Influences of Spatial and Temporal Variation on Fish–Habitat Relationships Defined by Regression Quantiles

—We used regression quantiles to model potentially limiting relationships between the standing crop of cutthroat trout Oncorhynchus clarki and measures of stream channel morphology. Regression quantile models indicated that variation in fish density was inversely related to the width:depth ratio of streams but not to stream width or depth alone. The spatial and temporal stability of model predictions were examined across years and streams, respectively. Variation in fish density with width:depth ratio (10th–90th regression quantiles) modeled for streams sampled in 1993–1997 predicted the variation observed in 1998–1999, indicating similar habitat relationships across years. Both linear and nonlinear models described the limiting relationships well, the latter performing slightly better. Although estimated relationships were transferable in time, results were strongly dependent on the influence of spatial variation in fish density among streams. Density changes with width:depth ratio in a single stream were responsible for the significant (P , 0.10) negative slopes estimated for the higher quantiles (.80th). This suggests that stream-scale factors other than width:depth ratio play a more direct role in determining population density. Much of the variation in densities of cutthroat trout among streams was attributed to the occurrence of nonnative brook trout Salvelinus fontinalis (a possible competitor) or connectivity to migratory habitats. Regression quantiles can be useful for estimating the effects of limiting factors when ecological responses are highly variable, but our results indicate that spatiotemporal variability in the data should be explicitly considered. In this study, data from individual streams and streamspecific characteristics (e.g., the occurrence of nonnative species and habitat connectivity) strongly affected our interpretation of the relationship between width:depth ratio and fish density. The history of habitat modeling to predict abundance or occurrence of stream fishes has shown that models often have low predictive ability, and those with high predictive ability have low transferability to different times or places (e.g., Fausch et al. 1988; Bozek and Rahel 1992; Leftwich et al. 1997). Habitat models that predict abundance often work only within narrowly defined temporal and spatial scales, whereas fish abundance, occurrence, and habitat conditions vary significantly in time and space (Matthews 1998). Density-dependent habitat selection (Bult et al. 1999), changes in habitat availability (Bozek and Rahel 1992), and interactions among habitat factors (Baltz et al. 1987) are common occurrences in the stream environment. Predictive habitat models that are applicable to a wide range of spatial and temporal scales will need to incorporate realistic assumptions for dealing with the wide range of variability * Corresponding author: [email protected] Received August 15, 2000; accepted July 27, 2001 in habitat and populations consistently associated