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Ecology, 0(0), 2019, e02930 © 2019 by the Ecological Society of America

At what spatial scales are alternative stable states relevant in highly interconnected ?

1,2,3 1 VADIM A. KARATAYEV AND MARISSA L. BASKETT 1Department of Environmental Science and Policy, University of California, Davis, 2004 Wickson Hall, One Shields Avenue, Davis, California 95616 USA 2Graduate Group in , University of California, Davis, One Shields Avenue, Davis, California 95616 USA

Citation: Karatayev, V. A., and M. L. Baskett. 2019. At what spatial scales are alternative stable states relevant in highly interconnected ecosystems? Ecology 00(00):e02930. 10.1002/ecy.2930

Abstract. Whether ecosystems recover from depends on the presence of alter- native stable states, which are theoretically possible in simple models of many systems. How- ever, definitive empirical evidence for this phenomenon remains limited to demographically closed ecosystems such as lakes. In more interconnected systems such as temperate rocky reefs, the local relevance of alternative stable states might erode as immigration overwhelms local and produces a single stable state. At larger spatial scales, dispersal might counter localized disturbance and feedbacks to synchronize states throughout a region. Here, we quan- tify how interconnectedness affects the relevance of alternative stable states using dynamical models of California rocky reef communities that incorporate observed environmental stochas- ticity and loops in kelp–urchin–predator interactions. Our models demonstrate the potential for localized alternative states despite high interconnectedness likely due to feedbacks affecting dispersers as they settle into local communities. Regionally, such feedbacks affecting settlement can produce a mosaic of alternative stable states that span local (10–20 km) scales despite the synchronizing effect of long-distance dispersal. The specific spatial scale and dura- tion of each state predominantly depend on the scales of environmental variation and on local dynamics (here, fishing). Model predictions reflect observed scales of states in Cali- fornia rocky reefs and suggest how alternative states co-occur in the wide array of marine and terrestrial systems with settlement feedbacks. Key words: alternative stable states; dispersal; disturbance; ; ; stochastic ; temperate rocky reefs; urchin barren.

conditions, even if changes in environment lead to dra- INTRODUCTION matic (nonlinear) ecological changes. Therefore, in addi- When qualitatively distinct, alternatively stable ecosys- tion to informing a basic understanding of the structure tem states occur under the same environmental condi- of ecological communities, resolving whether or not state tions, brief (“pulse”) disturbances can lead to abrupt and shifts represent alternative stable states can affect con- persistent ecological shifts (Scheffer et al. 2001). In such servation and management decisions such as the degree cases, the persistence of a given ecological state depends of restoration necessary for recovery of a target state on the magnitude of perturbations that ecosystems can (Suding et al. 2004). However, empirically establishing withstand and return to the target state (“ecological resi- the relevance of alternative stable states requires long- lience” hereafter; Holling 1973). Models and empirically term data of each state at large spatial scales under iden- observed feedbacks reinforcing distinct states suggest tical environmental conditions and therefore remains that alternative stable states could, theoretically, underlie debated in most systems (Petraitis and Dudgeon 2004, observed shifts following environmental change in many Petraitis 2013). ecosystems, including the collapse of , declines One of the factors that might affect the relevancy of in foundational species including corals and kelp, alternative stable states to many systems is demographic replacement of forests by -prone grasslands, and interconnectedness (Petraitis and Latham 1999, Petraitis algal in lakes (Scheffer et al. 2009). Alterna- and Dudgeon 2004). In particular, inputs of individuals tively, such state shifts may be readily reversed if only from outside areas may overwhelm the feedbacks main- one state is stable under a given set of environmental taining alternative stable states at small spatial scales and induce a “rescue effect” (Brown and Kodric-Brown 1977) that always allows eventual recovery of the origi- Manuscript received 9 February 2019; revised 5 September nal state after disturbance. Consequently, the best evi- 2019; accepted 11 September 2019. Corresponding Editor: Mark Carr. dence for the existence of alternative stable states and 3E-mail: [email protected] their relevance to management remains limited to

Article e02930; page 1 Article e02930; page 2 VADIM A. KARATAYEVAND MARISSA L. BASKETT Ecology, Vol. xx, No. xx relatively small, demographically closed, shallow lake dispersal and connectivity allow gradual recoveries from ecosystems (Scheffer et al. 1993, Schroder et al. 2005). disturbances. Specifically, urchin and predator dispersal By contrast, in most terrestrial and marine systems, on 50–100 km scales (Waples and Rosenblatt 1987, manipulative studies occur on small scales (e.g., <100 m; Edmands et al. 1996) largely decouples larval supply McGill 2010) while many animal taxa disperse above the from local densities (Okamoto 2014), and scale of kilometers (Kinlan and Gaines 2003), which can might rescue predators from local disturbance (Connell dynamically link communities across tens to hundreds and Sousa 1983) or propagate and synchronize urchin of kilometers (Gouhier et al. 2010). barrens over large scales (Hughes et al. 2005). Where At the larger spatial scale of an entire , high shifts to urchin barrens have occurred, resolving the rele- interconnectedness among locations raises the question vance and scale of alternative stable states can inform of whether alternative stable states, if relevant, manifest whether reduction in predator harvest alone allows kelp within local communities or at system-wide scales. On forest recovery, or whether additional restoration efforts the one hand, localized disturbances induce ecosystem (e.g., urchin harvest; House et al. 2017) might be neces- heterogeneity that can maintain localized alternative sary at specific scales. stable states: for instance, in models with Allee effects, Here, we quantify whether and at what spatial scales demographic stochasticity in a given year can reinforce alternative stable states and the associated concept of population persistence in some patches and pro- ecological resilience can be relevant in temperate rocky mote extinction in others (Martin et al. 2015). Analo- reefs given long-distance dispersal. We develop a tri- gous heterogeneity in savannas, coral reefs, and trophic community model with empirically grounded predator–prey communities might maintain localized feedback mechanisms that can drive alternative forested alternative stable states in spite of high external input and barren states by regulating settlement success. We (Durrett and Levin 1994, Mumby et al. 2007, Schertzer first use a one-patch model to explore how the fraction et al. 2015). On the other hand, dispersal at the ecosys- of external larval supply affects the presence of alterna- tem level can synchronize ecological states across space tive stable states, and then resolve their potential spatial and produce alternative stable states at system-wide and temporal scales using a spatially explicit model for- scales. In particular, spatial models emphasize that mulation that incorporates observed stochasticity. under high levels of dispersal sudden collapses to unde- Finally, we compare the predicted scales of the alterna- sired ecosystem states can propagate across large scales tive states from our model to long-term data. From these in a domino effect (Hughes et al. 2005, 2013, van Nes analyses, we find a potential for local relevance of alter- and Scheffer 2005), with recovery possible only through native stable states in systems with high connectivity and large-scale restoration efforts (van de Leemput et al. quantify how feedbacks and local disturbance interact 2015). Resolving the expected scale of alternative stable to determine community structure across locations and states and its drivers informs the scales at which empiri- through time. cal efforts could detect this phenomenon, the socioeco- nomic consequences of ecosystem collapses to undesired MATERIALS AND METHODS states, and which management approaches might effec- tively maintain desired states. Study system Temperate rocky reef ecosystems throughout the world exemplify systems with both extensive dispersal We base our analysis on temperate rocky reefs in the and a hypothesized potential for alternative stable states. northern California Channel Islands, USA, which repre- Two observed ecological states of these communities are sent a ~300 km total coastline with well-documented kelp forests with abundant urchin predators and barrens shifts between distinct community states (Filbee-Dexter where urchins overgraze kelp and predators are rare (re- and Scheibling 2014). Like many temperate rocky reefs viewed in Lawrence 1975, Steneck et al. 2002, Konar around the world, strong trophic interactions character- and Estes 2003, Ling et al. 2015). When fishing reduces ize this system, and primarily involve kelp (Macrocystis predator densities, transitions between these states often pyrifera), (Strongylocentrotus pur- follow localized, stochastic events such as pulses of puratus), and urchin predators: sheephead (Semicossy- urchin larvae and kelp loss during intense (Hart phus pulcher) and spiny lobsters (Panulirus interruptus; and Scheibling 1988, Cavanaugh et al. 2011). These Filbee-Dexter and Scheibling 2014, Hamilton and Case- community shifts typically occur on small scales lle 2015). Kelp facilitate urchin predators by providing (≤20 km of coastline) and can persist for years to dec- shelter that can double survival rates of settled predator ades (reviewed in Filbee-Dexter and Scheibling 2014). A larvae compared to exposed areas (Smith and Herrkind number of feedbacks have the potential to drive alterna- 1992, Lipcius et al. 1998; Appendix S1: Section S1). tive stable states on temperate reefs, such as when abun- Predator facilitation by kelp via settlement dant kelp facilitate recruitment of urchin predators cues or increased early post-settlement survival creates a (Ling et al. 2015) and barrens facilitate urchin recruit- strong feedback often invoked by empirical studies of ment (Baskett and Salomon 2010). Alternatively, urchin temperate rocky reefs (Ling et al. 2015) that can produce barrens might instead represent a transient state as high alternatively stable forest and barren states under Xxxxx 2019 ALTERNATE STABLE STATES AND CONNECTIVITY Article e02930; page 3 intensive predator fishing in closed-system models describe the one-patch and spatially explicit formula- (Appendix S1: Section S2, Fig. S5a; Marzloff et al. tions of the model (Fig. 1b, c). Within each patch x, our 2013). Note that predator recruitment facilitation, the model tracks kelp (, Ax) and densities of focus here, is one of many possible feedbacks hypothe- adult consumers (urchins, Ux, and predators, Px). We sized to drive alternative stable states in kelp systems use a semi-discrete (Mailleret and Lemesle 2009) model (Ling et al. 2015); additional possible mechanisms where kelp growth, herbivory, , and harvest include recruitment facilitation of urchins to crustose mortality occur continuously for one year (t 6¼ sK ), fol- coralline algae that increases in barrens (Baskett and lowed by an annual discrete-time pulse (at t ¼ sK ) with Salomon 2010) and intensified urchin behavior -induced kelp mortality and settlement of newly when kelp (Ebeling et al. 1985, Harrold and Reed 1985) produced urchins and predators into local communities. or predators (Cowen 1983) are rare. Throughout the year, kelp biomass grows logistically Local communities in this system are highly intercon- at a rate rA with K, and urchins graze nected because dispersal distances of some key species kelp at a rate dA. Urchins and predators experience natu- l l greatly exceed the scale of predominant environmental ral mortality at rates U and P, and predators consume stochasticity. Although adult consumer home ranges and urchins at rate dU and experience fishing mortality at a kelp dispersal occur within rocky kelp habitat patches (1– rate FP. Thus, the community dynamics within a year (at 6¼ sþ 5 km of coastline; Topping et al. 2005, Castorani et al. t K ) are 2015), consumer larvae disperse over much longer dis- tances (50–100 km on average; Table 1). We consider two dA A x ¼ A r 1 x d U (1) sources of local-scale stochasticity that regulate commu- dt x A K A x nity composition and can form persistent urchin barrens: winter storms, which annually lead to a 70% loss of kelp dU x ¼U ðd P þ l Þ (2) biomass (Dayton et al. 1999, Cavanaugh et al. 2011), and dt x U x U urchin larval survival, which varies temporally by an order of magnitude (Hart and Scheibling 1988, Schroeter et al. dP x ¼P ðl þ F Þ: (3) 1996). As with our focal feedback mechanism, these are dt x P P not the only possible sources of environmental stochastic- ity, which also include extreme warm water events leading Both urchins and predators experience an annual to kelp loss (Dayton et al. 1999) and disease outbreaks reproductive pulse at time sK (spring-early summer), affecting predators (Harvell et al. 2019) and urchins (Laf- where larvae produced within each patch disperse ferty 2004, Ling et al. 2015). between patches. Larval production in each patch is pro- portional to grazing or predation in the local community integrated over the previous year. Urchins convert con- Model description sumed kelp into larvae (accounting for larval mortality Here we describe the model of local community during development) given the conversion factor a.Two dynamics (Fig. 1a), and in the next subsections, we energetic sources contribute to predator fecundity:

TABLE 1. Definitions, base values, and sources of model parameters.

Parameter Default value Description Source 1 rA 12 yr kelp growth rate K 4 kg/m2 A kelp carrying capacity Cavanaugh et al. (2011) 1 1 dA 1.1 U yr urchin grazing rate on kelp Lauzon-Guay et al. (2009) 1 1 dU 11 P yr predator attack rate on urchins Tegner and Levin (1983) a 0.41 UA1 kelp to urchin conversion see Appendix S1 b 0.014 PU1 urchin to predator conversion see Appendix S1 fc 0.85 predator recruitment facilitation see Appendix S1 sAðsK ; xÞ 0.305 winter kelp survival (mean) see Appendix S1 rU ðsK ; xÞ 1 urchin larval survival stochasticity (mean) see Appendix S1 l 1 U 0.1 yr urchin natural mortality Marzloff et al. (2013) l 1 P 0.05 yr predator natural mortality Neilson (2011), Hamilton et al. (2011) 1 FP 0.19 yr predator harvest rate Neilson (2011), Hamilton et al. (2011) b 6.7 9 105yr1m2 non-urchin predator resources Dd 1.5 km length of patch along coast w U 80 km mean urchin dispersal distance Edmands et al. (1996) w P 80 km mean predator dispersal distance Waples and Rosenblatt (1987) w sA 20.8 km distance at 0.5 correlation in sA see Appendix S1 w r rU 12.0 km distance at 0.5 correlation in u see Appendix S1 Article e02930; page 4 VADIM A. KARATAYEVAND MARISSA L. BASKETT Ecology, Vol. xx, No. xx

FIG. 1. (a) Model schematic of kelp (A), urchin (U), and urchin predator (P) dynamics within a local community x, denoting losses to consumption and mortality and consumer settlement dynamics at the reproductive pulse t ¼ sK (time of annual reproduc- tive pulse). Arrow colors denote pre-settlement (red), settlement (blue), and post-settlement processes (black). (b) Prior to settle- ment, larvae of each consumer z disperse in both one-patch and spatially explicit models. (c) Kelp mortality and urchin larval survival (relative to average conditions) implemented at the reproductive pulse are determined from empirically observed environ- mental stochasticity.P (d) Time series illustrating two stochasticP metrics of resilience used in model analysis: state frequency calcu- 1 1 lated as tF Fi and mean state duration calculated as n Fi. Parameters are defined in Table 1 and in Materials and methods. consumption of urchins given the conversion factor b only weak effects on community dynamics because and feeding on alternative (non-urchin) prey species b, predators experience much lower population turnover, b l where P to prevent unbounded predator growth. so we ignore it here. To account for recruitment facilita- We multiply this per capita larval production by the tion, both the settlement of predator larvae and early number of individuals that live to reproduce in early post-settlement survival of predator juveniles together spring to arrive at the larval production for species i in increase proportionally with local kelp biomass by a fac- q ðs Þ patch x, i;x K : tor fc, where 1 fc is the baseline predator settlement Z success in the absence of kelp (Baskett and Salomon sK q ðs Þ¼ d ðs Þ ð Þ 2010). Finally, kelp biomass experiences stochastic sur- U;x K a AUx K Ax t dt (4) ¼sþ vival sAðsK ; xÞ due to storms and limited growth during t K 1 winter-spring. See Model implementation section below Z ! ðs ; Þ sK for details on the distributions of sA K x and q ðs Þ¼ ðs Þ b þ d ð Þ : r ðs ; Þ P;x K Px K b U Ux t dt (5) U K x for different model realizations. Thus, the t¼sþ K1 community state just after the reproductive pulse (at ¼ sþ t K )is

Given larval production in all n patches in the vector ðsþÞ¼ ðs ; Þ ðs Þ q ðs Þ Ax K sA K x Ax K (6) i K , we account for dispersal with the function D ðq ðs Þ; xÞ, which depends on the spatial model. i i K ðsþÞ¼r ðs ; Þ ðq ðs Þ; Þþ ðs Þ Urchin larvae can then experience stochasticity in the Ux K U K x DU U K x Ux K (7) number of dispersing larvae that end up in a population þ sAðsK ;xÞAx rU ðsK ; xÞ, which captures presettlement larval survival ðs Þ¼ ðq ðs Þ; Þ þ þ ðs Þ: Px K DP P K x 1 fc fc Px K and movement by water currents (Hart and Scheibling K 1988), settlement success dependent on factors such as (8) local cues, and post-settlement survival dependent on predation on recently settled juveniles (Schroeter et al. Spatial dynamics 1996), where our distinction between “presettlement”, “settlement”, and “post-settlement” phases follows We start with a one-patch model to link to existing Keough and Downes (1982) and Benton and Bowler theory and measurement of resilience as the size of a (2012). Because larval survival predominates stochastic- basin of attraction (see Model analysis). We then extend ity across these processes, from this point we refer to the framework to a spatially explicit model to test the rU ðsK ; xÞ as stochasticity in larval survival. In prelimi- robustness of our results to greater realism and nary simulations, we found that, compared to urchin lar- determine the spatial scale of alternative stable states val survival, stochasticity in predator larval survival had where relevant. In the one-patch model (Fig. 1b), we Xxxxx 2019 ALTERNATE STABLE STATES AND CONNECTIVITY Article e02930; page 5 incorporate external larval production as the proportion the stochastic case we calculate production over a tran- c i of urchin and predator larvae that originate from out- sient period that precedes eventual predator declines to c ¼ side communities. Thus, i 0 corresponds to demo- the long-term absorbing state of extinction c ¼ graphically closed and i 1 corresponds to (Appendix S1: Section S1) that occurs without external demographically open populations following Johnson larval supply. In deterministic simulations we omit (2005). Combining larval production in external areas stochasticity in urchin larval survival (rU ðt; xÞ¼1) and q ¼ : for species i i with local retention, dispersal into the kelp survival (sA 0 37, the average sA across all obser- local community is vations). In stochastic simulations we model sAðsK Þ as a beta distribution fitted to remote-sensed kelp biomass in ðq ðs ÞÞ ¼ c q þð c Þq ðs Þ; \c : Di i K i i 1 i i K 0 i 1 (9) the region (31 yr; Bell et al. 2015; Fig. 1c) and rU ðsK ; xÞ as a beta distribution fitted to observed age-1 In the spatially explicit model (Fig. 1c), the density of urchin densities (27 yr, 33 sites; Kushner et al. 2013). We species i larvae arriving in patch x depends on the dis- then rescale rU ðsK ; xÞ by its mean so that stochasticity persal kernel kiðx; yÞ, which describes the proportion of does not affect long-term larval survival (i.e., average larvae in patch y dispersing to x: rU ðsK ; xÞ¼1). In the spatial model, we account for w w observed scales of environmental stochasticity ( sA , rU ; Xn Appendix S1: Section S1) using multivariate beta distri- D ðq ðs Þ; xÞ¼ k ðx; yÞq ðs Þ: (10) i i K i i;y K butions, wherein correlations in kelp and urchin larvae y¼1 survival decline with distance according to a Gaussian distribution (discretized as in Eq. 11). For the discrete dispersal kernel, we integrate a con- tinuous Gaussian distribution with mean 0 and vari- w2p= w ance i 2 (i.e., mean dispersal distance i when Model analysis integrating absolute dispersal distances over all off- In one-patch models, we measure resilience R of the spring) over the length of coast Dd spanned by patch kelp forest state, with alternative stable states present for x to calculate 0 < R < 1, and absent for R 1 (indicating 100% for- 2 ests) and R 0 (indicating 100% barrens). In the deter- kiðx; yÞ¼Uðjy xjþDd=2; w p=2ÞUðjy xj i (11) ministic case, we quantify R as the proportion of 1,000 D = ; w2p= Þ d 2 i 2 uniformly spaced initial conditions that result in kelp forests. In stochastic simulations, we measure R as the using the Gaussian cumulative density function U. proportion of time local communities spend in a forested state (Scheffer et al. 2015). For stochastic simulations, we also measure the mean duration of forest and barren Model implementation states, where increasing durations signify increasing resi- We numerically simulate model dynamics using R lience of each state (Fig. 1d; Livina et al. 2010). In all 3.4.3 (R Core Team 2017; see Data S1 for model code), stochastic simulations, we first test for multimodality in 6¼ sþ ’ solving intrannual dynamics (t K ), and accounting the distribution of kelp biomass using Hartigans dip for dispersal and environmental stochasticity at the end test (Hartigan and Hartigan 1985) to see if alternative ¼ sþ of each year (t K ). We use a spatial resolution of stable states are present. We then identify each state by Dd ¼ 1:5 km (i.e., n ¼ 200 patches) to resolve the small- fitting mixed skewed-normal distributions to model est-scale stochasticity, and analyze simulations over results, and use these distributions to determine commu- 1,000 yr following a 3,000-yr burn-in period to exclude nity states in every patch and year (i.e., AxðsK Þ, UxðsK Þ). transient dynamics (Appendix S1: Section S3). Given Note that, while predators are largely extinct in patches the presence of kelp forests outside our study area, we with lengthy barren states, predator densities in stochas- exclude by assuming a linear coastline with tic models generally vary over longer time scales and do periodic boundary conditions in kiðx; yÞ (Gouhier et al. not exhibit a clear bimodality. 2010), placing organisms that disperse beyond the limits In spatially explicit simulations, we first test for sys- of our system into patches on the opposite end. tem-wide alternative stable states by investigating the ini- We parameterize our models based on published stud- tial-condition dependence of the system-wide outcome. ies (Table 1) and monitoring data (Appendix S1: Sec- Specifically, we measure the frequency of forest states, tion S1). In one-patch models, we calculate external aggregated across space, in simulations starting from q larval production i as would occur for a 75% frequency either all patches initially forested or nearly barren. In of kelp forests across all suitable habitat in the system stochastic simulations where disturbances might induce (observed in Castorani et al. 2015; we relax this assump- localized state shifts, we quantify the mean spatial extent tion in Appendix S1: Section S1, Fig. S4). Specifically, and duration of forests and barrens over the range of we separately determine larval production in each state fishing intensities. To verify that our stochastic dynamics q q for closed communities ( i;forested, i;barren) and use the reflect the presence of alternative stable states (Scheffer q ¼ : q þ : q weighted average of i 0 75 i;forested 0 25 i;barren.In et al. 2015), we run simulations with and without the Article e02930; page 6 VADIM A. KARATAYEVAND MARISSA L. BASKETT Ecology, Vol. xx, No. xx recruitment facilitation feedback (i.e., fc ¼ 0:85 and 0) the presence of alternative stable states and reduces for- and test for bimodality in kelp biomass. Bimodality with est resilience. The magnitude of annual urchin settle- and unimodality without facilitation indicates that feed- ment, coupled with fast growth of kelp biomass, also back-based alternative stable states drive community means that pulses of high and low urchin larval survival dynamics, while bimodality in both cases indicates are the primary source of environmental stochasticity stochasticity as the driver of observed patterns. Addi- that drives community shifts in our model tionally, to evaluate whether the scale of disturbance (vs. (Appendix S1: Section S5). dispersal) determines the scale of alternative stable In contrast to urchins, the fraction of external preda- states, we explore a range of spatial scales in urchin set- tor larvae increases the frequency and duration of kelp w tlement stochasticity rU. forests by increasing total settlement (which encapsu- lates presettlement, settlement, and early post-settlement processes that affect overall establishment) of predator Comparison to observed community scales larvae in urchin barrens. The feedback driving alterna- To test the realism of our spatial model predictions, tive stable states (recruitment facilitation) limits this out- we compare the spatial scale and durations of alternative come by controlling the number of dispersing states in the model to monitoring data from 83 sites individuals that successfully settle within a location. across the Channel Islands (Kushner et al. 2013, PISCO Taken together, external predator larval supply alone et al. 2011; see Appendix S1: Section S4 for analysis leads to loss of alternative stable states (only forests details). Monitoring sites span only kelp where stable), while at high external larval supply in both spe- kelp loss arises predominantly from urchin grazing; con- cies, effects of external urchin larval input predominate, sequently, we classify each site in every year as forested maintaining barrens locally even in regions dominated if adult plants are present (>1 individual/100 m2) or bar- by kelp forests. This presence of alternative stable states ren otherwise. Due to the limited length of time series under high external larval input requires feedbacks that (10–22 yr), most (76%) observations record only par- affect predator settlement, and disappears in a prelimi- tially observed state durations (i.e., start and/or end nary investigation of post-settlement feedback mecha- years unknown). To utilize all data, we compare obser- nisms that affect only established individuals vations with 10,000 equivalently long subsets of model (Appendix S1: Section S2, Fig. S5). simulations, each starting at a randomly selected patch and year (omitting model transients; see Appendix S1: Spatial scales of alternative stable states Section S4 for comparison of only fully observed states). Because data were recorded at individual sites, we calcu- Consistent with the one-patch simulations, our late the spatial scale of states in both simulations and stochastic spatially explicit model reveals forested and data as the distance at which Pearson correlation in barren states at localized but not global scales. While the community state j, calculated over a 5 km window mov- deterministic spatial model exhibits initial-condition- dependent system-wide alternative stable states at inter- qingffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi by 0.5 km, declines to zero (with standard error mediate levels of fishing intensity (the predominant ð j2Þ=ð Þ1 1 n 2 given n comparisons). source of predator mortality, Fig. 3a), in the presence of stochasticity the long-term, spatially aggregate ecosys- tem state is independent of initial conditions (Fig. 3b; RESULTS Appendix S1: Fig. S7). However, individual patches in the stochastic simulations typically occur in one of two Presence of alternative stable states under external larval distinct urchin- and kelp-dominated states (87% of input patches with <0.02 or >1 kg/m2 kelp, Fig. 4c) that span We find that the occurrence of alternative stable states localized 10–20 km scales and can persist for decades decreases (i.e., increasing forest resilience) with the frac- (Fig. 5a, b). This feature reflects tion of external predator larvae but increases with the dynamics because the stochastic model without the fraction of external urchin larvae in both the determinis- recruitment facilitation feedback exhibits a unimodal tic (Fig. 2a) and stochastic (Fig. 2b–d) implementations state distribution (Fig. 4b, c). of our model. Intuitively, external urchin larval input Our spatially explicit model also illustrates how the increases the persistence of barren states by maintaining spatial scale of alternative stable states depends on the high settlement when kelp are overgrazed to low levels. interaction between the scale of environmental stochas- External urchin larval input also can increase forest state ticity and the amount of ecological resilience based on persistence because greater urchin settlement increases within . By reducing forest resilience, predator consumption, which in turn increases predator higher fishing increases the frequency and duration of production and densities to reinforce forest states. This barrens (and vice versa for forests; Fig. 5a, b) as pulses outcome entails high urchin population turnover in for- of urchin larvae become more likely to produce barren est states, as observed in reality (Kenner and Lares states. The spatial scale of barrens simultaneously 1991). Overall, external urchin larval input maintains increases because, for a given disturbance level, nearby Xxxxx 2019 ALTERNATE STABLE STATES AND CONNECTIVITY Article e02930; page 7

FIG. 2. Effects of external predator and urchin larval supply from a partially (75%) forested environment on the presence of alternative stable states (i.e., kelp forest resilience between 0 and 1) (a) without and (b) with environmental stochasticity, and the effects of external larval supply on mean duration of (c) forest and (d) barren states in the stochastic model. For reference, autocor- relation in community dynamics without recruitment facilitation (fc ¼ 0) declines to zero in 4–5 yr. Boxes highlighting larval supply regimes in the top-right of each panel denote the proportion of external larval supply corresponding to our spatially explicit model w ¼ c ¼ : (dispersal distances i 80 km are approximately equivalent to a fraction of external larvae i 0 997; see Appendix S1: Fig. S1 c w for the full relationship between i and i). locations experience greater likelihood of being in a bar- P = 0.61, two-sample Kolmogorov-Smirnov tests here ren state. The spatial scale of urchin barrens peaks at and throughout). However, distributions of barren dura- intermediate spatial scales of environmental stochastic- tions differed more strongly (D = 0.27, P < 0.001), with w ity ( rU ; Fig. 5c, d): initial increases in the scale of vari- mean barren durations shorter in simulations compared ation in larval supply increase the scale of both states by to data (2.9 vs. 4.8 yr; see Discussion for possible expla- synchronizing environmental conditions among nearby nation). Omitting partially observed states yielded anal- w communities. Eventual increases in rU reduce the ogous results (Appendix S1: Section S4). The spatial capacity of urchin dispersal to mitigate stochastic popu- scale of community states was on a similar magnitude in lation declines via larvae from areas experiencing favor- simulations compared to data, albeit substantially larger able environments (i.e., the spatial ). The (15 vs. 30 km, distances where correlation declines to resulting declines in overall urchin densities and settle- zero in Fig. 6c). ment reduce the extent of barrens by reducing their resi- lience and the persistence of both states. DISCUSSION Our results show that alternative stable states can Comparison to observed community scales remain relevant in highly interconnected communities Duration and spatial scales of alternative states in the (Figs. 2, 4). This relevance of alternative stable states in spatial model were partially comparable to data (Fig. 6). our model most likely arises because the feedback mech- Overall, distributions of observed forest state durations anism maintaining urchin barrens (low predator facilita- differed little from model expectations (D = 0.07, tion) affects the settlement and early post-settlement Article e02930; page 8 VADIM A. KARATAYEVAND MARISSA L. BASKETT Ecology, Vol. xx, No. xx

FIG. 3. System-wide alternative stable states that occur in the (a) deterministic spatially explicit model disappear in the (b) stochastic model with environmental variation. Each plot shows long-term community dynamics of simulations starting from a forested (black, dashed lines) or near-barren (gray, solid lines) state, across levels of fishing intensity, the predominant source of predator mortality.

ab

cd

FIG. 4. Spatiotemporal kelp forest dynamics (top row) and frequency distributions of community states (bottom row) in our model with (fc ¼ 0:85, left column) and without (fc ¼ 0, right column) the recruitment facilitation feedback that produces alterna- tive stable states. Panels a and b show kelp biomass, with forested states in green-yellow and barren states in dark blue. The time period shown is from after the 3,000-yr burn in period from a spatially homogeneous kelp forest state. P values from the dip test in panels c and d indicate whether the distributions of kelp biomass are multimodal (P\0:05), indicating the presence of alternative stable states, or unimodal (P [ 0:05), with accompanying test statistics D. In panel c, contours denote the best-fit skew-normal bivariate distributions, and dashed line denotes the fitted boundary between forest and barren states. Xxxxx 2019 ALTERNATE STABLE STATES AND CONNECTIVITY Article e02930; page 9

FIG. 5. (a, b) Effects of fishing intensity (which determines forest resilience) and (c, d) the spatial scale of variability in urchin w larval survival ( rU ) on the average duration (a, c) and spatial extent (b, d) of kelp forests (solid lines) and urchin barrens (dashed lines). Shaded areas in panels a and b denote variation (25th and 75th percentiles) in state duration across patches (a) or spatial w extent across years (b). Parameters not varied in each plot (i.e., FP or rU ) held at default values (Table 1). survival of predators dispersing into local communities, and Scheffer 2005, Martin et al. 2015). In models with but not subsequent post-settlement processes (e.g., natu- settlement feedbacks similar to ours, fine-scale (0.1– ral predation and fishing mortality: Appendix S1: Sec- 100 m, below the scales of dispersal) patterning of dis- tion S2, Fig. S5). Specifically, dispersing predator larvae tinct states arises through self-organization when organ- do not overwhelm settlement feedbacks within patches isms facilitate each other locally and inhibit growth at as might otherwise be intuitively expected because few larger scales (Rietkerk and Van de Koppel 2008). dispersers successfully establish in the community. Our findings show the potential for analogous self- Across local communities, the settlement feedback organization mechanisms to structure ecosystems on reduces dispersal among communities in distinct states large (e.g., 10–20 km) spatial scales. Taken together, and maintains localized, alternatively stable forest and multiple sources of ecosystem heterogeneity can induce barren states (Fig. 4). In contrast, preceding spatially alternative stable states at local scales. explicit studies that predict dispersal-induced synchrony We also find that the spatial and temporal scales of of ecological states over large scales (van Nes and Schef- each stable state increase with its local-scale basin of fer 2005, Martin et al. 2015) have focused on post-settle- attraction and the scale of environmental variation, ment feedbacks as the drivers of alternative stable states. which outweigh the role of dispersal scale. The attraction This suggests that the relevance of alternative stable basin size of a given state (e.g., forests) depends on local- states in highly interconnected communities might ized dynamics (here, fishing intensity, Fig. 5a, b) and require settlement feedbacks, a hypothesis worth testing represents its ecological resilience. Our results integrate in alternate model structures. previous stochastic and spatially explicit models that Our results show that ecosystem heterogeneity have separately emphasized how greater resilience required for alternative stable states to be relevant increases the persistence (Livina et al. 2010) and spatial locally (here, spatially asynchronous stochasticity; scale (Bel et al. 2012) of alternative stable states. The Fig. 3) may occur below the scales of dispersal (e.g., spatial scales of alternative stable states can also increase w \\w rU U in our model, Fig. 5d). Conversely, in spa- with the spatial extent of environmental variation via tially explicit models with post-settlement feedbacks, environmentally induced synchrony (Fig. 5c, d; the alternative stable states co-occur among local communi- Moran effect; Gouhier et al. 2010) when disturbances ties only when stochasticity or habitat patchiness exceed are well below the scale of dispersal. However, larger- the scales of dispersal (Durrett and Levin 1994, van Nes scale disturbances can decrease the spatial extent of both Article e02930; page 10 VADIM A. KARATAYEVAND MARISSA L. BASKETT Ecology, Vol. xx, No. xx

FIG. 6. (a, b) Durations and (c) spatial scales of community states in model simulations compared to field data. Minimum dura- tions (i.e., both fully and partly observed states) of barrens (a) and forests (b) given for data (bars, frequencies) and model simula- tions (red). Spatial autocorrelation of community states in simulations (red) and data (black) is calculated over a 5 km window moving by 0.5 km; gray lines denote 99% confidence intervals. states by reducing the role of dispersal and weakening preferentially immigrate to areas of high coral cover dispersal-induced synchrony. Analogous dynamics occur (which offer predation refugia) when emigrating from in stochastic population models with single equilibria nursery habitats (Dixson et al. 2014). Consequently, dis- (Kendall et al. 2000), highlighting how extensive tinct states might co-occur among local reefs, especially research on population synchrony might inform the spa- when large-scale disturbances have reef-specific impacts tial scales of alternative stable ecosystem states. due to long-term, localized environmental differences (e.g., areas with protected vs. fished herbivores; Mumby et al. 2013). In terrestrial systems where competitively Systems where alternative stable states might be relevant inferior grasses impede tree seedling survival by amplify- locally ing fire severity, empirical studies find mounting evi- The settlement feedbacks expected to be necessary for dence for alternative stable savanna and forest states the local relevance of alternative stable states in our (Staver et al. 2011). Consistent with our results, spatially model are likely to occur in many taxa. In general, explicit models predict that these states co-occur locally plants and numerous marine species disperse during below (and independently of) the scale of tree dispersal seed, spore, or larval stages, which often are inferior (Schertzer et al. 2015) when propagate heteroge- competitors compared to individuals already established neously across landscapes. Numerous studies also docu- in the community or rely on facilitating species for sur- ment localized alternative stable states that arise as fine- vival (reviewed in Caley et al. 1996, Bruno et al. 2003, scale patterns in systems such as mussel beds, wetlands, Clobert et al. 2009). Additionally, actively moving adult and arid ecosystems when established individuals deplete animals and aquatic larvae avoid settling in areas of resources or displace growth-inhibiting factors (e.g., intense , high predation risk, or unfavorable snow fields in alpine forests; reviewed in Rietkerk and conditions (Morgan et al. 1996, Benton and Bowler Van de Koppel 2008). Given that both processes locally 2012). Thus, settlement feedbacks can arise from behav- inhibit settlement of new individuals, our results imply ior during or high mortality immediately after settlement that the scale of such patterns in general depends on the that prevents dispersers from establishing in the commu- scales of depletion or ecosystem engineering nity. rather than the scale of dispersal. Observed settlement feedbacks might in turn underlie localized alternative stable states in a variety of ecosys- Empirical evidence and tests for localized alternative tems beyond temperate rocky reefs. For tropical reefs stable states where coral larvae cannot settle or survive in algae- dominated areas, alternative stable coral and macroalgal The localized spatial and temporal scales of alterna- states occur in spatially explicit models on the scale of tive stable states predicted here are in line with empirical individual reefs (~500 m2) despite high levels of external observations of temperate and tropical rocky reef sys- larval supply (Mumby et al. 2007). Additionally, herbiv- tems. The duration of kelp forests in our model match orous fish that reinforce coral-dominated states observed community scales in the Channel Islands. The Xxxxx 2019 ALTERNATE STABLE STATES AND CONNECTIVITY Article e02930; page 11 greater duration of barrens observed compared to expec- presence of kelp. Alternatively, several feedbacks omit- tations might be due to lower urchin predator densities ted here might reinforce urchin barrens. First, changes in in the northern Channel Islands compared to the mod- urchin foraging behavior not modeled here can lead to eled region, which arise partly due to lower body growth intensified grazing at low predator densities (Cowen or higher mortality (Caselle et al. 2011). The smaller 1983) or at low levels of kelp biomass and therefore spatial scale of community states in the data compared reduced supply of drift kelp (Ebeling et al. 1985, Har- to expectations likely arises from spatial heterogeneity in rold and Reed 1985). Second, urchins might also experi- rocky reef habitat availability not accounted for here (see ence recruitment facilitation in barrens due to crustose Model robustness for details). Worldwide, studies on coralline algae, which might compete with kelp (Baskett temperate rocky reefs often find evidence for kelp- and and Salomon 2010). Additionally, predators preferen- urchin-dominated states (analogous to Fig. 3a) even tially avoid consuming starving urchins in barren areas when sampling at very fine scales (5 m2; Ling et al. (Eurich et al. 2014). All of these mechanisms could 2015). Among 51 transitions between these states docu- increase urchin densities or grazing at low kelp biomass. mented worldwide, two-thirds occurred at <100 km spa- Acting together, multiple feedbacks can produce alterna- tial scales (Filbee-Dexter and Scheibling 2014). These tive stable states even when individually each mechanism scales are likely at or below the mean dispersal distance is insufficient to do so (van de Leemput et al. 2016). The of urchins and their predators given the species’ long strength of most feedbacks posited to drive alternative pelagic larval duration and strong, large-scale genetic kelp and barren states, including our feedback of recruit- exchange (100–300 km; Waples and Rosenblatt 1987, ment facilitation, is often estimated in only a few small- Edmands et al. 1996). Similarly, in tropical coral reefs scale, system-specific studies (Ling et al. 2015). Ninio et al. (2000) found long-term shifts to algal-domi- Nevertheless, our qualitative results are not sensitive to nated regimes that were spatially localized (~10 km) and the level of facilitation (Appendix S1: Section S6), and asynchronous at larger (~100 km) scales. this mechanism is consistent with greatly reduced preda- The spatial scales of alternative stable states found here, tor densities in barrens vs. kelp forests in our system while local, still exceed the extent of feasible manipulative (Graham 2004). experiments and many ecological surveys, which impedes Our model also makes several simplifying assumptions efforts to detect this phenomenon. The two most com- that might quantitatively affect the extent and duration of monly used approaches to detect distinct states under the alternative stable states. For example, we ignore the fact same environmental conditions involve demonstrating that juvenile and adult predators (particularly lobsters) either (1) a lack of recovery of an original, stable state fol- can potentially move over long distances and, unlike lar- lowing experimental manipulations or natural distur- vae, might immigrate to and survive in barren areas with bances or (2) a bimodality in the distribution of ecological low kelp cover. Our model also does not account for kelp states observed across locations in field surveys (e.g., mortality during extreme warm water events, which can Fig. 4c; reviewed in Mumby et al. 2013, Scheffer et al. span much larger spatial scales than storm-driven kelp 2015). We highlight that both features occur only when loss (Dayton et al. 1999). Additionally, we parameterize the spatial extent of experiments or surveys is greater than stochasticity in urchin larval survival based on data from the spatial scale of alternative stable states; at finer scales, the Channel Islands, which experience stronger oceano- detection efforts might fail because dispersal or long- graphic variability compared to other California rocky distance interactions rapidly reverse the effects of manipu- reefs. Together, increased role of dispersal by adult preda- lations or disturbances, maintaining a single community tor movement, large-scale kelp mortality events, or lower state (Petraitis 2013). One approach toward resolving the intensity of localized stochasticity might produce larger- presence and scale of local alternative stable states can be scale community states than predicted here. Alternatively, to pair spatially explicit dynamical models with field data our model might over-estimate these scales due to limited (Scheffer et al. 2001). In particular, model selection given dispersal among communities separated by areas lacking observed data can quantify the extent to which observed kelp habitats, particularly between islands (1–5 km; Cava- spatiotemporal patterns are consistent with expectations naugh et al. 2013). Other forms of local environmental for multiple types of hypothesized feedback loops, as com- heterogeneity not modeled here, such as heterogeneity in pared to solely the effects of environmental heterogeneity fishing intensity due to distance from ports or the pres- known to occur in a given system. ence of marine protected areas (Hamilton et al. 2011) and variation in kelp growth conditions might also make forests and barrens manifest within more localized areas Model robustness of our system. For tractability, we omitted several factors that might affect the feedback loops that drive the relevance of Management implications alternative stable states under external larval input. One factor that might erode the recruitment facilitation feed- We find that increasing stress applied to the overall back maintaining urchin barrens in our model is strong ecosystem (here, fishing) can induce localized socioeco- predation on urchins by species less reliant on the nomically undesired states (here, urchin barrens) that Article e02930; page 12 VADIM A. KARATAYEVAND MARISSA L. BASKETT Ecology, Vol. xx, No. xx gradually increase in frequency, spatial extent, and ACKNOWLEDGMENTS duration (Fig. 5a, b). Our results suggest that while spatially synchronous state shifts expected in intercon- We would like to thank Robert Dunn, Tom Bell, David Kush- nected systems (Hughes et al. 2005, 2013) may be unli- ner, Jennifer Caselle, Katie Davis, Nicholas Shears, Daniel kely when settlement feedbacks reduce the role of Reed, Max Castorani, and the Santa Barbara Long Term Eco- logical Research for biological insights and providing data. We dispersal (Fig. 3b), collapsed states could span 10– also thank Alan Hastings, Sebastian Schreiber, Jay Stachowicz, 30 km of the coastline and persist for decades under and two anonymous reviewers for feedback that greatly intense exploitation (here, fishing). Where disturbances improved the manuscript. Funding for this project was provided induce localized undesired states, local management by a National Science Foundation Graduate Research Fellow- efforts can increase the probability of recovery by ship to V. A. Karatayev. increasing the attraction basin size of desired states, for example by reducing predator harvest (i.e., by imple- LITERATURE CITED menting ecologically sustainable yield sensu Zabel et al. Barnett, L. A. K., and M. L. Baskett. 2015. Marine reserves can 2003). Alternative management approaches to restoring enhance ecological resilience. Ecology Letters 18:1301–1310. desired states include manipulating species densities, for Baskett, M. L., and A. K. 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