1. Bioscience – Aarhus University Pin-point plant cover data Christian Damgaard Bioscience Aarhus University

2. 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

3. Bioscience – Aarhus University The pin-point (point-intercept) method Objective 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

4. 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  : 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)

5. Bioscience – Aarhus University Generalised binomial distribution q : mean cover at the site  : intra-plot correlation

6. 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)  : 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)

7. Bioscience – Aarhus University Relationship between plant cover and intra-plot correlation in dune grasslands

8. Bioscience – Aarhus University Important to include spatial correlation The cover of Calluna vulgaris and Deschampsia flexuosa on dry heathlands

9. Bioscience – Aarhus University Important to include spatial correlation If  was set to zero (no spatial correlation) then there was a strong significant effect (grey line, P < 0.0001) If  was allowed to vary then the effect was found to be insignificant (black line,  = 0.57, P = 0.19)

10. 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)

11. 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

12. 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