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

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

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

The Pearson coefficient of correlation Species Leaf mass [mg] Leaf size [mm 2 ] Life span Light Achillea_pa nnonica Agrostis_ca pillaris Species Leaf mass [mg] Leaf size [mm 2 ] Life spanLight Achillea_pan nonica Agrostis_cap illaris 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.

Output of the Ord software

SCaCO3SandpHSpeciesAbundance DNAcontent Grazingtolerance Leafmass[mg] Leafsize[mm2] Lifespan Light Meanseedweight Nitrogen Soilfertility Specificleafaream m ln(Seedspershoot) pH 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!

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

SES> SES< SCaCO3SandpHSpeciesAbundance Achillea_pannonica Agrostis_capillaris Agrostis_stolonifer Agrostis_vinealis Ajuga_genevensis Apera_spica_venti Arenaria_serpyllifo Artemisia_vulgaris_ Betula_pendula Brachypodium_sylvat Bromus_hordeaceus Bromus_tectorum Calamagrostis_epige Carex_arenaria_agg 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

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.

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

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 marks a tipping point from a random to a structured pattern.

: 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.

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

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