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

2. Early plant succession in the post brown cole mining area Chicken Creak 2005 2010 Succession starts with colonising species from a regional species pool and from the initial seed bank

3. Species abundance matrix MPhylogenetic distance matrix P Species trait matrix T Site GPS location matrix D Environmental variable matrix V Interdepen- dence matrix X Species Sites Variables Traits Multivariate approaches to biodiversity Why are species abundant or rare? What determines community composition? How does a community function in space and time? L

4. Species abundance matrix MPhylogenetic distance matrix P Species trait matrix T Species Sites Traits The interplay between traits, phylogeny, and species occurrences As species of the same genus have usually, though by no means invariably, some similarity in habits and constitution, and always in structure, the struggle will generally be more severe between species of the same genus, when they come into competition with each other, than between species of distinct genera. (Darwin 1859) Traits and phylogeny are closely related. Trait distance correlates positively with phylogenetic distance Niche conservatism Competition: niche conservatism causes phylogenetically close species to co- occur less common. Habitat filtering causes species with similar traits (close in phylogeny) to co- occur more frequent.

5. Local colonizers Regional pool of species Environmental filters Random colonization Regional pool of potential colonizers Regional pool of species No phylogenetic structure Phylogenetic clumping Early succession Facilitation Phylogenetic segregation Local community structure Competition No phylogenetic signal Phylogenetic clumping Later succession Positive interactions Phylogenetic segregation Neutral interactions

6. Phylogenetic distance matrix P Species trait matrix T Species Traits Mantel test A Mantel test is a correlation between two distance matrices. We have to transform the trait matrix into a distance matrix and correlate with the phylogeny matrix.

7. S Achillea _panno nica Agrosti s_capill aris Agrosti s_stolo nifera_ agg. Agrosti s_vinea lis Achillea_pannoni ca0.0179.0 Agrostis_capillari s179.00.02.5 Agrostis_stolonif era_agg.179.02.50.02.5 Agrostis_vinealis179.02.5 0.0 S Achillea _panno nica Agrosti s_capill aris Agrosti s_stolo nifera_ agg. Agrostis _vineali s Achillea_pannon ica0.0179.0 Agrostis_capillari s179.00.02.5 Agrostis_stolonif era_agg.179.02.50.02.5 Agrostis_vinealis179.02.5 0.0 R = -0.04; P(r=0) = 0.37 Plant traits and phylogeny in the year 2011 are not correlated. Why?? We averaged over all traits Mantel test

8. Blue eyes Trait Brown eyes Blue eyes Brown eyes Blue eyes Brown eyes The trait ‚brown eyed’ is phylogenetically conserved. Closely related species have the same eye colour Eye colour is phylogenetically not conserved. 10 5 8 12 Blue eyes: (10+5+10+15)/3=10 15 Blue eyes: (10+5+15++10+ 8+12)/3=20 10 12 Trait 10 5 8 12 15 10 12 Compare these phylogenetic distances per trait with those expected from a random (Brownian motion ) phylogeny.

9. Brownian motion Brownian motion is the standard method to generate random phylogenetic trees 1.Start with a pixel 2.Take a second pixel and move at random until it sticks to the first 3.Repeat two until the desired number of end-tips is reached. Brownian motion generates random trees and can simulate the evolution of traits along this trees.

10. Blue eyes Brown eyes Blue – brown boundary Brownian motion (random walk) along a phylogeny Compare the observed pattern of blue and brown with those generated by many Brownian motion trees. Start0 10.002168 2+B2+0.5*(LOS()-0.5)

11. MX-M nX -4.76-2.213.594.26-0.88 10.83-4.7622.6610.52-17.09-20.284.19 23.38-2.2110.524.88-7.93-9.411.94 39.183.59-17.09-7.9312.8915.29-3.16 49.854.26-20.28-9.4115.2918.15-3.75 54.71-0.884.191.94-3.16-3.750.77 Mean5.59 Wwij Diagonal sum59.35wij00.40.740.180.4 n5wij0.6900.150.530.47 wij0.460.8700.750.32 wij0.120.030.5600.27 wij0.450.020.640.940 Sum8.99 WM12345 104.2078-12.645-3.651.6755 27.258520-1.1901-4.98970.9141 3-7.8607-6.9025011.4701-1.011 4-2.4333-0.28248.56430-1.012 Sum-11.5151.884960.0389-2.0219-3.52390 I-0.108Expected I -0.25 Moran’s I as a test of phylogenetic signal where n is the number of data points. w defines the strength of distance effects. I is similar to a weighed coefficient of correlation.

12. SpeciesKP(K) Lamb da P(Lamb da) SpeciesKP(K) Lamb da P(Lamb da) Morphological traitsReproductive traits Canopy height (m)1.200.0011.00<0.001 Average month of seedling 0.110.0040.001.000 Emergent attached to substrate 0.070.3240.880.001Duration of flowering0.040.7430.130.135 Leaf mass [mg]0.110.1551.000.001Duration of seedling0.040.5050.001.000 Leaf size [mm 2 ]0.100.1380.980.003Early month flowering0.080.0280.80<0.001 Life span0.070.0140.500.020 Early month seed shedding 0.050.2260.001.000 Max releasing height [m]2.110.0011.00<0.001Latest month flowering0.140.0010.82<0.001 Min releasing height [m]0.780.0031.00<0.001 Latest month seed shedding 0.190.0010.520.085 Specific leaf area mm 2 /mg0.060.048<0.011.000ln (Seeds per shoot)0.060.0540.630.002 Stem ascending to prostrate % 0.100.0120.89<0.001Mean seed weight0.130.0841.00<0.001 Stem erect %0.110.0060.96<0.001Seed bank longevity0.060.0740.001.000 Terminal velocity m/s0.060.1200.58<0.001Type reproduction0.050.1790.220.011 Woodiness Stem0.650.0011.00<0.001 Pagel’s lambda

13. SpeciesKP(K) Lamb da P(Lamb da) SpeciesKP(K) Lamb da P(Lamb da) Habitat requirementsMolecular traits Light0.040.5060.220.063Polyploidy0.050.2510.400.001 Soil fertility0.060.154<0.011.000Chromosome number8.620.0011.00<0.001 pH0.050.251<0.011.000DNA content0.390.0010.75<0.001 Nitrogen0.050.126<0.011.000 Life strategy type0.060.1330.391.000 Grazing tolerance0.030.855<0.011.000 Hemerobic level0.050.142<0.011.000 Morphological and genetic plant traits are phylogenetically more conserved than life history, reproductive, and ecological traits.

14. Large size Body size Small size 10 5 8 12 15 10 12 Small home range Large home range Small home range Species daily home range Ungulates Mammal predators Without phylogenetic knowledge we would link body size to home range in a functional manner. Home range and body size are linked by common phylogeny. They are phylogenetically preserved. Phylogenetic pseudoreplication Phylogenetic regression accounts for the phylogenetic non-independence of variables

15. Phylogenetic distance matrix P Species trait matrix T Species Traits Eigenvector methods MUU  x Every square matrix M has a vector U so that U: Eigenvector : Eigenvalue I: Identity matrix Because both sides of the equation are equal the right side contains the same information as the left side. The eigenvector U contains the information in M in a condensed form.

16. Species Leaf mass [mg] Leaf size [mm 2 ] Life span Light Soil fertility pH Nitro gen ln (Seeds per shoot) Specific leaf area mm 2 /m g DNA content Mean seed weight Grazing toleran ce Achillea_pannonica82.3567.8573626.38.119.10.15.1 Agrostis_capillaris61.01147.9570445.326.87.10.15.0 Agrostis_stolonifera _agg. 61.01147.95870512.122.87.00.19.0 Agrostis_vinealis1.422.8599324.315.66.90.12.0 Ajuga_genevensis18.0365.55837212.125.85.91.85.1 Apera_spica_venti61.01147.9166508.50.010.80.15.1 Arenaria_serpyllifol ia_agg. 0.23.60.584706.016.11.70.15.1 Artemisia_vulgaris_ agg. 61.01147.95760812.80.06.00.15.1 Species Leaf mass [mg] Leaf size [mm 2 ] Life span Light Soil fertility pH Nitro gen ln (Seeds per shoot) Specific leaf area mm 2 /m g DNA content Mean seed weight Grazing toleran ce Achillea_pannonica1.32-0.260.58-0.58-0.660.76-0.35-0.66-0.632.31-0.38-0.05 Agrostis_capillaris0.600.940.58-0.58-1.800.000.45-0.981.23-0.20-0.38-0.10 Agrostis_stolonifera _agg. 0.600.940.58 0.85-1.510.841.130.83-0.22-0.382.17 Agrostis_vinealis-1.41-1.390.581.731.61-0.38-0.35-1.270.12-0.24-0.38-1.80 Ajuga_genevensis-0.85-0.680.58 -0.661.13-0.351.13 -0.452.65-0.05 Apera_spica_venti0.600.94 - 1.59 -1.730.470.38-1.140.04-1.430.57-0.38-0.05 Arenaria_serpyllifol ia_agg. -1.45-1.43 - 1.86 0.58-0.281.13-1.14-0.750.17-1.33-0.38-0.05 Artemisia_vulgaris_ agg. 0.600.940.58-0.580.47-1.512.031.36-1.43-0.43-0.38-0.05 =(S12- ŚREDNIA(S$4:S$11))/ODCH.STAND.POPUL(S$4:S $11) We use Z-transforms to normalize the trait values

17. Species Achillea_p annonica Agrostis_c apillaris Agros tis_st olonif era_a gg. Agrosti s_vine alis Ajuga_gen evensis Apera _spica _venti Arenari a_serp yllifolia _agg. Artemisia _vulgaris_ agg. Achillea_pannonica0.003.795.375.585.433.775.585.13 Agrostis_capillaris3.790.004.545.614.794.755.064.76 Agrostis_stolonifera_agg.5.374.540.006.015.455.446.183.61 Agrostis_vinealis5.585.616.010.005.356.044.285.96 Ajuga_genevensis5.434.795.455.350.005.934.695.98 Apera_spica_venti3.774.755.446.045.930.004.814.74 Arenaria_serpyllifolia_agg. 5.585.066.184.284.694.810.006.52 Artemisia_vulgaris_agg.5.134.763.615.965.984.746.520.00 The Euclidean distance matrix Eigenvalues Squared eigenvalues Explained variance -8.8077.430.05 -6.7845.960.03 -5.6732.160.02 -4.7422.440.01 -4.0916.700.01 -3.4411.810.01 -2.848.080.01 36.351321.430.86 Dominant eigenvector 2nd eigenvector 0.3400.139 0.3280.130 0.3560.406 0.374-0.449 0.364-0.283 0.3470.139 0.360-0.513 0.3570.484 The dominant eigenvector (DEV) contains 86% of variance in the distance matrix.

18. Traits2011Phylogeny Eigenvalue104786Eigenvalue19855 SDEVS Achillea_pannonica0.249299Achillea_pannonica0.296259 Agrostis_capillaris0.202592Agrostis_capillaris0.318521 Agrostis_stolonifer0.202402Agrostis_stolonifer0.318521 Agrostis_vinealis0.331781Agrostis_vinealis0.318521 Ajuga_genevensis0.271579Ajuga_genevensis0.323584 Apera_spica_venti0.202506Apera_spica_venti0.318354 Arenaria_serpyllifo0.336897Arenaria_serpyllifo0.318607 TraitSpearman's r Leaf_mass_[mg]0.12525 Leaf_size_[mm2]0.055584 Life_span0.14348 Light-0.13865 Soil_fertility0.007277 pH-0.01992 Nitrogen-0.06805 ln_(Seeds_per_shoot)0.10293 Specific_leaf_area_m m2/mg0.049542 DNA_content0.022556 Mean_seed_weight0.097499 Grazing_tolerance-0.03174 None of the traits is correlated to phylogenetic distance. DEV contains information on the average distance of species in niche space

19. Ecological niches Species Leaf mass [mg] Leaf size [mm 2 ] Life span Light Soil fertility pH Nitrog en ln (Seeds per shoot) Specific leaf area mm 2 /m g DNA content Mean seed weight Grazing toleranc e Achillea_pannonica1.32-0.260.58-0.58-0.660.76-0.35-0.66-0.632.31-0.38-0.05 Agrostis_capillaris0.600.940.58-0.58-1.800.000.45-0.981.23-0.20-0.38-0.10 Agrostis_stolonifera_ agg. 0.600.940.58 0.85-1.510.841.130.83-0.22-0.382.17 Agrostis_vinealis-1.41-1.390.581.731.61-0.38-0.35-1.270.12-0.24-0.38-1.80 Ajuga_genevensis-0.85-0.680.58 -0.661.13-0.351.13 -0.452.65-0.05 Apera_spica_venti0.600.94-1.59-1.730.470.38-1.140.04-1.430.57-0.38-0.05 Arenaria_serpyllifolia _agg. -1.45-1.43-1.860.58-0.281.13-1.14-0.750.17-1.33-0.38-0.05 Artemisia_vulgaris_a gg. 0.600.940.58-0.580.47-1.512.031.36-1.43-0.43-0.38-0.05 Dominant eigenvector 2nd eigenvector 0.3400.139 0.3280.130 0.3560.406 0.374-0.449 0.364-0.283 0.3470.139 0.360-0.513 0.3570.484 Convex hulls, eigenvector ellipses, and functional attribute diversity

20. EV1EV2 1 1 The area of the eigenvector ellipse is a measure of niche space Axes length are given by the respective eigenvalues The niche space spanned by light and soil fertility spans 3.47 units. Eigenvalues 1.580.70 EV1EV2 0.71 -0.710.71 Compare these value with those obtained from a null model The larger the niche space is the higher is the functional diversity of a community or a species. Eigenvectors are always orthogonal.

21. Convex hulls CH The area of a convex hull is a measure of total niche space. High dimensional convex hull are difficult to obtain. Two dimensional convex hulls are easy to calculate.

22. Functional attribute diversity FAD Species Achillea_ pannoni ca Agrostis_c apillaris Agrostis_ stolonife ra_agg. Agrosti s_vine alis Ajuga_ geneve nsis Apera_ spica_v enti Arenaria_ serpyllifol ia_agg. Achillea_pannonica0.003.795.375.585.433.775.58 Agrostis_capillaris3.790.004.545.614.794.755.06 Agrostis_stolonifera_agg.5.374.540.006.015.455.446.18 Agrostis_vinealis5.585.616.010.005.356.044.28 Ajuga_genevensis5.434.795.455.350.005.934.69 Apera_spica_venti3.774.755.446.045.930.004.81 Arenaria_serpyllifolia_agg.5.585.066.184.284.694.810.00 Sites 1 0 0 1 1 0 1 Raw FAD scores are meaningless. You have to compare these scores with an appropriate null model of species occurrences.

23. Total raw functional attribute diversity (grey bars) increased while the respective SES scores of FAD (red bars) and convex hulls (blue bars) decrease during succession when compared to a neutral null model. Regression coefficients High plant cover decreased an species richness increases standardized effect sizes of FAD (neutral null model) in all study years. Soil characteristics did not significantly influence SES FAD (functional diversity). 2006 2011

24. The evolutionary dimension of species occurrences Eigenvector mapping, eigenvector regression, logistic eigenvector regressiuon Species abundance matrix M Phylogenetic distance matrix P Species Sites EV1EV2 Significant eigenvectors The explained variance r 2 of this regression is a measure of the influence of evolutionary history on species abundances.

25. Net relatedness index S Achillea_p annonica Agrostis_c apillaris Agrostis_st olonifera_ agg. Agrostis_vi nealis Ajuga_gen evensis Apera_spic a_venti Achillea_pannonica0.0179.0 117.0179.0 Agrostis_capillaris179.00.02.5 179.06.7 Agrostis_stolonifera_agg. 179.02.50.02.5179.06.7 Agrostis_vinealis179.02.5 0.0179.06.7 Ajuga_genevensis117.0179.0 0.0179.0 Apera_spica_venti179.06.7 179.00.0 M7-2 0.5 0 0 0 Phylogenetic distance matrix Abundance vector The raw net relatedness index is the phylogenetic distance of all species present at a focal site. M7-2 0 0 0.5 0 Randomized bundance vector Calculate the raw NRI from 1000 randomized abundance matrices NRI increases with increasing phylogenetic clustering

27. Relating phylogenetic patterns to environmental variables NRI Phylogenetic eigenvector regression r 2 VariablesBError BtpB tp Constant1305.600121.69010.729<0.0001-15.4843.2963-4.697<0.0001 Study year-0.6510.061-10.746<0.00010.0080.00164.748<0.0001 Species richness 0.1930.01611.947<0.00010.0010.00042.5380.011 Abundance-0.0230.002-13.173<0.00010.0010.000022.931<0.0001 Soil carbon0.3450.0963.588<0.0001-0.0080.0026-3.1180.002 Sand0.0080.0110.6990.484-0.0010.0003-3.746<0.0001 pH-0.0080.127-0.0660.947-0.0020.0034-0.6100.542