Estimating Effects of Limiting Habitat Relationships with Regression Quantiles

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Blue sucker fish. Photo:
A blue sucker fish. Photo:

Unexplained heterogeneity in statistical models of animal responses to their physical environment is reasonable to expect, because the measured habitat resources are a constraint on—but not the sole determinant of—abundance, survival, fecundity, or fitness. Typically, it is impossible to know whether the habitat factors measured are actually limiting at the time and location of sampling. Our ecological understanding and reliability of management predictions based on animal habitat models can be improved by shifting focus from estimating expected values (means) of responses to estimating intervals of responses associated with multiple percentiles of a distribution. Regression quantiles are an easily implemented approach for estimating intervals of responses in multiple regression models of animal responses to habitat. Completed research under this task compared the statistical performance of the conventional asymptotic rank score test (used for testing hypotheses and constructing confidence intervals for regression quantile estimates) with a new permutation variant of the rank score test and a permutation drop in dispersion test. Evaluation conditions were structured to match the range of sample sizes, variable types, covariance among predictors, and hypotheses typically encountered by investigators building models of animal habitat relationships with multiple linear regression models. We also demonstrated how to extend the continuous-response quantile regression model to model discrete counts of organisms. In addition, case studies for selected terrestrial and aquatic species were used to demonstrate the utility of building more reliable habitat models. An online webinar course on the fundamentals of linear quantile regression was developed and presented.

Because the quantile regression methodology can be applied to a variety of ecological analyses where heterogeneity in responses need to be modeled, we have expanded our focus to include (1) improving models of fish body condition based on quantiles of allometric growth, and (2) use of quantile regression with equivalence testing. Fish weight and length data are commonly collected by fisheries scientists to help them evaluate differences in body condition of fish (weight at length) in different environments or under alternative management schemes. Following on prior efforts to evaluate and promote a more rigorous statistical approach based on quantile regression in 2008, FORT scientists and state cooperators refined the quantile regression approach and used it to evaluate the geographic variation in body condition of blue suckers, a threatened species inhabiting large rivers the central United States. Blue suckers had better body condition at more southern locations. The quantile regression approach models allometric growth of fish weight with length, allows for multiple forms of heterogeneity in growth, and provides estimates of percentiles of weight at length that can be compared among any factors included in the statistical model. Thus, this approach promotes assessment of fish condition in a manner consistent with that used for humans and avoids many of the statistical and interpretation issues associated with use of condition indices, such as relative weight. Our recent 2011 publication includes statistical code for R that can be modified for other investigations of fish body condition. We will continue our efforts to promote this approach by developing online webinar training materials. Other applications we have contributed to include relating remotely sensed spectral measures to plant biodiversity, and analysis of isotopes for detecting spatial origin of organisms. Statistical refinements being considered include development of hierarchical quantile regression models and necessary modifications to inferential statistics.