbance cycles, however, lead to increased robustness to changes in productivity and to demographic coupling. These testable predictions indicate that the occurrence and temporal scale of local disturbance recovery dynamics can drive large-scale variability in demographically open systems, and the response of metapopulations to changes in nearshore productivity. Key words: demographic coupling; demographically open system; dispersal limitation; disturbance cycles; metapopulation; mussels; rocky intertidal communities; synchrony. INTRODUCTION Understanding the maintenance of large-scale variability in the abundance of subdivided populations and communities still remains a great challenge for ecologists. An increasing number of studies contribute to elucidating the role of dispersal limitation and species interactions for species coexistence, stability, and spatiotemporal dynamics (Hassell et al. 1991, 1994, Mouquet and Loreau 2003). However, the role of the interaction between fundamental properties of ecological communities and dispersal limitation for the generation of large-scale dynamics remains largely unknown. One such property is the process of population disturbance and recovery. Disturbance dynamics has long been shown to be a major driver of community dynamics and species diversity in marine intertidal landscapes (Paine 1966, Levin and Paine 1974, Paine and Levin 1981, Sousa 1984). It has more recently been suggested to be a cause of hierarchical and cyclic ecosystem dynamics (Gunderson and Holling 2002). Here we present a hierarchical metapopulation model to Manuscript received 24 April 2006; revised 18 August 2006; accepted 1 September Corresponding Editor: P. T. Raimondi. 1 Corresponding author. frederic.guichard@mcgill.ca 647 elucidate the relative contributions of local landscape disturbance dynamics and limited dispersal to the maintenance of large-scale variability and synchrony in marine populations. The interplay between demographic processes and limited dispersal in spatially explicit systems can produce large-scale patterns in homogeneous environments including phase-locked oscillations (Blasius et al. 1999), stationary patterns, spiral waves (Hassell et al. 1991, 1994, Sole et al. 1992), and scale invariance (Guichard 2005). However, we still ignore the degree to which hierarchies of such spatial processes (linking local interactions at the individual level to large-scale dispersal limitation in metapopulations) can interact to control regional dynamics and stability. Such hierarchies have been suggested to control cycles of ecosystem connectivity and resilience (sensu Gunderson and Holling 2002), and to allow quantification of ecosystem complexity (Kolasa 2005). Here we adopt hierarchies of spatial processes to integrate current theories of marine coastal ecosystems across spatial scales. In rocky intertidal landscapes, wave disturbances play an important role in maintaining biodiversity by displacing competitively dominant species and allowing subordinate species to colonize vacant substrates (Levin and Paine 1974, Paine and Levin 1981, Paine 1984). The spatial interplay between abiotic disturbance and biotic

2 648 TARIK C. GOUHIER AND FRÉDÉRIC GUICHARD Ecology, Vol. 88, No. 3 recolonization has been shown to explain species composition and distribution (Wootton 2001a), and the effects of habitat fragmentation on the structure of competitive communities (Roy et al. 2004). It has further been shown to generate landscape-level patchiness and disturbance cycles in model systems that are suggested to explain strong temporal fluctuations in some natural mussel populations (Guichard et al. 2003). However, long-term data are still required to establish the causal relationship between local disturbance dynamics and temporal fluctuations. Also, because rocky intertidal habitats are naturally subdivided into fragmented landscapes, the role of these disturbance cycles at spatial scales larger than intertidal landscapes (;100 m) has yet to be elucidated. Many coastal species have a larval dispersal stage, and local disturbances can influence regional dynamics of subdivided populations provided they can feedback into large-scale processes through current-mediated larval dispersal. Because of the potential large-scale larval dispersal, initial theoretical frameworks of coastal ecosystems started from the assumption of demographically open populations (Johnson 2005) in which local reproductive output has no direct effect on local larval supply (Levin and Paine 1974, Roughgarden et al. 1985). Demographically open populations, therefore, constitute a specific case of open systems that are more generally defined by the input of larvae from nonlocal sources (Johnson 2005). Here we contrast demographically coupled with demographically open populations to elucidate the implications of open system theories for the maintenance of variability in coastal ecosystems. Coastal systems were also studied as well-mixed metapopulations (Iwasa and Roughgarden 1986, Roughgarden and Iwasa 1986) and closed communities (Connolly and Roughgarden 1998, 1999). However, because of their equilibrium behavior and their treatment of space and dispersal limitation, these theoretical frameworks provide limited opportunity for local disturbance dynamics to feedback into large-scale dynamics, relying instead on nearshore oceanographic heterogeneity to explain the large-scale distribution of abundance. Recent empirical studies showing strong larval dispersal limitation in many benthic species (Kinlan and Gaines 2003, Menge et al. 2003, Palumbi 2003) suggest the existence of hierarchies of spatial processes (from landscapes to the scale of larval dispersal) and directs us toward the study of their synergistic interaction. Here we incorporate disturbance cycles at the landscape level into a metapopulation framework, and investigate their ability to scale up and explain regional dynamics in relation to changes in onshore productivity, within both demographically coupled and demographically open systems (Roughgarden and Iwasa 1986, Alexander and Roughgarden 1996, Menge et al. 2003; but see Johnson 2000). Here local disturbance cycles are shown to play a critical role in explaining the maintenance of variability and the onset of regional synchrony in relation to onshore productivity. We further elucidate the role of temporal scales for predicting how disturbance cycles can maintain spatial heterogeneity across gradients of oceanographic productivity, and we predict onshore and nearshore conditions allowing the applicability of open system theory at multiple scales. THE MODEL Landscape dynamics The model incorporates the spatially explicit landscape mussel disturbance model developed by Guichard et al. (2003) within a metapopulation framework consisting of a series of spatially structured landscapes coupled through larval dispersal. Each landscape is represented by a square grid composed of cells. The spatial extent of each landscape corresponds to the fragmentation scale of rocky intertidal systems, and cells correspond to spatially homogeneous 1-m 2 areas that can be in one of three states: empty, occupied by mussels, or wave disturbed (Fig. 1A). Each cell interacts with its eight nearest neighbors with periodic boundary conditions applied within each landscape. More precisely, wave disturbances spread through cells in each landscape according to a disturbance parameter a 0. This parameter, which is always set to one, dictates the probability that a disturbance will spread from a wave-disturbed cell to a neighboring occupied cell. This local spread of disturbances emulates the natural propagation of waves through weakened gap edges in mussel beds (Paine and Levin 1981, Denny 1987). Local positive density-dependent mechanisms during recruitment and growth allow mussels to colonize empty substrata (Bayne 1964, Paine and Levin 1981). Specifically, if a cell is empty, colonization probability is a function of the proportion of occupied neighbors and of a colonization parameter, a 2, that corresponds to the probability that the colonization of an empty cell will be successful provided mussel larvae are available (Fig. 1A). Metapopulation dynamics We implemented the metapopulation as a onedimensional array of 100 landscapes where each landscape is coupled to a single neighboring landscape through unidirectional larval dispersal (Fig. 1). Periodic boundary conditions are implemented at the metapopulation level in order to avoid edge effects observed with absorbing boundary conditions. Larval supply in each landscape i is a saturating function of larval production. Within each landscape, larval supply is assumed to be well-mixed and its probability P i within each cell of landscape i is calculated as a Poisson process with a rate proportional to the larval contribution L i 1 of the neighboring landscape i 1 (Caswell and Etter 1999):

3 March 2007 DISTURBANCE CYCLES IN METAPOPULATIONS 649 FIG. 1. Model dynamics diagrams. (A) Each landscape in the model is composed of a lattice of cells. Each cell can be either empty (bare substratum), disturbed by waves, or occupied by mussels. Wave-disturbed cells transition to the empty state. Empty cells either remain empty, if there are no larvae available to colonize the empty space, or become colonized by larvae originating from a neighboring landscape through a positive density-dependent process proportional to a 2. Occupied cells become wave disturbed with a probability of a 0 if any neighboring cell is disturbed or if a new disturbance occurs. (B) Spatial coupling between each landscape defined as unidirectional and nearest-neighbor larval dispersal. The larval production (L i ) of each landscape is a function of mussel cover (q i ) and fecundity ( f ). (C) Larval supply is a saturating function of fecundity, which thus controls both demographic coupling between landscapes and onshore productivity: increases in fecundity below the saturation point generate a response to increased onshore productivity (demographically coupled regime), while increases above the saturation point result in a demographically open system. P i ¼ 1 e Li 1 : ð1þ Each landscape i is connected to its neighboring landscape i þ 1 through larval dispersal L i ¼ q i f ð2þ where L i represents the number of larvae dispersed from landscape i to landscape i þ 1, and q i and f are the mussel cover and fecundity in landscape i, respectively (Fig. 1B). These dispersed larvae are incorporated into the dynamics of landscape i þ 1 during the following iteration, where one iteration represents the average time needed to update all cells. Cells are randomly selected for update among cells in each landscape. This

4 650 TARIK C. GOUHIER AND FRÉDÉRIC GUICHARD Ecology, Vol. 88, No. 3 asynchronous update at the landscape level introduces stochasticity and has been shown to approximate a continuous time process (Durrett and Levin 1994). All simulations were run for 3000 iterations, the first 1000 iterations having been discarded in order to exclude transient behavior from our analysis. Unidirectional dispersal was implemented as a simplified version of nearshore currents observed along the coast of Oregon or California on the west coast of the United States (Gaylord and Gaines 2000), but we also used a Gaussian dispersal kernel that allowed larvae in each landscape to be exported to its 10 nearest neighbors (larval dispersal over 10% of the domain). Since this more computationally intensive implementation resulted in no qualitative (and very little quantitative) change in the overall results, the previously mentioned nearestneighbor discrete dispersal was used to generate all the results presented here. Elucidating the importance of landscape dynamics In order to elucidate the relative contribution of landscape spatial processes to regional dynamics, wellmixed models were created at both the landscape and the metapopulation scales and their results were compared to those of the main spatially explicit metapopulation and to closed population dynamics. Because the deterministic well-mixed model was not analytically tractable (Guichard et al. 2003), we used stochastic simulations in order compare well-mixed landscapes and metapopulations to the stochastic spatially explicit model described in the previous section. Specifically, the well-mixed landscape dynamics was created by randomizing the neighbors of each cell, which resulted in a lack of disturbance cycles, lower mussel cover, and smaller temporal fluctuations. Because the effects of the mean and variance of landscape mussel cover can be confounded with the specific effect of disturbance cycles, we obtained an adjusted well-mixed model (hereafter referred to as stochastic mean-field model) by adding stochastic fluctuations to the mussel cover of each landscape at the end of each iteration in order for the coefficient of variation of the stochastic mean-field model to match that of the spatially explicit model. The metapopulation mean-field model was obtained by randomizing each landscape s neighbor (i.e., larval input) at each iteration. The scale of landscape disturbance cycles was further controlled by varying the recolonization rate a 2. This rate determines the temporal scale of colonization as well as the landscape connectivity and thus controls the temporal signature of disturbance dynamics without having any strong effect on mussel cover and spatial patterns in demographically open landscapes (Pascual et al. 2002, Guichard et al. 2003). Onshore productivity and demographic regimes We use fecundity as a parameter driving both onshore productivity and demographic coupling in the metapopulation. Indeed, variability in fecundity has been observed in coastal invertebrate species and has been associated with nearshore properties such as primary productivity and upwelling events (Leslie et al. 2005). Varying fecundity below the larval saturation point in Eq. 1 thus allows us to explore the response of the metapopulation to increased onshore productivity. However, increases in fecundity beyond the larval saturation point result in demographically open systems as landscapes are saturated with larvae, and larval supply becomes completely independent of productivity and constant in a homogeneous environment. Thus, we vary fecundity across the saturation point f ¼ 5 defined by the saturating functional response of larval supply to fecundity in order to study metapopulation dynamics in demographically coupled (fecundity below saturation) and open (fecundity above saturation) systems (Fig. 1C). Analysis of results Regional time series analysis. At the metapopulation level, we analyzed the time series of total mussel cover obtained from all 100 landscapes by extracting all local minima and maxima found over 2000 post-transient iterations and then plotted these extremes in relation to fecundity. This analysis was conducted for both a single closed population and all metapopulations. Landscape time series analysis. For all metapopulation simulations, the minimum and maximum landscape cover along the metapopulation transect was recorded and subsequently averaged over 100 iterations. These mean maxima and minima were then plotted against the fecundity value in order to reveal the spatial variability in cover across the metapopulation. Synchrony. The Kendall coefficient of concordance was used as an index of metapopulation synchrony. Kendall s coefficient of concordance is a nonparametric statistic that measures the association between multiple ranked variables (Zar 1999). It is commonly used to measure the level of agreement among several rankings and, as such, has been suggested as the most effective method for determining synchrony between multiple data series (Buonaccorsi et al. 2001). Furthermore, it has already been applied in intertidal systems to characterize gap dynamics in mussel beds (Paine and Levin 1981). Here the coefficient of synchronization is calculated by first ranking (R i ) the mussel cover time series (2000 iterations) for each landscape i. Kendall s coefficient of concordance (W c ) is then calculated as follows (Zar 1999): X 2 X Ri R 2 i W c ¼ T L 2 ðt 3 TÞ L X ð3þ s 12 where L represents the total number of landscapes (100), T represents the total number of iterations (2000), and Rs is an adjustment for tied ranks within each landscape

5 March 2007 DISTURBANCE CYCLES IN METAPOPULATIONS 651 (Fig. 2A). In order to atone for this naturally occurring discrepancy, whose effects could potentially be confounded with those of space, an adjusted mean-field model (referred to as stochastic mean-field model) was devised by adding stochasticity in mussel cover so as to match the mussel cover and variance of the spatially explicit model (Fig. 2A). Temporal scale of disturbance cycles. The temporal scale of disturbance cycles decreases with a 2 (Fig. 2B) and can be characterized as slow (a 2 ¼ 0.2) or fast (a 2 ¼ 1). This temporal signature is important for landscapelevel dynamics as fast disturbance cycles become quickly subdued in response to larval saturation (Fig. 3A), whereas slow disturbance cycles maintain landscape mussel cover variability as the system becomes demographically open (Fig. 3B). Metapopulation dynamics Response to onshore productivity. Fast disturbance cycles produce highly synchronized oscillations in metapopulation mussel cover in response to increased but nonsaturating onshore productivity, whereas satu- FIG. 2. Mussel cover time series for single closed landscape simulations with nonsaturated fecundity ( f ¼ 3). (A) Time series of mussel cover with fast disturbance cycles (a 2 ¼ 1.0) featuring spatially explicit (dotted line), mean-field (heavy solid line), and stochastic mean-field landscape dynamics (thin solid line; see The Model: Elucidating the importance of landscape dynamics for details). (B) Time series of mussel cover with spatially explicit dynamics exhibiting either fast (a 2 ¼ 1.0, dotted line) or slow (a 2 ¼ 0.2, solid line) disturbance cycles. such that for t i number of ties in the ith group and j groups of tied ranks X X j s ¼ ðti 3 t i Þ: i¼1 RESULTS Disturbance cycles within closed landscapes Occurrence of disturbance cycles. Disturbance cycles are revealed by temporal oscillations in mussel cover (Fig. 2A), and are driven by the spatially explicit interplay between local colonization and disturbance. Disturbance cycles depend on the local (spatially explicit) nature of disturbance dynamics, and never appear in mean-field landscapes (Fig. 2A). A side effect of controlling for spatial structure at the landscape level is the resulting difference in mussel cover and variance between spatially explicit and mean-field simulations FIG. 3. Landscape time series of the mussel cover in relation to fecundity for a single closed landscape featuring spatially explicit landscape dynamics and either (A) fast (a 2 ¼ 1.0) or (B) slow (a 2 ¼ 0.2) disturbance cycles.

6 652 TARIK C. GOUHIER AND FRÉDÉRIC GUICHARD Ecology, Vol. 88, No. 3 rating productivity results in regional stability (Figs. 4A, 6). The importance of these landscape disturbance cycles for regional dynamics is revealed by the robustness of regional synchrony to the scale of larval dispersal (nearest neighbor vs. mean field; Figs. 4B, 6), as well as by the lack of such synchrony in the absence of spatially explicit disturbance cycles (Figs. 4C, D, 6). This is further corroborated by the absence of synchronized oscillations in the stochastic mean-field model results, which indicates that the difference in regional behavior produced by these models is attributable to landscape disturbance cycles and is not simply caused by the inherent differences in mussel cover and variance between the spatially explicit and mean-field models (Figs. 4E, F, 6). The temporal scale of these landscape disturbance cycles also plays an important role in regional pattern formation, as slow disturbance cycles maintain spatial heterogeneity (Fig. 5A), and thus never display synchronized oscillations (Fig. 6). Interestingly, spatial heterogeneity can also be observed with mean-field landscape dynamics, indicating that slow disturbance cycles are not necessary for the maintenance of spatial variability in response to increased onshore productivity (Fig. 5C). Maintenance of variability in demographically open systems. Slow disturbance cycles are robust to increases in nearshore productivity as both spatial heterogeneity and regional temporal stability are maintained (Fig. 5A), even in the face of saturating fecundity levels that drive both fast disturbance (Fig. 4C) and mean-field models (Figs. 4E, 5C, E) to spatial homogeneity. These results and their invariance to alternate metapopulation configurations reveal the robustness of local and slow disturbance cycles to regional processes (Fig. 5B). DISCUSSION A number of recent studies have revealed the role of nearshore productivity in predicting the response of local benthic communities (Connolly and Roughgarden 1998, 1999). However, observations still fail to broadly support large-scale nearshore heterogeneity as a general predictor of community structure (Menge et al. 2003, 2004). We showed that in a spatially subdivided population, the temporal scale of landscape disturbances determines their potential to (1) scale up and drive metapopulation dynamics as well as its response to changes in nearshore productivity, and (2) to render the system robust to regional processes. Here we start from well-documented local disturbance dynamics in rocky intertidal communities (Wootton 2001b, Guichard et al. 2003) to address assumptions of demographically open system theories, and to provide a set of testable predictions to explain variability and coherence in coastal ecosystems (Table 1). Our results further highlight the importance of hierarchies of spatial processes in predicting the persistence of ecological systems under changing environments. Disturbance cycles and regional dynamics Since the original formulation of metapopulation theory (Levins 1969), important progress originated from the realization that subdivided populations and communities can be characterized by nonequilibrium dynamics, which interact with dispersal limitation to predict the persistence of populations and long transients (Hassell et al. 1991, 1994). More recently, theories of ecosystem resilience (Gunderson 2000, Scheffer et al. 2001, Scheffer and Carpenter 2003), of panarchies (Gunderson and Holling 2002), and of criticality (Pascual and Guichard 2005) have relied on the dynamics of disturbance and connectivity to explain how cycles of disturbance and recovery can occur across scales and cause sudden and drastic shifts in homogeneous landscapes. In rocky intertidal communities naturally occurring wave disturbances dislodge the competitively dominant mussel species (Paine and Levin 1981, Paine 1984, Sousa 1984). This disturbance and the subsequent recolonization by mussels results in disturbance cycles that have been used to predict species distribution patterns at the landscape level (Wootton 2001a, b, Guichard et al. 2003). At larger scales, rocky intertidal communities are assumed to be naturally fragmented into landscapes and the prediction of large-scale variability has mostly relied on oceanographic and dispersal processes, which largely assumes linear averaging of spatial interactions within landscapes. Our results generalize previous applications of disturbance dynamics in intertidal landscapes and predict conditions allowing local dynamics to scale up: when local recovery rates and disturbance cycles are fast, changes in onshore reproductive potential (i.e., fecundity) can scale up and produce regional (coherent) fluctuations. In contrast, constraints on the recovery of populations after disturbance prevent such synchrony and rather lead to landscape disturbance cycles that are robust to regional processes (Table 1). Dispersal between regulated populations and communities and correlation in environmental fluctuations can cause spatial correlation in ecological systems (Bjornstad et al. 1999, Liebhold et al. 2004). The interplay between these factors can control large-scale patterns in homogeneous environments including synchronized oscillations (Earn et al. 2000) and phaselocked oscillations (Blasius et al. 1999). Here we contribute to theories of synchrony as they apply to ecology by showing how spatial ecological interactions at the individual level can synchronize dynamics at higher (metapopulations) organizational levels. We further demonstrate that this effect is caused by the temporal signature of ecological disturbance cycles resulting from spatially explicit disturbance dynamics. Our study is the first to predict the importance of hierarchies of spatially explicit processes involving individual and dispersal scales in coastal ecosystems. It more specifically elucidates conditions under which

7 March 2007 DISTURBANCE CYCLES IN METAPOPULATIONS 653 FIG. 4. Landscape and regional time series maxima and minima of the mussel cover in relation to fecundity for metapopulations of 100 landscapes with fast disturbance cycles (a 2 ¼ 1). Mean metapopulation mussel cover (solid line) was calculated by obtaining the average mussel cover along the transect for each iteration and subsequently averaging these values over 2000 iterations. The regional time series graph (dots) was generated by plotting the local minima and maxima of the metapopulation mussel cover in relation to fecundity. The landscape time series graph (open circles) was obtained by determining the minimum and maximum landscape mussel cover across the entire metapopulation at each iteration, and independently averaging these minima and maxima over 100 iterations. Mean-field landscape models (C and D) and stochastic mean-field landscape models (E and F) were used in order to elucidate the specific contribution of disturbance cycles. Stochastic mean-field landscapes (E and F) had their mussel cover coefficient of variation adjusted to match that of the spatially explicit landscapes (A and B) by adding random fluctuations with mean b and variance r. A, C, and E are based on spatially explicit metapopulation models, while B, D, and F represent mean-field metapopulation models.

8 654 TARIK C. GOUHIER AND FRÉDÉRIC GUICHARD Ecology, Vol. 88, No. 3 FIG. 5. Landscape and regional time series maxima and minima of the mussel cover in relation to fecundity for metapopulations of 100 landscapes with slow disturbance cycles (a 2 ¼ 0.2). Symbols and other parameter values are the same as in Fig. 4. localized processes at the landscape (i.e., disturbance/ recovery) rather than at the metapopulation (i.e., dispersal) level could be essential for the prediction of large-scale dynamics. In contrast with previous theoretical frameworks (Connolly and Roughgarden 1999), our results suggest that emergent phenomena scaling up from local processes could be the determinant for testing the assumption of demographic decoupling between populations and for predicting their regional response to oceanographic fluctuations. Disturbance cycles and open system theory Open system theory was initially applied to predict the local dynamics of marine populations and communities. Because recruitment was assumed to be limited by local supply of homogeneously distributed larvae rather than

9 March 2007 DISTURBANCE CYCLES IN METAPOPULATIONS 655 FIG. 6. Coefficient of synchrony in mussel cover as a function of fecundity for spatially explicit metapopulations with fast and slow disturbance cycles, and consisting of 100 spatially explicit, mean-field landscapes or stochastic mean-field landscapes. Only the metapopulation with spatially explicit landscapes and fast disturbance cycles showed a response of synchrony to fecundity. by their production, frameworks originally decoupled onshore community dynamics from larval production, which lead to the inherent stability of metapopulation models (Roughgarden and Iwasa 1986). Large-scale oceanographic processes such as supply-side theory were introduced to explain observed variability in recruitment (Roughgarden et al. 1987) and community structure (Menge and Sutherland 1987). Nearshore oceanography was similarly integrated into theories of bottom-up and top-down controls. While theoretical and recent empirical advances have promoted limited dispersal and a degree of demographic coupling between neighboring landscapes, the assumption of demographically open systems still proves to be a useful simplification (Hixon et al. 2002, Menge et al. 2003). In an effort to provide a more general framework integrating these two views and allowing their empirical validation, we formulated specific local and regional predictions related to demographic coupling between nearshore and onshore processes. For instance, we predict that populations experiencing slow onshore recovery rates relative to disturbance intensity can explain the maintenance of regional variability in open systems (Table 1). This prediction defines conditions allowing results that are based on local demographically open populations to be directly scaled up to regional dynamics. It more generally provides an alternative hypothesis to extrinsic environmental forcing (Lewin 1986) for the maintenance of regional heterogeneity in the distribution of onshore abundance and larval supply in coastal communities. Given the increasing availability of long-term data, predictions from our model will help testing for the occurrence of locally driven disturbance cycles and of demographic coupling, two phenomena that still lack strong empirical support in natural coastal systems. Regional response to changes in onshore productivity Predicting the causes and consequences of large fluctuations in nearshore and onshore physical condi- Response of local and regional population dynamics to local disturbance, to increase in regional larval production, and to demographic coupling. TABLE 1. Scale of Onshore productivity Demographically open systems biological response Fast local disturbance Slow local disturbance Fast local disturbance Slow local disturbance Regional synchrony (homogeneous) robust (heterogeneous) quasi-equilibrium quasi-equilibrium Local high-frequency cycles low-frequency cycles equilibrium low-frequency cycles (robust) Notes: Imposed variations include changes in regional productivity (increase in fecundity) in demographically coupled or open systems, and in the pace of local disturbance (fast or slow). Heterogeneity of regional (metapopulations) and local (landscape) populations are affected in terms of regional synchrony and of local fluctuations. In a demographically open system, local larval production and larval supply are decoupled. Productivity refers to changes in the per capita reproductive output (fecundity) across entire metapopulations (see The Model: Onshore productivity and demographic regimes for details).

10 656 TARIK C. GOUHIER AND FRÉDÉRIC GUICHARD Ecology, Vol. 88, No. 3 tions is crucial for the development of a predictive framework applied to coastal ecosystems (Menge et al. 2003, Hughes et al. 2005). For example, fluctuations in nearshore phytoplankton concentration have been associated with large-scale climatic drivers (Barber and Chavez 1986, Chavez et al. 1999), and have been shown to affect recruitment, growth, and fecundity of benthic invertebrates. Resulting patterns of recruitment and reproductive output can show large and uncoupled heterogeneity (Menge et al. 2003, Leslie et al. 2005), but we have yet to elucidate the regulation of recruitment by onshore reproductive output, and its response to environmental fluctuations. Our results are the first to suggest how changes in fecundity can affect regional dynamics and persistence of coastal ecosystems through the onset of synchrony, and should be used to guide the analysis and interpretation of large-scale coastal data sets. More precisely, when the recovery rate of disturbed populations is fast relative to disturbance and independent of reproductive output, local disturbance dynamics can control population response to environmental change at the regional level and most specifically predict the onset of regional synchrony in relation to onshore reproductive potential. Interestingly, the same increase in onshore reproductive potential fails to induce synchrony for metapopulations exhibiting slow recovery and high amplitude disturbance cycles. This result is compatible with existing metapopulation theories predicting increased probability of metapopulation synchrony with increasing demographic rates and fluctuations of abundance (Earn et al. 2000, Keeling and Rohani 2002, Guichard 2005). More importantly, our results predict the sensitivity of these predictions to the spatial nature and temporal signature of local dynamics (Table 1). CONCLUSION We have shown how local cycles of disturbance and recovery can scale up and govern regional dynamics in both demographically open and coupled marine metapopulations. Our study predicts how properties of onshore productivity and disturbance dynamics affect both local and regional behavior of coastal ecosystems. This hierarchical framework complements existing theories of marine ecosystems by demonstrating the importance of combining nonequilibrium dynamics and dispersal limitation as an endogenous cause of spatiotemporal dynamics and regulation. One important consequence of this work is the unsuspected importance of local processes for regional dynamics. This stresses the importance of incorporating knowledge of both local and regional processes when conducting empirical studies of large-scale coastal populations. More precisely, variability in local recovery and disturbance rates, as well as regional nearshore oceanographic processes strongly interact to predict the onset of synchrony and the maintenance of heterogeneity across scales. The model presented here should be extended to metacommunity dynamics in order to address problems of competitive and trophic interactions (Connolly and Roughgarden 1999), and constitutes an important step toward the full integration of local community ecology into a nonequilibrium theory of large-scale coastal ecosystems. ACKNOWLEDGMENTS We acknowledge support from the Natural Science and Engineering Research Council of Canada and from the James S. McDonnell Foundation. We thank M. Anand and two anonymous reviewers for useful comments on a previous version of the manuscript. LITERATURE CITED Alexander, S. E., and J. Roughgarden Larval transport and population dynamics of intertidal barnacles a coupled benthic/oceanic model. Ecological Monographs 66: Barber, R. 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