Title: Community assembly: alternative stable states or alternative transient states?
Abstract: Ecology LettersVolume 14, Issue 10 p. 973-984 IDEA AND PERSPECTIVEOpen Access Community assembly: alternative stable states or alternative transient states? Tadashi Fukami, Corresponding Author Tadashi FukamiE-mail: [email protected]Search for more papers by this authorMifuyu Nakajima, Mifuyu Nakajima Department of Biology, Stanford University, Stanford, CA 94305-5020, USASearch for more papers by this author Tadashi Fukami, Corresponding Author Tadashi FukamiE-mail: [email protected]Search for more papers by this authorMifuyu Nakajima, Mifuyu Nakajima Department of Biology, Stanford University, Stanford, CA 94305-5020, USASearch for more papers by this author First published: 25 July 2011 https://doi.org/10.1111/j.1461-0248.2011.01663.xCitations: 42 Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://wileyonlinelibrary.com/onlineopen#OnlineOpen_Terms AboutSectionsPDF Comments ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Ecology Letters (2011) 14: 973–984 The concept of alternative stable states has long been a dominant framework for studying the influence of historical contingency in community assembly. This concept focuses on stable states, yet many real communities are kept in a transient state by disturbance, and the utility of predictions for stable states in explaining transient states remains unclear. Using a simple model of plant community assembly, we show that the conditions under which historical contingency affects community assembly can differ greatly for stable versus transient states. Differences arise because the contribution of such factors as mortality rate, environmental heterogeneity and plant-soil feedback to historical contingency changes as community assembly proceeds. We also show that transient states can last for a long time relative to immigration rate and generation time. These results argue for a conceptual shift of focus from alternative stable states to alternative transient states for understanding historical contingency in community assembly. Introduction It is increasingly recognised that the species composition and diversity of ecological communities can be greatly influenced by the history of community assembly. Growing evidence indicates that the effect of biotic interactions on species abundances may depend on the order and timing of species immigration during community assembly, the phenomenon known as priority effect (e.g. Schoener 1976; Drake 1991; Almany 2003). The extent of historical contingency due to priority effect is difficult to quantify because immigration history is impossible to reconstruct in sufficient detail for most natural communities. Nevertheless, theory suggests that biotic historical effects can be substantial (Gilpin & Case 1976; Drake 1990; Law 1999; Fukami 2004b; Steiner & Leibold 2004), with profound implications for understanding and conserving species diversity. For example, priority effect can cause unexpectedly high variability in community structure, or high beta diversity sensuWhittaker (1960, 1972), among similar sites (Fukami 2004b; Chase 2010). Further, if historical contingency is important, restoring native diversity in degraded sites may require specific sequences of species removal and introduction to be successful (Fukami et al. 2005; Young et al. 2005; Suding & Hobbs 2009; Kardol & Wardle 2010). In this light, much research has been directed toward identifying the environmental factors that determine the importance of assembly history, such as habitat productivity (Steiner & Leibold 2004), ecosystem size (Fukami 2004a), disturbance frequency (Jiang & Patel 2008) and environmental heterogeneity (Shurin et al. 2004; Van Nes & Scheffer 2005). In the effort to understand the role of historical contingency in community assembly, the concept of alternative stable states (also known as multiple stable points, multiple stable equilibria, alternative attractors, multiple domains of attraction and other similar terms) has played a dominant role as the guiding theoretical framework (e.g. Lewontin 1969; Sutherland 1974; May 1977; Peterson 1984; Drake 1991; Petraitis & Dudgeon 1999; Beisner et al. 2003; Schröder et al. 2005; Suding & Hobbs 2009). According to this concept, there can be more than one final stable state of species composition that assembling communities may approach depending on immigration history, even under the same environmental conditions and the same species pool. Once a community reaches a stable state, it cannot move to another unless heavily disturbed (Lewontin 1969; Gilpin & Case 1976; Law 1999). This concept places a special emphasis on the analysis of stable states, not necessarily because stable states characterise natural communities, but primarily because of mathematical tractability (DeAngelis & Waterhouse 1987; Hastings 2004, 2010). As long recognised since at least Cowles (1899), many real communities are in a transient, not stable, state, because disturbance keeps communities from reaching a stable state (reviewed in Pickett & White 1985). Despite this mismatch between theory and reality, theoretical predictions about alternative stable states can be useful in understanding real communities if two further assumptions are met. One assumption (hereafter assumption 1) is that, even if natural communities are not in a stable state, theoretically predicted stable states help to explain transient communities (Chase & Leibold 2003; Didham et al. 2005; Schröder et al. 2005). In other words, transient and stable states do not differ qualitatively with respect to the conditions that make assembly history important to community structure, as measured by the level of beta diversity generated by priority effect. A second assumption (hereafter assumption 2) is that, even if assumption 1 is not always true, the transient states to which assumption 1 does not apply are so short-lived that any discrepancy between stable and transient states is of minor importance. These assumptions are, however, only tacitly implied in most studies thus far. Given the central role that the concept of alternative stable states has played in community assembly research, surprisingly little is known about the validity of these assumptions. In this paper, we examine their validity using a simple simulation model of plant community assembly. Our results suggest that both assumptions may be easily violated. The aim of this paper is not to downplay the well-appreciated importance of studying stable states, but rather to highlight the underappreciated importance of studying transient states. For example, we show that the environmental conditions under which community assembly is particularly sensitive to historical contingency can be understood only by studying transient states directly because it is often not possible to infer transient states from stable states. More generally, we seek to provide new perspectives on community assembly in order to stimulate more research on alternative transient states, which we believe will help to advance the understanding of historical contingency in community assembly and its effect on species diversity. We define alternative transient states as follows: communities are in alternative transient states when they have not reached a stable state, but vary in structure (e.g. species composition and diversity) and/or function (e.g. total biomass and carbon flux) because of variable immigration history and other stochastic processes, even though they have assembled under the same environmental conditions, have received the same set of species multiple times, and have undergone population dynamics over multiple generations of the species involved. This definition ensures that alternative transient states do not include obvious cases in which communities vary in composition simply because they vary in environmental conditions or species pool or because they are at an early stage of assembly where species composition is inevitably variable. Thus, our definition of alternative transient states is identical to that of alternative stable states proposed by Connell & Sousa (1983) and further articulated by Chase (2003), except that communities exhibiting alternative transient states have not reached a stable state, whereas those in alternative stable states have. Here, a community is considered stable when the locally coexisting species are permanent members of the community and are resistant to colonisation by any additional species in the region (Law 1999). In the following sections, after describing the main model employed, we will present results that indicate that assumptions 1 and 2 can easily be violated. We will then discuss implications of the violated assumptions for understanding how the importance of historical contingency varies along environmental gradients. Because any theoretical prediction needs to be evaluated by empirical evidence, we will also discuss empirical data relevant to our simulation results. We will end by suggesting several future research directions for further improving our understanding of alternative transient states. Model Description Overview Our model is a modification of the generalised competition model analysed by Chesson (1985), Pacala & Tilman (1994), Hurtt & Pacala (1995) and Mouquet et al. (2002). In our model, species are randomly chosen each year from a regional species pool. The chosen species immigrate as a small number of seeds to a local patch consisting of numerous cells that vary in habitat condition. Initially, all cells are empty. Subsequently, only one individual can establish in each cell even when multiple individuals arrive from the regional pool or from within the patch. Thus, individuals compete at the establishment stage. Of the individuals that arrive at a cell, the one that belongs to the species that best fits the environmental condition of the cell wins. Once established, individuals produce seeds once a year until they die. Individuals die with a fixed probability, and when they do, the previously occupied cells become empty and available for a new individual to establish. This process of immigration, arrival, establishment, reproduction and death is repeated for multiple years. Regional species pools and local patches Regional species pools each contain 30 species, with species i assigned a trait value, Ri, chosen randomly from a uniform distribution [0, 1]. Local patches consist of a linear, circular array of 2000 cells. The condition of cell j is defined by a value, Hj, chosen randomly between 0 and 1 from a beta distribution, where the probability density for value x is proportional to: xa−1 (1 – x)b−1. In our model, we set a = b and use h (=1/a), which takes values between 0 and 1 (see below), as a measure of the spatial environmental heterogeneity (e.g. soil temperature, soil moisture, soil pH) in the patch. Larger values of h indicate greater heterogeneity within the patch (Mouquet et al. 2002). Cells are distributed randomly in the patch with respect to Hj values. Community assembly Each year, each species in the regional species pool immigrates to the local patch with a probability I, equal for all species (I = 0.05). At each cell in the local patch, species i arrives with the probability: 1 – exp [−(Pi + F Ni)/(total number of cells, i.e. 2000)]. Here Pi is the number of individuals of species i that immigrate from the regional pool (20 individuals for species chosen that year for immigration from the regional pool, and 0 individual for all other species), F is fecundity (50 for all species), and Ni is the number of individuals of species i in the local patch (0 for all species in the first year, i.e. at t = 1). When the number of cells that are assigned to receive a seed of species i exceeds Pi + F Ni (which rarely happens), Pi + F Ni cells are randomly selected from these cells, and a seed of the species assigned only to the selected cells. Given this probability, there are three possibilities regarding individual establishment in each cell. First, if the cell is already occupied by an individual, that individual remains there. Second, if the cell is empty, of the species that arrive at that cell, the one with the greatest value of Cij establishes. The value of Cij, which defines the competitive ability of species i at cell j, is given as: 1–|Hj–Ri| if neither cell j− 1 nor cell j + 1 is already occupied by species i; 1–|Hj–Ri| + f if cell j− 1 or cell j + 1 is already occupied by species i; and 1–|Hj–Ri| + 2f if both cell j− 1 and cell j + 1 are already occupied by species i. The value of f is positive or negative, respectively, when the presence of conspecifics in neighbouring cells increases or decreases the competitive ability of species i relative to other species. A biological basis for such neighbouring effects is plant-soil feedback (Bever 2003; Eppstein & Molofsky 2007). We set f = 0, 0.05 or 0.1 for all species and for all cells. We use positive f values to simulate positive feedback in our model as a mechanism of priority effect (Knowlton 1992, 2004; Bever 2003; Eppstein & Molofsky 2007; Kardol et al. 2007; Suding & Hobbs 2009). In some plant communities, feedback may be negative rather than positive (e.g. Kardol et al. 2006), and may affect individuals in the same cell rather than neighbouring cells (e.g. Bever 2003; Levine et al. 2006). We will discuss these and other possibilities as future research directions, but focus in this paper on positive feedback as a simple example of a source of alternative stable states. Third, if the cell is empty and no species arrives at that cell, it remains empty. After individual establishment is completed for all cells, individuals occupying a cell die with the probability, m. We set m = 0.1 or 0.5 for all species. In our model, competitive ability, Cij, does not directly affect fecundity or mortality, but does affect the ability to ‘fight’ for a cell, which indirectly affects fecundity and mortality. The assumption that species are identical in mortality and fecundity is also made by the neutral theory (Bell 2001; Hubbell 2001), but in our model, species are not neutral, because competitive ability, Cij, differs between species. Moreover, the neutral theory focuses on explaining the structure of equilibrium communities, whereas we focus on explaining the structure of transient communities. Following these rules of immigration, arrival, establishment, reproduction and death for 1600 generations (for t = 1600 years), we assemble 10 communities using the same set and distribution of Hj values in the patch under each regional pool used. Two observations confirm that communities always reach a stable state by the 1600th generation in our model. First, there is no obvious long-term change in immigration and extinction rates from the 1200th to 1600th generations, indicating that communities have entered an equilibrium state by, conservatively, the 1600th generation (see Fig. S1 in Supporting Information). Second, between the 1200th and 1600th generations, there is virtually no immigration (indicating that communities are resistant to invasion by any additional species from the regional pool) or extinction (indicating that communities have stable species composition with no species lost over time) if immigration and extinction are measured for species having more than 100 individuals in the patches, indicating that communities have reached a stable state (see Fig. S1). In contrast, communities are still in a transient state at the 60th generation, as indicated by immigration and extinction rates still changing over time (see Fig. S1). Below we mainly compare communities observed at t = 60 and t = 1600 as those at transient and stable states, respectively. Species diversity We measure alpha diversity as the mean number of species present in a local patch (averaged over the 10 replicate communities), gamma diversity as the number of species present in one or more of the 10 patches, and beta diversity as gamma diversity divided by alpha diversity. This measure of beta diversity is the original multiplicative form of Whittaker (1960, 1972). Although other measures of beta diversity have been proposed (Koleff et al. 2003; Tuomisto 2010; Anderson et al. 2011), we use Whittaker’s measure for two reasons. First, it can be interpreted as indicating the number of alternative community states observed in different patches in the region (Jost 2010; Wilsey 2010), or more precisely, the effective number of distinct local communities in the region (Jost 2007, 2010; Wilsey 2010), applicable for both transient and stable states. Thus, multiplicative beta diversity can be used as a surrogate for the effective number of alternative states, which can be used to evaluate the importance of immigration history in community structuring. Second, unlike some other measures of beta diversity, the multiplicative measure is comparable between regions even when alpha diversity is variable between regions (Jost 2010; Wilsey 2010). We note, however, that further analysis indicates that our main conclusions regarding the validity of assumptions 1 and 2 hold true when we use the additive, rather than multiplicative, measure of beta diversity, calculated as gamma diversity minus mean alpha diversity (Lande 1996; Crist et al. 2003; Veech & Crist 2010). Mortality rate, environmental heterogeneity and the strength of intra-specific feedbacks To examine the effect of mortality rate (m), habitat heterogeneity (h) and the strength of plant-soil feedback ( f ) on the importance of historical contingency as measured by beta diversity, we run the simulation using all possible combinations (hereafter called scenarios) of the following parameter values: m = 0.1 and 0.5; h = 0.0125, 0.025, 0.05, 0.1, 0.2 and 0.4; and f = 0, 0.05 and 0.1 (Fig. S2). We analyse 20 replicates (20 independently created pairs of the regional pool and local patch) to examine alpha, beta and gamma diversity for each combination of m, h and f values (Fig. S2). Model Results Evaluating assumption 1: are stable states and transient states comparable? To investigate the validity of assumption 1, we now use several illustrative examples of simulation results. Some examples indicate that assumption 1 is sometimes valid. For instance, comparing two scenarios of community assembly, one with positive feedback and one without (Fig. 1), we find, for stable communities (i.e. at t = 1600), that beta diversity is higher when there is positive feedback. This is an expected result: in general, when the strength of positive feedback ( f ) = 0, there is only a single stable state that is approached by the assembled communities, but when f > 0, alternative stable states exist, as confirmed by the fact that beta diversity is greater than 0 at t = 1600, even when only species with more than 100 individuals in a given community are regarded as members of that community (Fig. S3; see also Figs S4–S7). In any case, except at very early stages of community assembly (until t = ∼20), the relative difference in the level of beta diversity between the two scenarios is the same, throughout all stages of assembly, as the eventual outcome for stable communities, despite the slow gradual decline in the absolute value of beta diversity in both scenarios (Fig. 1). Therefore, in this case, the prediction that the number of alternative states is greater in the presence of positive feedback than in its absence is consistent between stable and transient communities. Figure 1Open in figure viewerPowerPoint Illustrative example of community assembly where assumption 1 is valid: beta diversity is higher in one scenario (a) than in the other (b) for both transient and stable states, except at very early stages of assembly. Temporal changes in alpha, beta and gamma diversity are presented with means (dark lines) and standard deviations (pale lines). Transient dynamics (from t = 1 – 150) and stable states (t = 1580 – 1600) are shown. In (c), beta diversity is presented for both scenarios to facilitate comparison between them. Assumption 1 is not always valid, however. For example, comparing two scenarios, the number of alternative states can be indistinguishable for stable communities, but different in transient communities. In the example shown in Fig. 2, the two scenarios differ only in mortality rate. Beta diversity does not differ between the two scenarios for communities at a stable state, as expected from the same value of f shared between the scenarios. However, it continues to be different for a long time (until t = ∼150) during transient dynamics. Here, mortality rate determines the rate at which beta diversity approaches the final value, causing beta diversity to differ for transient, but not stable, states (Fig. 2). We will refer to these dynamics (Fig. 2c) as slow convergence of beta diversity between scenarios. Figure 2Open in figure viewerPowerPoint Illustrative example of community assembly where assumption 1 is violated: beta diversity differs between the scenarios during transient dynamics, but not at stable states. Symbols are as in Fig. 1. Conversely, beta diversity is in some cases different for stable communities, but indistinguishable for transient communities. In the example shown in Fig. 3, beta diversity of stable communities is again higher in the presence than absence of positive feedback, as expected. But this difference becomes apparent only after t = ∼150. The two scenarios differ from each other in the values of m and f. Here the rate at which beta diversity approaches the final value (which is influenced by m) and the level of the final value itself (which is determined by f ) cancel each other out for a long time in their influence on beta diversity before the eventual difference in beta diversity emerges (Fig. 3). We will refer to these dynamics (Fig. 3c) as slow divergence of beta diversity between scenarios. Figure 3Open in figure viewerPowerPoint Illustrative example of community assembly where assumption 1 is violated: beta diversity differs between the scenarios at stable states, but not during transient dynamics. Symbols are as in Fig. 1. The most troubling case is when beta diversity is higher in one scenario than in another for stable communities, but lower in the former scenario than in the latter for transient communities. In the example given in Fig. 4, the two scenarios differ in h, m and f values. The value of h determines the extent of initial ‘overshooting’ in alpha, gamma and beta diversity, with smaller h values (i.e. less heterogeneous environments) causing more extensive overshooting (Fig. 4). Because of the overshooting, small h values, like small m values, reduce the rate of the approach to the final value of beta diversity determined by the value of f. Consequently, the smaller m and h values in scenario 7 than in scenario 8 in Fig. 4 result in greater beta diversity until t = ∼70, even though beta diversity will eventually become higher in scenario 8 than in scenario 7 because of stronger positive feedbacks (i.e. larger f ). We will refer to these dynamics (Fig. 4c) as temporal reversal of beta diversity between scenarios. Figure 4Open in figure viewerPowerPoint Illustrative example of community assembly where assumption 1 is violated: beta diversity shows temporal reversal between the scenarios (see text for detail). Symbols are as in Fig. 1. A comprehensive pair-wise comparison of scenarios reveals that slow convergence (Fig. 2c), slow divergence (Fig. 3c) and temporal reversal (Fig. 4c) are not uncommon in the parameter space examined (Fig. 5). For example, slow convergence occurs frequently when two scenarios share the same f, but differ in m, whereas slow divergence occurs when one scenario has a higher f and either a higher m or h (or both) than the other. These conditions for slow divergence sometimes result in temporal reversal instead, especially when the scenario with a high f has a particularly high m or h (or both) relative to the other scenario. This is because strong positive plant-soil feedback (high f ) results in an increased number of alternative stable states, whereas low mortality (low m) and/or low environmental heterogeneity (low h ) result in an increased number of alternative transient states due to temporary ‘overshooting’ of gamma and beta diversity. Figure 5Open in figure viewerPowerPoint Summary of all possible pair-wise comparisons of the scenarios shown in Fig. S2. Additional simulations, in which 10 replicate communities are assembled using a single common immigration history (blue lines in Fig. S8), show that temporal reversal (Fig. 4c) would never occur if there was no variation between communities in immigration history (Fig. S9). Thus, these simulations reveal the importance of immigration history, relative to other sources of historical contingency (such as stochastic variation in individual establishment and mortality), in causing inconsistencies in diversity patterns between stable states and transient states. We also point out that occurrence of temporal reversal (Fig. 4c) does not seem to depend on specific characteristics of our model. As a representative example, we use a classic grazing model of vegetation that has been extensively used for studying alternative stable states, especially with the graphical representation of the model (Fig. 6a): dx/dt = rx(1 − x/K) –cx2/(x2 + 1), where r is the per capita growth rate (we assume r = 1), x is the total vegetation biomass of a plant community, K is the carrying capacity of total vegetation biomass and c is the maximum rate of grazing determined by herbivore density ( Van Nes & Scheffer 2005). Using this model originally developed by Noy-Meir (1975) and May (1977), we examine temporal changes in vegetation biomass (as an aggregate property of a plant community) after biomass is reduced by pulse disturbance to less than half of the maximum level. As this model does not consider plant species composition, but just total vegetation biomass, we use between-community variation in total vegetation biomass, instead of beta diversity, as an index of the degree of historical contingency. When grazing rate c is 1.60, there is only one stable state (Fig. 6c), whereas when it is 1.63, there are two alternative stable states that vegetation biomass will tend to after disturbance, depending on initial biomass (Fig. 6b). When c is 1.60 (Fig. 6c), if biomass starts with a very low value, it will first reach a value at which the rate of biomass increase is small. Vegetation biomass will stay there for some time before complete recovery (‘ghost of equilibrium,’sensuVan Geest et al. 2007). If biomass starts above the level at which this slow change occurs, it will increase rapidly toward the stable state. This difference in transient dynamics causes transient divergence (for time = ∼10 –∼40) and then eventual convergence (completed by time = ∼90) in vegetation biomass (Fig. 6c). In contrast, when c is 1.63 (Fig. 6b), divergence proceeds relatively slowly. Because of this contrast in the vegetation recovery dynamics under the two values of c, temporal reversal in the level of biomass variation (Fig. 6d) happens (see also Van Geest et al. 2007; Van Nes & Scheffer 2007). We have found similar results using the two other basic models of alternative stable states studied by Van Nes & Scheffer (2005). Figure 6Open in figure viewerPowerPoint Vegetation recovery in the model defined by dx/dt = rx (1 – x/K) –cx2/(x2 + 1) (see text for parameter details). In (a), black line indicates stable equilibrium, dotted line indicates unstable equilibrium, and arrows indicate the direction of change in vegetation biomass under a given value of c. Two alternative stable states exist for a certain range of c (indicated by shading), as indicated by two stable equilibria for a given c value. In (b) and (c), trajectories of vegetation biomass recovery from 50 different initial values (i.e. 1/100, 2/100, 3/100, 4/100, … 49/100 and 50/100 of the equilibrium value) are shown for each of the two values of c (c1 and c2) indicated in (a). In (d), temporal changes in maximum variation in vegetation biomass between recoveries from different initial values are shown under c1 and c2. In summary, our results indicate that the alternative stable states concept and the predictions derived from it can be potentially highly misleading in predicting the importance of historical contingency in community assembly. For example, as apparent in our results, the number of alternative stable states may be determined solely by the strength of plant-soil feedback, whereas the number of alternative transient states may be determined not only by the strength of feedback, but also by other factors such as mortality rate and environmental heterogeneity. These factors influence the trajectory and speed of community assembly as communities approach their final stable states, affecting transient, but not stable, community states. Consequently, there can be relatively many alternative transient states even when there are few alternative stable states (e.g. scenario 7 in Fig. 4c) and vice versa (e.g. scenario 8 in Fig. 4c). Evaluating assumption 2: are transient states trivial? If assumption 1 is not always valid, the next question is whether discre