  The relationships among ecological variables are usually obtained by fitting
statistical models that go through the conditional means of the dependent
variables. For example, the nonparametric loess and the parametric piecewise
linear regression models, which pass through the conditional mean of the
response variable given the predictor, are used to analyze simple to complex
relationships among variables. We used loess and bootstrapped confidence
interval to subjectively identify the number and positions of potential
ecological breakpoints in a bivariate relationship, and a piecewise linear
regression model (PLRM) to quantitatively estimate the location of breakpoints
and the associated precision. We also estimated breakpoint location and
precision using a piecewise linear quantile regression model (PQRM), which is
fitted to the quantiles of the conditional distribution of the response
variable given the predictor and provides much richer information in terms of
estimating relationships and breakpoints. We compared the precision of
breakpoints estimated by PQRM relative to PLRM. We compared the precision of
the methods using two examples from the ecological literature suspected to
exhibit multiple breakpoints: relating a Fish Index of Biotic Integrity (an
index of wetlands' fish community 'health') to the amount of human activity in
wetlands' adjacent watersheds; and relating the biomass of cyanobacteria to the
total phosphorus concentration in Canadian lakes. Statistically significant
breakpoints were detected for both datasets, demarcating the boundaries of
three line segments with markedly different slopes. We recommend the piecewise
linear quantile regression as an effective means of characterizing bivariate
environmental relationships where the scatter of points represents natural
environmental variation rather than measurement error.
