TY - JOUR
T1 - Function regression in ecology and evolution
T2 - FREE
AU - Yen, Jian D. L.
AU - THOMSON, Jim
AU - Paganin, David
AU - Keith, Jonathan
AU - MAC NALLY, Ralph
PY - 2015/1/1
Y1 - 2015/1/1
N2 - Summary: Many questions in ecology and evolutionary biology consider response variables that are functions (e.g. species-abundance distributions) rather than a single scalar value (e.g. species richness). Although methods for analysing function-valued data have been available for several decades, ecological and evolutionary applications are rare. We outline methods for regression when the response variable is a function ('function regression') and introduce the r package FREE, which focuses on straightforward implementation and interpretation of function regression analyses. Several computational methods are implemented, including machine learning and several Bayesian methods. We compare different methods using simulated data and real ecological data on individual-size distributions (ISDs) of fish and trees. No single method performed best overall, with several performing equally well for a given data set. Which method to use depends on sample sizes and the questions being considered; in many cases, a consensus approach should be used to combine or compare fitted models. Function regression allows the direct modelling of many function-valued data (e.g. species-abundance distributions) rather than having to reduce those functions to a single scalar response variable (e.g. species diversity or functional diversity indices). Our ecological examples using ISD data show that larger rivers support more-even fish-size distributions than smaller rivers and that low initial planting densities lead to more-even tree-size distributions than high initial planting densities. Function regression provided more informative and intuitive interpretations of these data than conventional non-function-valued approaches.
AB - Summary: Many questions in ecology and evolutionary biology consider response variables that are functions (e.g. species-abundance distributions) rather than a single scalar value (e.g. species richness). Although methods for analysing function-valued data have been available for several decades, ecological and evolutionary applications are rare. We outline methods for regression when the response variable is a function ('function regression') and introduce the r package FREE, which focuses on straightforward implementation and interpretation of function regression analyses. Several computational methods are implemented, including machine learning and several Bayesian methods. We compare different methods using simulated data and real ecological data on individual-size distributions (ISDs) of fish and trees. No single method performed best overall, with several performing equally well for a given data set. Which method to use depends on sample sizes and the questions being considered; in many cases, a consensus approach should be used to combine or compare fitted models. Function regression allows the direct modelling of many function-valued data (e.g. species-abundance distributions) rather than having to reduce those functions to a single scalar response variable (e.g. species diversity or functional diversity indices). Our ecological examples using ISD data show that larger rivers support more-even fish-size distributions than smaller rivers and that low initial planting densities lead to more-even tree-size distributions than high initial planting densities. Function regression provided more informative and intuitive interpretations of these data than conventional non-function-valued approaches.
KW - Bayesian statistics
KW - Ecological modelling
KW - Function-valued data
KW - Functional data analysis
KW - Functional responses
KW - Multivariate data
KW - Trait distributions
KW - r package
KW - ecological modelling
KW - functional data analysis
KW - function-valued data
KW - functional responses
KW - multivariate data
KW - trait distributions
UR - http://www.scopus.com/inward/record.url?scp=84921460720&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/function-regression-ecology-evolution-free
U2 - 10.1111/2041-210X.12290
DO - 10.1111/2041-210X.12290
M3 - Article
SN - 2041-210X
VL - 6
SP - 17
EP - 26
JO - Methods in Ecology and Evolution
JF - Methods in Ecology and Evolution
IS - 1
ER -