1. Advanced analytical approaches in ecological data analysis The world comes in fragments

2. Species abundance matrix MPhylogenetic distance matrix P Species trait matrix T Environmental variable matrix V Interdepen- dence matrix X Species Sites Variables Traits Multivariate approaches to biodiversity

3. Fourth corner statistics Species abundance matrix MSpecies trait matrix T Environmental variable matrix V k m n m l m species, n sites, k traits, l environmental variables The matrix X is a k  l matrix that contains information on the relationhips between traits and environmental variables mediated by species abundances or occurrences. n

4. The Pearson coefficient of correlation Species Leaf mass [mg] Leaf size [mm 2 ] Life span Light Achillea_pa nnonica 82.33567.8457 Agrostis_ca pillaris 60.981147.9357 Species Leaf mass [mg] Leaf size [mm 2 ] Life spanLight Achillea_pan nonica 0.79-0.560.97-0.02 Agrostis_cap illaris 0.250.270.97-0.02 Agrostis_stol onifera_agg. =(C5- ŚREDNIA(C$3:C$125))/ODCH.STAN D.POPUL(C$3:C$125) Using Z-scores in fourth corner analysis leads to correlations between traits (phylogeny) and environmental (geographical) variables.

5. Output of the Ord software

6. SCaCO3SandpHSpeciesAbundance DNAcontent-0.3470.534-0.5810.9841.119 Grazingtolerance-0.632-0.6210.2750.3430.161 Leafmass[mg]0.365-0.488-0.7820.1630.758 Leafsize[mm2]0.423-0.780-0.321-0.6490.053 Lifespan-0.348-2.0060.5671.9352.495 Light-0.0551.170-0.6330.847-0.283 Meanseedweight0.829-0.233-0.386-0.217-0.088 Nitrogen-0.141-0.889-0.4461.4542.341 Soilfertility-0.4290.0680.5820.412-0.624 Specificleafaream m2 -0.2781.6060.554-0.753-0.543 ln(Seedspershoot)1.430-1.2010.686-1.361-0.248 pH-1.3661.558-0.9010.670-1.919 The SES scores for traits of the proportional – proportional null model We detect three significances. Three significances is exactly the random expectation a the 5% error level. None of the relationships is really significant. Use Bonferroni corrected significance levels!

7. Correlation coefficients and a neutral null model (AA) Clumped species co- occurrences

8. SES>0035899089 SES<012388343334 SCaCO3SandpHSpeciesAbundance Achillea_pannonica-0.47-0.350.97 Agrostis_capillaris-0.200.38-0.72-0.21-0.30 Agrostis_stolonifer-0.210.39-0.72-0.21-0.30 Agrostis_vinealis-0.210.39-0.72-0.21-0.30 Ajuga_genevensis-0.40-0.210.430.970.80 Apera_spica_venti-0.200.37-0.74-0.22-0.30 Arenaria_serpyllifo-0.64-0.450.240.941.07 Artemisia_vulgaris_-0.49-0.330.870.950.96 Betula_pendula-0.59-0.120.340.850.62 Brachypodium_sylvat-0.210.38-0.71-0.19-0.28 Bromus_hordeaceus-0.210.37-0.71-0.21-0.29 Bromus_tectorum-0.220.36-0.71-0.21-0.29 Calamagrostis_epige-0.210.40-0.73-0.20-0.30 Carex_arenaria_agg.-0.280.31-0.52-0.05-0.16 Phylogenetic distance was negatively related to soil carbon content and sand. Phylogenetic distance was positively related to soil pH. Phylogenetic distance was positively related to soil species richness and abundance. The SES scores for phylogeny of the proportional – proportional null model

9. Phylogenetic species co-occurrences Count for all checkerboard, clumped and togethernerss pairs the average phylogenetic and variable distances. Compare these average with the random distribution after randomisation of the species occurrence matrix.

10. Each effect is linked to an ecological pattern that can be related to an ecological process.

12. Phylogenetic relatedness during succession : Clumping : Togetherness : Checkerboard Phylogenetic distances of co-occurring species increased during early succession. Phylogenetic distances of segregated species decreased. At the onset of succession phylogenetic community structure was random. 2008 marks a tipping point from a random to a structured pattern.

13. : Clumping : Togetherness : Checkerboard CaCO 3 Sand pH Co-occurrences in dependence on soil variables At the beginning of succession SES score were negative. Species co-occurred on similar soils (habitat filtering). At the end of the succession species co- occurred on different soils and co-occurred less often on soils osf similar structure. This points to competitive effects.

14. PCA, PCoA multiplots Eigenvector multiplots serve as a graphical representation of species associations with trait or soil variables. Chicken Creek 2011 data

15. Principal coordinates analysis (Bray Curtis metric of distance) links the eigenvectors of species, trait, and environmental variable eigenvectors Leaf features are linked to the pH gradient. Seed weight is connected to the sand gradient