Effects of interannual climate variability on tropical tree cover

Effects of interannual climate variability on tropical tree cover Milena Holmgren, Marina Hirota, Egbert H. Van Nes & Marten Scheffer Correspondence to: milena.holmgren@wur.nl Contents: 1. Climate Indexes. 2. Correlation of climate variables and multi-collinearity analysis (Tables S1, S2) 3. Interactive effects of MAP and CV on tropical tree cover (Table S3, S4). 4. Models for the distribution of tree cover in wet tropics (MAP > 600 mm) as a function of MAP, CV and MSI (Table S5, S6, S7). 5. Non-spatial models for the distribution of tree cover in dry tropics (MAP 600 mm) as a function of climate (Tables S8, S9, S10, S11). 6. Spatial models for the distribution of tree cover in dry tropics (MAP 600 mm) as a function of climate (Tables S12, S13, S14). 7. Analysis of the residuals for dry-land models. NATURE CLIMATE CHANGE www.nature.com/natureclimatechange 1

1. Climatic indexes Standardized Precipitation Index (SPI) The Standardized Precipitation Index estimates the probability of an anomalous precipitation event at a particular time scale 30. The SPI is defined as the number of standard deviations above or below the climatological mean precipitation for that period. Depending on the SPI value, the anomalous climatic event is classified as follows: SPI values +2σ +1.50σ to +1.99σ +1.00σ to +1.49σ -0.99σ to +0.99σ -1.00σ to -1.49σ -1.50σ to -1.99σ -2σ Category Extremely wet Severely wet Moderately wet Close to normal Moderately dry Severely dry Extremely dry Because we were interested in evaluating inter-annual variability, SPI values were calculated for each year as the deviations of the yearly mean precipitation from the long term Mean Annual Precipitation (MAP) for the period from 1961 to 2002 (42 years). Severely wet years were defined for our purpose as those with SPI +1.5σ (thus including the years classified as extremely wet in the original SPI system). For each pixel, we calculated the percentage of severely wet years (SPIW). Conversely, severely dry years were defined as those with SPI - 1.5σ to calculate the percentage of severely dry years (SPID). SPIW and SPID are good indicators of inter-annual variability because they are not correlated with MAP (see Table S1). Coefficient of Variation (CV) and Standard Deviation (SD) Coefficient of variation (CV) and standard deviation (SD) of mean annual precipitation (MAP) were calculated according to the usual statistical equations for the years 1961-2002. Markham s Seasonality Index (MSI) The Markham s Seasonality Index was proposed to show the tendency a certain location has to concentrate more precipitation in certain months of the year compared to others 31. Its calculation assumes that monthly rainfall totals are vectors, with the rainfall as the length, and the month as the direction of the vector. We calculated the magnitude of the summed vector of all months per year (which is an indication of the seasonal variation) and standardized this by dividing it by the mean annual precipitation. Subsequently we averaged the yearly values over the period of 1961 to 2002. 2 NATURE CLIMATE CHANGE www.nature.com/natureclimatechange

SUPPLEMENTARY INFORMATION 2. Correlation between climate variables and multi-collinearity analysis. Table S1 Pearson correlation coefficients among Mean Annual Precipitation (MAP) and the other climate variables: percentage of severely wet years (SPIW), percentage of severely dry years (SPID), Coefficient of Variation (CV), Standard Deviation (SD) and Markham Seasonality Index (MSI). Indexes SPIW SPID CV SD MSI MAP -0.023 +0.038-0.591 +0.762-0.469 Table S2 Variance Inflation Factor (VIF) values for the explanatory variables (MAP, SPIW, SPID, CV, MSI) to test for multi-collinearity. All VIF < 5 indicating there is no multicollinearity affecting the effect size and signal of the linear coefficients. Continent/ precipitation classification VIF for each linear regression setup f(map, SPIW, MSI) f(map, SPID, MSI) f(map, CV, MSI) /drylands (1.01, 1.06, 1.06) (1.00, 1.05, 1.05) (1.79, 1.79, 1.01) /wetlands (1.48, 1.00, 1.48) (1.48, 1.03, 1.50) (2.27, 1.82, 1.48) /drylands (1.38, 1.05, 1.41) (1.40, 1.04, 1.38) (2.52, 2.41, 3.11) /wetlands (1.23, 1.21, 1.36) (1.15, 1.12, 1.28) (1.71, 2.15, 2.30) /drylands (1.24, 1.08, 1.30) (1.35, 1.42, 1.42) (1.96, 2.30, 1.47) /wetlands (1.32, 1.02, 1.33) (1.34, 1.02, 1.33) (1.60, 1.25, 1.32) NATURE CLIMATE CHANGE www.nature.com/natureclimatechange 3

3. Interactive effects of MAP and CV on tropical tree cover. Table S3. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (log MAP) and the Coefficient of Variation (log CV) and their interaction for tropical regions in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent Intercontinental AIC Pseudo Adj. 2910.65 0.561 Constant -0.122* -0.154-0.089 MAP +0.071* +0.065 +0.077 CV +1.278* +1.249 +1.308 MAP*CV -0.195* -0.198-0.191-1130.38 0.352 Constant -1.008* -1.414-0.601 MAP +0.166* +0.099 +0.232 CV -0.042-0.390 +0.305 MAP*CV -0.227-0.078 +0.033 554.39 0.479 Constant -0.292* -0.414-0.170 MAP +0.118* +0.096 +0.141 CV +1.170* +1.036 +1.304 MAP*CV -0.169* -0.186-0.152 175.58 0.572 Constant -0.211* -0.343-0.078 MAP +0.089* +0.065 +0.113 CV +1.280* +1.155 +1.406 MAP*CV -0.192* -0.208-0.176 4 NATURE CLIMATE CHANGE www.nature.com/natureclimatechange

SUPPLEMENTARY INFORMATION Table S4. Spatial generalized least square (GLS) models fitting tree cover percent (arcsinsquared-root transformed) to Mean Annual Precipitation (log MAP), the Coefficient of Variation (log CV) and their interaction for tropical regions in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent Intercontinental AIC Pseudo Adj. -1804.51 0.793 Constant -0.339-0.881 +0.203 MAP +0.103 +0.022 +0.183 CV +0.078-0.310 +0.466 MAP*CV -0.013-0.070 +0.044-1712.12 0.516 Constant -1.167* - - MAP +0.215* - - CV +0.077 - - MAP*CV -0.024 - - -450.37 0.685 Constant +0.129-0.083 +0.342 MAP +0.035* +0.006 +0.065 CV +0.439* +0.179 +0.699 MAP*CV -0.080* -0.115-0.045-808.41 0.739 Constant -0.033-0.228 +0.162 MAP +0.047* +0.019 +0.075 CV +0.345* +0.151 +0.538 MAP*CV -0.066* -0.092-0.040 NATURE CLIMATE CHANGE www.nature.com/natureclimatechange 5

4. Models for the distribution of tree cover in wet tropics (MAP > 600 mm) as a function of MAP, CV and MSI (Tables S5, S6 and S7). Table S5. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (MAP) and the Coefficient of Variation (CV) for tropical regions with MAP > 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent AIC +106.48 0.354 Constant +0.343* +0.300 +0.387 MAP +0.929* +0.843 +1.014 CV -0.248* -0.357-0.139-223.55 0.103 Constant +0.475* +0.442 +0.508 MAP +0.163* +0.104 +0.222 CV -0.298* -0.355-0.240 +842.88 0.280 Constant +0.486* +0.449 +0.523 MAP +1.610* +1.479 +1.740 CV -0.177* -0.352-0.002 Table S6. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (MAP), the Coefficient of Variation (CV) and Markham Seasonality Index (MSI) for tropical regions with MAP > 600 mm. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. f(map, CV, MSI) -208.50 0.449 Constant +0.672* +0.619 +0.725 MAP +0.579* +0.492 +0.667 CV -0.207* -0.308-0.106 MSI -0.448* -0.496-0.401 f(map, CV, MSI) -460.01 0.234 Constant +0.483* +0.453 +0.514 MAP +0.507* +0.438 +0.576 CV +0.140* +0.065 +0.216 MSI -0.409* -0.460-0.359 f(map, CV, MSI) +827.89 0.286 Constant +0.582* +0.523 +0.641 MAP +1.461* +1.313 +1.609 CV -0.199* -0.374-0.024 MSI -0.162* -0.239-0.085 6 NATURE CLIMATE CHANGE www.nature.com/natureclimatechange

SUPPLEMENTARY INFORMATION Table S7. Spatial generalized least square (GLS) models fitting tree cover percent (arcsinsquared-root transformed) to Mean Annual Precipitation (MAP), the Coefficient of Variation (CV) and Markham Seasonality Index (MSI) for tropical regions with MAP > 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05; p < 0.10 ). Estimates and confidence intervals () are presented for each factor. f(map, MSI) -1373.60 0.692 Constant +0.532* +0.354 +0.710 MAP +0.252* +0.071 +0.433 MSI -0.326* -0.523-0.128 f(map, MSI) -704.54 0.350 Constant +0.500* +0.395 +0.604 MAP +0.392* +0.247 +0.537 MSI -0.300* -0.446-0.155 f(map, CV, MSI) -375.00 0.609 Constant +0.769* +0.589 +0.949 MAP +0.467* +0.240 +0.693 CV -0.282-0.586 +0.021 MSI -0.342* -0.527-0.157 NATURE CLIMATE CHANGE www.nature.com/natureclimatechange 7

5. Non-spatial models for tree cover in dry tropics (MAP 600 mm) as a function of climate (Tables S8, S9, S10, S11). Table S8. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (MAP) and the Coefficient of Variation (CV) for tropical regions with MAP 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent AIC -1647.81 0.198 Constant -0.076* -0.111-0.041 MAP +0.325* +0.288 +0.362 CV +0.036-0.047 +0.119-1846.20 0.226 Constant +0.198* +0.174 +0.222 MAP +0.181* +0.156 +0.205 CV -0.259* -0.292-0.226-936.04 0.425 Constant -0.126* -0.156-0.097 MAP +0.594* +0.557 +0.630 CV +0.289* +0.202 +0.376 Table S9. Non-spatial generalized least square (GLS) models fitting tree cover percent (arcsin-squared-root transformed) to Mean Annual Precipitation (MAP), the Coefficient of Variation (CV) and Markham Seasonality Index (MSI) for tropical regions with MAP 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. Continent Best Model AIC f(map, MSI) -1686.50 0.203 Constant -0.039* -0.062-0.016 MAP +0.318* +0.290 +0.346 MSI -0.049* -0.076-0.022 f(map, CV, MSI) -1961.52 0.270 Constant +0.109* +0.081 +0.137 MAP +0.336* +0.300 +0.373 CV -0.058* -0.106-0.009 MSI -0.232* -0.273-0.190 f(map, CV, MSI) -937.73 0.426 Constant -0.104* -0.141-0.067 MAP +0.591* +0.554 +0.627 CV +0.325* +0.231 +0.420 MSI -0.045* -0.090-0.001 8 NATURE CLIMATE CHANGE www.nature.com/natureclimatechange

SUPPLEMENTARY INFORMATION Table S10. As Table S9 with the percentage of severely wet years (SPIW) based on the Standardized Precipitation Index. f(map, MSI) -1686.50 0.203 Constant -0.038* -0.062-0.016 MAP +0.318* +0.290 +0.346 MSI -0.049* -0.076-0.022 f(map, SPIW, MSI) -1965.06 0.271 Constant +0.055* +0.034 +0.076 MAP +0.363* +0.336 +0.390 SPIW +0.060* +0.021 +0.100 MSI -0.276* -0.304-0.248 f(map, SPIW) -912.81 0.418 Constant -0.086* -0.111-0.061 MAP +0.518* +0.491 +0.545 SPIW +0.089* +0.049 +0.129 Table S11. As Table S9 with the percentage of severely dry years (SPID) based on the Standardized Precipitation Index. f(map, MSI) -1686.50 0.203 Constant -0.039* -0.062-0.016 MAP +0.318* +0.290 +0.346 MSI -0.049* -0.075-0.022 f(map, SPID, MSI) -1959.7 0.269 Constant +0.099* +0.075 +0.123 MAP +0.361* +0.333 +0.388 SPID -0.033-0.067 +0.001 MSI -0.270* -0.297-0.242 f(map) -895.82 0.413 Constant -0.043* -0.058-0.027 MAP +0.509* +0.482 +0.535 * and show statistical significances of 95% (p < 0.05) and 90% (p < 0.10) respectively NATURE CLIMATE CHANGE www.nature.com/natureclimatechange 9

6. Spatial models for the distribution of tree cover in dry tropics (MAP 600 mm) as a function of climate (Tables S12, S13, S14). Table S12. Spatial generalized least square (GLS) models fitting tree cover percent (arcsinsquared-root transformed) to Mean Annual Precipitation (MAP), the Coefficient of Variation (CV) and Markham Seasonality Index (MSI) for tropical regions with MAP 600 mm in each continent. Significance of the explanatory variables assessed with L-Ratio (* p < 0.05). Estimates and confidence intervals () are presented for each factor. f(map) -3318.18 0.648 Constant +0.060* -0.066 +0.187 MAP +0.165* +0.096 +0.235 f(map, MSI) -2549.55 0.456 Constant +0.100* +0.051 +0.148 MAP +0.286* +0.207 +0.365 MSI -0.221* -0.313-0.129 f(map) -2233.50 0.700 Constant +0.201* +0.089 +0.313 MAP +0.202* +0.119 +0.286 Table S13. As Table S12 with the percentage of severely wet years (SPIW) based on the Standardized Precipitation Index. f(map) -3318.18 0.648 Constant +0.060* -0.066 +0.187 MAP +0.165* +0.096 +0.235 f(map, MSI) -2549.55 0.456 Constant +0.100* +0.051 +0.148 MAP +0.286* +0.207 +0.365 MSI -0.221* -0.313-0.129 f(map, SPIW) -2235.60 0.700 Constant +0.175* +0.058 +0.292 MAP +0.200* +0.117 +0.284 SPIW +0.058* +0.002 +0.293 Table S14. As Table S12 with the percentage of severely dry years (SPID) based on the Standardized Precipitation Index. f(map) -3318.18 0.648 Constant +0.060* -0.066 +0.187 MAP +0.165* +0.096 +0.235 f(map, MSI) -2549.55 0.456 Constant +0.100* +0.051 +0.148 MAP +0.286* +0.207 +0.365 MSI -0.221* -0.313-0.129 f(map) -2233.50 0.700 Constant +0.201* +0.089 +0.313 MAP +0.202* +0.119 +0.286 10 NATURE CLIMATE CHANGE www.nature.com/natureclimatechange

SUPPLEMENTARY INFORMATION 7. Analysis of the residuals for dry-lands Figure S1: Variograms of the residuals for the models with and without the inclusion of spatial correlation. Covariates are Mean Annual Precipitation (MAP), the percentage of severely wet years (SPIW) based on the Standardized Precipitation Index, and the Markham Seasonality Index (MSI) for tropical regions with MAP 600 mm in each continent (Increases in semi-variances as a function of the distances indicate the presence of spatial correlation within the datasets. Blue and red lines represent models without and with spatial correlation respectively. NATURE CLIMATE CHANGE www.nature.com/natureclimatechange 11