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

2. Species abundance matrix M Site GPS location matrix D Environmental variable matrix V Species Sites Variables Multivariate approaches to biodiversity L Spatial regression Co-occurrence mapping Regression tree Impact analysis

3. S G6-3A2-2C4-4J4-4D2-4K7-2K7-4F1-3M7-2 Achillea_pannonica 00.120.50000 Agrostis_capillaris 0.5 0 0 Agrostis_stolonifera_agg. 000000000 Agrostis_vinealis 000.5000000 Ajuga_genevensis 000000000.5 SG6-3A2-2C4-4J4-4D2-4K7-2K7-4F1-3M7-2 CaCO 3 0.950.110.851.531.930.58 0.380.63 Sand85.6681.3174.4274.24 83.45 78.4582.15 pH8.698.017.978.058.088.23 8.258.4 PlotG6-3A2-2C4-4J4-4D2-4K7-2K7-4F1-3M7-2 Longitude317.78187.24237.32322.62217.79388.38382.38226.3412.75 Latitude266.85307.27299.92188.9259.69209.6 221.79177.88 The raw data Basic questions: Do soil characteristics influence species abundances and diversity? How do these relationships change in time? Starting hypotheses: Neighboured plots are similar in species composition. CaCO 3 is of major importance for plant diversity. Species occurrences is not random with respect to soil characteristics

4. Neighboured plots are similar in species composition We calculate the Soerensen (Dice) index of species similarity and transform to a distance matrix (D = 1 – S) We calculate the distance matrix of GPS data Mantel test

5. CaCO 3 is of major importance for plant diversity PlotLongLatYearSpecies Abundanc e CaCO3SandpH A3-2203.09319.46200630.70.9585.668.69 A3-3197.09325.462006610.1181.318.01 A3-4197.09319.46200640.80.8574.427.97 A4-2218.95331.64200640.81.5374.248.05 A4-3212.95337.64200641.21.9374.248.08 B3-3209.28309.6200630.70.5883.458.23 B4-2231.14315.78200640.80.5883.458.23 B4-4225.14315.78200631.50.3878.458.25 B5-2247327.97200630.70.6382.158.4 B5-4241327.97200630.72.2180.017.78 C1-1195.75269.37200661.81.5179.168.02 C2-2211.61275.55200630.30.184.097.9 The SAM input file CaCO 3 Species richness

6. 5 5 1 1 5 5 7 7 17 41 35 Species richness at sites of different area AreaSpecies 3135 55 95 157 2217 5041 51 We did not include the spatial distance into the regression Spatial autocorrelation is inevitable in ecology General linear models in the face of spatial autocorrelation

7. TemperaturePrecipitationAridity 8.956.50.15 10.9799.50.94 8.4343.50.94 1.2305.20.00 8.3952.30.75 15.0286.30.69 5.6651.50.59 3.2572.10.11 0.5836.60.83 3.4399.00.45 0.2984.30.56 5.7655.60.11 13.7269.60.26 9.0561.80.56 18.5457.80.94 5 5 1 1 5 5 7 7 17 41 35 Abundance 28.3 17.7 13.5 16.1 26.2 29.0 11.7 17.4 3.7 10.1 1.5 3.2 21.2 14.4 0.7 Spatial autocorrelation Spatial autocorrelation is inevitable. All ecological field data sets have a spatial structure. Collinearity Autocorrelation

8. Bivariate case F increases proportionally to the degrees of freedom n, that is to the number of data points. P decreases with increasing number of data points (sample size). Any statistical test will eventually become significant if you only increase the sample size. Statistical significance at the 1% error level PlotSpeciesCaCO3SandpH A3-230.9585.668.69 A3-360.1181.318.01 A3-440.8574.427.97 A4-241.5374.248.05 A4-341.9374.248.08

9. 5 5 1 1 5 5 7 7 17 41 35 Spatial autocorrelation 7 7 17 35 7 7 17 35 7 7 7 7 7 7 7 7 7 7 Spatial autocorrelation reduces the effective degrees of freedom. Using spatially autocorrelated data we artificially increase the degrees of freedom and the F-score. We get too often statistically significant results. What to do??? First, test for spatial autocorrelation: Moran’s I

10. Reduce the degrees of freedom N = 15 N eff = 4 Neighbor joining cluster analysis What to do??? UPGMA cluster analysis

11. Correct for the effects of spatial autocorrelation What to do???

12. Correct for the effects of spatial autocorrelation Trend surface analysis is able to capture broad scale trends What to do??? Eigenvector regression or eigenvector mapping  Euclidean distances G6-3A2-2C4-4J4-4D2-4 G6-30.0136.787.078.1100.3 A2-2136.70.050.6179.856.5 C4-487.050.60.0140.044.7 J4-478.1179.8140.00.0126.5 D2-4100.356.544.7126.50.0 Eigenvalues 2140.4-938.7 Eigenvectors 0.1910.046 0.3070.394 0.2440.316 0.176-0.146 0.2360.284

13. Autocorrelation models Multiply Y and X by a spatial corrective Spatial weights of C Often all the whole variance goes into the spatial component leaving no room for the predictors. The larger  the more variance goes into space.  = means no spatial effect (OLS).  is an additional weight factor (  < 1).  = 0 means no spatial effect (OLS).  = 1 means all variance goes into space.

14. PlotLongitudeLatitudeEV1SCaCO3SandpH G6-3317.78266.850.01639150.9585.668.69 A2-2187.24307.27-0.03864170.1181.318.01 C4-4237.32299.92-0.02015160.8574.427.97 J4-4322.62188.90.04304161.5374.248.05 D2-4217.79259.69-0.01349131.9374.248.08 K7-2388.38209.60.05755210.5883.458.23 K7-4382.38209.60.05561150.5883.458.23 F1-3226.3221.790.001452160.3878.458.25 M7-2412.75177.880.0756130.6382.158.4 I3-1300.57198.580.03283122.2180.017.78 The input tab delimited text file for SAM No clear spatial trend in species richness

15. OLS VariablesCoeff.Std.err.tpR^2 Constant6.145.621.090.280.00 CaCO3-0.100.37-0.270.790.00 Sand-0.020.04-0.420.670.00 pH1.270.502.520.010.02 r2r2 P0.08 Trend surface analysis VariablesCoeff.Std.err.tpR^2 Constant6.135.581.100.270.00 Longitude0.010.003.000.000.02 Latitude0.010.001.750.080.00 CaCO3-0.350.38-0.910.360.00 Sand-0.060.05-1.310.190.00 pH1.000.511.970.050.02 r2r2 0.04 P0.007 Eigenvector mapping VariablesCoeff.Std.err.tpR^2 Constant6.345.621.130.260.00 EV18.085.721.410.160.01 CaCO3-0.190.38-0.510.610.00 Sand-0.010.04-0.260.800.00 pH1.160.512.270.02 r2r2 P0.06 The dependence of richness on pH vanishes after accounting for spatial structure. Do soil properties influence species richness? The Hühnerwasser catchment is divided into a western and an eastern part with different sand soil content and pH. Trend surface analysis captures this gradient.