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

Abstract

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 stream-specific 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.

Multispatial-scale variation in benthic and snag-surface macroinvertebrate assemblages in mid-continent US great rivers

“…Similar to macroinvertebrate densities on the UMRS, many biotic components in diverse aquatic ecosystems exhibit high temporal variability (Gido et al 1997;Bunn and Davies 2000;Dunham et al 2002;Quist et al 2003). Much of the year-to-year variability seen in the target taxa collected by the LTRMP is actual change and not error variance.…”

A Gentle Introduction to Quantile Regression for Ecologists

“…Changes in the upper quantiles of densities of mature plants were essentially a 1:1 mapping of germination density when it was low (< 100/0.25-m 2 ), whereas there was a strong decrease in density of mature plants at higher germination densities consistent with density-dependent competition. Global temperature change over the last century Koenker and Schorfheide 1994 Animal habitat relationships Terrell et al 1996;Haire et al 2000;Eastwood et al 2001;Dunham et al 2002 Prey and predator size relationships Scharf et al 1998 Plant Quantile regression was developed in the 1970s by econometricians (Koenker and Bassett 1978) as an extension of the linear model for estimating rates of change in all parts of the distribution of a response variable. The estimates are semiparametric in the sense that no parametric distributional form (eg normal, Poisson, negative binomial, etc) is assumed for the random error part of the model , although a parametric form is assumed for the deterministic portion of the model (eg, ␤ 0 X 0 + ␤ 1 X 1 ).…”

“…The Dunham et al (2002) analyses relating the abundance of Lahontan cutthroat trout (Oncorhynchus clarki henshawi) to the ratio of stream width to depth illustrates the value of the additional information provided by quantile regression (Figure 1). The ratio was used as a predictor variable because it was an easily obtained measure of channel morphology that was thought to be related to the integrity of habitat in small streams like those typically inhabited by cutthroat trout.…”

“…A regression model with heterogeneous variances implies that there is not a single rate of change that characterizes changes in the probability distributions. Focusing exclusively on changes in the means may underestimate, overestimate, or fail to distinguish real nonzero changes in heterogeneous distributions (Terrell et al 1996;Cade et al 1999).The Dunham et al (2002) analyses relating the abundance of Lahontan cutthroat trout (Oncorhynchus clarki henshawi) to the ratio of stream width to depth illustrates the value of the additional information provided by quantile regression (Figure 1). The ratio was used as a predictor variable because it was an easily obtained measure of channel morphology that was thought to be related to the integrity of habitat in small streams like those typically inhabited by cutthroat trout.…”

Polymorphic mountain whitefish (Prosopium williamsoni) in a coastal riverscape: size class assemblages, distribution, and habitat associations

“…Because mountain whitefish occur in neighboring drainages within the Quileute basin, my study also did not account for basin-scale factors affecting the spatial distribution of whitefish. I also did not account for temporal variation in fish distribution (e.g., seasonal migration), which is an important factor that may influence salmonid distribution (Schlosser 1985, Taylor et al 1996, Dunham et al 2002, Dunham et al 2007) (see Appendix A for springsummer variation in distribution).…”