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Modeling Stream Fish Habitat Limitations from Wedge‐Shaped Patterns of Variation in Standing Stock
Author(s) -
Terrell James W.,
Cade Brian S.,
Carpenter Jeanette,
Thompson Jay M.
Publication year - 1996
Publication title -
transactions of the american fisheries society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.696
H-Index - 86
eISSN - 1548-8659
pISSN - 0002-8487
DOI - 10.1577/1548-8659(1996)125<0104:msfhlf>2.3.co;2
Subject(s) - homoscedasticity , heteroscedasticity , quantile regression , statistics , ordinary least squares , segmented regression , regression analysis , mathematics , linear regression , econometrics , regression , stock (firearms) , polynomial regression , geography , archaeology
A wedge‐shaped pattern of variation in stream fish standing stock estimates relative to a habitat variable, in which range of standing stocks increases as a function of the variable, is consistent with the concept that the habitat variable is a limiting factor for fish populations. This pattern of variation complicates interpretation of parameter estimates and significance of ordinary least‐squares (OLS) regression models of conditional mean standing stock; slopes of these regression models may have little or no relation to slopes of models describing standing stock limits. We modeled standing stock limits by testing for homoscedastic error distributions, screening plots of coordinate pairs for evidence of a wedge‐shaped pattern of data, and estimating 90th regression quantiles for simple linear models. Application of this technique to data sets supporting 35 previously published OLS regression models of stream fish standing stocks led to rejection of homoscedasticity ( P < 0.10) in 13 of the 35 data sets. Eight of these heteroscedastic data sets had wedge‐shaped patterns of variation in standing stock and slopes of 90th regression quantiles that differed from slopes of OLS regression models. For three of these eight data sets, tests rejecting homoscedasticity were more significant than tests rejecting zero slope parameters in OLS regression models. In a separate exercise, analysis of simulated standing stock data generated from known distributions indicated that our technique can detect heteroscedastic error distribution patterns and yield 90th regression quantile models of standing stock limits from data sets characterized by OLS regression as having no correlation between mean standing stock and a habitat variable. Identification of correlations between habitat variables and standing stock by OLS regression is a common method of determining whether a variable is to be used for habitat assessment. Application of our technique to data sets that display wedge‐shaped patterns of variation should help identify variables that may be limiting standing stock from data sets that do not yield significant OLS regression models of mean standing stock.