Using Quantile Regression to Investigate Ecological Limiting Factors Active
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. The 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.
Trust Species and Habitats scientists have refined quantile regression to provide novel insights on trout densities in stream habitat, allometric growth of fish to assess body condition, monitoring habitat management objectives at National Wildlife Refuges, and evaluating changes in streamwater quality over 40 years. Additional refinements include modifying quantile regression for small counts to evaluate effects of climate, demographic characteristics of parents, and landscape habitat on California spotted owl fl edglings produced on territories over 20 years on the Lassen National Forest.
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 improving models of fish body condition based on quantiles of allometric growth, and 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. Quantile regression can provide managers with modeled relationships that more realistically reflect the variation in animal responses observed in their physical environments.
Below are other science projects associated with this project.
Below are publications associated with this project.
Macrophyte decomposition in a surface-flow ammonia-dominated constructed wetland: Rates associated with environmental and biotic variables
Estimating fish body condition with quantile regression
A permutation test for quantile regression
Evaluating redband trout habitat in sagebrush desert basins in southwestern Idaho
Rank score and permutation testing alternatives for regression quantile estimates
The effect of multiple stressors on salt marsh end-of-season biomass
User manual for Blossom statistical package for R
Evaluation of models and data for assessing whooping crane habitat in the central Platte River, Nebraska
Quantile regression reveals hidden bias and uncertainty in habitat models
Linear models: permutation methods
Determinants of woody cover in African savannas
Quantile regression models of animal habitat relationships
- Overview
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. The 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.
Trust Species and Habitats scientists have refined quantile regression to provide novel insights on trout densities in stream habitat, allometric growth of fish to assess body condition, monitoring habitat management objectives at National Wildlife Refuges, and evaluating changes in streamwater quality over 40 years. Additional refinements include modifying quantile regression for small counts to evaluate effects of climate, demographic characteristics of parents, and landscape habitat on California spotted owl fl edglings produced on territories over 20 years on the Lassen National Forest.
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 improving models of fish body condition based on quantiles of allometric growth, and 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. Quantile regression can provide managers with modeled relationships that more realistically reflect the variation in animal responses observed in their physical environments.
- Science
Below are other science projects associated with this project.
- Publications
Below are publications associated with this project.
Filter Total Items: 30Macrophyte decomposition in a surface-flow ammonia-dominated constructed wetland: Rates associated with environmental and biotic variables
Decomposition of senesced culm material of two bulrush species was studied in a surface-flow ammonia-dominated treatment wetland in southern California. Decomposition of the submerged culm material during summer months was relatively rapid (k = 0.037 day-1), but slowed under extended submergence (up to 245 days) and during fall and spring sampling periods (k = 0.009-0.014 day-1). Stepwise regressiAuthorsJ.S. Thullen, S. M. Nelson, B.S. Cade, J.J. SartorisEstimating fish body condition with quantile regression
We used quantile regression to compare the body condition of walleye Sander vitreus and white bass Morone chrysops before (1980-1988) and after (1989-2004) the establishment of alewives Alosa pseudoharengus in Lake McConaughy, Nebraska. Higher quantiles (percentiles = 100% x quantiles [0, 1]) of weight (W) at the same total length (TL) were indicative of better body condition in an allometric growAuthorsB.S. Cade, J.W. Terrell, M.T. PorathA permutation test for quantile regression
A drop in dispersion, F-ratio like, permutation test (D) for linear quantile regression estimates (0≤τ≤1) had relative power ≥1 compared to quantile rank score tests (T) for hypotheses on parameters other than the intercept. Power was compared for combinations of sample sizes (n=20−300) and quantiles (τ=0.50−0.99) where both tests maintained valid Type I error rates in simulations with p=2 and 6 pAuthorsBrian S. Cade, Jon D. RichardsEvaluating redband trout habitat in sagebrush desert basins in southwestern Idaho
We estimated abundance quantiles of redband trout Oncorhynchus mykiss gairdneri relative to five site-specific habitat variables (stream shading, bank cover, bank stability, fine sediment in the stream substrate, and cover for adults) and one landscape variable (distance from stream headwaters) on 30 streams in southwestern Idaho during 1993–1998. In addition, the five site-specific habitat variabAuthorsB.W. Zoellick, B.S. CadeRank score and permutation testing alternatives for regression quantile estimates
Performance of quantile rank score tests used for hypothesis testing and constructing confidence intervals for linear quantile regression estimates (0 ≤ τ ≤ 1) were evaluated by simulation for models with p = 2 and 6 predictors, moderate collinearity among predictors, homogeneous and hetero-geneous errors, small to moderate samples (n = 20–300), and central to upper quantiles (0.50–0.99). Test staAuthorsB.S. Cade, J.D. Richards, P.W. MielkeThe effect of multiple stressors on salt marsh end-of-season biomass
It is becoming more apparent that commonly used statistical methods (e.g., analysis of variance and regression) are not the best methods for estimating limiting relationships or stressor effects. A major challenge of estimating the effects associated with a measured subset of limiting factors is to account for the effects of unmeasured factors in an ecologically realistic matter. We used quantileAuthorsJ.M. Visser, C.E. Sasser, B.S. CadeUser manual for Blossom statistical package for R
Blossom is an R package with functions for making statistical comparisons with distance-function based permutation tests developed by P.W. Mielke, Jr. and colleagues at Colorado State University (Mielke and Berry, 2001) and for testing parameters estimated in linear models with permutation procedures developed by B. S. Cade and colleagues at the Fort Collins Science Center, U.S. Geological Survey.AuthorsMarian Talbert, Brian S. CadeEvaluation of models and data for assessing whooping crane habitat in the central Platte River, Nebraska
The primary objectives of this evaluation were to improve the performance of the Whooping Crane Habitat Suitability model (C4R) used by the U.S. Fish and Wildlife Service (Service) for defining the relationship between river discharge and habitat availability, and to assist the Service in implementing improved model(s) with existing hydraulic files. The C4R habitat model is applied at the scale ofAuthorsAdrian H. Farmer, Brian S. Cade, James W. Terrell, Jim H. Henriksen, Jeffery T. RungeQuantile regression reveals hidden bias and uncertainty in habitat models
We simulated the effects of missing information on statistical distributions of animal response that covaried with measured predictors of habitat to evaluate the utility and performance of quantile regression for providing more useful intervals of uncertainty in habitat relationships. These procedures were evaulated for conditions in which heterogeneity and hidden bias were induced by confoundingAuthorsB.S. Cade, B.R. Noon, C.H. FlatherLinear models: permutation methods
Permutation tests (see Permutation Based Inference) for the linear model have applications in behavioral studies when traditional parametric assumptions about the error term in a linear model are not tenable. Improved validity of Type I error rates can be achieved with properly constructed permutation tests. Perhaps more importantly, increased statistical power, improved robustness to effects ofAuthorsB.S. CadeDeterminants of woody cover in African savannas
Savannas are globally important ecosystems of great significance to human economies. In these biomes, which are characterized by the co-dominance of trees and grasses, woody cover is a chief determinant of ecosystem properties 1-3. The availability of resources (water, nutrients) and disturbance regimes (fire, herbivory) are thought to be important in regulating woody cover1,2,4,5, but perceptionsAuthorsM. Sankaran, N.P. Hanan, Robert J. Scholes, J. Ratnam, D.J. Augustine, B.S. Cade, J. Gignoux, S.I. Higgins, Roux X. Le, F. Ludwig, J. Ardo, F. Banyikwa, A. Bronn, G. Bucini, K.K. Caylor, M.B. Coughenour, A. Diouf, W. Ekaya, C.J. Feral, E.C. February, P.G.H. Frost, P. Hiernaux, H. Hrabar, K.L. Metzger, H.H.T. Prins, S. Ringrose, W. Sea, J. Tews, J. Worden, N. ZambatisQuantile regression models of animal habitat relationships
Typically, all factors that limit an organism are not measured and included in statistical models used to investigate relationships with their environment. If important unmeasured variables interact multiplicatively with the measured variables, the statistical models often will have heterogeneous response distributions with unequal variances. Quantile regression is an approach for estimating the cAuthorsBrian S. Cade