Using the beta distribution to analyse plant cover data

TY - JOUR

T1 - Using the beta distribution to analyse plant cover data

AU - Damgaard, Christian

AU - Irvine, Kathryn M

PY - 2019

Y1 - 2019

N2 - Most plant species are spatially aggregated. Local demographic and ecological processes (e.g. vegetative growth and limited seed dispersal) result in a clustered spatial pattern within an environmentally homogenous area. Spatial aggregation should be considered when modelling plant abundance data. Commonly, plant abundance is quantified by measuring cover within multiple areal plots or along multiple lines randomly placed within a study area. A common practice for analysing plant cover is to use statistical methods that rely on the normal distribution for quantifying uncertainty. This is problematic because plant cover data tend to be left-skewed (J-shaped), right skewed (L-shaped) or U-shaped and, therefore, commonly violate classic statistical assumptions, such as normality. We outline statistical analyses that explicitly account for spatial aggregation by assuming that plant cover is beta-distributed. The beta distribution is a flexible choice because within the open unit interval it can take on a wide range of shapes (L, J, U, or a bell-shaped). We discuss and introduce extensions to the beta distribution that address common analysis issues encountered in plant cover datasets, such as (a) the treatment of zero and one cover values, (b) hierarchical data structures and (c) observations errors. For heuristic purposes, we focus on single species analyses, but we demonstrate how the outlined methods can be generalized to more species. The assumption that plant cover is beta-distributed allows us to estimate the degree of spatial aggregation, and the ecological significance of this new knowledge is discussed. We provide a summary of available software for analyses (emphasizing standard R packages) and include worked examples and a simulation study comparing analysis options as supplemental information. Synthesis. Previously, the state of the statistical software made it practically difficult for empirical plant ecologists to analyze their cover data correctly, but new theory and R-packages have been developed, and this difficulty no longer exists. We recommend that empirical plant ecologists embrace the new statistical possibilities for exploring the exciting ecological features in spatial variation of plant cover.

AB - Most plant species are spatially aggregated. Local demographic and ecological processes (e.g. vegetative growth and limited seed dispersal) result in a clustered spatial pattern within an environmentally homogenous area. Spatial aggregation should be considered when modelling plant abundance data. Commonly, plant abundance is quantified by measuring cover within multiple areal plots or along multiple lines randomly placed within a study area. A common practice for analysing plant cover is to use statistical methods that rely on the normal distribution for quantifying uncertainty. This is problematic because plant cover data tend to be left-skewed (J-shaped), right skewed (L-shaped) or U-shaped and, therefore, commonly violate classic statistical assumptions, such as normality. We outline statistical analyses that explicitly account for spatial aggregation by assuming that plant cover is beta-distributed. The beta distribution is a flexible choice because within the open unit interval it can take on a wide range of shapes (L, J, U, or a bell-shaped). We discuss and introduce extensions to the beta distribution that address common analysis issues encountered in plant cover datasets, such as (a) the treatment of zero and one cover values, (b) hierarchical data structures and (c) observations errors. For heuristic purposes, we focus on single species analyses, but we demonstrate how the outlined methods can be generalized to more species. The assumption that plant cover is beta-distributed allows us to estimate the degree of spatial aggregation, and the ecological significance of this new knowledge is discussed. We provide a summary of available software for analyses (emphasizing standard R packages) and include worked examples and a simulation study comparing analysis options as supplemental information. Synthesis. Previously, the state of the statistical software made it practically difficult for empirical plant ecologists to analyze their cover data correctly, but new theory and R-packages have been developed, and this difficulty no longer exists. We recommend that empirical plant ecologists embrace the new statistical possibilities for exploring the exciting ecological features in spatial variation of plant cover.

KW - beta distribution

KW - hierarchical models

KW - ordinal cover data

KW - pinpoint cover data

KW - plant cover

KW - spatial aggregation

KW - statistical models

UR - http://www.scopus.com/inward/record.url?scp=85066311812&partnerID=8YFLogxK

U2 - 10.1111/1365-2745.13200

DO - 10.1111/1365-2745.13200

M3 - Journal article

SN - 0022-0477

VL - 107

SP - 2747

EP - 2759

JO - Journal of Ecology

JF - Journal of Ecology

IS - 6

ER -