Bioscience – Aarhus University

Pin-point plant cover data

Christian Damgaard

Bioscience

Aarhus University

Bioscience – Aarhus University

Hierarchical plant cover data

Large-scale ecological processes (among-sites): environmental drivers extinction / colonization of sites

Small-scale ecological process (within-sites): size of individuals density-dependent population growth inter-specific competition

Plant cover data has too many zero values and too much variance compared to a binomial distribution

U- shaped distributions of plant cover are typical

Bioscience – Aarhus University

The pin-point (point-intercept) methodObjective method for measuring plant cover

Place a frame with a grid pattern

A pin is inserted vertically through one of the grid points into the vegetation

The pin will typically touch a number of plants and the different species are recorded

This procedure is repeated for each grid point

Bioscience – Aarhus University

Distribution of pin-point cover data within a site

The distribution of plant cover is modelled using a generalised binomial distribution with two parameters q : mean plant cover d : intra-plot correlation

The probability density function of the generalised binomial distribution (=Pólya-Eggenberger distribution) is equal to the beta-binomial mixture distribution but is somewhat more general in that negative intra-plot correlation is allowed (Qu et al. 1993)

Bioscience – Aarhus University

Generalised binomial distribution

n

ynq

yq

y

nqnyfY

,11

,)1)(1(

,11

),,;(

)1()1()()(),( nxxxxnxnx

qnYE )(

))1(1()1()( nqqnYVar

q : mean cover at the site d : intra-plot correlation

Bioscience – Aarhus University

The parameters

q : mean plant cover – may be regressed to environmental gradients test hypotheses on the effect of environmental gradients on plant

abundance (Damgaard 2008, Damgaard 2012)

d : intra-plot correlation - depends on size of individuals and spatial arrangements test hypotheses on the effect of environmental gradients on the spatial

variation The intra-plot correlation parameter may be generalized to a

multispecies case and be used to test for different hypotheses on the level of the community test of neutrality (Damgaard and Ejrnæs 2009)

does climate change or nitrogen deposition change the spatial structure or increase size of plants? (Damgaard et al. 2012)

Bioscience – Aarhus University

Relationship between plant cover and intra-plot correlation in dune grasslands

Bioscience – Aarhus University

Important to include spatial correlation

The cover of Calluna vulgaris and Deschampsia flexuosa on dry heathlands

Bioscience – Aarhus University

Important to include spatial correlation

If d was set to zero (no spatial correlation) then there was a strong significant effect (grey line, P < 0.0001)If d was allowed to vary then the effect was found to be insignificant (black line, d = 0.57, P = 0.19)

Bioscience – Aarhus University

Among site-variation in cover

The zero-inflated beta-distribution is a good candidate distribution to model among-site variation in plant cover (Damgaard, in prep)

Bioscience – Aarhus University

Analysing trends in plant cover Framework for analysing trends of plant cover data has been

developed Bayesian state-space model Separation of process and sampling error Efficient treatment of missing values Effect of treatment or co-variable on change in cover Possible auto-correlation

Published in Ecology 93(6), 2012, pp. 1269–1274

Bioscience – Aarhus University

Conclusions The parameters in the generalised binomial distribution may

be used to test ecological hypotheses

Erroneous conclusions if the spatial variation is ignored also when assuming a naïve model with normally distributed

data