Abstract Species abundance data from a horizontal transect at Hopkins Marine Station were combined with data about the physical environment of these sites to study horizontal variation in intertidal community structure. Cluster analysis validates traditional ecological descriptions of population structure, in that the statistical clusters of species are similar to those communities described by marine ecology texts (such as Ricketts and Calvin, 1992). Regression analysis suggests that some species commonly found together had different physical parameters driving their distribution. For example, the limpet Lottia gigantea is positively correlated with wave force, but shows no correlation with maximum temperature, azimuth and site slope angles, or the presence of crevices in the rocks. In contrast, L. gigantea’s cluster-mate and prey, the encrusting alga Hildenbrandia spp., has a positive correlation with slope angle, but no correlation with wave force, azimuth angle, maximum temperature, or presence of crevices. A smooth, continuous, horizontal gradient of species does not exist along the experimental transect. The complex shape of the shoreline causes physical parameters at each site to be uncorrelated with those at neighboring sites and as a result, the horizontal distribution of species at HMS is patchy. Horizontal variation can be attributed both to the expansion and contraction of vertical zones with variation in wave exposure, as well as community changes caused directly by wave exposure. Introduction One of the most easily observable ecological features of rocky shores is the pattern of zonation that occurs in the intertidal zone. Horizontal bands of distinct communities exist from high on the shore to subtidal areas (Stephenson and Stephenson, 1949). Causes of vertical zonation patterns are generally well understood by marine ecologists. The upper limits of organisms are often set by physical factors, such as threat of desiccation (Carefoot 1977). Lower limits are generally set by biological factors, such as competition or predation (Carefoot 1977). In addition to vertical zones, and less easily observed, are horizontal zones of communities. Causes of horizontal zonation, however, are less known, and much less studied. Ricketts and Calvin (1992) and Burrows et al (1954) point to exposure to wave action as a cause for a variation in community structure horizontally along a shore. Ricketts and Calvin (1992) identify six types of communities, divided both horizontally and vertically, that exist on rocky intertidal shores (Fig. 1). They focus mainly on invertebrates, thus some of these groups don’t include all the algae that are commonly found in these communities. Group I, characteristic of low intertidal, highly wave-exposed areas, is distinguished by large amounts of algae, particularly corallines, laminarians, and the sea palm, Postelsia palmaeformis. On especially wave-exposed headlands, the sea urchin, Stronglyocentrotus purpuratus also occurs in this zone. In the protected, low intertidal areas, a second community exists (Group II). Characteristic invertebrates that are found in this community are sea stars, sponges, hydroids, and the large green anemone, Anthopleura xanthogrammica. The primary alga in this zone is eelgrass, Phyllospadix spp. Further up the shore is a community, (Group III), dominated by what Ricketts and Calvin (1992) call the "Mytilus-Pollicipes-Pisaster association." Mytilus californicus, and Pollicipes polymerus, are filter feeders that form large beds in this mid-intertidal zone, and Pisaster ochraceus is the sea star that preys upon them. These three species generally dominate the exposed mid intertidal shoreline. Also commonly found with this assemblage are the chiton Nuttallina californica, the barnacle Tetraclita rubescens, the predatory snail Nucella emarginata, and three limpet species, Lottia gigantea, L. limatula, and Tectura scutum. The corresponding mid-intertidal community on protected shores includes Tegula funebralis, an intertidal snail, Patiria miniata, the bat star, and Tonicella lineata, a chiton (Group IV). Sponges, such as Haliclona spp. and Plocamium spp. are also found in this community. Located just above the mid-intertidal community is an upper community, dominated by the alga Endocladia muricata, as well as the limpets Lottia scabra and L. pelta (Group V). When this assemblage occurs in more wave-exposed areas, it shares the limpet L. gigantea and snail N. emarginata with the mid-intertidal exposed community. At the upper end of the intertidal emersion gradient, is the high wave splash zone. The community that characterizes this zone (Group VI) includes the littorines, as well as the limpet Lottia digitalis, and the barnacles Balanus glandula, and Chthamalus spp. These species are able to withstand the threat of desiccation in this high intertidal region. These last two communities (Groups V and VI) occur on both protected and wave-exposed shores, although with greater species abundance and lower down in protected areas (Ricketts and Calvin, 1992). Wave-induced hydrodynamic forces and the resulting splash of waves are the primary factors that drive the changes between exposed and protected shores. The force of a wave (due to drag, acceleration, and lift (Denny et al, 1985)) can remove delicate species. Wave splash may increase the height of the shore that remains wet at low tide. Researchers have shown that an increase in wave splash causes both expansion and upward shift of the vertical zones seen in the intertidal zone (Fig. 2) (Burrows et al, 1954; Lewis, 1964; Carefoot, 1977; Ricketts and Calvin, 1992; Raffaelli and Hawkins, 1996). This prediction of how intertidal zones vary with exposure, combined with the six communities that Ricketts and Calvin (1992) describe, should allow one to characterize species distribution in the intertidal zone (Fig. 3). This descriptive model predicts that given a horizontal transection of a shoreline that spans the entire range of exposure (from fully exposed to fully sheltered), the most wave-exposed areas of the transect will have a species assemblage characteristic of the lowest vertical zone. Likewise, the most sheltered area of the transect will have a species assemblage characteristic of the highest vertical zone. The number of vertical zones that are crossed with this horizontal slice of the intertidal zone will depend on the horizontal difference in exposure. A section of shoreline that has great differences in exposure will have many different vertical zones represented along a horizontal transect, whereas on a shoreline that has only one type of exposure a transect will all fall within a single zone. The Hopkins Marine Station shore, where this study took place, is comprised of both highly exposed headlands of rocky shore as well as protected sandy beaches. Both sheltered and exposed areas were interspersed along the 325-meter transect that was the study site for this project,. Because of the large range in exposure, I expected that the horizontal transect would include multiple vertical zones and their corresponding species assemblages. Following the model described above, I predicted that the most exposed areas of the transect should contain organisms from the mid-intertidal exposed community (Group III). The section of the transect with the lowest wave exposure should contain an assemblage characteristic of the upper limits of the intertidal zone (Group VI). At the areas of the transect with medium wave exposure, a combination of the mid-intertidal protected and the high-intertidal communities (Groups IV and V) was expected. To test this conceptual model, I first had to verify that groupings of species actually did exist along the transect. Cluster analyses were used to statistically identify species assemblages. The analyses, indeed, discerned clusters along the transect. Secondly, I hypothesized that these clusters would be similar to those described by Ricketts and Calvin (1992). In most cases, there is in fact a strong similarity between the species assemblages discerned by cluster analyses and the groupings that Ricketts and Calvin (1992) report. With these verified assemblages in hand, I then used them to test the tidal height-exposure model. Finally, if the model correctly predicts how species are distributed in the intertidal zone, and community composition can be predicted by wave exposure, does that mean that all species in a grouping are correlated with wave exposure? Regression analysis was used to explore the relationship between species, clusters, and various physical factors. These analyses, combined with the cluster analyses, suggest that within clusters, different environmental factors are driving species distribution. Materials and Methods Fieldwork The transect is located along the Hopkins Marine Station shoreline in Pacific Grove, California (Fig. 4). The length of shoreline studied is approximately 325 m, with 221 measurement sites. All points along the transect are 1.5 m + 0.3 m above mean lower low water. Sites are situated at various spacings along the shoreline. Starting at the east end of the transect 46, sites are spaced approximately four meters apart. The next 46 points are approximately two meters apart; the next 97 points are approximately one half meter apart; the final 29 points are approximately two meters apart. These distances are measured following the relief of the shoreline (Denny et al, submitted). Quadrats, 22 cm wide by 31.5 cm high, were used to estimate percent cover of species adjacent to each site. Quadrats were located with their center nine inches to the right of the meter hole (looking at the shore with your back to the ocean). Percent cover was estimated for all macroscopic species located in each quadrat. Bare rock was included as a "species." As a result, the proportional cover sums to 1 for every site. Data were taken twice at each site during October 2002. Replicates were reconciled, checked and averaged. Physical data for each site includes the azimuth angle, the slope angle, a measure of maximum wave force, a maximum temperature, and an index number for the amount of cracks and crevices in the quadrat area. Azimuth angle (horizontal direction of the site normal vector relative to north) was measured at each site using a compass. Slope angle (the slope of the rock face, where horizontal sites have a slope angle of O degrees and vertical sites are 90 degrees) was measured at each site using an electronic level. At each site along the transect, maximum water velocity was estimated as a function of offshore wave height (Helmuth and Denny, 2003). Wave force data was obtained by using a dynamometer installed into the rock at each site. Each meter consists of a spring scale attached to a small ball that the wave’s force pulls. Further description of the dynamometers can be found in Bell and Denny (1994) and Denny and Wethey (2001). The meters have been calibrated in previous studies so that the record on the spring scale can be equated to a certain wave force, and measurements were made for a large number of known offshore wave heights. These data, were used to predict wave force at each site along the transect for a typical offshore wave height of two meters (Helmuth and Denny, 2003). To a first approximation, wave force along the transect changes proportionally at every site as a function of offshore wave height. That is, one site will not suddenly jump from a wave force of 35N at a two-meter wave height to 85N at three-meter wave height if all the other sites that have 35N forces at two-meter wave heights only increase to 5ON with a three meter wave height. Temperature was logged at all sites along the transect for two weeks during April 2002 using iButton digital temperature loggers. From this record, the maximum temperatures achieved at each site along the transect during those two weeks was noted. It was assumed that the relative temperatures among the sites would not change drastically through time (i.e. the hottest sites would remain the hottest on both the hottest and the coldest days, and the coldest sites would be the coldest on both the hottest and coldest days). Topography at each site was quantified using an index of the amount of cracks and crevices in the rock found at each quadrat area. Any cracks or crevices found in the quadrat area at each site and their width and depth, were measured and recorded, and these measurements were transformed into an index value. Length of cracks was unnecessary to record, as nearly al of the cracks extended far beyond the quadrat area. Quadrats containing no cracks or crevices were assigned a value of 1. Quadrats with cracks at least 3 cm in width were assigned a 2, those at least 5 cm in width were assigned a 3, those at least 10 cm in width were assigned a 4, and those 15 cm in width or more were assigned a 5. A crack with a depth double its width was assigned the next higher value. A crack with a depth less than half its width was assigned the next lower index value. If a quadrat contained multiple cracks, the sum of the widths and depths of the cracks was used to estimate the topographic index. For example, a site with a crack 7 cm wide by 3 cm deep would be assigned a 2, a site with a crack 3 cm wide by 10 cm deep would be assigned a 3, and a site with both of those cracks would be assigned a 4 (from the sum of the widths and depths). The topographic data were collected during April and May 2003. Some of the sites on the transect had been removed by storms during winter 2002-2003. Thus, data were not available for topography at six sites. Statistical Methods Cluster analysis can be used as a method of summarizing large data sets by helping to detect patterns or relationships (Gordon,1999). Clustering has not been as widely used in biology as other methods of statistical analysis, possibly because it is primarily a descriptive tool. One drawback of cluster analysis is that it remains difficult to validate clusters, as it is often possible to produce different clustering patterns from the same data depending on the parameters used (Arabie and Hubert, 1996). Recently, clustering has been used more frequently in biology to create phylogenetic trees based on molecular data (Arabie and Hubert, 1996), and this increase in usage might spur creation of better methods of evaluating cluster validity. The process of cluster analysis is based on grouping objects in a data set so that the grouped objects are more similar to objects in their own group than they are to objects in other groups. Various methods of obtaining clusters exist. Hierarchical clustering, where each group is entirely contained in the next group higher up in the structure, was used in this study, and will be the only type of clustering discussed. Further discussion of other methods of classification can be found in Arabie, Hubert, and De Soete (1996), as well as in Gordon (1999). Cluster analysis proceeds in two stages. First, measures of similarity (or dissimilarity) are calculated to obtain a matrix of values representing the relationship between all objects in the set. Many methods of calculating similarity or “distance" exist. Secondly, objects are joined into groups based values in the similarity matrix. Again, many methods of creating these linkages are available. Different types of similarity and linkage calculations generally result in different cluster diagrams. Similarity calculations affect the matrix representing the data, and thus can affect the cluster groupings (Milligan, 1996). Some different similarity metrics include the Pearson correlation coefficient, and indices of distance, such as the Euclidean method or the City-block distance. Pearson’s correlation metric is a measure of the covariance in pairwise comparisons between variables, whereas the Euclidean and City-block metrics are based on an arithmetic distance formulae and often are strongly influenced by large values in the data (Quinn and Keough, 2002). Gordon (1996) describes the effects of different linkage methods on clusters. Complete linkage, which characterizes each cluster by the furthest member of the group, typically produces balanced, even dendrograms, where objects in clusters are highly similar to one another. Single linkage produces clusters that are more distinctly separate from the other groupings but contain objects that are less similar to one another. Complete linkage tends to produce more clusters than single linkage methods. Various other types of linkages take a middle road between these two extremes. Two different cluster analyses were performed in this project. The first compared species, regardless of their location along the transect. The comparison was accomplished by doing a pairwise comparison of species by their abundances along the transect. This yielded a dendrogram that had clusters of species that occurred together. The second type of analysis compared sites along the transect to each other. These comparisons were performed by doing pairwise comparisons of all species abundances for each site. This analysis yielded a dendrogram of that had clusters of sites with related species abundances. Both analyses excluded rare species, where "rare" is defined as being found in five percent or fewer of the total quadrats along the transect. This exclusion minimized groupings that didn’t accurately represent the real structure of the data. Rare species tend to cluster with relationships that are artificial, as a result of the cluster structure imposed on them. The cluster analyses that were performed in this study utilized two different types of distance methods. The R“ distance metric (which is the square of the Pearson correlation coefficient) was used when clustering the sites as a function of species composition. Because the alternative methods (Euclidean and City-block measures) are highly influenced by large values, the R“ metric was chosen so as to include all values at an approximately equal weight in the clustering. The gamma metric, a measure of association, was used when creating the clusters of species regardless of sites. Gamma correlation is a metric used when clustering variables that have large quantities of cases to describe them. It is especially useful when comparing data that have large quantities of "tied observations" or observations that are the same among variables or among cases (Wilkinson et al, 1996). In this case, many quadrats contained none of a particular species, which made the gamma correlation ideal. Complete linkage was used rather than single or average linkages. One of the goals of the cluster analysis in this project was to identify different communities in the intertidal zone. To achieve that, the complete linkage was a better metric because it only groups objects that are highly similar. The dendrograms produced by cluster analysis branched to the left off of the main stem of the cluster tree. Lengths of the branches are known as moats. Estabrook (1966) defines the moat of a cluster as the difference between the distance at which a cluster is formed and the distance at which it is combined with another cluster (Fig. 5). Clusters can be identified by drawing a line down the dendrogram at a specified distance from the origin, crossing various cluster branches. Each branch that is crossed denotes a cluster (Fig. 6). Branches that are crossed that have only a single object attached (one site) are outliers. When choosing where to place my cluster denotation line, I wanted to obtain sizable clusters that were very general groupings, but still maximize the distance of the moats that 1 was crossing. All cluster analyses in this project were undertaken using SYSTAT’s cluster analysis module. Additionally, this project used multiple regression analysis to quantify the relationship between physical factors and the biological diversity at each site. To obtain unbiased residuals when conducting the correlations, biological data were transformed using the arcsine-square-root transformation and physical data were transformed using a log transformation. The model used for all regressions was: Species abundance = constant + azimuth angle + slope angle + wave force + temperature + crevice index Azimuth and slope angles were measured in degrees. Azimuth angle was transformed to cosine of degrees so that a value of 1 represented due north and -1 due south. Slope angle was transformed to sine of degrees so that a value of 1 represented a perfectly vertical site, and -1 represented a perfectly horizontal site. Wave force was measured in Newtons. Temperature was measured in degrees Celsius. Results Cluster Analyses The first type of cluster analysis performed was on species, regardless of their location along the transect. The dendrogram for the species clusters (Fig. 7) shows three distinct clusters, separated at a distance of 1.5 from the base of the tree. There appears to be a connection between the composition of these clusters and the way individual species respond to the physical factors. The first group, cluster I, (containing M. californianus, Lottia paradigitalis, and L. pelta) has a significant positive correlation with wave force in half of the species (eight out of 16). The middle cluster (containing L. digitalis, Chthamalus spp., and E. muricata) shows less correlation with wave force (only one species out of six, and a negative correlation), but instead, a negative correlation with slope angle in three of the six species. The last cluster (containing Porphyra spp., Ralfsia pacifica, and Cladophora columbiana) has a negative correlation with wave force in four out of ten species, but no other strong cluster-wide trends. The second type of cluster analysis performed was done on sites, grouping them by the species present at each location. The cluster analysis of sites clustered by species abundance (Fig. 8) yielded nine clusters and one outlier, with the cluster denotation line placed so that clusters were very large (at a distance of 0.93). To characterize the species assemblages in the groups of sites found in the cluster diagram, the means and standard deviations of each species abundances were calculated for every cluster (Table 1). Five of the nine clusters could easily be characterized by the unusually large abundance of a particular species. For example, cluster IX, has sites that all have significantly high abundances of M. californianus as compared to all other sites on the transect (mean M. californianus species abundance for cluster IX is 64.8%) (p50.01, Student’s t-test). The cluster with the next highest mean M. californianus species abundance is cluster VII, with 28.9%. Cluster II sites contain significantly large amounts of E. muricata as compared to all other sites on the transect (p£0.01, Student’s t-test). Average abundance for this group is 53.7%, while the group with the next highest E. muricata abundance is cluster III, at 27.2%. From this, those clusters that are dissimilar from one another are evident (those that have 12 a significantly high quantity of one species), as well as clusters that may not be significant (those that do not have any distinguishing species). Because of the difficulty in validating clusters (see Arabie and Hubert, 1996), this distinction between the clusters was used to choose which clusters to analyze. The most notable clusters, IX, VII, II, VI, and I, are those that have a distinguishing species, and will be the only ones discussed here. Clusters III, IV, V, and VIII did not have a large quantity of a certain species or other distinguishing characteristic. Cluster IX is characterized by significantly high abundances of M. californianus, P. polymerus, and N. californica (p#0.01, Student’s t-test). Along the transect, the sites in this group occur on headlands (Fig. 9), that is, in areas that are the most exposed. Average wave force for the sites in this cluster is 56.8 N, the highest average for all nine clusters. Also, the average azimuth angle of sites in this cluster is 322.0 degrees, northwest, only two degrees off the estimated direction of wave approach (324 degrees). Sites in cluster VII are characterized by significantly high abundances of Hildenbrandia spp. (average percent cover for sites in this cluster is 46.2%), L. gigantea, and M. scabra as compared to all other sites (pS0.01, Student’s t-test). This cluster occurs slightly further away from the tips of the headlands than cluster IX, but still covers areas that are wave-impacted. The average wave force at the sites in this cluster feel (55.8 N) is just slightly less than the average wave force for sites in cluster IX. In the regression analysis, it was found that Hildenbrandia spp. has a strong positive correlation with slope of the substrate. This might imply that this cluster, which is characterized by high abundances of Hildenbrandia spp., would have a high slope angle. In actuality, the slope angle of these sites is exactly equal to the average slope angle for all the sites along the transect (64 degrees). E. muricata and T. funebralis characterize the population in cluster II. It is found even fürther back from the headlands than cluster VII. Sites in cluster II have a medium wave force, but the average maximum temperature at these sites is the highest of all the groups (33.8 °C). The sites also average a westerly azimuth angle, 263 degrees. Sites in cluster VI are characterized by a significantly large quantity of bare rock (average percentage of quadrat space at these sites that is bare rock is 58.9%) compared to all other sites along the transect (p20.01, Student’s t-test). The organisms at these sites are littorines, Chthamalus spp., L. digitalis, and Verrucaria spp., in significantly higher abundance at sites in this cluster than all other sites along the transect (p#0.01, Student’s t-test). Sites in this cluster are in some of the most protected areas of the transect (average wave force at these sites is 26.9 N), either because they don’t face oncoming waves or because the site is protected from the waves by offshore rocks. The average direction that sites in this cluster face is 237 degrees, southwest. Also located in the most wave protected areas of the transect is Cluster I. It is comprised of sites that contain significantly large amounts of M. papillatus (56.2% cover on average at the sites in this group) as compared to the rest of the transect (p#0.01, Student’s t-test). This cluster averages the lowest wave force of all the clusters (25.3 N). In the regression analysis, it was found that M. papillatus was highly negatively correlated with wave force, which is shown again in this cluster data. Regressions The regressions for the most part reinforced previously held notions about which species corresponded with which physical factors. Data for the multiple regression model relating species abundance and physical factors are shown in Table 1. Wave force was the most significant physical factor, contributing significantly to 15 out of the 55 total species. Nine species (articulated coralline algae, B. glandula, Callithamnion paschal, Cryptopleura lobuliferam, L. gigantea, L. pelta, M. californianus, N. californica and P. polymerus) showed significant positive trends with wave force. Six species exhibited a significant negative trend with wave force: crustose corallines, Cumagloia andersonii, L. limatula, L. scutulata, M. papillatus, Porphyra spp., and T. funebralis. Six algae (crustose and articulated corallines, C. columbiana, Gelidium coulteri, Mazzaella affine, and Porphyra spp.) showed a significant positive correlation with azimuth angle, (or more prominence of the species on northern-facing rocks). The species that showed a significant negative trend with azimuth angle (meaning more south-facing) were Littorina keenæe, L. digitalis, and Verrucaria spp. Verrucaria spp. and Hildenbrandia spp. were the only species that had a positive correlation with slope angle, while A. xanthogrammica, E. muricata, M. californianus, N. emarginata, and T. funebralis showed significant negative correlations with slope. Temperature also was found to be important in determining the distribution of species. Six algae, Analipus japonicus, articulated corallines, C. andersonii, E. muricata, Mazzaela leptorhynchus, and Petrocelis spp. showed a significant trend with temperature. Most of the algae were negatively correlated with temperature; E. muricata was the only alga to have a positive correlation. R* values range from 0.038 for A. japonicus to 0.248 for E. muricata. L. pelta, (R°= 0.066, ß = 0.086, p = 0.012), was the only animal species that had a significant trend with temperature. However, the low r-squared value shows that this trend does not explain much of the species' distribution. Cracks and crevices in the rocks were significant positive factors in influencing the distribution of crustose corallines, N. emarginata, P. polymerus, R. pacifica, and T. funebralis, as well as worm tubes, which were included in the study as a species. L. digitalis showed a significant negative relationship with the presence of crack and crevices. Of the 55 species examined, 22 species showed no significant correlations with any of the physical factors. Of these 22, 16 were considered rare species, found in five percent or fewer of the total quadrats along the transect. Discussion Are there statistical clusters in the data? Cluster analysis provided a useful method of grouping species and sites along the transect. The dendrogram for the first cluster analysis, of species, appears to be an accurate representation of the species assemblages that are actually seen in the intertidal zone. The moat distance for these species clusters is large (20.5 for each of the branches out of the total distance of 2.5 for the entire cluster diagram), suggesting that the three clusters are quite distinct. In addition to being distinct, the clustering makes ecological sense. In each of the three species clusters, there are smaller groupings that are indicative of intertidal zone relationships. For example, in cluster I, L. gigantea and Hildenbrandia spp. join together before joining any other group. It is possible that the closeness of these two species in the cluster diagram is a result of the their relationship in the intertidal zone. Limpets have been shown to "garden" algae, removing all competing organisms so that one alga can grow (Shanks, 2001; Williams and Little, 2001). It has been hypothesized that L. gigantea has this relationship with the encrusting alga Hildenbrandia spp. The second type of cluster analysis, of sites by species abundance, contained some clusters that seemed valid, as well as some clusters that seemed less valid. In terms of moat distance, these clusters appeared less distinct from one another. Moat distances crossed to create the clusters are around 0.1 to 0.15 for most of the clusters, out of the total dendrogram distance of 1.2. However, despite the smaller moat distances, five of the clusters contained species abundances that created fairly obvious distinctions between clusters. The clusters that were not deemed significant (because they did not have any distinguishing feature) had unusual species compositions (such as slightly higher than average abundances of both coralline algae and B. glandula in cluster VIII). Statistical clusters versus Ricketts and Calvin's (1992) groups The clusters of species match the groups described by Ricketts and Calvin (1992) quite well. M. californianus, T. rubescens, P. polymerus, N. californica, and L. gigantea appear in both the species cluster I and Ricketts and Calvin’s group III. Species in the cluster group that diverge from Ricketts and Calvin’s (1992) group III include L. pelta (Ricketts and Calvin’s (1992) group V), articulated and crustose corallines (Ricketts and Calvin’s (1992) group 1), B. glandula (Ricketts and Calvin’s (1992) group V), and M. scabra (Ricketts and Calvin’s (1992) group V). Grouping the corallines in this cluster makes sense, as the mid-intertidal exposed grouping is the next closest group to the low intertidal exposed group, where the corallines occur, according to Ricketts and Calvin (1992). Cluster II in the species clusters is very well correlated with Ricketts and Calvin’s (1992) group VI. L. digitalis, Chthamalus spp., L. scutulata, and L. keenæ are species found in both. Additionally, this cluster includes E. muricata, which Ricketts and Calvin denote as a high intertidal alga. Given that this analysis did not produce a cluster that represented the high intertidal zone, cluster II of the species clusters is the best fit for E. muricata. Cluster III represents a combination of the mid-intertidal protected and exposed species assemblages described by Ricketts and Calvin (1992) (groups IV and III). The cluster includes T. funebralis, a species in Ricketts and Calvin’s (1992) group IV, as well as L. limatula and N. emarginata, which are both in Ricketts and Calvin’s (1992) group III. It is unknown why L. limatula and N. emarginata clustered with T. funebralis in cluster III rather than the mid- intertidal exposed species in cluster I. Also in cluster III are six algae that are not discussed by Ricketts and Calvin (1992). The cluster of sites was performed by grouping sites with similar species composition. For five of the nine clusters the cluster analysis of sites also yielded characteristic species assemblages. The species assemblage of Cluster IX corresponded well with Ricketts and Calvin’s (1992) group III. Cluster IX contains significantly large quantities of M. californianus (average for sites in this cluster is 65.4% cover) as compared to all other sites on the transect (p50.01, Student’s t-test) as well as large abundances of species that were expected in the mid¬ intertidal exposed community, according to Ricketts and Calvin (1992), such as P. polymerus (average for sites in this cluster is 1.2% cover, compared to 0.50% cover all other sites along the transect, p#0.01, Student’s t-test) and N. californica (average for sites in this cluster is 0.75% cover compared to 0.40% cover for the whole transect, p«0.01, Student’s t-test). It also contained very low abundances of those species that would not be common in the mid-intertidal exposed community (Chthamalus spp.: 0.15% cover for sites in this cluster, 1.2% cover for all other sites on transect, p#0.01, Student’s t-test; L. scutulata: 0.040% cover for sites in this cluster, 0.21 % cover for all other sites on transect, p#0.01, Student’s t-test; L. keenæ: 0.00046% 18 cover for sites in this cluster, 0.013% cover for all other sites on transect, p«0.01, Student’s t- test; and E. muricata: 1.5% cover for sites in this cluster, 13.2% cover for all other sites on transect, p#0.01, Student's t-test) Likewise, Cluster VI was a good match with Ricketts and Calvin’s (1992) upper limits assemblage, group VI. Cluster VI, which contained large quantities of bare rock (average 58.9% cover for sites in this cluster versus 20.5% for all other sites on the transect, p«0.01, Student’s t- test), also contained above average quantities of L. scutulata (average percent cover on sites in this cluster is 0.37% versus 0.11% cover for all other sites on the transect, p«0.01, Student’s t- test), L. keenæ (average for sites in this cluster is 0.029% versus 0.0047 % cover for all other sites on the transect, p20.01, Student’s t-test), Chthamalus spp. (average 2.2% cover in these sites, and 0.55% cover for all other sites on the transect, p#0.01, Student’s t-test) and L. digitalis (average 1.2% cover in these sites and 0.23% cover for all other sites on the transect, p«0.01, Student’s t-test), but contained little M. californianus (average1.6% cover in these sites, 23.8% cover for all other sites on the transect, p#0.01, Student’s t-test) or coralline algae (average 1.1% cover in these sites and 6.4% cover in all other sites on the transect, p#0.01, Student’s t-test). The species assemblage represented in Cluster I of the site clusters is characterized by large amounts of M. papillatus (average percent cover in these sites is 56.2% compared to 2.4% for all other sites on the transect, p#0.01, Student’s t-test), which Ricketts and Calvin (1992) do not discus. Cluster II of the site clusters contained significantly large quantities of E. muricata (average percent cover for sites in this cluster is 53.7%, versus 5.8% cover for all other sites on the transect) and T. funebralis (average for sites in this cluster is 0.24% cover while average for all other sites on the transect is 0.073% cover) (p#0.01, Student’s t-test). E. muricata is described by Ricketts and Calvin (1992) as an upper-intertidal alga present with all wave exposures while T. funebralis is a mid-intertidal, protected shore snail. Since both of these species are present in large quantities in Group II, it might represent a blending of the two Ricketts and Calvin (1992) assemblages. Group VII of the site clusters (Fig. 8) has a significantly high abundance of both Hildenbrandia spp. (average percent cover of these sites is 46.2% compared with 12.9% for all other sites on the transect, p#0.01, Student’s t-test) and L. gigantea (average percent cover of these sites is 1.6% compared with 0.76% for all other sites on the transect, p«0.01, Student’s t- test). Ricketts and Calvin (1992) state that L. gigantea can be found in both mid and high intertidal areas with high exposure. If we assume that Hildenbrandia spp. can be found in both these areas as well, it is possible that this cluster represents the blending of the mid and high intertidal exposed areas (Ricketts and Calvin’s (1992) groups III and V). Other species in the cluster seem to represent both Ricketts and Calvin’s (1992) mid-intertidal exposed species assemblage (group III) and their high intertidal species assemblage (group IV). N. californica (also of Ricketts and Calvin’s (1992) group III) has a significantly high abundance at sites in this cluster as compared to all other sites on the transect (0.82% for these sites, 0.46% for other sites on the transect, p«0.02, Student’s t-test). M. scabra (of Ricketts and Calvin’s (1992) group V) also has a significantly higher average percent cover in these sites (1.3%) than across the rest of the transect (0.53%) (p#0.01, Student’s t-test). The tidal height-exposure model and species distribution The tidal height-exposure model (Fig. 3) accurately predicts the species assemblages at most sites along the transect. The protected areas of the transect, at the backs of protected coves 20 and on surfaces that are protected from wave action, were covered by the upper limits species assemblage (the same as Ricketts and Calvin’s (1992) group VI, cluster II of the species clusters, and cluster VI of the site clusters). The most exposed areas of the transect contained the mid- intertidal exposed assemblage (the same as Ricketts and Calvin’s (1992) group III, cluster I of the species clusters, and cluster IX of the site clusters) as predicted by the model. Additionally, some overlapping between zones did occur at sites with a medium wave force. Group II of the site clusters represented both Ricketts and Calvin’s (1992) mid-intertidal protected assemblage (group V) with its high quantities of both E. muricata, and their high- intertidal assemblage (group IV) with the above average abundance of T. funebralis. This indicates that the boundaries on the model are not precise. Additionally, mapping the sites of the fall site clusters shows that there are distinct spatial patterns to where clusters occur (Fig. 9). Group IX (containing large amount of M. californianus) occurs on the headlands of the points, while group VI (containing large amounts of bare rock and Littorina spp.) generally occurs in more protected areas. The gradient of cluster members from the headlands to the coves is evident, and there does seem to be a gradient of clusters relative to wave exposure. We also see that despite this gradient in communities, there are patches of each cluster that occur along the whole transect. There is no smooth east to west gradient of species; species distribution is dependent on the shape of the shoreline and the physical factors at each site. Correlation between physical factors and species in each assemblage Although theses species assemblages are distinct and we can see patterns of where they exist relative to wave exposure, it is not wave exposure alone that is driving species’ distribution. 21 Only some of the species in each grouping have a significant correlation with wave exposure, not all of them. The regressions revealed that some of the species have correlations with other, unrelated factors, such as presence of cracks or the slope of the rock face. If anything changes the environment of these assemblages, the assemblages will change. According to the regression relationships found here, if climate change occurs, as predicted by many scientists, certain species in an assemblage will respond positively to the temperature change, others negatively, and still other species in the same grouping might not respond at all. These reactions could dramatically change the species assemblages in each area. Since the algae appear to be more sensitive to temperature than the invertebrates, they will be more susceptible to undergoing population-wide geographical distribution shifts as a result of climate change. Conclusion The cluster and regression analyses revealed many instances of organisms whose distribution patterns could reasonably be explained by the physical factors with which they had significant correlations. Cluster analysis produces a practical, objective method of dividing the species found on our horizontal transect into distinct assemblages. A model used to predict species assemblage at a given tidal height and wave exposure was found to correctly determine species assemblages with my analyses. Further study of intertidal species distribution should be conducted to better understand cause of species groupings. Acknowledgements First and foremost, thanks go to all the members of the Denny lab past and present who thanklessly collected the species abundance data for this project. Without their input of time, this project never would have happened. Special thanks also go to my advisor, Mark Denny, for the inspiration and creativity behind this project. Not only did he give me tremendous amounts of input, he patiently helped me through the writing process by editing this paper countless times and offering ideas. Secondly, my thanks go to Chris Harley for his immeasurable amounts of intertidal zone knowledge, daily input of ideas, and amusing conversations. Also, thanks to Jim Watanabe who helped with all the statistics in this project. Thank you to Luke Miller, who accompanied me on various field expeditions and gave me encouragement. Finally, thanks go to all the 175H professors and students for promoting the curiosity necessary for all research endeavors. References Arabie, P., Hubert, L. J., De Soete, G. (Eds). (1996) Clustering and Classification. Singapore: World Scientific. 490 pp. Arabie, P., Hubert, L. J. (1996) An overview of combinatorial data analysis. In Clustering and Classification: 5-64. Arabie, P., Hubert, L. J., De Soete, G. (Eds). Singapore: World Scientific. Bell, E.C. and Denny, M.W. (1994) Quantifying "wave exposure": a simple device for recording maximum velocity and results of its use at several field sites. J. Exp. Mar. Biol. Ecol. 181:9-29. Carefoot, T. (1977) Pacific Seashores. Seattle: University of Washington Press. 208 pp. Denny, M. W., Daniel, T. D., Koehl, M. A. R. (1985) Mechanical limits to size in wave-swept organisms. Ecol. Monogr. 55:69-102. Denny, M. W. and Wethey, D.S. (2000) Physical processes that generate patterns in marine communities. In Marine Community Ecology: 1-37. Bertness, M. D., Gaines, S. D., and Hay, M. E. (Eds). Sunderland, Mass.: Sinauer Associates. Denny, M.W., Helmuth, B., Leonard, G.H., Harley, C.D.G., & Hunt, L. Submitted. Quantifying scale in ecology: lessons from a wave-swept shore. Estabrook, G. F. (1966) A mathematical model in graph theory for biological classification. J. of Theoretical Biology 12:297-310. Gordon, A. D. (1996) Hierarchical classification. In Clustering and Classification: 65-122. Arabie, P., Hubert, L. J., De Soete, G. (Eds). Singapore: World Scientific. Gordon, A. D. (1999) Classification. Boca Raton: Chapman and Hall. 256 pp. 24 Helmuth, B., and Denny, M. W. (2003) Predicting wave exposure in the rocky intertidal zone: do bigger waves always lead to larger forces? Limnol. Oceanogr. 48(3):1338-1345. Lewis, J. R. (1964) The Ecology of Rocky Shores. England, English Universities Press. 323 pp. Milligan, G. W. (1996) Clustering validataion: Results and implications for applied analysis. In Clustering and Classification: 341-376. Arabie, P., Hubert, L. J., De Soete, G. (Eds). Singapore: World Scientific. Quinn, G. P. and Keough, M. (2002) Experimental Design and Data Analysis. Cambridge University Press. Raffaelli, D. and Hawkins, S. (1996) Intertidal Ecology. London: Chapman and Hall. Ricketts, E. and Calvin, J. (1992) Between Pacific Tides. Stanford, Calif.: Stanford University Press. Stephenson, T. A. and Stephenson, A. (1949) The universal features of zonation between tidemarks on rocky coasts. J. Ecol. 38:289-305. Wilkinson, L., Blank, G., and Gruber, C. (1996) Desktop Data Analysis with SYSTAT. Upper Saddle River, NJ: Prentice Hall. 798 pp. Table Legend Table 1. Means and standard deviations of proportional cover of each species in the site clusters. Table 2. Results of the multiple regression performed with each species. 8 . 3 - 58. . 8. . 8 . . - a- 38 oo 8. 85 . o aaaaaaaaaaa ata- kaata. 8. 88 5 88 25 S aaa- 5 8 8 8 S. 5 S 8. 8 88 : 88 8 kaataatai 8 18 . 88 8 8 V 8. 2 38 80 . 28 8 - o 8 S . 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S- 8 i. 83 ooe - . saaaaaa- 85. 81 ooo s- . . 385 ii. 8. ooood 88 85 38 — — aataaa- 55 . oooo . 388 . 38 ooo. aaaaa- . . 8- 28. ooo 38. aaaaa- - . s. . 3. 88 oooo . 8 Figure Legend Figure la. Graph showing locations of Ricketts and Calvin’s (1992) intertidal groups relative to tidal height and wave exposure. Figure lb. Summary of species that characterize Ricketts and Calvin’s (1992) intertidal groups. Figure 2. Chart showing the expansion and upward shift of vertical intertidal zones with exposure. Figure 3. The tidal-height exposure model, highlighting groups at the 1.5m tide height. Figure 4. Aerial photo of Hopkins Marine Station showing transect location. Figure 5. A simple dendrogram showing moat distance. Figure 6. A simple dendrogram shoing cluster denotation. Figure 7. Dendrogram of the species clusters. Figure 8. Dendrogram of the site clusters. Figure 9. Map showing locations of each of the site clusters along the transect. 2 — — L 0 — — — 8 8 — 2 2 O a S 2 . — O 0 — Q 0 — — k 0 — 1 — L ) 0 L — + - - - — — — - +--- a 1 — — 0 5 1 — 1 ————————————— 1 — 1 0 — -------------------------------+----- S SS . . — 1 0 L Fig. 8 outlier S cluster I — cluster II — — cluster III cluster IV¬ cluster — — cluster VI S —— — cluster VII — — cluster VIII cluster IX 0.0 0.2 0.4 0.6 0.8 1.0 1.2 —— 4 . I oAA 8 EEPSSSE aa. aaaa- Kenleio E