including known habitats). For Bluntface Shiner (Cyprinella camura), one of the species studied by McNyset (2005) in Kansas, the omission error was calculated to be 17%, although essentially all streams occupied by Bluntface Shiner were included. Overprediction errors are much more problematical because their actual verification would require knowing the true range of the species at the pixel level of the distribution map (in which case running a niche model would be somewhat superfluous). Although no training or test data for Bluntface Shiner were from Walnut River (Figure 4.8), they are known to occur there (McNyset 2005). However, GARP modeling also predicted that Bluntface Shiner would occur in Kansas tributaries of the Kansas and Marais des Cygnes rivers—drainages where they are not known to occur. In this situation, it could be that the species actually occurs in these areas but the areas have not been adequately sampled, that the species once occurred in these drainages but has been eliminated, or, as seems to be true in this instance (Miller and Robison 2004), Bluntface Shiner have never occurred in these drainages, perhaps because of geographic or ecological barriers.
Niche models are also useful in the context of predicting ranges, or locations for refugia, of rare, threatened, or endangered species, as well as determining the probability of invasions by alien species. For instance, Chen et al. (2007) successfully modeled the North American distribution of two large minnows native to eastern Asia, Silver Carp (Hypophthalmichthys molitrix) and Bighead Carp (H. nobilis) that were originally brought into North America for aquaculture purposes. First Chen et al. (2007) constructed niche models using data associated with the natural distribution of these fishes in China, and then projected this information onto North American streams showing where invasions were likely to occur. Such information is useful to resource managers to be alert to the occurrence of nonnative species. Presently, the field of niche modeling is extremely active and includes development and application of new algorithms, such as Maxent, that show different strengths and weaknesses when compared to GARP (A. T. Peterson et al. 2007).
One or Several Models?
No single model of how fish assemblages are formed or identified would likely ever be sufficient. Each approach illustrated here, as well as the many others available in the literature, offer different insights into assemblage formation and spatial or temporal occurrence. A priori models provide an opportunity to infer what functional groups or species traits are likely to occur in an area. These approaches can be particularly powerful in efforts to understand how faunas might change as a consequence of anthropogenic factors such as eutrophication, desertification, construction of impoundments, increasing aridity, or elevated temperatures. Although a priori models are useful because of their generality, in most cases they are limited in their ability to predict the occurrence and/or abundance of a particular species. A posteriori models tend to be more restricted in their application, such as to a particular stream or geographic region, with the notable exception of recent advances in niche modeling using GARP or similar approaches. What a posteriori models might lack in generality they gain in their ability to relate the occurrence of particular species, or suites of species, to particular physical factors and to provide an objective means of defining recurring groups of species (i.e., fish assemblages).
LOCAL VERSUS REGIONAL EFFECTS ON ASSEMBLAGES
Any fish assemblage is the outcome of a myriad of factors operating over a broad range of spatial and temporal scales. Depending on the strength of the factors, the structure of some assemblages might be determined more by local temporal or spatial effects, whereas others by historical or broadscale factors. Focusing on spatial dimensions, one recent approach compares the relative importance of local to regional effects. Local effects on fish assemblages include the nature of the local habitat—especially how it varies spatially and temporally. Regional effects could encompass the regional species pool, as well as landscape features such as climate, elevation, and geographic location.
Much of the role of regional or landscape factors in shaping fish assemblages has been discussed earlier in this chapter. In this section I focus on what has been a primary issue in the study of local versus regional factors, the relationship of the species richness of the local fauna to that of the regional fauna. The principal question is whether local faunas are saturated with species and thus resistant to the addition of new elements, or whether local faunas will increase in species richness as a function of regional species richness (Ricklefs 1987; Cornell and Lawton 1992). In other words, the question is to what degree local fish assemblages are determined by processes acting within the local area versus processes operating at a regional level. Asymptotic relationships between local and regional species diversity (i.e., saturation) suggest the primacy of local control over assemblages; in contrast, if the relationship remains linear (i.e., unsaturated), then local processes would be subordinate to the effect of the regional species pool (Ricklefs 1987). Although it seems clear to contrast local versus regional effects, local assemblages obviously contribute to the regional species pool thus creating a “chicken and egg” problem (Cornell and Lawton 1992).
FIGURE 4.9. The relationship between native fish diversity of local assemblages to regional fish diversity in Virginia streams at the drainage and local scales (based on Angermeier and Winston 1998) and Wisconsin lakes (based on Tonn et al. 1990). Dashed lines indicate a hypothetical direct relationship between regional and local diversity; for Virginia streams, solid lines indicate actual relationships between regional and local diversity. The closed circle and vertical line indicate the mean and 95% confidence interval of local species richness for Wisconsin lakes. Used from Ross and Matthews (in press) with permission from Johns Hopkins University Press.
A study on stream fish assemblages in Virginia showed that regional diversity generally explained more of the variation in local native fish assemblages than did local variables, but local variables also showed some, albeit reduced, explanatory power, with the most important being habitat complexity (Angermeier and Winston 1998). Graphs of local versus regional species richness, although not reaching asymptotes, had low slopes when comparisons were on large spatial scales, such as the drainage level, and all intercepts with the y-axis were significantly greater than zero, both suggesting a tendency for an asymptotic relationship (Figure 4.9). However, when analyzed at a local scale such as site, diversity was strongly related to regional diversity, indicating that the local sites were not saturated with species. The number of introduced species in a local area was also positively related to the regional number of introduced species and, in contrast to native species, showed no evidence of saturation. In addition, the number of native fish species did not influence the number of nonnative species, suggesting that high nativefish diversity does not preclude invasion by nonnative fishes.
The strong influence of regional compared to local factors has also been shown for lakes. Jackson and Harvey (1989) demonstrated that fish faunas of watersheds within the Laurentian Great Lakes showed the effect of large-scale regional processes reflective of postglacial dispersal or climate but were much less related to measures of environmental similarity (e.g., lake depth, area, and pH), although such factors likely have some role in affecting species composition. In a study comparing small lakes in Wisconsin and Finland, Tonn et al. (1990) showed that species richness in individual lakes was related to regional species richness but that local richness reached an asymptote, suggesting that individual lake faunas became saturated with species (Figure 4.9). However, regional factors alone could not explain local species composition because biotic factors, particularly the presence of large predators, also influenced species composition. Tonn and Magnuson (1982) also showed the effects of predator composition, as well as lake morphometry and winter oxygen levels, on the structure of fish assemblages in small Wisconsin lakes.
These studies all suggest a general, but highly variable, link between regional and local species richness. In contrast, in a study of fishes of the Interior Highland region (Ozark and Ouachita mountains of Arkansas, Oklahoma, Missouri, and Kansas) Matthews and Robison (1998) found that regional (river basin) species richness accounted only marginally for species richness at local sites if
