1. Bioscience – Aarhus University Modelling the joint abundance of more plant species - pin-point cover data Christian Damgaard Department of Bioscience Aarhus University

2. Bioscience – Aarhus University Joint distribution of species Why model the joint distribution of spatial plant abundance data? If we know a species is present at a position then the probability that another species is present at the same position is reduced More used information → More statistical power Knowledge on spatial covariance patterns

3. Bioscience – Aarhus University Complementary vegetation classes In species rich communities it is not feasible to model the cover of all species, instead it may be relevant to group the species into complementary vegetation classes Different functional types Different life history strategies CSR strategies ….

4. Bioscience – Aarhus University Monitoring of habitat types since 2004 Plot 0.5x0.5 m: Cover of plant species (pin-point) Vegetation height pH in soil/water C/N – ratio in soil Phosphorous N and P in leaves 5 m circle: Presence plant data Cover of woody species Grazing or moving Gaps in vegetation/bare soil/sand Cover of plants affected by herbivory Hollows in bog structure

5. Bioscience – Aarhus University Dry heathlands The cover of the two dominating species on dry heathlands, Calluna vulgaris and Deschampsia flexuosa, and all other higher plant species covary 179 Danish dry heathland sites with 20 – 40 plots Mean cover was 0.257,0.208,and 0.535, respectively

6. Bioscience – Aarhus University Spatial aggregation – single species The beta-binomial distribution adequately model the distribution of pin-point cover data

7. Bioscience – Aarhus University Joint pin-point cover distribution

8. Bioscience – Aarhus University Environmental gradient

9. Bioscience – Aarhus University Estimation Hierarchical Bayesian modelling approach Mean site cover was modelled by latent variables MCMC - Metropolis-Hastings algorithm Statistical inferences on the parameters of interest were based on the marginal posterior distribution of the parameters

10. Bioscience – Aarhus University Spatial aggregation within sites Parameter2.50%50%97.50%P(X > 0) 0.1970.2060.215- -0.1940.0250.1900.59 0.1860.3450.5141 -4.12E-060.0001930.0004590.9725 -0.00041-0.00022-2.60E-050.0113 0.1220.1390.159- 0.1070.1200.136- -0.299-0.1420.03170.0544

11. Bioscience – Aarhus University Spatial aggregation parameter () If we do not take the spatial aggregation into account then statistical inference is biased (Damgaard 2013) Like pseudo-replication A serious and often made error in the analysis of plant cover The spatial aggregation parameter may be used to test different hypotheses on the role of spatial aggregation at the level of the community Test of neutrality (Damgaard and Ejrnæs 2009) Does species aggregation reduce the importance of competitive interactions? (Damgaard 2011) Does climate change or nitrogen deposition change the spatial structure or increase size of plants? (Damgaard et al. 2012)

12. Bioscience – Aarhus University Effects of precipitation on dry heaths Parameter2.50%50%97.50%P(X > 0) 0.1970.2060.215- -0.1940.0250.1900.59 0.1860.3450.5141 -4.12E-060.0001930.0004590.9725 -0.00041-0.00022-2.60E-050.0113 0.1220.1390.159- 0.1070.1200.136- -0.299-0.1420.03170.0544

13. Bioscience – Aarhus University Spatial covariation among sites Parameter2.50%50%97.50%P(X > 0) 0.1970.2060.215- -0.1940.0250.1900.59 0.1860.3450.5141 -4.12E-060.0001930.0004590.9725 -0.00041-0.00022-2.60E-050.0113 0.1220.1390.159- 0.1070.1200.136- -0.299-0.1420.03170.0544

14. Bioscience – Aarhus University Conclusions The framework allows modelling of the spatial covariation in cover at two levels Local – among individual plants Regional – among communities / sites We know from manipulated experiments that drought increase the competitive effect of Deschampsia on Calluna (Ransijn et al. in prep) Negative spatial covariation at the site level and significant effects of precipitation on the observed cover of Deschampsia and Calluna It is suggested that the oceanic–continental climatic gradient determine the relative abundance of the two species Effects of soil may be confounded with precipitation gradient? The cover ratio of the two species may be used to monitor the effect of climate change on dry heathlands

15. Bioscience – Aarhus University Time series

16. Bioscience – Aarhus University No significant changes in cover at dry heathlands since 2007 Parameter2.50%50%97.50%P(X > 0) 0.1800.1890.199- -0.269-0.0860.0820.159 -0.1360.0080.1520.548 -0.110-0.0050.1010.460 0.7130.8260.971- 0.6040.7010.826- 0.4420.5140.605-