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.
A gentle introduction to quantile regression for ecologists
Influences of spatial and temporal variation on fish-habitat relationships defined by regression quantiles
No consistent effect of plant diversity on productivity
Estimating effects of constraints on plant performance with regression quantiles
The role of landscape and habitat characteristics in limiting abundance of grassland nesting songbirds in an urban open space
Estimating effects of limiting factors with regression quantiles
- 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: 30A gentle introduction to quantile regression for ecologists
Quantile regression is a way to estimate the conditional quantiles of a response variable distribution in the linear model that provides a more complete view of possible causal relationships between variables in ecological processes. Typically, all the factors that affect ecological processes are not measured and included in the statistical models used to investigate relationships between variableAuthorsB.S. Cade, B.R. NoonInfluences of spatial and temporal variation on fish-habitat relationships defined by regression quantiles
We used regression quantiles to model potentially limiting relationships between the standing crop of cutthroat trout Oncorhynchus clarki and measures of stream channel morphology. Regression quantile models indicated that variation in fish density was inversely related to the width:depth ratio of streams but not to stream width or depth alone. The spatial and temporal stability of model predictioAuthorsJ. B. Dunham, B.S. Cade, J.W. TerrellNo consistent effect of plant diversity on productivity
Hector et al. (1) reported on BIODEPTH, a major international experiment on the response of plant productivity to variation in the number of plant species. They found “an overall log-linear reduction of average aboveground biomass with loss of species,” leading to what the accompanying Perspective (2) described as “a rule of thumb—that each halving of diversity leads to a 10 to 20% reduction in prAuthorsM.A. Huston, L.W. Aarssen, M.P. Austin, B.S. Cade, J.D. Fridley, E. Garnier, J.P. Grime, J. Hodgson, W.K. Lauenroth, K. Thompson, J.H. Vandermeer, D.A. WardleEstimating effects of constraints on plant performance with regression quantiles
Rates of change in final summer densities of two desert annuals, Eriogonum abertianum and Haplopappus gracilis, as constrained by their initial winter germination densities were estimated with regression quantiles and compared with mechanistic fits based on a self-thinning rule proposed by Guo et al. (1998); Oikos 83: 237–245). The allometric relation used was equivalent to S=Nf (Ni)−1=cf (Ni)−1,AuthorsB.S. Cade, Q. GuoThe role of landscape and habitat characteristics in limiting abundance of grassland nesting songbirds in an urban open space
We examine the relationships between abundance of grassland nesting songbirds observed in the Boulder Open Space, CO, USA and parameters that described landscape and habitat characteristics, in order to provide information for Boulder Open Space planners and managers. Data sets included bird abundance and plant species composition, collected during three breeding seasons (1994–1996), and landscapeAuthorsS. Haire, C.E. Bock, B.S. Cade, B.C. BennettEstimating effects of limiting factors with regression quantiles
In a recent Concepts paper in Ecology, Thomson et al. emphasized that assumptions of conventional correlation and regression analyses fundamentally conflict with the ecological concept of limiting factors, and they called for new statistical procedures to address this problem. The analytical issue is that unmeasured factors may be the active limiting constraint and may induce a pattern of unequalAuthorsBrian S. Cade, J. W. Terrell, Richard L. Schroeder