Northern Prairie Wildlife Research Center
Several univariate and multivariate statistical methods have been used to explain the distribution of fish species in streams. Assumptions that must be considered when using these techniques for the analysis of ecological data are provided by Zar (1984) for univariate analyses and Gauch (1982), Ludwig and Reynolds (1988), and Johnson and Wichern (1992) for multivariate analyses.
Hawkes et al. (1986) placed 39 fish species from 410 stream sites in Kansas into 10 ecologically meaningful assemblages using principal components analysis (PCA). Hughes and Gammon (1987) used cluster analysis (CA) to group fishes into upriver and downriver assemblages of the Willamette River, Oregon; and Sepkoski and Rex (1974) grouped mussels of coastal rivers into meaningful assemblages using CA, which does not require species abundance data (Ludwig and Reynolds 1988).
Cluster analysis is a technique that sorts objects (such as sampling units) into groups or clusters based upon their overall resemblance to one another (Ludwig and Reynolds 1988). There are several CA methods, including single-linkage, average-linkage, and complete-linkage, all having different ways in which clusters are formed (Johnson and Wichern 1992); and although most of the CA strategies give similar results, several methods should be explored and the results compared. Clusters can then be determined from one of the CA methods based on the "underlying ecological knowledge of the data" (Ludwig and Reynolds 1988). Interpretation of CA results can often be highly subjective.
Cluster analysis has been widely used for analysis of lakes and streams. Sepkoski and Rex (1974) clustered 49 rivers of the Atlantic Coast and eastern Gulf of Mexico based on the similarities of their unionid faunas. The analysis defined five distinct clusters or faunal "provinces." The distributional patterns in the provinces were strongly influenced by distance from species "source" rivers, supporting the theory that isolated coastal rivers can be studied as biogeographic islands (MacArthur and Wilson 1967). Hughes et al. (1987) used historical fish survey records from 1300 sites in Oregon to classify 85 streams. Cluster analysis of presence-absence data produced a dendrogram which was truncated to form 8, 10, and 18 distinct clusters of streams, corresponding to 8 ecoregions, 10 physiographic provinces, and 18 river basins, respectively.
Cluster analysis can also be used to group streams based upon environmental variables. Poff and Ward (1989) analyzed flow patterns of 78 streams from across the United States. Using 11 flow variables, the streams were clustered into nine groups separated primarily by intermittency, flood frequency, and flood predictability. The groups were somewhat geographically associated.
Principal components analysis is an ordination technique (Pielou 1984) which breaks down or partitions a resemblance matrix (variance-covariance or correlation) into a set of orthogonal (perpendicular) axes or PCA "components" (Ludwig and Reynolds 1988). The first few PCA components will explain the largest percentage of variation in the data set (Gauch 1982), and ordinations of sampling units on these axes provide information about the ecological relationships between them.
Matthews (1985) used PCA to ordinate 101 stream localities in the central and southwestern United States with respect to 19 physical and biological characters. The analysis was used to determine the limits of environmental conditions where fish taxa typically occurred within the study area. Matthews and Robison (1988) used historical fish survey records from 2323 sites in Arkansas to identify similarities among drainage units based on fish assemblages. The analysis defined fish faunal regions within the state and related fish distributions to gradients in environmental conditions. Results of Matthews and Robison (1988) were combined with long-term USGS water-quality data for Arkansas watersheds by Matthews et al. (1992) to determine if the distribution of fishes was related to patterns in water quality. In this analysis, PCA was used to ordinate drainage units based on 14 water-quality variables. A relationship among ordination axis scores based on fish distribution and axis scores based on water quality was determined using product moment correlation.
Paller (1994) used PCA to identify the relationships between 47 sample sites in South Carolina coastal plain streams. Two separate analyses were conducted. In one case, sampling sites were ordinated with respect to fish species abundances; and in the second case, the sites were ordinated with respect to 12 habitat variables. Changes in assemblage structure and habitat characteristics of sites were noticed along a stream order gradient.
Principal components analysis has also been applied to lake studies. Tonn et al. (1990) compiled records for fish assemblages and environmental characteristics of 113 Finnish and 51 Wisconsin lakes and used PCA along with several other statistical techniques to compare species-environment relationships, and Schupp (1992) utilized 9 limnological variables from 3029 Minnesota lakes to classify the lakes into 44 types for fisheries management.
Canonical correspondence analysis is a technique developed by ter Braak (1986) to relate community composition to environmental variation. In this "direct gradient analysis" technique (Gauch 1982), a set of species is related directly to a set of measured environmental variables. The CCA ordinations have an environmental basis and detect patterns of variation in community composition best explained by the environmental variables (ter Braak 1986). It is one of the most popular gradient analysis techniques in ecology (Palmer 1993).
Few analyses of stream fishes have utilized CCA; but it has been widely used for distributional studies of other organisms, including chrysophytes (Dixit et al. 1989), protozoans (Charman and Warner 1992), insects (Williams 1991), and birds (Hill 1991). Edds (1993) used DCA, CCA, and detrended CCA (ter Braak 1986) to explain the distributions of 52 fish species in the Gandaki River, Nepal. Species distributions were correlated with 34 environmental variables in five categories, which included geography, water quality, season, substrate, and vegetation. Canonical correspondence analysis was also used successfully by Taylor et al. (1993), who examined fish assemblages in the Red River, Oklahoma, along measured environmental gradients and Copp (1992), who predicted habitat preferences of 24 juvenile fish species in streams of eastern England.
Ecoregions have been shown to be useful for classifying streams in a number of studies. Hughes et al. (1987) and Whittier et al. (1988) used multivariate analyses of fishes, macroinvertebrates, water quality, and physical habitat measures to demonstrate that ecoregions could be used as a broad scale geographic framework for classifying streams in Oregon. Lyons (1989) used multivariate analyses of fish and habitat data from three size classes of streams in Wisconsin to determine differences among sampling stations associated with ecoregion classification, and Rohm et al. (1987) examined fish, habitat, and water quality data from 22 streams in Arkansas. Ordination analysis determined greater similarity among streams within the same ecoregion than streams in different ecoregions. Similar results were obtained in Ohio, where regional differences in fish assemblages were related to ecoregions (Larsen et al. 1986). Heiskary et al. (1987) analyzed total phosphorus concentrations of 1100 lakes and determined that the aquatic ecoregion approach is a valid method for grouping lake data in Minnesota.