and present address: M. J. Papaik, University of Quebec at Montreal, CP 8888 Succ. Centre-Ville, Montreal, Quebec H3C 3P8, Canada (tel. +1 514 987 3000 × 2357, fax +514 987 4647, e-mail firstname.lastname@example.org).
1Severe winds are the predominant cause of natural disturbance in temperate forests of north-eastern and north-central North America. Conceptual models of the effects of wind disturbance have traditionally focused on the impacts of catastrophic disturbances and have painted a simple picture of how disturbance acts to maintain tree species diversity. These models ignore variation among species characteristics that could have important consequences for both resistance to and recovery from disturbance.
2We integrated an empirically parameterized, mechanistic model of windstorm mortality (WINDSTORM) and a seed-mass-based dispersal and recruitment model into a spatially explicit, individual tree model of forest dynamics (SORTIE) in order to create simulated long-term ‘experiments’ designed to explore the sensitivity of forest composition and structure to species-specific resistance to and recovery from disturbance.
3We found that species-specific variation in resistance to wind mortality interacted strongly with: (i) shade tolerance characteristics, (ii) the medium-term history of disturbances, (iii) the long-term average severity of the disturbance regime and (iv) seedbed substrate dynamics to influence tree population dynamics and successional trajectories.
4We also examined how local and long-distance dispersal affect response to wind disturbance. Ignoring differences among local dispersal characteristics overestimates the importance of dispersal-limited species. Our results show that long-distance immigration maintains species coexistence only if the immigration rate is very high relative to local dispersal. Despite this, stand-scale models that ignore long-distance dispersal can underestimate population dynamics of dispersal-limited species.
5Our results indicate that landscape-scale heterogeneity in structure and species composition in these forests is facilitated by synergisms between the stochastic nature of wind disturbance and complex interactions between species traits that govern: (i) resistance to disturbance, (ii) local dispersal and seedling establishment and (iii) competitive (i.e. growth/survival) traits that do not adhere to strict tradeoffs.
6We conclude that wind disturbance has much more complex and variable effects on long-term dynamics of forest structure and composition than suggested by previous models. In particular, non-catastrophic disturbances can generate important variation in forest dynamics that can either lead to dominance by a single or small number of species, or facilitate species coexistence.
Disturbance is a major force influencing the species composition and structure of ecosystems throughout the world (Pickett & White 1985). Disturbances (particularly catastrophic disturbances) promote diversity at the landscape scale by maintaining populations of shade-intolerant and early-successional species (Loucks 1970; Bormann & Likens 1979). The effects of natural disturbances can be difficult to characterize, however, because disturbances operate over such a wide range of spatial and temporal scales. Historically, disturbance theory has relied on two key concepts, resistance to disturbance and community resilience after disturbance, to describe how ecosystems react to and recover from disturbances (e.g. Attiwill 1994). These concepts are difficult to quantify because, among many other reasons, they require specification of a reference, predisturbance or equilibrial condition. Recently, however, empirical approaches have been developed that allow us to estimate directly the species-specific resistance of trees to disturbance as a function of disturbance severity (e.g. Canham et al. 2001). Together with the development of spatially explicit, individual-based forest simulation models (e.g. Pacala et al. 1996), we can directly explore the consequences of key processes that determine community susceptibility to and recovery from disturbance.
Severe winds are the predominant cause of natural disturbance in temperate forests of north-eastern and north-central North America (e.g. Lorimer 1977; Canham & Loucks 1984; Frelich & Lorimer 1991b). Both theoretical and empirical studies of wind disturbance in temperate forests have generally focused on the effects of catastrophic storms (e.g. Loucks 1970; Lorimer 1977; Bormann & Likens 1979; Canham & Loucks 1984) that create a landscape-scale mosaic of patches of various sizes and ages (Canham & Loucks 1984) in which the species composition of each patch is assumed to be largely a result of successional processes (e.g. Loucks 1970). In effect, these studies assume that catastrophic wind disturbances simply reset stands to an earlier successional stage.
Non-catastrophic disturbances may also have important, underappreciated ecological consequences. The susceptibility of canopy trees to damage or death as a result of severe winds varies as a function of species, size, and a host of other individual traits and site-specific factors (e.g. Foster & Boose 1992; Canham et al. 2001). Catastrophic disturbances overwhelm the abilities of trees to resist disturbance, rendering differences among species moot. In the far more frequent non-catastrophic storms, however, variation in resistance to disturbance among trees has a profound effect on both the immediate and the long-term effects of any given storm, and may have pervasive impacts on forest composition and structure, at both the stand and the landscape scales (e.g. Lorimer & Frelich 1989; Frelich & Lorimer 1991a; Foster & Boose 1992; Canham et al. 2001). Despite awareness that species composition influences the severity of the effect of a given storm, there has been little explicit consideration of species-specific differences in resistance to disturbance as a factor in determining post-disturbance community development.
Post-disturbance colonization is also strongly dependent on differences among species in local and long-distance dispersal, and subsequent seedling establishment (i.e. recruitment). Highly localized dispersal patterns are an important feature of seedling recruitment patterns in forest trees (Janzen 1970; Connell 1971; Ribbens et al. 1994) and many theoretical studies have shown the importance of dispersal for finding suitable germination and establishment substrates (Levin et al. 2003; Levine & Murrell 2003). Windthrows create gaps that increase light and free other resources for understorey tree and seedling growth (Mladenoff 1987; Canham et al. 1990). As they decay, fallen trees become a favourable seedbed germination substrate for small-seeded species such as yellow birch (Betula alleghaniensis Britton) and hemlock (Tsuga canadensis L.) moreso than larger seeded species (Godman & Lancaster 1990; Peterson & Pickett 1995; McGee 2001). These pulses of rotting coarse woody debris (CWD) combined with higher understorey light levels in large windthrow gaps (Peterson & Pickett 1995) could have long-term impacts on subsequent community dynamics.
Long-distance dispersal (LDD) also presumably plays an important role in post-disturbance colonization. The importance of long-distance dispersal is clear in studies of island colonization and in the reconstruction of post-glacial plant migrations (e.g. Clark 1998; Higgins & Richardson 1999; Cain et al. 2000). Recent studies have shown that our ability to predict the effects of climate change critically depends on high-quality information and on models of long-distance dispersal (Cain et al. 2000). Historically, diffusion spread models have underestimated spread rates (e.g. Weinberger 1982), in part because they assumed that the spread rate was constant and exponentially bounded (Weinberger 1982). Current empirical approaches to estimating LDD have made progress in approximating the spread of populations, but have proved sensitive to assumptions of constant mean reproductive rates and the proportion of seeds that disperse long distances (Clark et al. 2001). Thus, the importance of long-distance dispersal for community dynamics following wind disturbance remains an open question.
In the absence of suitable long-term empirical studies, models parameterized using field data can be used to improve our understanding of how natural ecosystems function (Levin et al. 2003; Levine & Murrell 2003); they are a powerful alternative to purely empirical studies (Pacala et al. 1996); they can bridge the gap between the theoretical and empirical literature (Levine & Murrell 2003); and they can be used to choose between alternative hypotheses generated by different theories (DeAngelis & Mooij 2003). In this paper, we use SORTIE (Pacala et al. 1996), a spatially explicit model of forest dynamics, to undertake long-term, simulation ‘experiments’ to explore the sensitivity of forest composition and structure, to the resistance of individual trees to wind disturbance and the roles of local and long-distance dispersal and seedling establishment in community recovery. Specifically, we address five questions:
1How does variation in the severity of a wind disturbance regime affect long-term patterns of composition, structure and diversity of canopy tree species?
2How important is species-specific resistance to windthrow for patterns of relative abundance and diversity in forests subject to storms with a broad range of severity?
3How does variation among species in local dispersal of seeds affect patterns of relative abundance and species coexistence in forests subject to recurrent wind disturbance?
4Are forest composition and structure sensitive to species-specific responses to and spatial and temporal variation in recruitment opportunities (particularly seedbed substrates) created by wind disturbance?
5How important is long-distance dispersal for patterns of succession and tree species diversity in forests subject to wind disturbance?
For the purposes of the present study, we focus our simulations on the transition oak – northern hardwood forests where SORTIE was originally developed (Pacala et al. 1996). There are a variety of forest types in this region, with a transition from oak-dominated forests on the drier and more southern and eastern sites, to northern hardwood species on more mesic and northern sites. The six species used in our simulations include the most common northern hardwood species found in mid- and late-successional stands across the region. The species are (in approximate decreasing order of shade tolerance; Kobe et al. 1995): American beech (Fagus grandifolia Ehrh.), eastern hemlock (Tsuga canadensis L.), yellow birch (Betula alleghaniensis Britton), sugar maple (Acer saccharum Marsh), red maple (A. rubrum L.) and black cherry (Prunus serotina Ehrh).
None of the previous studies using SORTIE has explicitly considered the role of canopy disturbance. Incorporating disturbance in the model required that we develop two new submodels and we adopt a new approach for estimating fecundity. First, we have developed a wind disturbance submodel, WINDSTORM, which is based on our previous work (Canham et al. 2001) to parameterize species-specific functions for the susceptibility of canopy trees to windthrow as a function of tree size and storm severity. The submodel also allows us to specify the characteristics of the regional, long-term disturbance regime. Second, we have incorporated a new submodel for the dynamics of seedbed substrates (Papaik et al. 2005) that allows us to track the effects of windstorms on the availability of tip-up mounds and rotted logs as substrates for seedling establishment. Third, we are using an alternative approach to estimating seedling establishment to that developed by Ribbens et al. (1994). This approach is based on work by Greene & Johnson (1994, 1998), and uses seed mass as a basis for estimating fecundity and substrate-dependent seedling establishment. These additions to SORTIE allow us to explore how species-specific variation in: (i) resistance to a wide range of windstorm severity, and (ii) dispersal characteristics (both local and long-distance) and seedling recruitment following disturbance can shape the structure and composition of forested landscapes.
the disturbance submodel
Integrating the new WINDSTORM submodel into SORTIE requires specifying: (i) parameters that define species-specific resistance to windthrow and (ii) the wind disturbance regime.
Resistance of trees to windthrow
Canham et al. (2001) developed a method of simultaneously estimating an index of local (i.e. stand-scale) storm severity and the parameters of functions that quantify species-specific variation in probability of windthrow (i.e. defined as either uprooting or stem break) as a function of storm severity and tree size. The method follows directly from the principles of likelihood estimation and takes advantage of the fact that most severe (i.e. landscape-scale) windstorms contain considerable variation in severity. The model calculates the log of the odds ratio of mortality as a function of species, individual tree size and the estimated index of local storm severity (Canham et al. 2001):
( eqn 1)
where pisj is the probability of windthrow for the jth individual of species s in plot i; Si is the estimated storm severity for plot i (on an arbitrary scale of 0–1); DBHisj is diameter at breast height (d.b.h.; in cm at 1.35 m height) of the jth individual of species s in plot i; and as, bs and cs are estimated, species-specific parameters (see Canham et al. 2001). The resulting probability of mortality is a response surface that is expected to increase with both d.b.h. (i.e. bs > 1) and storm severity index (i.e. cs > 0). For our analyses of wind disturbance in temperate forests, we do not consider damage that results in only partial loss of the crown. In tropical forests, crown damage is far more common than outright mortality (Walker 1991), and our empirical methods have been extended to predict levels of damage rather than simply survival vs. mortality as a function of storm severity (e.g. Uriarte et al. 2004).
The wind disturbance regime
A disturbance regime is typically defined in terms of four characteristics: spatial extent, severity (i.e. the amount of tree and plant mortality in a disturbed area), return frequency and type of disturbance (Frelich 2002). In this study, we hold spatial extent (i.e. the SORTIE stand size) and disturbance type (wind) constant. The disturbance regime is characterized by variation in the frequency and severity of individual windstorms. We use a synthetic index of storm severity (ranging from 0 to 1) representing the approximate proportion of trees killed in a well-mixed plot with broad size distribution of trees of all species (Canham et al. 2001). There are a number of benefits to using an index rather than more operational measures such as wind speed, not the least of which is the scarcity and difficulty of obtaining direct local measurements of severe winds during storms. Storms are episodic and occur with a frequency equal to the inverse of their return interval (Fig. 1).
We use three different disturbance regimes in our simulations (mild, moderate and major) (Fig. 1). Each regime has the same expected long-term, average annual mortality from wind (0.6%). The moderate storm regime is equivalent to the historical regime derived by Frelich & Lorimer (1991a); the mild storm regime specifies more frequent, less severe storms; and the major storm regime specifies less frequent but more severe storms (Fig. 1). The sum of all other sources of stochastic mortality of canopy trees is set to 1% per year for each species. All non-disturbance simulations are set to 1.6% per year, keeping the long-term expected mortality equal for all disturbance and non-disturbance simulations.
changes to the sortie recruitment submodel
The original recruitment submodel in SORTIE (Ribbens et al. 1994) predicts the number and spatial locations of new seedlings produced by a parent tree of a given species as an increasing function of parent tree size and a decreasing function of distance from a parent (Ribbens et al. 1994):
( eqn 2)
where Fx is the number of seedlings per m2 at distance x from the parent tree, STR is the number of first-year seedlings produced by a tree of 30 cm d.b.h. and R(x) is the Weibull dispersal kernel function that describes how seeds are dispersed as a function of distance x from the source tree (Ribbens et al. 1994). Ribbens et al. (1994) based their estimates of STR on only a few years of field data. Without longer-term data, their approach does not capture the high interannual variability of seed production in these forests, nor generate reasonable estimates of mean fecundity (Ribbens et al. 1994; Clark et al. 2004).
Many studies have shown that seed production, subsequent seedling germination and seedling establishment are all influenced by seed mass (e.g. Westoby et al. 1992, 1996; Greene & Johnson 1994, 1998). Our approach estimates the number of 1-year-old seedlings produced by a parent tree as a function of seed mass, seedbed substrate characteristics and the basal area of the parent tree (Greene & Johnson 1994, 1998; Greene et al. 2002; D. Greene, personal communication). Mean annual fecundity is calculated as:
( eqn 3)
(Greene & Johnson 1994) where α and β are empirically derived parameters (reproduced in Table 1), ms is seed mass in grams and B is the basal area of the tree. Seed germination and 1-year seedling survival is determined by:
Table 1. Fecundity and substrate favourability parameters used in the model. (a) Calculating standard total recruitment of seedlings (STR) from seed mass using eqn 6 and parameters from Green & Johnson (1998). (a) Seed mass (ms) in grams (Greene & Johnson 1994); µ is the number of established seedlings per 2 × 2 m quadrat per year. The parameter µ creates the same number of seedlings for a 16-ha stand as STR. (b) Values for α and β are derived from Greene & Johnson (1994; D. Greene, personal communication), all others from Greene & Johnson (1998)
( eqn 4)
where mg is mortality from granivory, w is the proportion of favourable seed bed area, and γL, δL, γH and δH are empirical coefficients for favourable and unfavourable substrates, respectively (Greene & Johnson 1998) (parameter values are reproduced in Table 1b). The product of f1 × f2 is the number of 1-year seedlings per unit basal area of source tree. The result when multiplied by 0.0707 (the basal area of a 30-cm d.b.h. tree) is equivalent to STR in eqn 2 (Fig. 2).
The substrate model used in this investigation is derived from LePage et al. (2000) and described in detail in Papaik et al. (2005). The model is composed of four different seedbed substrate types: fresh CWD, rotting CWD, mineral soil from pit-mound complexes and litter, where substrate creation is driven by tree mortality, and substrate change is driven by eqn 5. Each substrate type has a species-specific ‘favourability’ that is determined empirically (Greene & Johnson 1998; LePage et al. 2000). Substrates are either favourable for establishment (e.g. mineral soil, humus, rotted logs, see Table 4), where a high proportion of seeds germinate and establish, or unfavourable for establishment (e.g. undisturbed sites, freshly fallen trees, see Table 4), those on which many fewer seeds germinate and establish. Favourable substrates are considered to be equally favourable. The favourability index of an unfavourable substrate (Table 4) is determined by eqn 2 and is defined as the ratio of seedling establishment on an unfavourable substrate to the ratio of seedling establishment on a favourable substrate. Substrate creation occurs when a tree dies. A specified proportion of trees that die are uprooted, creating new mineral soil substrate as a function of tree size (Papaik et al. 2005). Fallen trees, whether uprooted or not, create fresh CWD that is also a function of tree size (Papaik et al. 2005). The area of fresh CWD and mineral soil substrates ‘decay’ as a logistic function of time since creation in 5-year timesteps:
Table 4. Initial abundances (no. ha−1). Even abundance initial conditions and seed-mass-weighted initial conditions both sum to 150 trees ha−1 between 0 and 1 cm d.b.h. Field demographics calculated from pooled plot data that were used in the long-distance dispersal runs
Initial abundances for LDD test from field data by d.b.h. class (cm)
( eqn 5)
where S(t) is the proportion of the area of the original substrate remaining at t, 5-year timesteps since the creation of fresh CWD, and ν and η are substrate-specific decay parameters. Fresh CWD is transformed to rotting CWD (ν = −0.5 and η = 2.6; Papaik et al. 2005), which in turn decays to litter, and mineral soil is transformed to the background litter layer (ν = −1.0 and η = 4.4; Papaik et al. 2005). A constant proportion of rotting CWD (0.45; Papaik et al. 2005) transforms to forest litter at each timestep, completing the cycle of substrate dynamics.
The substrate model also defines the species-specific probabilities of successful germination and seedling establishment for each substrate type (eqn 4). Establishment of large-seeded species at our study sites (e.g. Quercus, Acer, Fagus) is relatively insensitive to substrate conditions (Ribbens et al. 1994; our personal observations), and all substrates are considered uniformly favourable. Rates of establishment of the smallest-seeded species, particularly T. canadensis and B. alleghaniensis, however, are sensitive to substrate conditions. They require either bare mineral substrates or elevated seedbeds on well-rotted logs, with little effective establishment on either litter or fresh CWD (Godman & Lancaster 1990; McGee 2001).
We tested sensitivity of forest dynamics to seedbed favourability, both with and without disturbance. In both cases, we tested the control, in which only the small-seeded species find decaying CWD and mineral soil a favourable substrate, against all substrates being favourable for all species. In the disturbance tests, we also determined the case in which all substrates are unfavourable for all species (Table 2).
Table 2. Overview of research questions and the specification of the simulation treatments designed to address them. Blank cells are the same as control
How does variation in the severity of a wind disturbance regime affect long-term patterns of composition, structure, and diversity of canopy tree species?
Mild; moderate; major
25 per sp. ha−1 vs. seed-mass based
How important is species-specific variation in resistance to windthrow for patterns of relative abundance and diversity in forests subject to storms with a broad range of severity?
Mild; moderate; major
How does variation among species in local dispersal of seeds affect patterns of relative abundance and species coexistence in forests subject to recurrent wind disturbance?
Local dispersal: spatially explicit vs. non-spatial ‘bath’
Are forest composition and structure sensitive to species-specific responses to, and spatial and temporal variation in, recruitment opportunities (particularly seedbed substrates) created by wind disturbance?
Seedbed favourability: control vs. all substrates favourable
Control vs. no substrates favourable vs. all substrates favourable
How important is long-distance dispersal for patterns of succession and tree species diversity in forests subject to wind disturbance?
Dispersal local: control vs. long-distance: κ varies ∝ 0.1%, 1% and 10% total fecundity (for 10 m2 ha−1 per species in landscape)
Local and long-distance bath dispersal
The default dispersal model in SORTIE disperses seeds from each parent tree according to spatially explicit dispersal functions (Ribbens et al. 1994). In order to isolate the role that spatially explicit dispersal has in these forests and to explore the consequences of omitting the effects of long-distance dispersal for forest succession following windthrow, we added a submodel to SORTIE that generates stochastic seedling establishment with a uniform mean across the plot (i.e. without respect to the locations of parent trees). This mode of dispersal and seedling establishment can be termed ‘bath’ recruitment by analogy with the settling of invertebrate larvae in marine intertidal zones. We divide the plot up into 2 × 2 m quadrats and disperse the calculated number of seedlings as a uniform random process within each quadrat. Bath recruitment is assumed to follow a Poisson distribution with the expected mean number of seedlings of a given species for each quadrat (λ) specified as a linear function of the basal area (BA) of the species in the plot:
( eqn 6)
In effect, eqn 6 contains two components: (i) adult biomass-dependent (but non-spatial) local dispersal, which is determined by parameter µ; and (ii) input that is independent of local adult abundance (presumably primarily due to long-distance dispersal), which is determined by parameter κ.
The basal area coefficients, µ, are calculated (Table 1a) to construct a density-dependent, non-spatial model of local dispersal that is quantitatively equivalent to the default spatial dispersal model, but which distributes seeds independently of the locations of parent trees. We used µ to explore the importance of spatially explicit local dispersal in these forests (Table 2, question 3), both with and without disturbance.
Both the default spatially explicit dispersal model and the local bath dispersal model will disperse seedlings only if there are adult trees of that species present in the plot. The intercept term in eqn 6, κ, represents LDD from source trees outside the plot. Thus, even if there are no adult trees of a given species in the plot, there will be immigration via LDD if κ is non-zero. In order to examine the relative importance of LDD vs. local dispersal, we kept track of locally dispersed individuals separately from LDD-dispersed individuals. To set κ, we assume a constant matrix of species across the landscape outside of our simulation plot at an abundance of 10 m2 ha−1. We made this assumption to constrain the boundary conditions of these simulations, and to provide tests that render the simulation results interpretable in biological terms. We look for thresholds regarding the ability of the four wind-dispersed species to persist in or invade already existing forested stands by taking advantage of the fact that where the tail is flat (i.e. far from the parent), the density of propagules scales with fecundity (Clark 1998). We tested three levels of LDD by setting κ to approximate 0.1%, 1% and 10% of the total fecundity of each wind-dispersed species (given the assumed constant landscape-level abundance of 10 m2 ha−1) (Table 3).
Table 3. Species parameters used in the model. Species are listed in order of increasing seed mass. ‘F’ denotes favourable substrate; ‘U’ denotes unfavourable substrate; NA denotes not applicable
From eqn 2. This is the ratio of STR for unfavourable substrate to STR for favourable substrate.
1.0 × 10−7
6.87 × 10−3
3.62 × 10−4
7.44 × 10−4
7.75 × 10−4
1.96 × 10−3
set-up of the simulation experiments
Parameters for our simulated ‘experiments’ are detailed in Table 3. All other parameters used in these simulations are from Pacala et al. (1996). The ‘experimental’ set-ups are detailed in Table 2. Each of the tests varied one or more of the features of our control simulations. All simulations used a 400 × 400 m (16 ha) plot and ran for 1000 years. There were 10 replicate runs of each test. Initial conditions for the control runs had 25 trees ha−1 per species distributed randomly between 0 and 1 cm d.b.h. and dispersed randomly throughout the stand. The test for sensitivity to initial conditions apportioned initial abundances among species proportionately by seed mass (Table 4). We calculated the initial conditions for the LDD tests from field data (Table 4). All other simulations used the same initial conditions as the control. The three disturbance regimes were set according to Fig. 1. Bath dispersal parameters for the long-distance tests are shown in Table 1 (µ) and non-spatial local dispersal tests are shown in Table 2 (κ).
Results and discussion
the effects of wind disturbance on tree population dynamics
Sensitivity to initial conditions
In the absence of disturbance, SORTIE forecasts of forest dynamics are very sensitive to initial conditions (both abundance and size structure) (Pacala et al. 1996). Initial conditions influence stand development well beyond the age of most stands in north-eastern North America, indicating the importance of understanding the processes controlling colonization following disturbance (Pacala et al. 1996). We tested how disturbance influences sensitivity to initial conditions by keeping total plot abundance the same (150 trees ha−1) between 0 and 1 cm d.b.h., but distributing the relative abundance among species in two ways: uniformly among species (25 trees ha−1 per species), and proportionally according to seed mass (Table 4). In the absence of disturbance, relative and absolute basal area changed in a manner that follows from the initial advantages in abundance given to the smaller seeded species in the proportional seed-mass-weighted initial conditions (Fig. 3a,e). The higher initial abundance ratio (∼3 : 1) of T. canadensis relative to F. grandifolia was sufficient to make Tsuga the dominant species for a 200-year period from about 350 to 550 years stand age, and delayed F. grandifolia dominance by ∼100 years (Fig. 3a,e). Basal area increases of the smaller seeded species (T. canadensis and B. alleghaniensis) in the seed-mass-weighted runs were offset by decreases in the larger seeded species (P. serotina and F. grandifolia) such that there was only a modest increase in total basal area throughout the duration of the simulation (Fig. 3a,c). These changes were all moderate, reflecting the modest differences in initial conditions, and were consistent with previous studies (Pacala et al. 1996).
Incorporating wind disturbance complicates the role that initial conditions play. The modest advantage in the initial abundance of B. alleghaniensis relative to F. grandifolia (∼3.5 : 1 per ha, see Table 4) was amplified by the superior wind resistance of B. alleghaniensis (Fig. 4). As a result, there was a sustained increase in total stand basal area and a 400-year delay in the time it took for F. grandifolia to become the dominant species (Fig. 3c,g). The reverse is true for T. canadensis. Low resistance to mild and intermediate-severity storms of medium and large T. canadensis (Canham et al. 2001; Fig. 4) virtually offsets the early abundance advantage such that there was only a minimal increase in the basal area of T. canadensis (Fig. 3c, g). The two heavier-seeded species, P. serotina and F. grandifolia, became less important in relative and absolute basal area when wind disturbance was included. Their greater susceptibility to wind, relative to B. alleghaniensis, increasingly prevented them from becoming more important as the disturbance regime increased toward major storms (Fig. 3). As the severity of the disturbance regime increased, the peak basal area and persistence of B. alleghaniensis increased significantly and delayed succession to F. grandifolia (Fig. 3f–h). In addition, total basal area increased significantly as the disturbance regime increased owing to the response of B. alleghaniensis (Fig. 3f–h). Consequently, if a wind-resistant species (e.g. B. alleghaniensis) has even a slight initial advantage, it can persist virtually indefinitely because of disturbance.
Species-specific resistance to disturbance
Species-specific resistance to non-catastrophic disturbances interacted strongly with shade tolerance of the species, the medium-term history of disturbances (time scales of 1–3 centuries) and the long-term average severity of the disturbance regime to influence the relative importance of species throughout succession. For example, the abundance of B. alleghaniensis was positively correlated with the severity of the disturbance regime (Fig. 3) because it is the most resistant species across a broad range of tree sizes and wind severities (Fig. 4). Conversely, P. serotina is highly susceptible across all tree sizes (Canham et al. 2001; Fig. 4), and its importance was inversely related to the severity of the disturbance regime (Fig. 3). However, resistance to disturbance is not a trait by which all species can be simply ordered as being more or less resistant. For instance, T. canadensis is the most susceptible species in low-severity storms for all tree sizes but becomes more windfirm, relative to other species in the same size range, as storm severity increases (Fig. 4, and see Canham et al. 2001). Therefore, milder storms act as a bottleneck limiting the long-term abundance of T. canadensis in all disturbance regimes (Fig. 3). As a second example, large F. grandifolia are highly susceptible to wind disturbance (in part because of the presence of beech bark disease; Papaik et al. 2005), but small F. grandifolia have the highest resistance (Canham et al. 2001; Fig. 4). Thus, F. grandifolia persisted as an abundant understorey species (Fig. 3) because of the resistance to wind disturbance of small trees (Fig. 4) and its shade tolerance (Kobe et al. 1995). In effect, species-specific resistance to disturbance adds variance to community dynamics that cannot be predicted by models that ignore it.
Intermediate-severity windstorms do not simply reset succession to an earlier state or advance it to a later state as is often assumed. The response of the community in our simulations depended on the temporal pattern of storms over an extended period and the relative importance of wind-susceptible vs. wind-resistant species. Succession of young stands was accelerated in the moderate disturbance regimes (Fig. 3) because the less shade-tolerant P. serotina is more susceptible to low- and moderate-severity disturbances than later successional species (Canham et al. 2001; Fig. 4). However, the most important intermediate successional species predicted in the disturbance-free simulations changed from the more shade-tolerant T. canadensis to the more disturbance-resistant B. alleghaniensis as the severity of the disturbance regime increased (Fig. 3).
stand vs. landscape dynamics
We are able to parse out the general trends described above because we have been considering the average response of replicate runs for a given disturbance regime. This is analogous to a landscape-scale analysis. Consider, however, that averaging eliminates important information by masking the effects of transient events. The temporal patterns of storms are stochastic, and individual runs have distinct histories that vary considerably within each disturbance regime. Individual runs within one regime can resemble those in other regimes and the average response of another regime (Fig. 5). Thus, individual runs are analogous to stand-scale dynamics. To illustrate how specific temporal patterns of storm events (i.e. disturbance history) shape community composition and succession at the stand scale, we selected three runs from the moderate disturbance regime (Fig. 5). Plot 10 is similar to the mild storm disturbance regime (Fig. 3b), plot 7 is similar to the mean of the moderate storm disturbance regime (Fig. 3c) and plot 9 is similar to the mean of the major storm regime (Fig. 3d).
First, note that although individual, non-catastrophic storms change structure, they had minimal effect on succession when compared with the disturbance-free simulations, despite substantial differences among species in resistance to disturbance (Fig. 4, based on Canham et al. 2001). A series of storms were necessary to alter succession and the length of time to the onset of old growth conditions. For example, consider early in succession when P. serotina dominated. The importance of P. serotina was extended when this period was relatively quiet (Fig. 5b), whereas it was curtailed by a series of storms that occurred at or near the peak abundance of P. serotina (Fig. 5d) and we see a similar pattern shortly later in succession. P. serotina and F. grandifolia were the most important species when two mild storms with a combined severity index of 0.369 occurred in plot 10 in year 360 (Fig. 5b). The more susceptible species (P. serotina) was effectively removed from the stand, but F. grandifolia recovered because, being shade-tolerant, it had established abundant saplings in the understorey. The major storm (index 0.445) that occurred 100 years later knocked back F. grandifolia. However, in this case, F. grandifolia recovery was forestalled because one major and four mild storms quickly followed the major storm. This sequence of storms, which occurred later in succession, created suitable sustained conditions (i.e. gaps and decaying CWD from previous storms) for B. alleghaniensis to establish and increase, but not become dominant. By contrast, a similar series of storms that occurred earlier in succession in plots 7 and 9, before F. grandifolia became fully established, led to the dominance of B. alleghaniensis (Fig. 5). It took sustained quiet periods in both plots for F. grandifolia to regain dominance (Fig. 5). A substantial understorey of F. grandifolia developed during these periods, and it remained the dominant species regardless of the subsequent pattern of storms.
Thus, quiet periods in excess of 100–150 years allowed the most shade-tolerant species (F. grandifolia) to increase in all regimes. Periods during which storms occurred more frequently allowed the more wind-resistant species (B. alleghaniensis) to increase. In effect, resistance to disturbance dominated competitive ability as a trait determining relative abundance during stormy periods. Lasting differences in succession among the regimes were a result of changes in the probability of relatively disturbance-free periods of at least 100–150 years. This cannot be inferred from the aggregated runs showing the differences among the average landscape responses to the disturbance regimes (Fig. 5a). We can only infer stand-scale processes by examining individual plot histories. By contrast, variation among individual stand histories masks important differences in expected successional trajectories that are only revealed by a landscape-scale analysis. In summary, species-specific resistance to disturbance interacts with the stochasticity of disturbance events and initial conditions to have dramatic and long-lasting effects on the patterns of community development (Fig. 3) at both the stand and the landscape scales.
interactions between local dispersal and species-specific resistance to disturbance
The importance of modelling local dispersal as a spatially explicit process is made clear in Fig. 6a & b. In the absence of disturbance, bath recruitment resulted in higher total stand basal area than spatially explicit, local dispersal (Fig. 6a,b). This was due almost entirely to increases in the basal areas of the most dispersal-limited species of this community (i.e. T. canadensis and F. grandifolia–Table 3) when dispersal was modelled as a bath process (Fig. 6a,b). Limited local dispersal of the shade-tolerant species (T. canadensis and F. grandifolia) led to an increase in establishment opportunities for more broadly dispersed, less competitive species and fostered coexistence in the absence of disturbance. Disturbance interacted with spatially explicit dispersal to facilitate a shift in composition to B. alleghaniensis from T. canadensis early in succession (Fig. 6c,d) and, later, resulted in co-dominance between B. alleghaniensis and F. grandifolia (Fig. 6c). Given equal dispersal characteristics, the superior competitive ability of T. canadensis relative to B. alleghaniensis (Pacala et al. 1994; Kobe et al. 1995) was more advantageous than the superior windthrow resistance of B. alleghaniensis (Canham et al. 2001). We conclude that: (i) abundance of B. alleghaniensis was strongly dependent on broad dispersal relative to the other later successional species (e.g. T. canadensis and F. grandifolia), (ii) T. canadensis was strongly dispersal limited and (iii) F. grandifolia eventually overcame both dispersal limitation and relatively lower resistance to windthrow because of superior competitive ability (i.e. shade tolerance) in this community. Our results support theories that suggest localized dispersal improves species coexistence (Chave et al. 2002) and delays competitive exclusion (Bolker & Pacala 1999; Murrell & Law 2003) (Fig. 6a,b), but argues against the need for strict tradeoffs between dispersal traits and competitive ability. Tilman (1994) showed that by including variation in resistance to disturbance, coexistence could occur without strict competition-dispersal trait tradeoffs. Our results support this and suggest that species-specific resistance to windthrow obviates the need for strict trait tradeoffs between mean dispersal and competitive ability (Fig. 6c,d).
Interactions between windstorms and dispersal – a caveat
It is tempting to use the model to assess how disturbance and dispersal interact. Dispersal is clearly a factor in community response to wind disturbance, as strong winds will disperse seeds much further, and in addition, smaller seed will disperse further than large seeds. But the focus of our analysis was to explore those factors that govern the community response to wind disturbance for which we have good empirical measures (e.g. growth as a function of light, regeneration as a function of seedbed). We do not address specific ‘disturbance–dispersal’ interactions because we do not have the appropriate data to support modelling dynamics of dispersal changes as a function of wind disturbance severity (i.e. is the kernel shape sensitive to wind intensity? How much does the mean dispersal increase as a function of disturbance severity?).
interactions between seedling recruitment and species-specific resistance to disturbance
Effects of substrate limitations
When substrate limitation was removed the initial basal area of all species increased relative to the control (Fig. 7a,b). This was most dramatic for P. serotina and B. alleghaniensis. This is largely an artefact of the absence of density-dependent seedling mortality in SORTIE and the initial conditions of the test (Pacala et al. 1996). As the initial cohort of saplings matured (150 ha−1) they dispersed a dense carpet of seedlings that is ∼10-fold greater than when substrate limitation was included. All these seedlings grew in this open environment and led to very high basal areas early in succession. After approximately 100 years, the canopy closed and all species declined (Fig. 7b). Subsequently, with the exception of B. alleghaniensis, community dynamics followed the same pattern as the control (Fig. 7a). However, B. alleghaniensis maintained a very high basal area well after the canopy closed, and shading effects on seedling and small sapling mortality came to dominate. The dramatic increase in B. alleghaniensis at this time was due to its considerable advantage over other species in finding suitable establishment sites that resulted from its broad dispersal. Without strong substrate limitations on establishment, the broad dispersal ability of B. alleghaniensis enabled its establishment throughout the plot. T. canadensis, for which establishment is limited by the same factors as B. alleghaniensis, does not experience a similar secondary peak in basal area because it is dispersal limited in these simulations (Table 3). As a cautionary note regarding our model predictions, Greene et al. (2004) have pointed out that Ribbens et al. (1994) probably underestimated mean dispersal for T. canadensis. We tested whether our predictions were sensitive to the precise estimate of the local dispersal characteristics of T. canadensis by removing all establishment limitation for this species (Fig. 7g). In this case, extremely dense, light-limited, fine-scale patches of T. canadensis regeneration occurred such that canopy recruitment by T. canadensis was self-limiting. This was the reason T. canadensis failed to replace B. alleghaniensis in our simulations and was not a result of underestimating the mean dispersal for this species.
Effects of differences among species in favourability of CWD substrates
Many studies have shown that decaying CWD is a more favourable establishment substrate for small-seeded species (i.e. B. alleghaniensis, T. canadensis) than large seeded-species (e.g. LePage et al. 2000; McGee 2001). However, empirical evidence suggests that recruitment into the sapling stage and canopy may be more dependent on light than favourable seedbed substrates (McGee 2001). The population dynamics of small-seeded canopy tree species are thought to be more dependent on light, because seeds that land in the moist litter layer in canopy gaps are able to germinate and subsequently grow faster and survive better through the sapling stage than seedlings on decaying logs and other more favourable germination sites. We examined the influence of decaying CWD on canopy tree dynamics, both with and without disturbance, by removing the species-specific advantage of decaying CWD for the small-seeded species (i.e. T. canadensis and B. alleghaniensis; Table 3). This was undertaken in two ways: (i) decaying CWD was first made equally favourable for all species, then (ii) equally unfavourable. In the absence of disturbance, the results are consistent with empirical findings and show that the advantage given to establishment of small-seeded species on decaying CWD does not have a noticeable effect on canopy dynamics (Fig. 7c,d). Including disturbance, however, changes this. The ability of small-seeded species to establish on decaying CWD had a noticeable influence on successional dynamics (Fig. 7e–g). B. alleghaniensis, in particular, appears to be limited by establishment rather than light.
interactions between ldd and species resistance to disturbance
The LDD model is non-spatial and generates a species-specific, constant annual rate of seed rain (defined by the parameter κ in eqn 5). There are precious little data on LDD in forest stands to guide us in setting reasonable values for κ. However, one modelling study found that as little as 0.1% of total fecundity dispersing further than 1 km increased the population dispersion rate 10-fold (Higgins & Richardson 1999). Our model and the dispersion model of Higgins & Richardson (1999) have different goals. Higgins & Richardson (1999) were interested in how rapidly trees can spread across a landscape and establish new populations; however, we are exploring how LDD influences the establishment and dynamics of a species within an existing community.
Our results clearly show an absence of an effect of LDD near the rates (0.1%) responsible for a 10-fold increase of geographical dispersion found by Higgins & Richardson (1999) (Fig. 8a). That is, none of the four LDD species established significant numbers of individuals via LDD. By contrast, long-distance immigrants of two of the wind-dispersed species (i.e. T. canadensis and B. alleghaniensis) quickly swamped the high LDD stand (10%, Fig. 8c). There was a noticeable and persistent increase in the abundance of B. alleghaniensis and T. canadensis in the 1% LDD stands over the 0.1% LDD conditions (Fig. 8b). There is no evidence that either of the maples benefited from LDD even at the 10% level (Fig. 8c). This suggests a spatial mass effect (Shmida & Ellner 1984) for B. alleghaniensis and T. canadensis somewhere between 0.1% and 1% LDD, but not for the two maple species, which are present but uncompetitive at this site because of soil nutrient limitations (Kobe et al. 1995).
In our simulations, density independence of the LDD seed pool leads to one of two consequences (Clark & Ji 1995). Either diversity is high, because a continuous seed supply maintains less competitive species, or it is low, because more dispersal-limited, competitive species become more broadly established. Our simulations do not allow the latter as neither F. grandifolia nor P. serotina have effective LDD, and support the former only for extremely high LDD (Fig. 8c). In general, our results support the hypothesis that increased dispersal results in increased recruitment and abundance (see Turnbull et al. 2000), but they do not support the hypothesis that long-distance immigration maintains species coexistence (Hubbell et al. 2001) unless the immigration rate is very high (Fig. 8b). They are also consistent with predictions of lottery models (Chesson & Warner 1981) and Janzen–Connell escape hypotheses (Janzen 1970; Connell 1971) for T. canadensis and B. alleghaniensis because the high colonization rates of these species allow them to dominate the system (Fig. 8c, and less so for Fig. 8b). Nevertheless, for these effects to be important, the proportion of LDD relative to local dispersal must be very high.
Conceptual models of the effects of wind disturbance (e.g. Loucks 1970; Bormann & Likens 1979) have traditionally focused on the impacts of catastrophic disturbances and have painted a simple picture of how disturbance acts to maintain tree species diversity. Our results suggest that wind disturbance has much more complex and variable effects on long-term dynamics of forest structure and composition. In particular, non-catastrophic disturbances can generate important variations in forest dynamics that can either lead to dominance by a single or small number of species, or facilitate species coexistence. We have also shown that there are important scale-dependent characteristics of wind disturbance that depend at the landscape scale on the disturbance regime, and at the stand scale on the particular history of disturbances. Furthermore, our results fail to show evidence of simple tradeoffs between the effects of traits related to resistance to disturbance vs. colonization following disturbance. Diversity of structure and species composition is maintained by the stochastic nature of disturbance and complex interactions between: (i) species traits that govern resistance to disturbance, (ii) local dispersal and seedling establishment and (iii) competitive (i.e. shade tolerance) traits that strongly influence community responses to disturbance.
This research was supported by National Science Foundation grant No. DEB-0087214 and by the US Environmental Protection Agency through the STAR Graduate Fellowship Program, Award # U91578401-0. The views expressed herein are those of the authors and do not represent positions taken by the EPA. This study is a contribution to the programme of the Institute of Ecosystem Studies, Millbrook, NY. We would also like to thank David Greene, Ed Johnson and Kiyoko Miyanishi for their comments on earlier versions of the manuscript.