SPECIES RICHNESS OF CORAL ASSEMBLAGES: DETECTING REGIONAL INFLUENCES AT LOCAL SPATIAL SCALES

Transcription

1 Ecology, 83(2), 2002, pp by the Ecological Society of America SPECIES RICHNESS OF CORAL ASSEMBLAGES: DETECTING REGIONAL INFLUENCES AT LOCAL SPATIAL SCALES RONALD H. KARLSON AND HOWARD V. CORNELL Department of Biological Sciences, University of Delaware, Newark, Delaware 976 USA Abstract. Coral assemblages are generally open to immigration from regional species pools and thus are regionally enriched rather than saturated with species. Previously we have documented the sensitivity of local richness in these assemblages to a number of regional factors including the size of the regional species pool. Here we focus on the local scale used to determine the local regional richness relationship. We examine the sensitivity of local richness to regional richness and to two environmental variables (depth and habitat type) across a range of locality sizes. In general, local richness is sensitive to the environmental variables regardless of locality size. In contrast, it is relatively insensitive to regional richness in very small -m 2 quadrats but highly sensitive when sampled with 0-m line transects. Thus our analysis suggests a spatial threshold somewhere below 0 m for the detection of regional enrichment in coral assemblages. There are four biological mechanisms that may allow regional effects to be expressed at this spatial resolution: () disturbance and slow recovery toward competitive equilibrium, (2) heterogeneous biological interactions involving aggregated resources, neighborhood competition, or nonrandom dispersal among local neighborhoods, (3) spatially variable predation by specialists, and (4) probabilistic recruitment coupled with equal competitive ability. Empirical tests are now needed to discriminate among these mechanisms. Key words: aggregation; coexistence; competitive exclusion; coral assemblages; dispersal; disturbance; immigration; pseudoreplication; pseudosaturation; regional enrichment; saturation; spatial heterogeneity; spatial scale. INTRODUCTION Although the high diversity of coral communities has been recognized for many years, the processes that generate and maintain it are only just becoming evident. A renewed awareness of the influence of history and geography on local communities (see Ricklefs and Schluter 993, Giller et al. 994) has made it clear that regional phenomena (e.g., geologic and evolutionary history, oceanic transport, and atmospheric oceanographic coupling) as well as local phenomena (e.g., storms and other disturbances, environmental gradients, habitat specialization, and species interactions) can affect coral community structure. In order to understand the dynamics of coral communities more fully, we now must integrate these phenomena into a single conceptual framework (Cornell and Karlson 996, 997, Caley and Schluter 997, Karlson and Cornell 998, 999, Karlson 999). Species saturation is an aspect of local community structure that provides a focus for the development of this framework. Classical equilibrium explanations for the high diversity observed in tropical communities held that local habitats were saturated with species and that high regional richness occurred because different species specialized on different habitats (MacArthur Manuscript received 6 March 2000; revised 26 November 2000; accepted 6 February 200; final version received 25 May rkarlson@udel.edu ). One can test for saturation by examining the relationship between local and regional richness (Cornell and Lawton 992). Saturation is indicated when local richness reaches an upper limit and becomes independent of the number of species in a region. In contrast, unsaturated communities do not reach such a limit. In the extreme, they are characterized by a linear, proportional relationship between local and regional richness (Cornell 985, Ricklefs 987, Cornell and Lawton 992). Central to the exploration of saturation are the spatial dimensions at which local and regional richness are measured. Logically, these dimensions should be chosen because they are ecologically meaningful in that they reflect some reality as to what is a region and what is a community (Cornell and Karlson 996, Huston 999). Regional richness is typically measured over large geographical areas. The ideal scale for a region should be that within which regional characteristics such as climate and evolutionary age are homogeneous, and within which propagules of all species are available to all localities within the region. Since different species have different dispersal abilities, this ideal scale would... have indistinct boundaries (Cornell and Karlson 996). In previous analyses, we searched the literature for estimates of coral regional richness at spatial dimensions spanning km (references in Karlson and Cornell 998). We found that the sensitivity of local richness to regional richness can vary depending

2 February 2002 REGIONAL INFLUENCES AT LOCAL SCALES 453 on the geographical scale of the analysis (Karlson and Cornell 998). Local richness was highly sensitive to regional richness at the global scale (Indo-Pacific and Atlantic provinces combined). But when the provinces were evaluated separately, this sensitivity occurred only in Indo-Pacific coral assemblages. Local richness is measured over more restricted spatial dimensions. Ideally, a locality should be at a scale within which all species interact, and within which the local environment is homogeneous. Since different species interact at different scales.... andenvironments that are homogeneous for one species may be heterogeneous for others, the ideal locality would, like the ideal region, have indistinct boundaries. (Cornell and Karlson 996). For example, it may circumscribe the number of decapod species associated with a single coral head, multiple coral heads on a single reef, or multiple coral heads on multiple reefs at one locality (e.g., Abele 979, 984). Local samples must be standardized in some way so that they are comparable among regions. Typically the number of individuals or the unit area assessed is uniform, or local assemblages are sampled until the species/sampling effort curve levels off (Cornell 985, Hawkins and Compton 992). In the former case, single samples are used to infer richness in relatively small areas. In the latter, multiple samples are added together to generate species-accumulation or species area curves (Colwell and Coddington 994). These curves are then used to infer the richness of the entire habitat, site, or community. Our previous analyses of coral assemblages employed single samples (spanning spatial dimensions of m) from 00 sites around the world (Cornell and Karlson 996, Karlson and Cornell 997, 998). Since sample unit size was variable, we first conducted log log regressions of local richness vs. sample unit size (see Cornell and Karlson [996] for details of this analysis and Karlson and Cornell [997] for figures of local richness vs. sample unit size for quadrat, linetransect, and point-intercept samples). The residuals (unexplained variation) were then analyzed in stepwise regressions against multiple independent variables. The analysis showed that local richness was sensitive to regional richness (being higher in more speciose regions) and that the magnitude of this sensitivity was comparable to that along local depth and habitat gradients (Cornell and Karlson 996). Although local richness was previously known to vary along local gradients (Huston 985a), variation across differentially rich regions was a novel result. The relationship between local and regional richness is affected by the relative scales at which these two variables are measured. As locality and region size converge, local and regional richness become more similar and the slope of the local regional richness plot approaches one. Thus as a conservative test for regional enrichment, we used widely divergent locality and region sizes: small individual samples (and some mean values per sample unit size) to estimate local richness and broad surveys over large geographic areas to estimate regional richness. This conservative test provided evidence for significant regional enrichment of coral assemblages across differentially rich regions (Cornell and Karlson 996). The use of small individual samples also ensures that estimates of local richness do not transcend individual habitats, a critical requirement for tests of saturation (see Westoby [998] and Huston [999] for similar arguments). Because of well-known species area relationships, larger localities should provide even higher local richness estimates and thus increase the probability of finding significant regional enrichment. For example, one might use species-accumulation curves over multiple samples to estimate the richness of an entire habitat. As a test for regional enrichment, this approach is less conservative. However, its primary limitation is that sufficient coral data from differentially rich regions are not currently available for the generation of species-accumulation curves. The effect of locality size on the similarity of local and regional richness is clear from several coral reef studies. For example, Caley (997) reported that the local richness of fishes within 4-m 2 samples differed by 0% between One Tree Island (2.0 species) and Lizard Island (3.2 species) on the Great Barrier Reef. Ten percent represents only one quarter of the roughly 40% difference in regional richness (859 vs. 200 species). Moreover, local richness at the 4-m 2 scale comprised only % of the regional fauna at each site. In contrast, Westoby (985, 993) reported that the local richness of fishes in 00-km 2 areas differed by 4% between St. Croix in the Virgin Islands (420 species) and One Tree Island (900 species). This was the same as the regional difference between the Caribbean Sea (700 species) and the Great Barrier Reef (500 species). At each site, local richness across a range of habitats represented 60% of the regional fauna. A result comparable to Westoby s was reported by Caley and Schluter (997) using a region size of km 2 and locality sizes of % and 0% of the region. At both of these large locality sizes, richness was strongly and linearly related to regional richness.... for multiple taxa. Average local richness was 6% and 68% of regional richness. As one example, coral species in six areas off the coast of Western Australia were combined to generate a regional richness estimate of 335 species. Fifty-eight percent of these species occurred at one locality (Rowley Shoals) representing 8% of the regional area. Caley and Schluter (997) acknowledged that localities this large include species from multiple habitats. Thus their analysis could be used to detect regional enrichment across multiple habitats, but not saturation within individual habitats (see Westoby 998). Although the use of small localities provides a con-

3 454 RONALD H. KARLSON AND HOWARD V. CORNELL Ecology, Vol. 83, No. 2 servative test for regional enrichment, it can also bias local regional richness relationships towards curvilinearity as rare species become increasingly undersampled in speciose regions (Hawkins and Compton 992, Caley and Schluter 997). This curvilinearity (pseudosaturation) can be confused with the curvilinear relationship described for Type II saturated communities (Cornell and Lawton 992). As Caley and Schluter (997) specifically noted, pseudosaturation can also make the linear pattern described by Cornell and Lawton (992) for Type I unsaturated communities more difficult (if not impossible) to attain. Thus caution is warranted when local regional richness plots based on small localities generate curvilinear patterns. Strong linear patterns provide evidence for regional enrichment, whereas curvilinear patterns may be consistent with regional enrichment or saturation depending on the degree of bias. Our previous analyses of coral assemblages used small local samples and we detected some curvilinearity in the local regional richness plots (the slopes of all log-transformed richness plots regardless of geographic scale or method were less than one (see Karlson and Cornell 998, 999). We thus re-examine our original database keeping in mind the problem of pseudosaturation. In particular, we consider the effects of locality size on the relationship between local and regional richness. We argue that most, if not all, regional influences on local richness are lost in very small localities because such samples can include only one or a few colonies (species coexistence is precluded by severe spatial constraints on the co-occurrence of individuals; see also Huston [999]). In large localities, population phenomena, spatiotemporal heterogeneity, and environmental uncertainty can promote species coexistence and elevate local richness (Cornell and Lawton 992, Cornell and Karlson 2000). Thus there may be some minimum locality size or sample resolution at which the regional species pool begins to influence local richness (i.e., a threshold). Does such a threshold exist, and if so, at what scale does it occur? The answers to these questions will determine the minimum locality size for future empirical studies of regional enrichment and species coexistence in coral assemblages. METHODS In order to determine how locality size influences the inferred relationship between local and regional richness, we return to our original database comprising 653 quadrat and 542 line-transect samples (Cornell and Karlson 996, Karlson and Cornell 998); we ignore the limited point-intercept data. Since quadrats and line transects differ substantially in terms of sampling resolution and the manner in which they assess spatial heterogeneity, we analyze them separately as in Cornell and Karlson (996:239). Our first objectives are to identify the sampling resolution at which local richness is most sensitive to regional richness and to determine Summary statistics for local richness of corals sampled at multiple spatial scales. TABLE. Scale of analysis -m 2 quadrats 5-m 2 quadrats 0-m line transects 9.3-m 2 quadrats 30-m line transects 25-m 2 quadrats Scale rank Mean Local richness Maximum SD n Notes: Scale rank is based on the mean and maximum local richness and is merely presented to illustrate overlap between quadrat and transect sampling. This ranking is inversely related to sampling resolution. Data were used in two previous analyses (Cornell and Karlson 996, Karlson and Cornell 998). Location with maximum local richness (superscript numbers):, Reunion Island (Bouchon 978); 2, Canton Atoll (Jokiel and Maragos 978); 3, Indonesia (Moll 986); 4, Addu Atoll (Davies et al. 97); 5, Guam (Randall 973); 6, Gulf of Aqaba (Mergner and Schuhmacher 98). the shape of the local regional richness relationship at this scale. Since some large quadrats sample more species than do small transects (Table ), there is overlap in the space sampled by these different methods. In order to minimize this overlap, we partition the quadrat and transect samples into large and small categories using the median sample unit sizes as criteria (i.e., 6.7 m 2 and 20 m). We then identify the category, and subsequently the specific spatial dimension within this category, providing the strongest evidence for regional enrichment. Lastly, we examine local regional richness relationships at higher spatial resolutions (smaller dimensions) for a possible threshold at which regional enrichment occurs. Using the forward selection procedure for stepwise regression analysis (using F 4.00 and P 0.05 as the rejection criteria), we examine the sensitivity of local richness to sample unit size, regional richness, depth, and habitat type. This procedure allows us to rate the variables in order of their importance (Snedecor and Cochran 967). In Cornell and Karlson (996), local richness was sensitive to each of these independent variables when data were pooled across all sampling methods and locality sizes. Depth, habitat, and regional richness are evaluated as linear and quadratic terms and as part of all possible two- and three-way interactions. As in Cornell and Karlson (996), sample unit sizes, depth, and regional richness values are log-transformed prior to analysis. This transformation not only stabilizes variances, but also permits estimation of the best power relationships between local richness and sample unit size (e.g., the species area relationship) and between local and regional richness. The continuum of expected local regional richness relationships described by Cornell and Lawton (992) ranges from Type I communities (in which local richness is a function of regional richness

4 February 2002 REGIONAL INFLUENCES AT LOCAL SCALES 455 FIG.. Local richness (number of species) along 0-m line transects plotted against depth (in meters below mean low water). Data are categorized into four groups based on regional richness: #, 9 2 species;, species;, species;, species. to the first power, a linear relationship) through a family of curvilinear relationships (in which local richness is a function of regional richness to a power less than one). Habitat type is a ranked variable based on the relative distance from shore through reef-flat, crest, and seaward-slope habitats. All variables are standardized (with mean 0 and SD ) to give them equal weighting in the analyses (see Cornell and Karlson 996). Lastly, we use ridge regression (Hoerl and Kennard 970a, b) to identify and eliminate terms generating unstable regression coefficients (especially those cases in which a sign reversal occurs). This problem (sometimes referred to as the multicollinearity problem ) occurs when the explanatory variables are too highly intercorrelated (Sokal and Rohlf 995:663). Local richness data from the literature were originally collected for a variety of purposes. Consequently, the data are highly variable and unbalanced relative to depth, habitat, and regional richness. Mean local richness estimates per habitat are presented in Appendices A (quadrats) and B (transects) in order to illustrate these problems across depth and habitat gradients. Nevertheless, mean local richness appears, in general, to vary consistently across habitats. It increases from inner reef flats outwards from shore to reach a maximum on upper and mid-slopes. This is a widely recognized pattern on coral reefs (Huston 985a, b, Cornell and Karlson 996, 2000, Karlson 999). In order to illustrate further how local richness varies with respect to depth and habitat over a range of differentially rich regions, we present the data on local richness per 0-m line transect (mean 8.6 species, 236 samples, Table ). Local richness in the most depauperate regions is below the mean across all regions ( 8 species) and samples are restricted to shallow water ( 8 m, Fig. ). In regions with species, local richness reaches a maximum of 6 species at two depths (4.5 and 7 m, Fig. ); the latter is from a midslope habitat (Fig. 2). In regions with species, local richness reaches a maximum of 30 species at a depth of 30 m (Fig. ) on a lower slope (Fig. 2). In the most speciose regions with species, there are few data reported with corresponding depth information (only three samples with, 8, and 20 species at depths of.0, 2.7, and 4.5 m, respectively, Fig. ). In contrast, there are several samples collected in lower slope habitats (depth not given) including a maximum value of 33 species (Fig. 2). This is the highest value among all 0-m line transects regardless of region (Table ). The general pattern of higher local richness in more speciose regions is evident in both Figs. and 2. Since reef habitats generally differ in local richness, local regional richness relationships are also likely to vary among habitats. Furthermore, unbalanced sampling, intercorrelations among variables (in spite of our use of ridge regressions), or differential interactions among variables across habitats, may have influenced these relationships in the previous stepwise regressions FIG. 2. Local richness along 0-m line transects plotted against habitat ranked by distance from shore ( inner flat, 2 mid- and outer flat, 3 crest and upper slope, 4 midslope, 5 lower slope). Data are categorized into four groups based on regional richness as in Fig..

5 456 RONALD H. KARLSON AND HOWARD V. CORNELL Ecology, Vol. 83, No. 2 Stepwise regression of local richness ( ) in small line-transect samples 20 m in length. TABLE 2. Source of variation df SS MS F Model (R 2 76.%) Depth (D) Regional richness (S) D S Error Total Notes: Richness and depth (relative to mean low water) are log-transformed. Habitat (ranked based on distance from shore) and sample unit size do not enter the regression model. All variables are standardized in the analysis. P Total variance due to depth 48.53, habitat 0.0, and regional richness Quadratic term; terms appear in the order they enter this model: Y D.04S 0.33D S 2. due to pooling of data. Thus we present a separate, habitat-specific analysis to augment the analysis of data pooled among habitats. The 0-m line transect data are selected for this procedure based on strong regional enrichment observed at this scale. We restrict this analysis to habitats with more than one local richness estimate per region in at least four regions. We consider four regions minimal to detect significant curvilinearity and at least some curvilinearity is indicated in the data pooled across habitats. Stepwise regressions are used to examine the sensitivity of local richness to the linear and quadratic terms for regional richness and depth as well as the interaction between these two variables. We include depth here only to insure that significant variation in local richness across regions is not confounded with depth. When only one term in the stepwise procedure is significant, we report the results from simple regression. Ridge regression is used again to reduce the multicollinearity problem. RESULTS Among four sampling categories (i.e., small quadrats, large quadrats, small transects, and large transects), small transects provide the strongest evidence for regional enrichment (Table 2). This is consistent with our previous report of strong regional enrichment from all transect samples combined (Cornell and Karlson 996). Not only does the linear term for log-transformed regional richness account for much more of the explained variation in local richness than does the quadratic term, but the regression coefficient associated with this best-fit power relationship (the linear term) is higher than any we have previously reported ( [mean SE]). Since it is not significantly different from one (t 0.676, P 0.05), it signifies a linear (rather than curvilinear) relationship between untransformed local regional richness values. Because both local and regional richness are standardized in these analyses (with mean 0 and SD ), this linear term also indicates a constant proportional increase in local richness as regional richness increases. However, the quadratic term for regional richness is also significant (but weaker) thus indicating some additional curvilinearity not explained by the best power relationship. The negative regression coefficient ( , [mean SE]) for this quadratic term is consistent with convex curvilinearity in the local regional richness relationship (see Cornell and Lawton 992, Cornell and Karlson 997). Together these two regional terms account for 62% of the explained variation in local richness; depth accounts for only 38% (Table 2). In quadrat samples, regional richness accounts for less of the explained variation in local richness than do depth and habitat. Regional richness accounts for only 32% and 6% of the explained variation in small and large quadrats, respectively (Tables 3 and 4). The fact that local richness is less sensitive to regional richness in larger (rather than smaller) quadrats is most likely due to unbalanced sampling across differentially rich regions in these two categories [e.g., a higher proportion of large-quadrat samples come from the relatively homogeneous western Atlantic where regional enrichment has not been detected (Karlson and Cornell 998)]. More importantly, the linear term for regional richness in small-quadrat data is not significant (Table 3). Thus local richness does not increase directly with regional richness (i.e., regional enrichment is not detected). The quadratic term is significant, but the regression coefficient is slightly positive ( [mean SE]) and not consistent with a convexly curvilinear relationship. In large-quadrat data, the linear term for regional richness is significant and the regression coefficient is less than one ( ; t 5.857, P ) thus indicating convex curvilinearity as the best power relationship (Table 4). The 0-m line-transect data as a subset of the smalltransect category also show strong regional enrichment (Table 5). The linear term for regional richness accounts for most of the explained variation (77%) and Stepwise regression of local richness ( ) in small-quadrat samples 6.7 m 2 in size. TABLE 3. Source of variation df SS MS F Model (R %) Regional richness (S) Depth (D) Habitat (H) H S D Error Total Notes: Richness and depth are log-transformed. Sample unit size does not enter this model. All variables are standardized in the analysis. P 0.00; P Total variance due to depth 26.07, habitat 37.50, and regional richness Quadratic term; terms appear in the order they enter this model: Y S D 0.84H 0.43H (S D).

6 February 2002 REGIONAL INFLUENCES AT LOCAL SCALES 457 Stepwise regression of local richness ( ) in large-quadrat samples 6.7 m 2 in size. TABLE 4. Source of variation df SS MS F Model (R %) Habitat (H) H Sample unit size (U ) Regional richness (S) Depth (D) D S D H S H Error Total Notes: Richness, depth, and sample unit sizes are log-transformed. All variables are standardized in the analysis. * P 0.05; P 0.00; P Total variance due to depth 68.04, habitat 26.48, and regional richness 9.7. Quadratic term; terms appear in the order they enter this model: Y H 0.23H S 0.59S 0.43D 0.29D S(D H) 0.6(S H). TABLE 5. Stepwise regression of local richness ( ) in 0- m line-transect samples. Source of variation df SS MS F Model (R 2 8.0%) Regional richness (S) Depth (D) S D Habitat (H) D Error Total Notes: Richness and depth are log-transformed, and all variables are standardized in the analysis. The model using untransformed richness values is as follows: Y S 0.59S D; R 2 72.%. * P 0.05; P 0.0; P 0.00; P Total variance due to depth 2.5, habitat.67, and regional richness 84.. Quadratic term; terms appear in the order they enter this model: Y S 0.8D 0.28S (D H) 0.8D 2. the regression coefficient ( , [mean SE]) again is not significantly different from one (t 0.67, P 0.05). The quadratic term indicates significant, but relatively weak, curvilinearity (Table 5). The relationship between log-transformed local and regional richness is depicted in Fig. 3 for all of the 0-m linetransect data ( studies, 8 regions, 236 samples, Table ). A duplicate analysis of untransformed richness data yields a similar result, but with a lower R 2 (72.%, Table 5). Ten meters is the minimum distance sampled along line transects in most studies. Thus quadrat samples need to be examined for local regional richness relationships at higher sampling resolutions. The three most common quadrat sizes in this data set are m 2, 5m 2, and 9.3 m 2. At least 63 samples were taken at each of these scales (Table ). However, 9.3-m 2 quadrats were used in only a single study at one location (Davies et al. 97). Consequently, the local regional richness relationship cannot be evaluated at this scale and we restrict further analysis to -m 2 and 5-m 2 quadrats. Local richness in small quadrats is much more sensitive to the local variables (depth and habitat) than to regional richness. Depth and habitat account for 90% of the explained variation at the -m 2 scale (Table 6). Regional richness was significant only in a relatively weak interaction term with habitat. Fig. 4 depicts the relationship between log-transformed local and regional richness for -m 2 quadrats (7 studies, 7 regions, 63 samples, Table ). At the 5-m 2 scale, only the linear term for habitat is significant (Table 7). Although three regions are represented at this scale, most of the data (96%) are from a single study in one region (Jokiel and Maragos 978). Duplicate analyses of untranformed richness data yield very similar results in both -m 2 and 5-m 2 quadrats (Tables 6 and 7). We now evaluate the 0-m transect data to examine habitat-specific differences in local regional richness relationships. There are sufficient data to examine these relationships in four of the five habitat categories: () mid- and outer reef flats, (2) reef crests and upper slopes, (3) mid-slopes, and (4) lower slopes. A summary of the results appears in Table 8. Overall, the linear term for regional richness is most significant in each of eight regression models (using log-transformed or untransformed richness). Thus regional enrichment is detected in all four habitats. This linear relationship is especially strong on mid-slopes where the best-fit FIG. 3. Local richness along 0-m line transects plotted against regional richness. These data are also used in Tables and 5. Duplicate values among 236 samples are not depicted (from sources cited in Karlson and Cornell [998]).

7 458 RONALD H. KARLSON AND HOWARD V. CORNELL Ecology, Vol. 83, No. 2 TABLE 6. Stepwise regression of local richness ( ) in - m 2 quadrat samples. Source of variation df SS MS F Model (R %) Depth (D) Habitat (H) H Regional richness (S) H Error Total Notes: Richness and depth are log-transformed, and all variables are standardized in the analysis. The model using untransformed richness values is as follows: Y D 2.40H.02H (S H); R 2 72.%. P 0.0; P Total variance due to depth 3.47, habitat 24.85, and regional richness Quadratic term; terms appear in the order they enter this model: Y D 2.38H 0.82H (S H). power relationship between local and regional richness indicates no significant curvilinearity ( [mean SE], t.625, P 0.05) and the quadratic term for regional richness does not enter either model (Table 8). Very strong evidence for curvilinearity appears only on lower slopes where both linear and quadratic terms for regional richness are significant regardless of the transformation (Table 8). Furthermore, use of the log transformation supports strong curvilinearity in this habitat because () the coefficient for the linear term representing the best-fit power relationship is significantly less than one ( , t 5.67, P 0.025) and (2) the quadratic term is relatively large and negative ( ). Evidence for curvilinearity is ambiguous on midand outer reef flats and on reef crests and upper slopes (Table 8). Although the quadratic term for regional richness does not enter the regression models using untransformed data, the regression coefficients for the linear term in log-transformed analyses are significantly less than one ( [mean SE], t 7.200, P and , t 4.667, P 0.025, respectively). However, sample sizes are very small (Table 8) and the results are not consistent with those from all small transects (Table 2) or all 0-m line transects (Table 5). DISCUSSION FIG. 4. Local richness in -m 2 quadrats plotted against regional richness. These data are also used in Tables and 6. Duplicate values among 63 samples are not depicted (from sources cited in Karlson and Cornell [998]). Our evidence indicates that the 0-m line transect represents the smallest locality at which regional enrichment is detected in coral assemblages. Within small quadrats, local richness appears not to increase directly with regional richness (the linear term for regional richness is not significant in Tables 3, 6, and 7). In contrast, 0-m line transects provide strong support for this linear component of variation (Tables 5 and 8). In addition, there is weak support for curvilinearity in these data. Local richness begins to level off as regional richness increases (Fig. 3), but more data are needed from the most speciose regions ( 400 species) to support or reject the saturation hypothesis (e.g., note that the upper limits on regional richness indicated in Table 8 are 350 species). Local richness is much less sensitive to regional richness at higher sampling resolutions. Thus we infer a threshold below the 0-m scale at which regional enrichment can be detected. In contrast, local richness is sensitive to local variables (depth and habitat) across a wide range of sampling resolutions. Below we discuss the relevance of these results to four topics germane to the study of local regional richness relationships: locality size, curvilinearity and saturation, pseudoreplication, and possible mechanisms promoting regional enrichment. TABLE 7. Simple regression of local richness ( ) in 5-m 2 quadrat samples. Source of variation df SS MS F Model (R %) Habitat (H) Error Total Notes: Regional richness and depth do not enter the regression model using stepwise procedures. Both variables are standardized in the analysis. The model using untransformed richness values is as follows: Y H; R %. P 0.0. Total variance due to depth 0.0, habitat 2.52, and regional richness 0.0. Terms appear in the order they enter this model: Y H.

8 February 2002 REGIONAL INFLUENCES AT LOCAL SCALES 459 Summary of regression analyses of local richness (Y ) vs. regional richness (S) and depth (D) in four separate habitat categories (numbered as in Fig. 2) sampled with 0-m line transects. TABLE 8. Habitat category 2) Mid- and outer reef flats 3) Reef crests and upper slopes 4) Mid-slopes 5) Lower slopes Regression models Y S 0.50D 0.35SD Y S 0.45D Y S 0.43D Y S 0.4D 0.20D 2 Y S Y S 0.58D 0.35D 2 Y S 0.78S 2 Y S 2.25S 2 Variation explained (R 2,%) No. samples No. regions Regional richness range (no. spp.) Notes: Terms for linear, quadratic, and interaction effects are included when significant and appear in the order they enter the regression models. Results from lower-slope data represent the only cases where both linear and quadratic terms for regional richness are significant. Analyses using both log-transformed and untranformed richness data are included to emphasize the robustness of these results. All variables are standardized as in previous analyses. Log-transformed richness data. Untransformed richness data. Locality size Local regional richness relationships can take several forms depending on the size of the locality and the scale at which local processes influence species richness (Ricklefs 987, Cornell and Lawton 992, Huston 999). These relationships may be linear as for Type I assemblages, curvilinear with no leveling off, or curvilinear with leveling off as for Type II assemblages (Cornell and Karlson 997). The larger the locality, the larger the proportional representation of the regional biota (e.g., Westoby 985, 993, 998) and the greater the tendency toward a linear relationship. The selection of large localities can thus obscure saturation at smaller spatial dimensions. In other words, a linear relationship might occur because local habitats are regionally enriched, or alternatively, because the locality circumscribes multiple habitats that are saturated with species. A possible way to discriminate between these alternatives is to select smaller localities within habitats where processes such as competition actually occur (Huston 999). However, small localities present their own problems. They may introduce curvilinearity into the local regional richness relationship as rarer species become increasingly undersampled in speciose regions (Caley and Schluter 997). The sampling resolution needed to quantify local richness must be large enough to avoid the false conclusion of saturation. Caley and Schluter (997, 998) and Westoby (985, 993, 998) suggest that the appropriate size of a locality is quite large (e.g., km 2 ). However, localities this large reintroduce the difficulty of discriminating between saturation within habitats and regional enrichment among habitats (see Huston [999] for a similar argument regarding scale and local processes). Within habitats, local richness may be assessed with small individual samples as we have done (Cornell and Karlson 996, Karlson and Cornell 998) or by means of species-accumulation curves to estimate local richness for an entire habitat. The former approach may introduce severe curvilinearity into the local regional richness relationship (although it did not appear to do so in our study), whereas the latter should reduce this sampling bias and avoid the pseudosaturation problem (sensu Caley and Schluter 997). However, the data required to generate convincing species-accumulation curves are more difficult to acquire and there are a variety of assumptions underlying each of several approaches to the generation of these curves (Colwell and Coddington 994). In any case, we found insufficient data in the coral literature to evaluate these estimation procedures. There are other potential problems that might be overcome by using small individual samples rather than species-accumulation curves. Since the latter require multiple samples, the area covered might be large enough to sample heterogeneous portions of a single habitat. Furthermore, not all habitat boundaries are clearly distinct so some degree of intergrading among different habitats is possible. Sampling protocols designed to estimate local richness should minimize edge effects at habitat boundaries and the between-habitat component of variation. Another potential problem is the mismatching of locality size with the actual processes controlling local richness. The locality size one uses should match the local processes one wishes to investigate (Huston 999). The pooling of all samples within a habitat to generate a single estimate of local richness may make it difficult to discriminate among the alternative mechanisms contributing to regional enrichment in smaller localities (see Discussion: Mechanisms promoting regional enrichment). Perhaps species-accumulation curves are best for making inferences concerning saturation when regional processes are not strongly influencing the local assemblage and processes such as com-

9 460 RONALD H. KARLSON AND HOWARD V. CORNELL Ecology, Vol. 83, No. 2 petitive exclusion are occurring at a scale encompassing the entire habitat. On the other hand, smaller localities may be best for making inferences concerning the lack of saturation due to such processes as local disturbances and neighborhood competition. At the present time, we believe it is premature to proclaim either of these approaches as best in all situations. We need better data and more rigorous analyses. Curvilinearity and saturation Although our study did not detect strong curvilinearity in the local regional richness relationship (except on lower slopes, Table 8), we note that very few data have been collected in the most speciose region of the central Indo-Pacific (i.e., the Philippines and parts of Malaysia and Indonesia). This is a coral diversity hotspot, where regional richness may exceed 450 species (Veron 995). If saturated coral assemblages actually exist, this is where we would expect to find them. In our previous analyses, we found only three quantitative studies from this region (Karlson and Cornell 998). Two of these employed point-intercept sampling (Ross and Hodgson 982, Wood and Tan 987) and thus could not be used in the present analysis. Sy et al. (982) used 5-m line transects in the Philippines (Appendix B). Thus our conclusion that coral assemblages are not saturated (Cornell and Karlson 996, Karlson and Cornell 997, 998) is based largely on data collected from less speciose regions of the world. Clearly, more extensive data are needed from more speciose regions to rigorously evaluate the saturation hypothesis. The analysis provided in Table 8 suggests that local regional richness relationships may differ among habitats. We know that seaward slope environments are generally more speciose than are reef flats and this difference may account for the curvilinear local regional richness relationship detected in the former. Seaward slopes may be providing evidence for saturation. Alternatively, the sampling bias causing pseudosaturation may be more severe on slopes due to the underrepresentation of rare species in small local samples. As with other aspects of this study, these alternatives need to be tested with better data than are presently available. Pseudoreplication Our analyses have focused on the joint influence of the local environment and regional phenomena on the local richness of corals (Cornell and Karlson 996, Karlson and Cornell 998). Thus they required multiple estimates of local richness per region across habitat and depth gradients. Regional richness was estimated as the number of coral species within a radius of each sampling location (i.e., km [Cornell and Karlson 996]). These procedures were necessary in order to assess simultaneously the relative sensitivity of local richness to local and regional variables. In general, the local richness of coral assemblages is sensitive to depth and habitat regardless of locality size, whereas sensitivity to regional richness varied strongly with locality size. Srivastava (999) has criticized the use of multiple estimates of local richness per region on the grounds that spatiotemporally correlated data can introduce pseudoreplication into the analysis thus inflating the apparent significance of regional effects. Caley and Schluter (998) also noted this problem as one drawback to the species area approach recommended by Westoby (985, 993, 998) for studying saturation. They noted that the earth provides us with few biogeographic regions with which to study species area and local regional richness relationships, so pseudoreplication is a statistical consequence of upscaling ecological studies to regional dimensions. Pseudoreplication was originally noted as a problem in the design of field experiments in which treatments were not replicated or when replicates were not statistically independent (Hurlbert 984). A recent review of this problem again was restricted to experimental studies (Heffner et al. 996). Our coral study was not a planned experiment or observational study. Rather it represents a retrospective examination of the literature to determine, as a first approximation, local regional richness patterns in scleractinian corals. These patterns should be tested empirically in planned studies of saturation and regional enrichment with particular emphasis on currently undersampled speciose regions where saturation is more likely to occur. Srivastava (999) specifically extended the notion of pseudoreplication to local regional richness plots. She argued that the use of multiple estimates of local richness within a region violates the fundamental assumption of statistical independence. In fact, as ANOVA by definition requires multiple measurements per treatment level, any local regional plot analyzed using ANOVA-type tests must be pseudoreplicated. As a solution to the pseudoreplication problem, Srivastava advocated the exclusive use of mean local richness values when using ANOVA methods. This is an extremely conservative solution in that it precludes multivariate analyses and does not allow one to use more than one independently generated local richness estimate per region. However, it does solve the problem. But local regional richness plots are not really like experiments in which one might fertilize a single field and then collect multiple samples from it, a classic case of pseudoreplication. Instead, defining regions is just a convenient way to specify an average species pool for particular local sites. If the system is viewed from the perspective of a local site, the species pool for the site could in theory be defined by intercepting all individuals arriving there over a specified period of time. If two sites are close together, their species pools would be similar. For sites farther apart, species pools would become progressively more different. From this view-

10 February 2002 REGIONAL INFLUENCES AT LOCAL SCALES 46 point, the problem has more to do with spatial autocorrelation in nearby samples rather than pseudoreplication within a region. One solution is to select sites that are far enough apart so that their species pools could be considered independent. Another would be to examine the possibility that there are independent species pools for different habitats. Yet a third is to use randomization tests as suggested by Sokal and Rohlf (995) when the assumptions of parametric tests are violated. We conclude that it is currently premature to undertake any of these solutions to the pseudoreplication problem in our study. The degree of curvilinearity in the local regional richness relationship for corals needs to be documented with better data from speciose regions. If strong curvilinearity is indicated by these data, we suspect that randomization methods will be required to discriminate between saturation and pseudosaturation (as suggested by Caley and Schluter [997]). While the exclusive use of mean local richness values can solve the pseudoreplication problem, it is unlikely to be sufficiently powerful to solve the pseudosaturation problem. Mechanisms promoting regional enrichment Among the putative mechanisms promoting regional enrichment in ecological communities (Cornell and Lawton 992), there are four which may be particularly relevant to coral assemblages. They are as follows: () disturbance and slow return to competitive equilibrium (Connell 978, Huston 979, 985a, b), (2) heterogeneous biological interactions (e.g., aggregated resources [Shorrocks 990, Ives 99, Shorrocks and Sevenster 995], neighborhood competition [Pacala 986a, b, Pacala and Levin 997], and nonrandom dispersal among local neighborhoods [Hassell et al. 994, Holmes et al. 994, Tilman 994]), (3) spatially variable predation by specialists (Janzen 970, Armstrong 989), and (4) probabilistic recruitment and equal competitive ability (Sale 977, 99, Hubbell and Foster 986). None of these have been rigorously tested for their influence on the regional enrichment of coral assemblages. However, there is supportive evidence for each of them and we have previously ranked them in the above order based on their plausibility (Cornell and Karlson 2000). In addition, we have emphasized three specific aspects of these general mechanisms that may be particularly relevant, namely local disturbances and predation, neighborhood competition, and intraspecific aggregation (Karlson and Cornell 999). Each of the general mechanisms stresses biological rather than purely physical processes and each can operate within quite small localities. Thus we suggest that they are suitable for empirical tests of their contribution to the regional enrichment of coral assemblages. It is our hope that the evaluation of the published literature will stimulate a renewed interest in factors generating and maintaining the diversity of coral assemblages. This effort will necessarily include consideration of both local and regional phenomena and thus the integration of processes across multiple spatial scales. ACKNOWLEDGMENTS A number of individuals have significantly contributed to this project. We are grateful for the support and constructive criticism from J. Caley, S. Harrison, T. Hughes, J. Lawton, J. Pandolfi, and D. Schluter. M. Huston, P. Sale, J. Witman, and two anonymous reviewers made several helpful suggestions for improving this manuscript. J. Fox and J. Witman suggested possible statistical solutions to the pseudoreplication problem. This work has been supported in part by grants from the Australian Research Council, the National Science Foundation, and the National Geographic Society. LITERATURE CITED Abele, L. G The community structure of coral-associated decapod crustaceans in variable environments. Pages in R. J. Livingston, editor. Ecological processes in coastal and marine systems. Plenum Press, New York, New York, USA. Abele, L. G Biogeography, colonization, and experimental community structure of coral-associated crustaceans. Pages in D. R. Strong, Jr., D. Simberloff, L. G. Abele, and A. B. Thistle, editors. Ecological communities: conceptual issues and the evidence. Princeton University Press, Princeton, New Jersey, USA. Armstrong, R. A Competition, seed predation, and species coexistence. Journal of Theoretical Biology 4: Caley, M. J Are local patterns of reef fish diversity related to patterns of diversity at a larger spatial scale? Pages in Proceedings of the Eighth Coral Reef Symposium (Panama City, Panama, June 996). Volume one. Caley, M. J., and D. Schluter The relationship between local and regional diversity. Ecology 78: Caley, M. J., and D. Schluter The relationship between local and regional diversity: reply. Ecology 79: Colwell, R. K., and J. A. Coddington Estimating terrestrial biodiversity through extrapolation. Philosophical Transactions of the Royal Society of London, Series B 345: 0 8. Connell, J. H Diversity in tropical rain forests and coral reefs. Science 99: Cornell, H. V Local and regional richness of cynipine gall wasps on California oaks. Ecology 66: Cornell, H. V., and J. H. Lawton Species interactions, local and regional processes, and limits to the richness of ecological communities: a theoretical perspective. Journal of Animal Ecology 6: 2. Cornell, H. V., and R. H. Karlson Diversity of reefbuilding corals determined by local and regional processes. Journal of Animal Ecology 65: Cornell, H. V., and R. H. Karlson Local and regional processes as controls of species richness. Pages in D. Tilman and P. Kareiva, editors. Spatial ecology: the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, New Jersey, USA. Cornell, H. V., and R. H. Karlson Coral species richness: ecological vs. biogeographical influences. Coral Reefs 9: Davies, P. S., D. R. Stoddart, and D. C. Sigee. 97. Reef forms of Addu Atoll, Maldive Islands. Symposia of the Zoological Society of London 28: Giller, P. S., A. G. Hildrew, and D. G. Rafaelli, editors Aquatic ecology: scale, pattern and process. Blackwell Scientific Publications, Oxford, UK. Hassell, M. P., H. M. Comins, and R. M. May Species