Abstract Abstract. Theory and empirical evidence suggest that spatial and temporal variation in propagule availability can have as great or greater an influence on community structure as post-recruitment biotic interactions, a phenomenon known as supply-side ecology. One of the first theories to invoke supply-side dynamics, D. Rabinowitz's Tidal Sorting Hypothesis (TSH), attributed the tidal zonation of mangrove tree species to the interacting effects of water depth and propagule size on dispersal and establishment. According to the TSH, smaller propagules are carried farther inland by flood tides than larger ones, stranding and establishing in greater numbers at upper tidal elevations. In contrast, larger propagules are better able to establish in deeper, more seaward areas because their size affords greater access to the soil surface and resistance to buffeting by moving water. Here we present results of the first comprehensive investigation of the TSH. In a series of experiments conducted at Punta Galeta on the Caribbean coast of Panama, we quantified patterns of propagule dispersal and establishment of the three dominant species: Avicennia germinans, Laguncularia racemosa, and Rhizophora mangle. Abstract To measure dispersal patterns, we monitored movements (directions and distances) of marked propagules released at three elevations along each of three transects. On all transects, regardless of species or elevation, propagules moved seaward rather than being carried inland by tides, as predicted by the TSH. Rates of seedling establishment were monitored in experiments conducted at different tidal elevations. Contrary to the TSH, all three species established best in the lower intertidal, where they were in prolonged contact with the soil surface during low tides, and established more poorly in the upper intertidal basin, where standing water made rooting difficult. Seedling establishment was lowest in the wave-exposed, back reef habitat, but in accordance with the TSH, the large propagules of Rhizophora rooted and persisted better in this turbulent habitat than did the smaller propagules of the other species. Abstract We conclude that the TSH does not explain the vertical distributions of mangrove species on Punta Galeta. Rather, a different form of supply-side dynamics imposed by the strong seaward movement of dispersing propagules is important in structuring our study forests. INTRODUCTION in marine benthic ecology shifted to the role of POSI-TS , , , , ., . ,. , , recruitment biotic interactions in determining commuIt has long been recognized that dispersal can strongly . ..... INTRODUCTION • , , ~. " i x-J • J -^ * mty structure. These biotic interactions could be atiect population dynamics and community structure (e.g., Hutchinson 1951 , Skellam 1951 , Andrewartha and Birch 1954 , Huffaker 1958 rigorously investigated with the then-novel technique of manipulative field experimentation. The 1980s saw a renewed interest by marine ecologists in the influence of 1967, Krebs et al. 1969) . Detailed studies of mvemle . , ,individuals arriving and recruiting to a site (i.e., dispersing larvae or diaspores) than by post-recruitment biotic interactions. This idea was formalized in a number of mathematical models (e.g., Gaines and Roughgarden 1985 , Dial and Roughgarden 1998 . While this supply-side paradigm was developing in marine ecology, terrestrial-plant ecologists independently began to focus their attention on the role of a spatially and temporally variable seed supply in structuring terrestrial plant assemblages (Schupp and Fuentes 1995 , Tilman and Kareiva 1997 , Nathan and MullerLandau 2000 , Hubbell 2001 , Levin et al. 2003 , Levine and Murrell 2003 . Much of this work has focused on the role of dispersal limitation, and its interplay with competition, in determining the membership and coexistence of species in plant assemblages. While the terminology is somewhat different, this concept is directly analogous to the concept of supply-side dynamics on sessile marine assemblages. Work in this area has given rise to a rich body of mathematical theory that, as discussed by Levine and Murrell (2003) , has largely outpaced empirical evidence concerning the role of seed limitation in structuring plant assemblages. These authors call for more empirical studies that (1) measure seed dispersal patterns, (2) correlate these patterns with spatial or temporal variation in the species composition and structure of vegetation, and (3) experimentally manipulate seed shadows to confirm a causal relationship between seed dispersal patterns and the distribution and structure of plant assemblages. INTRODUCTION One of the earliest supply-side theories of community structure, Rabinowitz's (1978a) Tidal Sorting Hypothesis (hereafter TSH), predates the coining of the term and has been largely overlooked in discussions of the phenomenon (excepting Levine and Murrell [2003] ). The TSH attributes the differential distribution of mangrove tree species with tidal elevation (i.e., zonation) to the interacting effects of water depth and propagule size on propagule dispersal and seedling establishment. Mangrove forests, like the biota of rocky seashores, lakeshores, salt marshes, and mountainsides, have often been cited as a classic example of the zonation of species along environmental gradients (but see Ellison et al. [2000] ). Rabinowitz (1978a) proposed the TSH as an alternative to prevailing hypotheses that invoked species-specific physiological specialization to, or preference for, differing edaphic conditions as explanations for mangrove zonation (e.g., Watson 1928 , Macnae 1968 , Lind and Morrison 1974 , Chapman 1976 see Smith [1992] for a comprehensive discussion of alternative models of mangrove zonation). Rabinowitz developed the TSH after reciprocally transplanting different species of mangrove seedlings along the tidal gradient and observing that they grew and survived as well or better in zones dominated by adults of other species than they did in zones dominated by adults of their own species. This finding did not support the idea that the species were physiologically adapted to survive and grow best under distinct regimes of tidal inundation and soil salinity. INTRODUCTION Mature mangrove propagules are buoyant when first released from the parent plant; the length of time that they remain buoyant varies among species, populations of the same species in some cases, and with water conditions (e.g., Rabinowitz 19786, Steinke 1986 , Clarke and Myerscough 1991 , Clarke et al. 2001 . While afloat, propagules may be dispersed by tidal currents or runoff following rain storms. According to the TSH (Fig. 1) , mangrove zonation results from a combination of (1) the directional dispersal of floating propagules that passively sorts them spatially according to species-specific differences in size and (2) the differential size-related ability of propagules to establish as rooted seedlings as a function of water depth. More specifically, it was hypothesized that incoming tidal currents, especially during higher spring tides, carry smaller propagules farther inland than larger propagules and that, due to their size, the latter are physically restricted from dispersing into these shallower areas. Thus, smaller propagules strand and establish as seedlings farther inland than larger propagules. Conversely, larger propagules are better able to establish in deeper, more seaward portions of the swamp because their large size affords both greater access to the soil surface and more resistance to buffeting by moving water, and therefore they have a better chance of taking root. The TSH was consistent with Rabinowitz's (1978a) observation that, in her study areas on both coasts of Panama, the species that dominates near the water's edge where water depth is greater, has larger, heavier propagules than species that dominate more landward areas of the swamps where the water is generally shallower. She argued that this pattern was characteristic of mangrove distributions along tidal gradients in many parts of the world. While Rabinowitz's original findings have been criticized and observations at some sites do not fit its predictions (see Discussion), a complete test of the TSH has yet to be conducted at a single site. We present here the results of what we believe to be the first comprehensive investigation of the TSH. Our study was designed to specifically evaluate both the dispersal and establishment components of the hypothesis, and it was conducted in the forests of Punta Galeta on the Caribbean coast of Panama, one of Rabinowitz's primary study sites. Thus, our results provide a highly relevant test of her model. In addition, our study is one of very few that has directly quantified the propagule dispersal patterns of several co-occurring, forest tree species (Levine and Murrell 2003) . METHODS Study area and species Our study was conducted in mainland mangrove forests near the Smithsonian Tropical Research Institute's Galeta Marine Laboratory (9°24T8" N, WL Tidal sorting hypothesis Rhizophora Avicennia Laguncularia 5^ ** WL Stranded positions as tide recedes, followed by seedling establishment FIG. 1. Schematic of the Tidal Sorting Hypothesis (Rabinowitz 1978a ). The top panel shows the expected differential movement of propagules by incoming tidal flow: species with smaller propagules are dispersed farther inland and to higher elevations than species with larger propagules. Water levels (WL) at these higher elevations are shallower, and flow is less strong and turbulent than at lower tidal heights. The bottom panel shows that the differential dispersal of propagules results in smaller propagules being stranded farther inland as the tide recedes. This passive sorting process, combined with the expectation that larger propagules are better able to establish a root hold in deeper, more turbulent, nearshore locations, results in species with larger propagules dominating at lower elevations and those with smaller propagules dominating at upper elevations. Illustrated propagules represent the three common canopy species in mangrove forests on the Caribbean coast of Panama (see Methods: Studyarea and species); images are adapted from Rabinowitz (19786) . 79°51'48.5" W) at Punta Galeta on the Caribbean coast of Panama, approximately 8 km northeast of the city of Colon (see Fig. 2 ). Three tree species (hereafter referred to by their generic names) comprise the canopy of the study forests: Avicennia germinans (Avicenniaceae), Laguncularia racemosa (Combretaceae), and Rhizophora mangle (Rhizophoraceae). In these forests, as elsewhere (Davis 1940 , Schaeffer-Novelli et al. 1990 , McKee 1995 , Imbert and Menard 1997 , Sherman et al. 2000 , these species are distributed differentially with distance from the water's edge, forming several zones of differing canopy composition along the tidal gradient. WL The typical pattern of species distributions in our study area is illustrated in Fig. 3A with data from one of the three transects used in this study (Methods: Propagule dispersal: Direction and distance). Rhizophora grows in a pure stand at the seaward forest edge. About 10-20 m from the water's edge, Laguncularia joins the canopy, forming a nearly even mixture with Rhizophora in the low intertidal. Avicennia enters the canopy in the mid-intertidal, creating a mixed canopy of the three species, and it then gradually monopolizes most upper intertidal stands. Laguncularia often reappears in the canopy near the upland edge, growing as scattered individuals or small monospecific stands along the mangrove-rain forest ecotone. WL The topographic profile of the intertidal zone (Fig. 3B ) is more complex than the monotonic rise in surface elevation assumed by the TSH (Fig. 1) . Moving inland from the water's edge, surface elevation increases over the first ~50 m, remains roughly constant for another 50 m, then declines again to form a shallow (5-15 cm deep) upper intertidal basin that holds standing water throughout the wet season. Such inland basins are a common geomorphic feature of many mainland Caribbean mangrove forests (Lugo and Snedaker 1974 , Cintron et al. 1985 , McKee 1993 , Ewel et al. 1998 . WL All three species disperse their propagules during the rainy season, which runs roughly from May to late December. More than 90% of the 200-400 cm of rainfall Punta Galeta receives annually occurs during these months (Cubit et al. 1988 , Duke et al. 1997 . Within the rainy season, the dispersal periods of the species overlap to differing degrees (Rabinowitz 19786, Duke and Pinzon 1993; W. Sousa, personal observation) . Mature Rhizophora propagules are dispersed primarily between April and October, with a peak from May to July. Avicennia propagules are released only between June and early August, although unrooted, dispersing seedlings of this species can be found on the forest floor into September or October (W. Sousa, personal observation FIG. 2. (A) Location of study area within Panama; (B) Punta Galeta, Panama and environs (the four-pointed star in the upper right panel is at 9°25' N, 79°50' W); and (C) enlargement of the Punta Galeta study area showing the three study transects: Minas South (MS), Bahia Margarita (BM), and Pipeline (PL). In the study area, light gray shading indicates mangrove forest, and dark gray shading indicates upland forest and developed areas. species are buoyant and dispersed by water (hydrochory) but differ in the duration and pattern of floating and time to establishment as rooted seedlings (Rabinowitz 19786) . Dispersing propagules are transported across the forest floor by runoff following rainfall and by tidal action. FIG. 2. (A) The size and shape of the three species' propagules differ markedly (see Plate 1; Sousa et al. 2003a ; also see drawings in Rabinowitz [19786] and Tomlinson [1986] ). Rhizophora has the largest propagules, averaging 223 mm in length and 17.5-g fresh mass. The species is viviparous; the hypocotyl is rod-like in shape with pointed ends, one being the plumule (embryonic shoot) and the other the radicle. Avicennia propagules have a flattened, ovoid shape with a short stylar beak; they average 19 mm in length and 1.0-g fresh mass. When released from the parent tree, Avicennia propagules are covered by a thin pericarp, which separates from the propagule soon after it falls into water on the forest floor. The fleshy cotyledons of Avicennia germinans are positively buoyant; buoyancy of the propagule does not depend on the presence of the pericarp, as seems to be the case for its Indo-Pacific congener Avicennia marina (Steinke 1986, Clarke and Myerscough 1991) . Laguncularia propagules have a flattened, obovoid shape and are the smallest of the three species' propagules, averaging Distance from lagoon edge (m) FIG. 3. Plots of the relative (A) abundances of three mangrove species and (B) soil surface elevations along the BM transect. The transect was sampled on 2 December 1994. Tree data are proportions of living individuals >4 cm diameter at breast height (1.3 m) within the indicated sections of a 10 m wide belt transect running from a lagoon edge to the lower edge of upland rain forest (Fig. 2) . Relative elevation was measured with an auto level every 10 m along the transect; plotted points are means of three replicate stadia-rod positions at each distance. The dotted line on the elevational profile (B) demarcates the inland basin habitat. 20 mm in length and 0.6-g fresh mass. Laguncularia propagules have a thick, cork-like, and very buoyant seed coat, which remains attached until the propagule develops into a rooted, upright seedling. FIG. 2. (A) Based on these differences in propagule size, we would expect, under the TSH, that (1) the rank order of propagule dispersal distances would be Laguncularia > Avicennia > Rhizophora and (2) the expected relative tidal elevations at which the species would strand and establish at maximum density would be from highest to lowest elevation: Laguncularia > Avicennia > Rhizophora. Propagule dispersal: direction and distance To evaluate whether patterns of propagule dispersal matched the predictions of the TSH, we released marked propagules at three elevations/distances along each of three permanent transects (Fig. 2C ) and monitored the directions and distances of their movement. The three transects were established as part of an earlier descriptive study of mangrove species distributions and ran from the water's edge to the lower edge of upland rain forest; BM (Bahia Margarita; 270 m long) originated on the edge of a brackish lagoon; PL (Pipeline; 210 m long), on a small, tidal river; and MS (Minas South; 310 m long), on a large bay. These transects were intentionally established in areas where relatively undisturbed, closed canopy forest was distributed along uninterrupted, intertidal gradients. For logistical reasons, we selected sites that were accessible by foot, rather than choosing a strictly random sample of sites with similar physiognomy. The chosen transect locations were widely dispersed across the study area (Fig. 2) and incidentally in three somewhat distinct environmental settings (i.e., one each originating on a lagoon, river, and bay). We did not intend to compare propagule dispersal and establishment among these specific habitats; rather, we considered these three transects to be samples drawn from a larger population of undisturbed sites. Consequently, "transect" was treated as a random factor in our statistical analyses. Propagule dispersal: direction and distance The elevations/distances at which propagules were released along each transect were selected to represent the major forest types along the tidal gradient (Table 1) . At each elevation/distance, replicate groups of propagules of each species were released during low tide at three different points along a 60-70 m line running perpendicular to the main transect. The locations of these release points were determined in a stratified random manner, such that adjacent release points for a given species were separated by at least 25 m. The number of marked propagules released at each replicate release location was 30 for Avicennia and Laguncularia, and 20 for Rhizophora. For each species, the size distributions of the released propagules were held constant across all release points (ranges of propagule lengths: Avicennia, [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] Laguncularia, [20] [21] [22] [23] [24] [25] [26] [27] [28] Rhizophora, . Propagule dispersal: direction and distance Propagules used in this dispersal study and the following experiment on propagule establishment were drawn from large pooled collections of propagules that had recently dropped from canopy trees in several forest Note: Data are percentages of canopy trees along 60-70 m long, 10 m wide belt transects running perpendicular to the main transects along the linear array of release points and/or establishment pens. stands of each type within the study area. This ensured that the source of propagules did not vary among treatments and that the propagules were in an early stage of development, not yet having developed roots or an expanded shoot with leaves. As described earlier, the pericarp had fallen off the Avicennia propagules before they were collected and marked, but their cotyledons remained tightly closed. The rolled cotyledons and other embryonic tissues of Laguncularia propagules were fully enclosed within the seed coat when the propagules were released. Rhizophora propagules had a tightly closed stipule. All propagules were inspected for predispersal insect damage; only undamaged ones were used in the study. Minchinton (2006) found that insect-damaged propagules of Avicennia marina were initially more buoyant than undamaged ones. This enhanced buoyancy did not, however, increase the effective dispersal distance of the propagules, as had been predicted, because their viability declined over time due to continuing damage from insect feeding and tissue decay. Propagule dispersal: direction and distance Avicennia and Rhizophora propagules were released in mid-July 1995, during the peak annual period of natural propagule release for both species. Because a full day was required to monitor both species at each site, releases on the three transects were staggered by one day (19, 20, 21 July) to allow intertransect comparisons of movement after equal time intervals. A consistent search protocol was followed each time a transect was monitored: over a period of about four hours, four or five people searched for marked propagules within a ~100 m wide strip that extended from the uppermost release points to the water's edge, a distance that ranged from 185 to 255 m. We measured the compass direction and distance from the point of release of each relocated propagule at 1, 5, 14, 19, and 28 d following release. We also recorded whether the propagule was still floating or had sunk, what object or barrier, if any, it was in contact with, and whether it had firmly rooted into the soil. Laguncularia propagules were released on 8 (BM and PL transects) or 9 (MS transect) September 1995, during the peak period of natural propagule release by this species. Propagule dispersal: direction and distance Using the same procedure as for Avicennia and Rhizophora, we mapped the position of each relocated Laguncularia propagule at 1, 6, and 14 d after release, collecting the same ancillary information on propagule condition. Because Laguncularia propagules dispersed much more rapidly than those of Rhizophora and Avicennia (see Results) and began to lose their buoyancy more quickly, searches conducted 21 d following release failed to relocate a sufficient number of marked Laguncularia to meaningfully characterize their directional and spatial distributions. Therefore, our analysis examined movements of this species' propagules over 14 d. Propagule dispersal: direction and distance At each release point, the propagules were deposited within 25 cm of a PVC pipe that marked the location. On subsequent visits, propagules that remained within this radius of the pipe were scored as not having moved. To aid in the relocation of released propagules, they were marked with a thin coat of fluorescent paint (red [ServiStar, Gary, Illinois, USA] or pink [Plasti-Kote, Medina, Ohio, USA]) sprayed on the exterior of the propagule. To ensure that propagules of the same species released at different distances along a transect could be distinguished, propagules released at the three distances were painted with different color schemes (all red, all pink, or half pink/half red). We tested for the potentially confounding effect of paint marks on propagule buoyancy with a laboratory experiment (Appendix A). We did not detect a significant effect of the fluorescent paint marks on flotation patterns of any of the three mangrove species' propagules. Therefore, it is unlikely that paint marks had any significant effect on patterns of propagule dispersal in the field. Propagule dispersal: direction and distance Mean proportions of marked propagules relocated two and four weeks following their release were compared among transects, elevations, and species using mixed-model ANOVA. There were three levels of each factor: transect (BM, PL, or MS), tidal elevation (high, mid, or low), and species of propagule (Avicennia, Laguncularia, or Rhizophora) . Transect was considered a random factor; elevation and species were fixed factors. Propagule dispersal: direction and distance We compared propagule recovery rates over the different periods of time with two analyses. The first analysis compared rates for the three species' propagules over equal two-week time intervals (starting 19-21 July for Avicennia and Rhizophora and 8-9 September for Laguncularia). The second analysis compared recovery rates of Avicennia and Rhizophora over the full fourweek duration of our monitoring effort. For both analyses, proportions were arcsine transformed to ensure homogeneity of variance (Cochran's C = 0.234 and 0.189, respectively; P > 0.05). Propagule dispersal: direction and distance The directions of propagule movement were summarized and compared with circular statistics (Batschelet 1981 , Fisher 1993 , Anderson and Wu 1996 , Zar 1999 . These analyses examined angular data collected at 28 d for Avicennia and Rhizophora and 14 d for Laguncularia. We restricted the analyses to the 66 release points (out of 81) for which angular measurements could be made on at least four propagules. At the remaining 15 release points fewer than four of the released propagules moved out of the 25 cm radius circle in which they had been deposited; in these cases, small sample sizes precluded accurate estimates of the mean direction of propagule dispersal. We analyzed data from the longest available sampling intervals because this maximized the number of release points meeting our minimum sample size criterion and because mean directions of propagule movement at two vs. four weeks were very similar. To determine if the direction of movement differed among species, transects, or elevations, we calculated the mean angle of propagule dispersal and its circular variance (V = 1 -R, where R is the length of the mean resultant vector), which varies from 0 to 1. A value of 0 indicates no variation in the direction of movement, while a value of 1 indicates maximal dispersion of the directions, i.e., a mean angle cannot be described. While a uniform distribution has a V = 1, so will some symmetrical multimodal distributions (e.g., diametrically bimodal distributions that are centrally symmetrical; Fisher 1993 , Zar 1999 . We used Rayleigh's test to evaluate whether the distribution of directions measured at each release point differed significantly from uniform. Since the orientations of the three transects with respect to the water's edge-upland gradient were different (Fig. 2) , we conducted separate statistical comparisons of mean directions of dispersal within transects. Treating the mean vectors of dispersal from each release point as replicate measures of angular movement, we used separate Watson-Williams F tests to compare the grand mean directions of movement among species and elevations along each transect. Ideally, we would have employed the equivalent of a multi-way ANOVA to examine the effects of these two main factors (species and elevation), the nested factor (release point), and their interactions. However, the application of such techniques to circular data is at an early stage of development (Anderson and Wu 1995) . Since summary statistics indicated no evidence of interaction among the factors, we chose to conduct more conventional univariate tests of the two main factors within each transect. The angular distributions were unimodal in form (approximating von Mises distributions) with very similar variances, meeting the assumptions of the parametric Watson-Williams F tests. All circular statistics were calculated with Oriana software (Kovach 2003) . Propagule dispersal: direction and distance We compared the mean distances moved by marked and released propagules among transects, elevations, species, and points of release using mixed-model ANOVA. There were three levels of each factor: transect (BM, PL, or MS), tidal elevation (high, mid, or low), species of propagule (Avicennia, Laguncularia, or Rhizophora), and release point (each species was released at three points per elevation on a transect). Transect and release point were considered random factors, and elevation and species fixed factors. Release point was nested within transect, elevation, and species. We compared the mean distances moved over different periods of time with two different analyses. The first analysis compared movements of the three species' propagules over equal two-week time intervals (starting 19-21 July for Avicennia and Rhizophora, and 8-9 September for Laguncularia). The second analysis compared movement over the full duration of our monitoring effort: four weeks for Avicennia and Rhizophora vs. two weeks for Laguncularia. The latter analysis determined whether interspecific differences seen at two weeks would persist or disappear if slower dispersing species (Avicennia and Rhizophora) were allowed more time for movement. For both analyses, distances were log 10 (X + 1) transformed to improve homogeneity of variances (Cochran's C = 0.104 and 0.087, respectively; P > 0.05 in both cases). Seedling establishment at different distances from the water's edge To evaluate the hypothesis that the establishment success of seedlings of the three species of mangroves differs with elevation/distance from the water's edge in the size-dependent manner predicted by the TSH, we conducted a series of three experiments, each in a different year. These experiments measured propagule establishment rates in a landward to seaward sequence of habitats: three elevations within interior forests (1994), fringing stands (1999), and the back reef (2004) . In each experiment, we stocked open-topped, plastic-mesh (6 mm wide opening) pens with propagules of each of the mangrove species and monitored their rates of establishment as seedlings. A propagule/seedling was considered to be established when it became firmly rooted in the soil. Seedling establishment at different distances from the water's edge The 1994 experiment was conducted along the three transects used for the propagule dispersal study. On each transect, at the same three elevations/distances employed in the dispersal study (Table 1) , we installed and stocked four replicate pens for each species. The replicate pens at a particular distance were located, like the release points Ecological Monographs Vol. 77, No. 1 in the propagule dispersal study, along a 60-70 m line running perpendicular to the transect; they were positioned in a stratified random manner with adjacent replicate pens of a particular species no closer than 5 m apart. Because the prediction of the TSH with regard to seedling establishment specifically concerns the effects of water depth on propagule establishment, the positions of several of the pens were slightly displaced (<1 m) to avoid spots that had particularly high densities of herbivorous crab burrows. At our sites, crabs consume a considerable number of dispersing propagules, particularly in the lower intertidal zone (Sousa and Mitchell 1999) . Even with the repositioning of the pens, crabs consumed a modest number of propagules (<3) in some pens during the two-week interval between the first and second censuses. In these cases, the propagules lost to crabs were excluded when calculating the proportion of propagules that established. The pens were circular and 60 cm tall; those used for Rhizophora propagules were 80 cm in diameter, while the pens used for Avicennia and Laguncularia were 40 cm in diameter. These pen sizes afforded each propagule roughly equal soil surface area relative to its projected size (i.e., length X width). Each pen was stocked with 20 propagules of the target species; the resulting densities were moderate relative to natural ranges of propagule and seedling density (W. Sousa, unpublished data). Replicate groups of each species' propagules had a common size distribution (ranges of propagule lengths: Avicennia, 24-34 mm; Laguncularia, 23-30 mm; Rhizophora, 150-300 mm). All propagules were visually screened for predispersal insect infestations; only insect-free propagules were used. After stocking each pen, a roof of fiberglass insect screening was secured over the top opening to prevent propagules released from overhanging trees from falling in. Seedling establishment at different distances from the water's edge The establishment rates of Avicennia and Rhizophora propagules were monitored concurrently over 12 weeks, beginning 23 August 1994. At the end of this period, Avicennia seedlings and propagules were removed from their pens, which were then stocked with Laguncularia propagules on 16 November 1994. At the time of their removal, Avicennia seedlings were only 10-15 cm tall with modest root development. They were easily pulled from the firm, peat-dominated soil with little or no disturbance of the surface sediments. We continued to monitor the establishment of both these Laguncularia propagules and the original Rhizophora propagules for another seven weeks. At each census, we recorded the numbers of propagules that had firmly rooted in the soil and those that had not. Seedling establishment at different distances from the water's edge Because the timing and durations of the trials differed among the three species, patterns of propagule establishment were examined with two separate analyses. For the 12 weeks of concurrent monitoring of Avicennia and Rhizophora propagules, the mean proportions of propagules that established were compared among transects (BM, PL, or MS), elevations (low, mid, or high), and species using a mixed-model, three-factor ANOVA. Transect was treated as a random factor, and elevation and species treated as fixed factors. Establishment rates of Laguncularia propagules after seven weeks were examined with a separate mixed-model, two-factor ANOVA testing the independent and interactive effects of transect (random factor) and elevation (fixed factor). The same analysis was applied to Rhizophora propagules after a total of 19 weeks. For all three analyses, proportions were arcsine transformed to improve homogeneity of variances (Cochran's C = 0.164, 0.256, and 0.342, respectively; P > 0.05 in all cases). Seedling establishment at different distances from the water's edge While the 1995 propagule dispersal study was designed to measure the distance and direction of propagule dispersal, it also yielded information on patterns of seedling establishment at different elevations in the forest interior; in essence, it provided temporal replication of the 1994 seedling establishment experiment. For Rhizophora and Avicennia, we used a mixedmodel, two-factor ANOVA to test for the independent and interactive effects of transect (random factor) and elevation (fixed factor) on the mean proportion of marked propagules dispersing from a release point that were found to be firmly rooted in the soil at the final census dates (i.e., after four weeks for Rhizophora and Avicennia). Proportions were arcsine transformed to ensure homogeneity of variance (Cochran's C = 0.353 and 0.241, respectively, P > 0.05). Too few Laguncularia propagules established on the BM and PL transects for meaningful statistical analysis, so for this species we simply compared the two-week seedling establishment rates among the three different elevations on the MS transect. An arcsine transformation homogenized the variances (Cochran's C = 0.541; P > 0.05). Seedling establishment at different distances from the water's edge The other two establishment experiments (1999 and 2004) were designed to compare establishment rates of the three species at even lower tidal levels, where the influence of water depth on seedling establishment might be stronger. The 1999 experiment was conducted within the 10-20 m wide pure Rhizophora stands that fringe the lagoon at the BM site (Table 1) . At each of three haphazardly chosen sites along the lagoon edge, separated by 75-100 m, we established four pens for each species 1.5-4 m landward of the water's edge at low tide. These pens were identical in design to those employed in the 1994 trials, and each was stocked with 20 propagules of the target species on 4 September 1999. The length distributions of the three species matched those used in the 1994 trials, and all were free of insect damage. Unlike the 1994 trials, this experiment tested all three species simultaneously and over the same length of time. Overlapping fruiting times in this particular year allowed a concurrent test of the three species. The condition of these propagules was monitored at 21, 29, 38, and 130 d (the last data set gathered on 12 January 2000, after almost 19 weeks). We used a mixed-model, two-factor ANOVA to test the independent and interactive effects of site (random factor with three levels) and species of propagule (fixed factor with three levels) on the proportion of propagules establishing over the 130-d period. These proportions were arcsine transformed to homogenize variances (Cochran's C = 0.242; P > 0.05) prior to analysis. Seedling establishment at different distances from the water's edge The 2004 experiment was conducted at the lower edge of the fringing Rhizophora stands at the back of the Galeta reef, about 75 m southwest of the main laboratory building (Fig. 2) . Ten small and ten large pens were installed in pairs (one of each size) along a 30 m length of fringing forest, among or just beyond the prop roots of the most seaward trees. They were constructed of the same materials and had the same diameters as used in the first two experiments, but the height of their walls was increased from 60 to 90 cm so that waves would not break over them at high tide and displace floating propagules. The pens were placed in locations where there was adequate sediment for seedling establishment and where reinforcing bars could be driven into the underlying dead coral pavement to support the pens. Water depth was spatially variable in this back reef area; blocking the pens as pairs ensured that water depths were matched between cages containing propagules of different species. Measurements of water height at low tide indicated that the tidal height of the enclosed areas ranged from 0.05 to 0.15 m below Mean Lower Low Water. Seedling establishment at different distances from the water's edge The temporal sequence of trials for the different species was similar to the 1994 experiment in that Rhizophora and Avicennia propagules were stocked first (on 13 July 2004) in the large and small pens, respectively. Each pen was stocked with 20 propagules of the appropriate species; replicate groups of each species' propagules had a common size distribution (ranges of propagule lengths: Avicennia, 20-35 mm; Rhizophora, 150-270 mm). All propagules were prescreened for insect infestations, as in the earlier trials. The fates of these propagules were monitored weekly until 2 December 2004, by which time all the Avicennia propagules had either established as seedlings or died. At that time, established Avicennia seedlings were removed from the 10 small pens, which were then stocked with 20 insect-free Laguncularia propagules, with a common distribution of lengths in each pen (range 25-30 mm). As in the 1994 experiment, removal of the small Avicennia seedlings caused little disturbance to surface sediments. The condition of the Laguncularia and remaining Rhizophora propagules was monitored weekly until 5 January 2005. The Rhizophora pens were censused a final time on 29 July 2005. Mean proportions of propagules that rooted firmly in the substrate were compared between species with paired / tests on arcsinetransformed data. RESULTS Rates of marked propagule recovery Mean rates of marked propagule recovery varied among species (two weeks, F 2i4 = 168.78, P = 0.0001; . Species-specific rates of marked propagule relocation two and four weeks after release. Bars show grand mean proportions (+SE) of the propagules deposited at individual release points that were relocated during the indicated census (data from replicate release points were averaged over transect and elevation, neither of which significantly affected relocation rates; Appendix B). There were no data for Laguncularia at four weeks. Rates of marked propagule recovery four weeks, F l2 = 93.47, P = 0.011) and through time (Fig. 4) but did not differ among transects (two weeks, F 2 . 54 = 0.36, P = 0.701; four weeks, F 236 = 0.44, P = 0.649) or elevations (two weeks, F 2A = 1.43, P = 0.340; four weeks, _F 2 ,4 = 0.96, P = 0.457), and there was no evidence that the influence of any of these factors interacted (P > 0.05 in all cases; Appendix B). The mean recovery rate for Rhizophora propagules exceeded 95% at each monitoring date (release point median = 100%). On average, more than 80% of Avicennia propagules released at a particular point were recovered after two weeks (release point median = 90%), and over 60% were recovered after four weeks (release point median = 67%). Laguncularia propagules were followed for two weeks, with a mean recovery rate of 60% (release point median = 60%). As discussed in Results: Propagule dispersal distance, some of the propagules that were not relocated, particularly those of Laguncularia, may have dispersed out of the monitored areas. There are, however, good reasons to believe that most of the propagule disappearances were the result of predation or sinking. During our searches, we found a number of marked Avicennia and Laguncularia propagules that had been torn apart by herbivorous crabs. In an earlier study (Sousa and Mitchell 1999) , we found that crabs consumed 30-40% of tethered propagules in the lower intertidal over a period of four weeks. Therefore, marked propagules dispersing into or through this zone probably experienced high rates of predation, accounting for many, if not most, of the disappearances. Sinking was probably another important cause of propagule disappearance, particularly for Laguncularia. When tested in the laboratory under the low salinity conditions typical of the rainy season (the period of natural dispersal, also when our study was conducted), more than half of Laguncularia propagules had lost their 5. Circular plots of the mean directions and distances moved by propagules of the three species along the BM transect. Each plot displays values for the three replicate release points at each elevation. The black and gray arrowheads on the periphery of each plot point toward the upland and low intertidal, respectively (see Fig. 2 for a large-scale view of transect orientations). Rates of marked propagule recovery buoyancy by 16 d (Appendix A), the length of time that their movements were monitored in the field. When these small propagules sink to the bottom among dense stands of pneumatophores and leaf litter, they become difficult to find. Direction of propagule dispersal The movement of propagules away from release points was highly directional and practically linear in many cases. Of the 66 releases for which the direction of movement was measured for four or more propagules, 63 (95.5%) had F < 0.20 and 54 (81.8%) had F < 0.10, indicating very little variation in the direction of propagule dispersal from individual release points. Rayleigh's tests showed that the distributions of propagule dispersal directions were significantly different (P < 0.05) from random in 64 of the 66 releases (97.0%). The two cases that could not be distinguished from random (one Avicennia and one Rhizophora release) were characterized by small numbers of dispersing propagules (fewer than seven in both cases) that moved short distances, resulting in greater variance (V = 0.392 and 0.348, respectively) and therefore less power to reject the null hypotheses of random movement. Direction of propagule dispersal On each transect, the propagules moved downward, towards lower elevations and the water, be it a bay (MS), lagoon (BM), or river (PL): exactly opposite the direction predicted by the TSH (Fig. 1) . The 27 propagule releases on the BM transect illustrate this consistency of dispersal direction (Fig. 5) . The propagules were moved by sheet-flow runoff across the forest floor following rain storms (W. P. Sousa, personal observation). The range of mean dispersal directions from the release points on each of the transects was less than 90° (Fig. 6) propagule movement on each of the transects did not differ among species or elevations (Table 2) . On the BM and PL transects, the grand mean direction of movement corresponded quite closely (within 10°) to the landward to seaward direction of the transects, while on the MS transect the propagules moved at a 35.8° angle to the transect. The transects had been established to cut across visually apparent forest zones, running roughly perpendicular to the water's edge, without attention to patterns of surface water flow. The contours of the watershed that contributes surface flow to the MS region are more heterogeneous than those of the other sites, making the relationship between flow and zonation more complex. Nonetheless, the direction of the MS transect fell within the range of mean dispersal angles measured at the site (Fig. 6) . Propagule dispersal distance Propagules of the three species exhibited very different rates of dispersal (Fig. 7) . On average, over a two-week period Laguncularia propagules moved more than 10 times farther than Avicennia propagules and more than 200 times farther than Rhizophora propagules. Even after an additional two weeks of dispersal by Avicennia and Rhizophora propagules, large differences persisted. Laguncularia propagules moved much farther over a two-week period than propagules of Avicennia or Rhizophora did over a four-week period (5 and 25 times, respectively). While there was a significant transect X species interaction at both two {F^5 4 = 5.47, P < 0.001) and four weeks (F 4M = 3.49, P = 0.013; Appendix C), Tukey's hsd tests comparing species differences within transects (Fig. 7) confirmed that Laguncularia propagules consistently dispersed greater distances than those of Avicennia, which in turn moved farther than propagules of Rhizophora. Propagule dispersal distance The transect X species interactions resulted from differences in the influence of transect on species dispersal rates (Fig. 7) . There was little variation in the dispersal of Rhizophora propagules among the transects; they moved very short distances regardless of where they were released. On the other hand, the more vagile propagules of Avicennia and Laguncularia moved greater distances on some transects than others. There was no significant effect of elevation on dispersal distance at either two or four weeks, and this factor exhibited no significant interactions with transect or species (P > 0.05 in all cases; Appendix C). Maximum dispersal distances showed very similar patterns of variation among transects and species (Fig. 7) . Propagule dispersal distance Note: The number of release points is given in parentheses. Box plots of the distributions of mean distances moved by propagules from individual release points along each of the three study transects. Propagules of each species were released at nine points on each transect; see Methods: Propagule dispersal: Direction and distance for details. Mean distances moved did not differ with elevation along a transect, nor did this factor interact significantly with either transect or species (Appendix C). In each plot, upper and lower hinges represent the 75th and 25th percentiles, upper and lower whiskers represent the 95th and 5th percentiles, and the median and mean are shown, respectively, as solid and dashed lines across the box. The range of the maximum distances (m) moved by a species' propagules from each of the nine release points is enclosed in parentheses to the right of the respective box plot. Two-week values are presented for Laguncularia (L2), and two-week and four-week values are presented for Avicennia (A2, A4) and Rhizophora (R2, R4). Propagule dispersal distance The results of Tukey's hsd tests comparing mean distances moved by propagules of the three species on each study transect are reported on the left of each panel. Separate results are presented for analyses of movement over two-week periods (Analysis I) and over the entire periods of monitoring (Analysis II; four weeks for Avicennia and Rhizophora and two weeks for Laguncularia). Lowercase letters summarize test results: within the column for a given analysis, species marked with different unprimed or primed letters exhibited significantly different (P < 0.05) rates of propagule dispersal. Propagule dispersal distance Consistent with these differences in dispersal rate, the average percentages of propagules that failed to move out of the 25 cm radius circle surrounding a release point differed markedly among the three species: 76.7% after four weeks for Rhizophora, 29.2% after four weeks for Avicennia, and 4.3% after two weeks for Laguncularia (F 2A = 192.01, P < 0.001). These proportions did not vary significantly among transects (i<2,54 = 2.98, P = 0.059) or elevations (F 2A = 3.53, P = 6.131), nor were there any significant interactions among the three factors (range of P = 0.107-0.905; Appendix D). Propagule dispersal distance Groups of propagules released at different points within an elevation exhibited significant differences in mean dispersal distance at both two and four weeks ( Fig. 8 ; Appendix C). Some of this variation was due to small scale spatial variation in sheet flow across the forest floor. In other cases, propagules dispersing from particular release points were blocked by physical barriers such as (Fig. 9A, B) , or they accumulated along strandlines of rivers (Fig. 9C) or bays (Fig. 9D) . Propagule dispersal distance We believe that the four-week dispersal distances measured for Rhizophora and Avicennia propagules and the two-week dispersal distances measured for Laguncularia propagules represent nearly the full extents of their movements. This conclusion is supported by the observation that the average and maximum distances that Rhizophora and Avicennia propagules dispersed changed little between the second and fourth week (Fig. 7) . By four weeks, an average of 64.3% of viable Avicennia propagules associated with individual release points had firmly rooted into the soil, and 74.0% of these had developed into erect seedlings and flushed their first pair of leaves. Rhizophora was slower to become rooted; by four weeks, an average of 14.1% of viable Rhizophora propagules associated with individual release points had become firmly rooted and none had flushed leaves. A small proportion of Laguncularia propagules had become rooted within two weeks of being released (an average of 6.7% of those associated with individual release points). By this time, however, most Laguncularia propagules were no longer buoyant and had either sunk to the soil surface within dense stands of pneumatophores or become trapped in leaf litter and were therefore unlikely to be moved much farther by currents. Propagule dispersal distance Due to their high vagility, Laguncularia propagules, particularly those released at lower tidal elevations, were the most likely to be carried to a tidal river, bay, or lagoon and be transported greater distances. We relocated 14 marked Laguncularia propagules in the strandline of the Rio Coco Solo at the bottom of the PL transect and 13 at the edge of Bahia Las Minas at the bottom of the MS transect (see Fig. 2 ). Therefore, some Laguncularia propagules may have been carried greater distances, but these represented a modest proportion of those relocated after two weeks. Propagule establishment In the 1994 experiment, the three species exhibited very similar patterns of seedling establishment (Fig. 10A) . In the first trial of this experiment, which involved Rhizophora and Avicennia propagules, the species did not differ in mean rates of establishment (F, 2 = 5.33, f = 0.147), but rates of propagule establishment differed among transects (F 2 . 54 = 10.08, P < 0.001) and elevations (F 2A = 25.96, P = 0.005), with no significant interactions among the factors (range of P = 0.095-0.977; Appendix E). Propagules of both species established better at the lower elevation, in mixed Rhizophora-Laguncularia stands (Fig. 10A ), than at mid-or high elevations (Tukey's hsd test: P < 0.05); rates did not differ between the latter two elevations. These patterns persisted for Rhizophora propagules over the additional seven weeks that they were monitored. In early January 1995, 19 weeks after being stocked in the pens, the proportion of Rhizophora that had established as rooted seedlings differed among transects (F2.27 = 8.30, P = 0.002) and elevations (F 2A = 9.49, P = 0.03), with no transect X elevation interaction (F 4t27 = 198, P= 0.126). The proportion of Rhizophora that had established as rooted seedlings was higher at low (x = 0.921) than mid-(0.716) or high (0.617) elevations (Tukey's hsd test: P < 0.05), which did not differ. Propagule establishment In the second 1994
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