map. In contrast, a biologist might favor an approach where first-order streams are classified as the smallest perennial unbranched tributaries that have persisted long enough to contain plants and animals (Hynes 1970). Obviously the second approach requires field verification, so the methodology suggested by Leopold et al. (1964) tends to be the approach of choice for all but the smallest of watersheds. In addition, GIS technology now provides an automated means of determining stream order (Lu et al. 1996).
A useful property of stream order based on the Horton-Strahler system is that a number of physical properties of streams are correlated with stream order. For instance, discharge and drainage area tend to be positively correlated with stream order whereas gradient is negatively correlated (Knighton 1984). The number of stream lengths of each order are negatively related to order so that there tends to be 3–4 times more streams of order n-1 compared to order n. Comparing order n-1 and n, the former has sections that are about half as long and drain somewhat more than one fifth of the area (Hynes 1970). Of course, stream order is a geographical-level variable and does not give information on microhabitat features such as pools, runs, or riffles. In addition, while it is a useful descriptor of the drainage network, streams of equivalent orders but from wet versus arid climates tend to be greatly different in size and biological attributes.
Medium-sized streams (orders 4–6) tend to be more open, have increased autochthonous production, and have greater diversity of insect functional groups (Figure 4.6). This general trend increases in large streams (order 6 and greater), except that increased turbidity can reduce light penetration and thus reduce photosynthesis (P/R ≤ 1). Medium and large streams have increased amounts of fine particulate organic materials (FPOM) produced by the upstream processing of coarse particulate organic materials (CPOM), such as leaves being processed by aquatic insects and bacteria.
Predictions of RCC about fish assemblage composition is at best limited to trophic groups and is based on food resources available in low-order, medium-order, and high-order streams. Vannote et al. (1980) also reasoned that low-order streams would tend to be cooler than high-order streams, although this could certainly vary depending on canopy cover and geographic region. In low-order streams, food resources for fishes would primarily be terrestrial invertebrates, with less importance of aquatic invertebrates or fishes as prey. In medium streams, food resources would expand to include more aquatic prey, both insects and fishes, and in large streams, the increased amount of autochthonous production could lead, in the absence of high turbidity, to the presence of planktivorous and herbivorous fishes. Although Vannote et al. (1980) said nothing about how invertivores might vary in abundance in high-versus mediumorder streams, later work (e.g., Goldstein and Meador 2004) has inferred that RCC predicted a decline. Several early papers, not cited by Vannote et al. (1980), did provide information on changes in functional groups of fishes along a gradient of stream order, including a classic paper by Shelford (1911). Shelford’s work on several small Michigan streams showed that headwaters of the streams were consistently occupied by several species, especially Creek Chub (Semotilus atromaculatus), and that fish species composition changed longitudinally in streams as a function of the physical changes in habitat. The headwater occurrence of Creek Chub (and in general the other three species within the genus) turns out to be a general pattern (Starret 1950; Kuehne 1962; Lotrich 1973; Ross 2001; Boschung and Mayden 2004). As predicted by RCC, in very small headwater streams, Creek Chubs consume primarily allochthonous materials, including insects and even berries (Lotrich 1973; Moshenko and Gee 1973; Ross 2001).
As stream order increases, there is a general trend for both trophic groups and species richness to increase (e.g., Kuehne 1962; Sheldon 1968; Schlosser 1982, 1987; Paller 1994), although species richness may plateau or even decline in large streams (stream orders > 5) (Whiteside and McNatt 1972; Platts 1979; Fairchild et al. 1998). Changes in faunas are generally gradual and do not closely correspond with changes in stream order (Matthews 1986a). Also, the faunal characteristics of small streams that are tributary to lower reaches of large streams (termed adventitious streams) are different when compared to a similarly sized headwater stream (Gorman 1986). For instance, adventitious streams can have greater fish diversity than similarly sized headwater streams and, in fact, have faunas that are more similar to the main channel than to headwater streams (Thomas and Hayes 2006).
The RCC predictions of changes in functional groups, such as fewer insect predators and more planktivores and detritivores with increasing stream size, are generally supported (Goldstein and Meador 2004). For instance, in large eastern and southeastern rivers, including the Missouri and Mississippi rivers, fishes that primarily consume plankton include Paddlefish (Polyodon spathula) and Bigmouth Buffalo (Ictiobus cyprinellus) (Rosen and Hales 1981). Other species also consume phytoplankton or zooplankton, but from on or near the substratum, such as River Carpsucker (Carpiodes carpio) (Brezner 1958; Ross 2001). Detrital materials also contribute to the diet of Bigmouth Buffalo and its congeners, Smallmouth Buffalo (I. bubalus) and Black Buffalo (I. niger) (Walburg and Nelson 1966; McComish 1967; Ross 2001).
The RCC continues to be an important heuristic tool in understanding stream ecosystems. However, among its shortcomings, it did not treat a stream or river as a landscape such that the great variety and complexity of aquatic habitats was largely ignored (Fausch et al. 2002).
A Posteriori Models
Models that use large data sets on fish occurrence and environmental characteristics of lakes and streams in an attempt to find predictive suites of physical characters, or to identify fish assemblages characteristic of locations or environmental conditions, typify a posteriori approaches. Such studies depend on some form of multivariate statistical analysis (Box 4.2) so that their popular use has paralleled that of modern, high-speed computers, and especially the powerful personal computers that are now common. Although widespread use of such approaches is relatively recent, the underlying statistical techniques, such as factor analysis, were developed early in the twentieth century (Sokal and Rohlf 1995; Gotelli and Ellison 2004). The application of multivariate approaches in fish ecology also benefitted from the interest in numerical taxonomy during the same time period (Sneath and Sokal 1973). Many of the computer programs developed for numerical taxonomy, such as cluster analysis and ordination, were used as well in ecological applications.
BOX 4.2 • Multivariate Statistics
In contrast to univariate models, such as linear regression where the response of the dependent variable is related to change in the independent variable or multiple linear regression where the response of the dependent variable is related to change in two or more independent variables, multivariate statistics deal with the simultaneous variation in two or more dependent variables (Manly 1986; Sokal and Rohlf 1995). As such, multivariate statistical techniques are ideally suited to dealing with the complexity of fish assemblages, both in comparing assemblages across space and/or time and for examining relationships among species and the physical and biological components of their environment. Multivariate statistics have become easy to use given the wide choice and availability of statistical software programs. However, this ease of use belies the underlying statistical complexity and the need for the user to have at least a conceptual understanding of what the statistical program is doing. In addition, such tests often assume that each of the variables has a certain structure, such as showing a normal distribution, that all the variables combined have a multivariate normal distribution, that variances among variables are homogeneous, or that the samples were collected randomly. Given the complexity and specialized nature of multivariate approaches, I have given only a brief introduction to some of the approaches that are referred to in the text. Principal components analysis, factor analysis, discriminant function analysis, correspondence analysis, and nonmetric multidimensional scaling can be considered ordination techniques because all are ways of ordering objects based on an array of variables or of ordering variables based on objects. Classification analysis provides another approach for recognizing patterns in multivariate data. Grouping objects (i.e., sites, individual organisms, or sampling units) based on measured variables (i.e., current speed, water depth, turbidity, or species composition) is termed Q analysis. For both ordination and classification, grouping measured variables
