Supplementary material

Table S1. Climate variables according to Quian and Ricklefs (2008); Rahbeck and Graves (2001); Schweiger et al. (2008); and Walther et al. (2005) derived from Arc Egmo Modelling, used as a basis for the PCA to derive the sample scores of the first four axes.

Parameter explanation / Min / Max / Mean
Mean annual temperature (°C) / 3.6 / 6.6 / 5.3
Mean annual sum of precipitation (mm) / 1326.6 / 1929.0 / 1606.4
Mean annual sum of global radiation (mm) / 1255.4 / 1747.3 / 1503.1
Mean annual relative humidity (%) / 70.0 / 80.0 / 80.0
Range mean annual temperature (°C) / 2.5 / 6.4 / 3.3
Range mean annual sum of precipitation (mm) / 861.9 / 1265.1 / 995.4
Mean temperature March–May (°C) / 2.6 / 6.1 / 4.5
Range mean temperature March–May (°C) / 16.8 / 19.5 / 17.9
Mean temperature June–August (°C) / 11.4 / 14.8 / 13.3
Range mean temperature June–August (°C) / 7.5 / 12.4 / 9.7
Mean temperature September–November (°C) / 4.0 / 7.0 / 5.7
Range mean temperature September–November (°C) / 14.9 / 18.6 / 16.9
Mean temperature December–February (°C) / –4.5 / –1.1 / –2.6
Range mean temperature December–February (°C) / 9.9 / 13.5 / 11.1
Mean sum of precipitation March–May (mm) / 90.3 / 137.5 / 112.8
Range mean sum of precipitation March–May (mm ) / 274.6 / 535.5 / 389.7
Mean sum of precipitation June–August (mm) / 123.5 / 156.1 / 138.1
Range mean sum of precipitation June–August (mm) / 322.2 / 423.4 / 373.8
Mean sum of precipitation September–November (mm) / 98.2 / 141.3 / 119.5
Range mean sum of precipitation September–November (mm) / 242.8 / 436.0 / 327.9
Mean sum of precipitation December–February (mm) / 130.2 / 213.2 / 165.0
Range mean sum of precipitation December–February (mm) / 291.4 / 484.3 / 384.1
Mean temperature coldest month (°C) / –5.1 / –1.5 / –3.1
Range mean temperature coldest and warmest month (°C) / 16.2 / 19.0 / 17.2
Mean temperature May–August (growing season, °C) / 10.4 / 13.8 / 12.4
Mean temperature >5°C daily mean (growing season, °C) / 10.6 / 12.2 / 11.4
Mean sum of precipitation driest month (mm) / 69.5 / 113.5 / 89.7
Range mean sum of precipitation driest and wettest month (mm) / 66.7 / 126.3 / 92.7
Mean sum of precipitation May–August (mm) / 114.3 / 146.2 / 129.6
12×(precipitation max – precipitation min)/mean precipitation sum year (mm) / 0.5 / 0.8 / 0.7
Mean annual sum of precipitation – Transpiration / –192.9 / 538.1 / 103.2
Range mean annual sum of precipitation – Transpiration / 211.3 / 290.1 / 240.8
Minimum of mean annual maximum temperature (°C) / 2.0 / 5.8 / 3.8
Mean maximum temperature May–August (°C) / 17.5 / 20.7 / 19.1
Maximum of mean annual maximum temperature (°C) / 19.1 / 22.1 / 20.6
Highest – lowest mean annual maximum temperature (°C) / 16.0 / 18.3 / 16.9
Mean annual minimum temperature (°C) / –14.5 / –9.8 / –11.5
Mean minimum temperature May–August (°C) / 3.4 / 7.5 / 6.0
Maximum of mean annual minimum temperature (°C) / 5.8 / 9.9 / 8.3
Highest – lowest mean annual minimum temperature (°C) / 18.3 / 22.5 / 19.9
Mean annual minimum global radiation (mm) / 15.7 / 65.7 / 39.7
Mean global radiation May–August (mm) / 188.0 / 209.8 / 199.7
Mean annual maximum of global radiation (mm) / 199.4 / 216.0 / 208.6
Highest – lowest mean annual global radiation (mm) / 150.0 / 187.9 / 168.9


Table S2. Soil variables from plot sampling and laboratory analyses, used as a basis for the PCA to derive the sample scores of the first four axes.

Parameter explanation / Min / Max / Mean
Mineral soil
pH / 2.25 / 4.82 / 3.25
H+ (µeq/g) / 0.43 / 118.81 / 17.14
Al3+ (µeq/g) / 6.10 / 266.26 / 89.38
Ca2+ (µeq/g) / 0.68 / 277.24 / 14.91
Fe2+ (µeq/g) / 0.31 / 37.62 / 10.00
K+ (µeq/g) / 0.69 / 14.37 / 3.12
Mg2+ (µeq/g) / 0.65 / 43.82 / 5.36
Mn2+ (µeq/g) / 0.01 / 11.65 / 1.44
Na+ (µeq/g) / 0.00 / 4.78 / 1.00
Cation-exchange capacity (µeq/g) / 42.12 / 383.20 / 142.35
Base saturation (µeq/g) / 3.12 / 328.98 / 24.39
Humus layer
pH / 2.32 / 4.42 / 3.03
H+ (µeq/g) / 0.17 / 74.90 / 25.64
Al3+ (µeq/g) / 0.95 / 186.72 / 44.04
Ca2+ (µeq/g) / 3.09 / 277.24 / 49.70
Fe2+ (µeq/g) / 0.13 / 35.37 / 5.27
K+ (µeq/g) / 2.04 / 17.05 / 7.30
Mg2+ (µeq/g) / 2.30 / 43.62 / 11.63
Mn2+ (µeq/g) / 0.09 / 36.50 / 4.82
Na+ (µeq/g) / 0.00 / 4.68 / 1.34
Cation-exchange capacity (µeq/g) / 88.70 / 357.19 / 149.74
Base saturation (µeq/g) / 12.27 / 328.98 / 69.97
H/N ratio / 0.83 / 4.04 / 1.83
C/N ratio / 9.52 / 41.81 / 22.20
Soil moisture index / 1.38 / 10.00 / 5.54


Table S3. List and frequency of the vascular plant species used to predict Natura 2000 habitat types.

Species / Plot frequency
Abies alba / 72
Acer pseudoplatanus / 49
Agrostis capillaris / 18
Ajuga reptans / 22
Anemone nemorosa / 24
Athyrium distentifolium / 46
Athyrium filix-femina / 95
Betula pendula / 7
Betula pubescens / 6
Blechnum spicant / 32
Calamagrostis villosa / 123
Caltha palustris / 11
Cardamine amara / 8
Carex brizoides / 19
Carex canescens / 18
Carex echinata / 20
Carex leporina / 8
Carex nigra / 8
Carex pilulifera / 18
Carex remota / 22
Carex sylvatica / 13
Chaerophyllum hirsutum / 6
Chrysosplenium alternifolium / 7
Circaea alpina / 16
Circaea lutetiana / 5
Cirsium palustre / 7
Deschampsia cespitosa / 12
Deschampsia flexuosa / 69
Dryopteris dilatata / 195
Dryopteris filix-mas / 16
Epilobium angustifolium / 44
Epilobium montanum / 8
Equisetum sylvaticum / 18
Fagus sylvatica / 134
Frangula alnus / 6
Galeopsis tetrahit / 16
Galium odoratum / 6
Galium palustre / 9
Galium saxatile / 17
Gymnocarpium dryopteris / 22
Homogyne alpina / 29
Impatiens noli-tangerer / 23
Juncus effusus / 27
Lamium montanum / 31
Luzula pilosa / 11
Luzula sylvatica / 64
Lycopodium annotinum / 24
Lysimachia nemorum / 21
Maianthemum bifolium / 67
Melampyrum pratense / 10
Molinia caerulea / 5
Mycelis muralis / 6
Myosotis scorpioides / 15
Nardus stricta / 6
Oreopteris limbosperma / 17
Oxalis acetosella / 115
Paris quadrifolia / 12
Petasites albus / 24
Phegopteris connectilis / 24
Picea abies / 170
Polygonatum verticillatum / 15
Populus tremula / 7
Prenanthes purpurea / 88
Ranunculus repens / 10
Rubus fruticosus / 23
Rubus idaeus / 79
Salix caprea / 7
Sambucus racemosa / 16
Senecio ovatus / 34
Soldanella montana / 38
Sorbus aucuparia / 118
Stachys sylvatica / 7
Stellaria nemorum / 18
Trientalis europaea / 36
Urtica dioica / 9
Vaccinium myrtillus / 147
Veronica officinalis / 6
Viola reichenbachiana / 6


Table S4. Cross-tabulation of the predicted versus observed habitat types for 6487 additional plots in the Bavarian Forest National Park (for details see Material and Methods. The prediction is based on discriminant analyses using our 237 plots along the transects). Bold values indicate correct predictions. The confusion matrices were derived from linear discriminant analysis (above) and from flexible discriminate analysis (below). Bold values along the diagonal of the confusion matrix indicate the number of correct predictions. The producer’s and user’s accuracy and conditional Kappa coefficients as well as the errors of omission are given (in %).

Observed
Luzulo-Fagetum / Asperulo-Fagetum / Bog woodland / Acidophilous Picea forest / Row
total / User`s accuracy / Errors of
omission / User`s
Kappa
Predicted by linear discriminant analysis / Luzulo-Fagetum / 2772 / 745 / 135 / 468 / 4120 / 67.3% / 32.7% / 0.38
Asperulo-Fagetum / 24 / 8 / 2 / 18 / 52 / 15.4% / 84.6% / 0.04
Bog woodland / 64 / 34 / 192 / 244 / 534 / 36.0% / 64.0% / 0.32
Acidophilous Picea forest / 183 / 6 / 52 / 1540 / 1781 / 86.5% / 13.5% / 0.79
Column total / 3043 / 793 / 381 / 2270 / 6487
Producer`s accuracy / 91.1% / 1.0% / 50.4% / 67.8% / Overall accuracy 69.6%
Errors of omission / 8.9% / 99.0% / 49.6% / 32.2% / Overall Kappa 0.49
Producer`s Kappa / 0.76 / 0.002 / 0.46 / 0.56
Predicted by flexible discriminant analysis / Luzulo-Fagetum / 2338 / 480 / 133 / 497 / 3448 / 67.8% / 32.2% / 0.39
Asperulo-Fagetum / 331 / 189 / 0 / 34 / 554 / 34.1% / 65.9% / 0.25
Bog woodland / 208 / 118 / 186 / 332 / 844 / 22.0% / 78.0% / 0.17
Acidophilous Picea forest / 166 / 6 / 62 / 1407 / 1641 / 85.7% / 14.3% / 0.78
Column total / 3043 / 793 / 381 / 2270 / 6487
Producer`s accuracy / 76.8% / 23.8% / 48.8% / 62.0% / Overall accuracy 63.5%
Errors of omission / 23.2% / 76.2% / 51.2% / 38.0% / Overall Kappa 0.43
Producer`s Kappa / 0.51 / 0.17 / 0.41 / 0.49

Fig. S1. Overall accuracy of linear discriminant analysis (lda) and flexible discriminant analysis (fda) for randomized data. The blue lines indicate the overall accuracy from the original discriminate analyses.

The four habitats differ considerably in occurrence (see Fig. 1). Only two habitats are common, and thus simply by making a random guess, we have a good chance to predict the correct habitat type. In the histogram labeled “random guess”, we simply randomized habitat types across plots and checked how often the randomized habitat types match the observed habitat types (a total of 1000 times). Note that the success is much lower than the success using linear discriminant function analysis (blue line). In the histograms labeled “lda, posterior” and “lda, CV”, we randomized habitat types across plots, calculated a linear discriminant analysis, and predicted the randomized classification either a posterior or by cross-validation (CV). The histogram labeled “fda, posterior” presents a similar analysis, except that flexible discriminant analysis was used. The much lower success of predicting randomly assigned habitat types compared to the original analyses (blue lines) shows that the LiDAR variables measure inherent structural differences between habitat types.

Note: During the analyses of randomized data using flexible discriminant analysis, the program sometimes failed to find lines for separating the groups. These failures of the program to converge to a solution were discarded from the analysis and may be one reason why the distribution of the success values is not as symmetric as for the other analyses.


Fig. S2. Overall accuracy using LiDAR, climate and soil, as well as vegetation data to predict Natura 2000 habitat types when using 50% of the data set as the training data set to predict the remaining plots (test data set). The blue line represents the overall accuracy when using the leave-one-out cross-validation. We used a stratified procedure so that for each habitat approximately 50% of the data were in the training data set and 50% were in the test data set. Note that only with vegetation data is the leave-one-out cross-validation optimistic.


References

Quian H, Ricklefs RE (2008) Global concordance in diversity patterns of vascular

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Rahbeck C, Graves, GR (2001) Multiscale assessment of patterns of avian species

richness. PNAS 98: 4534-4539

Schweiger O, Settele J, Kudrna O, Klotz S, Kühn I (2008) Climate change can cause

spatial mismatch of trophically interacting species. Ecology 89: 3472-3479

Walther GR, Berger S, Sykes MT (2005) An ecological "footprint" of climate change.

PNAS 272: 1427-1432