terminology, study system, model, and previous results
We define ‘long-distance’ dispersal as displacement of a seed by at least 150 m. This threshold is similar in magnitude to arbitrary thresholds of long-distance dispersal used by others (Cain et al. 2000; Russo et al. 2006), but is objectively linked to the spatial scale of our study system. In particular, 150 m is the minimum distance seeds must travel to be dispersed into a patch of habitat other than the one in which they originated; it represents non-local dispersal.
We conduct landscape-level analyses, meaning that we take into account not only the conditions at particular locations (e.g. habitat type and plant cover) but also the landscape context of those locations (e.g. connectivity and distance to edge). By ‘edge’ we mean the boundary between the habitat of our patches and the habitat of the surrounding matrix.
Our study system consists of eight experimental landscapes, each consisting of five patches (Fig. 1a). All landscapes contain a central patch (100 × 100 m) and four peripheral patches. The peripheral patches are located 150 m from each of the four sides of the central patch. There are three types of peripheral patches: connected, winged, and rectangular. Connected patches have a 150 × 25 m-wide corridor of the same habitat type that joins them to the central patch. Winged patches have two blind-end corridors (75 × 25 m) projecting from opposite sides of the patch in a direction parallel to the nearest edge of the central patch. Rectangular patches have an area the size of the corridor added to the side of the patch furthest from the central patch, creating a rectangle (137.5 × 100 m). Because patch types were randomly assigned and all have the same total area (1.375 ha), any differences among them in seed dispersal can be solely attributed to differences in patch shape and connectivity. All experimental landscapes contain all four patch types. In four of the landscapes the fifth patch is a second winged patch and in the remaining four landscapes the fifth patch is a second rectangular patch. Randomization of patch types within a given experimental landscape resulted in three configurations of patch types: two winged patches on opposite sides of the central patch (n = 2), two winged patches adjacent to each other (n = 2), and two rectangular patches on opposite sides of the central patch (n = 4; see Fig. 1).
Figure 1. (a) Aerial photograph of one of eight experimental landscapes; this one has two winged patches on opposite sides of the central patch, a connected patch at the top of the landscape and a rectangular patch at the bottom. It matches the schematic in the upper left of panel b. There were two other arrangements of patches, as illustrated in panel b. (b) Isoclines of occupancy density, 45 min after starting from random locations within each of the three types of landscapes. Contours represent predicted seed rain densities, with the highest densities in and around patches. Each landscape had 750 000 simulated dispersal events, of which approximately 500 000 end points were within the illustrated region. Numbers show distance in metres.
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Our study site is the Savannah River Site (33.20′°N, 81.40′°W), a National Environmental Research Park near Aiken, South Carolina. Habitat patches were created in the winter of 1999–2000 by harvesting trees in a mature forest dominated by loblolly (Pinus taeda) and slash pine (P. elliotii), with some oaks (Quercus spp.). Timber and other debris were removed and the sites burned several months later. After burning, we erected a grid of 3 m-tall polyvinyl chloride poles, 25 m apart and at least 12.5 m from the nearest edge. From the top of all poles, we suspended seed traps made from 25 cm-diameter flowerpots.
Our study species was the eastern bluebird, Sialia sialis (Turdidae). It is highly frugivorous and prefers the open habitat of our patches over the forested matrix between the patches, although it readily enters the forest and tends to move along the forested side of edges. It also prefers to sit on high and exposed perches, such as our pole tops. Of 90 independent observations of fruit-eating birds perched on pole tops, the vast majority (80%) were of bluebirds. Thus, we are confident that patterns of seed rain described from the seed trap data resulted mostly from the movement of bluebirds across our experimental landscapes.
Details of our model are provided in Levey et al. (2005) and in the Appendix. We summarize the model's general structure and our previous results because they form the basis of the current study. In brief, we used empirical measures of perching time, move length, and move direction to simulate movements of a bluebird from the centre of the central patch, where it had consumed fruit. We first described the distributions of perch time, move length, and move direction as functions of the habitat the bird was occupying (patch or matrix), its distance to edge, whether it was near a single edge or two edges (e.g. if it were near a patch corner), and for move direction, the direction of the nearest edge and the bird's previous move. Perch time was best described by an exponential distribution and move lengths by a lognormal distribution. Perch time was dependent on habitat (patch vs. matrix) and distance from edge. Move length was dependent on habitat. Movement direction was described by a mixture of von Mises distributions, one focused in the previous movement direction (this component alone would lead to a correlated random walk) and one focused in a direction parallel to the nearest patch edge. We simulated movements by randomly picking a perch time based on the observed distribution of perch times in the occupied habitat and distance from edge, then randomly picking a move direction based on habitat, orientation and distance from edge, and direction of previous move, and then randomly picking a move length based on habitat. The bird then moved from one point to the next. In our original model, this process was repeated for 45 min of simulated movements to match the approximate average gut passage time for seeds in bluebirds. The landscapes are unbounded and not modelled as a torus; birds are neither reflected off nor absorbed by artificial borders when they move away from the patches. The model was programmed in r, versions 2.5.0–2.6.1 (r Development Core Team 2007).
To test the model's results in the field, we placed branches of fruiting wax myrtle (Myrica cerifera) in the centre of the central patches and sprayed the fruits with a dilute solution of fluorescent powder (Levey & Sargent 2000). Bluebirds readily consumed these fruits and defecated the seeds into our pole-top seed traps. Observed seed rain agreed closely with the model's predicted distribution of seeds among connected, winged, and rectangular patches (Levey et al. 2005). For both observed and predicted results, seed inputs from the central patch into winged and rectangular patches were nearly identical. Also, connected patches received 31–37% more M. cerifera seeds from the central patch than did winged and rectangular patches. The model revealed that the effect of corridors on seed dispersal was driven by edge-following behaviour – bluebirds frequently followed the corridor edges, preferentially staying in matrix habitat as they moved between habitat patches. Upon arriving at a patch edge, they often entered the patch to forage.
The objective of this article is to apply the model more broadly, using it to predict how landscape heterogeneity (i.e. the occurrence of patches in matrix habitat) and patch shape affect the distribution of dispersal distances (‘dispersal kernels’). Our previous study focused on corridor use, examining bird movement that always started in the centre of the central patch and ended in the peripheral patches. Here we treat the same study system as a set of five habitat patches in an unbounded landscape, with birds and seeds originating within all patches or from random locations, not solely from the central patch.
We use the model to address five questions. (i) Given that bluebirds preferentially follow edges and that winged patches have proportionally more edge than rectangular patches, why was there no difference in the observed number of seeds deposited in winged and rectangular patches when birds started in the centre of the central patch? This question surfaced as paradox in our previous study (Levey et al. 2005). Intuitively, winged patches should act as ‘drift fences’ to edge-following birds – the wings should intercept individuals dispersing through the matrix and redirect them towards the patch (Anderson & Danielson 1997; Haddad & Baum 1999). We use the model to explain why this phenomenon was not apparent in observed patterns of seed rain. (ii) How do connected, rectangular, and winged patches differ in their ability to attract dispersers and ‘catch’ seeds that originate anywhere in the landscapes? This question focuses on the model's ability to discern spatial differences in seed rain across heterogeneous landscapes; unlike the next two questions, it does not explicitly consider dispersal distances. (iii) How does landscape heterogeneity affect dispersal kernels? This question is motivated by the difficulty of empirically measuring long-distance dispersal events. The model, which accurately predicts long-distance dispersal in our landscapes (Levey et al. 2005), can provide dispersal kernels. By comparing dispersal distances in our experimental landscapes to those in homogeneous landscapes, we show that habitat patches influence the pattern of long-distance dispersal of seeds, thereby setting the stage for the following two questions. (iv) How do dispersal kernels differ for seeds that originate in patches of different shape and how do they differ for seeds that originate in one patch and are deposited in another patch? We are most interested in the dispersal of seeds between patches because such events represent long-distance dispersal into favourable habitats. (v) Where are seeds that originate in different types of patches most likely to be dispersed? This question takes us from the perspective of dispersal kernels, which are one-dimensional representations of dispersal (i.e. single probability distributions), to two-dimensional landscapes, allowing us to visualize exactly where seeds go.
model modification and application
To explore why edge-following behaviour does not result in greater seed dispersal into winged than rectangular patches (question i), we parameterized and ran the model as previously (Levey et al. 2005). All birds started in the centre of the central patch. We focused on two metrics of bird behaviour: how often birds dispersing from the central patch visit each peripheral patch type and once in a patch, how long they spend there. A visit is defined as entry into a patch from the matrix or from the end of the corridor. Our rationale is that seed rain is determined by the total time a bird with seeds in its gut spends in a patch. Because the total time in a patch is a product of number of visits and average visit time, a higher rate of visitation by birds following edges into patches may be countered by a shorter duration of visit, as birds follow edges out of patches. The net result might be no difference in total time spent (and number of seeds dispersed) in winged and rectangular patches.
To assess how patch shape may affect spatial patterns of seed rain (question ii), we again ran the model as previously, except that simulated birds were started in random locations throughout the landscapes. Although fruiting plants do not occur in random locations and hence seed dispersal does not originate from random locations, for this exercise we were more interested in where seeds go than where they originate. Randomization of starting points allowed us to eliminate any effects of starting location on ending location. We completed 750 000 simulated dispersal events for each of the three types of landscapes at the study site.
To determine how the presence and shape of patches affect dispersal kernels (questions iii and iv), we modified our simulations in two ways. First, we started birds in the centres of all patch types. We did so to better reflect true dispersal events; seeds are most likely to originate from within patches because fruiting plants are relatively rare in the matrix. For this exercise we were more interested in dispersal distances (displacement) than actual coordinates of dispersed seeds. Second, we used a shifted gamma distribution based on gut retention times in a related species, American robins (Turdus migratorius; Turdidae; Levey & Karasov 1992), to determine when each simulated bluebird defecated the seed it consumed at time = 0 (see Appendix S1 in Supplementary material). This modification yielded a gut passage time distribution ranging from 16 to 145 min with a mean of 45 min and a median of 41 min. To the extent that robins and bluebirds are similar in their movement patterns and digestive physiology, it provides a more realistic estimate of dispersal kernels than the fixed time of defecation (45 min) we had used previously. For each of the three landscape types, we ran approximately 122 000 simulated dispersal events (c. 24 500 starts in each patch), recorded starting and ending points, and calculated dispersal distances. We compared dispersal kernels of seeds dispersed within our landscapes to an identical landscape without patches (i.e. all matrix habitat; question iii). We plotted dispersal kernels for seeds originating in the three patch types and for seeds that landed in each patch type but that had originated in another patch (question iv).
To visualize the spatial distribution of seeds dispersed from patches of different shapes (question v), we used the same runs that provided the dispersal kernels (questions iii and iv) and constructed probability density isoclines around one patch of each type (rectangular, winged, and connected).