Function regression in ecology and evolution

FREE

Jian D. L. Yen, Jim THOMSON, David Paganin, Jonathan Keith, Ralph MAC NALLY

    Research output: Contribution to journalArticle

    14 Citations (Scopus)

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)17-26
    Number of pages10
    JournalMethods in Ecology and Evolution
    Volume6
    Issue number1
    DOIs
    Publication statusPublished - 1 Jan 2015

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    ecology
    biogeography
    methodology
    planting
    species diversity
    rivers
    artificial intelligence
    functional diversity
    Bayesian theory
    fish
    evolutionary biology
    method
    diversity index
    river
    species richness
    Biological Sciences
    modeling
    sampling
    distribution

    Cite this

    Yen, Jian D. L. ; THOMSON, Jim ; Paganin, David ; Keith, Jonathan ; MAC NALLY, Ralph. / Function regression in ecology and evolution : FREE. In: Methods in Ecology and Evolution. 2015 ; Vol. 6, No. 1. pp. 17-26.
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    Function regression in ecology and evolution : FREE. / Yen, Jian D. L.; THOMSON, Jim; Paganin, David; Keith, Jonathan; MAC NALLY, Ralph.

    In: Methods in Ecology and Evolution, Vol. 6, No. 1, 01.01.2015, p. 17-26.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Function regression in ecology and evolution

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    AU - Yen, Jian D. L.

    AU - THOMSON, Jim

    AU - Paganin, David

    AU - Keith, Jonathan

    AU - MAC NALLY, Ralph

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    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.

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    KW - r package

    KW - ecological modelling

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    KW - functional responses

    KW - multivariate data

    KW - trait distributions

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    UR - http://www.mendeley.com/research/function-regression-ecology-evolution-free

    U2 - 10.1111/2041-210X.12290

    DO - 10.1111/2041-210X.12290

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    ER -