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Ecological models for estimating breakpoints and prediction intervals.

Jabed H Tomal1, Jan J H Ciborowski2,3

  • 1Department of Mathematics and Statistics Thompson Rivers University Kamloops BC Canada.

Ecology and Evolution
|December 11, 2020
PubMed
Summary
This summary is machine-generated.

Piecewise linear quantile regression models (PQRM) offer superior accuracy and precision in detecting environmental breakpoints compared to traditional piecewise linear regression models (PLRM). This method enhances ecological analysis by revealing nonlinear relationships and variation across environmental gradients.

Keywords:
bootstrapchlorophyll phosphorusecological breakpointsenvironmental stressloessmultimetric indexpiecewise linear regressionquantile regression

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Area of Science:

  • Ecology
  • Environmental Science
  • Statistical Modeling

Background:

  • Ecological responses to environmental variables are often modeled using conditional means, potentially missing nonlinearities.
  • Nonparametric loess and parametric piecewise linear regression models (PLRM) are common but may not fully capture response variations.
  • Piecewise linear quantile regression models (PQRM) can reveal nonlinearities across the response range by analyzing various quantiles.

Purpose of the Study:

  • To assess breakpoint detection using loess and compare the efficiency of PLRM and PQRM for quantitative breakpoint determination.
  • To propose a nonparametric method for generating bootstrap confidence intervals for breakpoints using PQRM.
  • To illustrate the application of these methods in aquatic studies with suspected environmental breakpoints.

Main Methods:

  • Utilized loess for identifying candidate breakpoints and compared PLRM and PQRM for breakpoint location and precision.
  • Developed a nonparametric bootstrap method for confidence intervals with PQRM.
  • Applied methods to datasets relating fish health (MMI) to agricultural activity and cyanobacterial biomass to phosphorus concentration.

Main Results:

  • Identified two significant breakpoints in each dataset, defining three distinct linear segments with varying slopes.
  • PQRM demonstrated less bias, higher accuracy, and narrower confidence intervals and prediction bands than PLRM, particularly with small samples or high variability.
  • Relationships showed weak/nonsignificant effects below lower thresholds, strong effects in the midrange, and weak/nonsignificant effects above upper thresholds.

Conclusions:

  • PQRM offers advantages over PLRM for characterizing environmental relationships, especially when scatter reflects natural variation.
  • The proposed PQRM methodology is valuable for detecting multiple breakpoints in ecological studies.
  • Understanding limits of variation is crucial, alongside the conditional mean, in ecological analysis.