Additional file 8: of Signatures of ecological processes in microbial community time series

Figure S6. The test for temporal structure with noise types is robust to noise. (a) Noise-type profile in the presence of noise generated with the Poisson distribution for each species and each sample. (b) Noise-type distribution in the presence of noise generated with the multinomial distribution for each sample. Labels for time series are colored according to the level of non-zero intrinsic noise (sigma) for Ricker, according to the death rate if larger than one for Hubbell, according to the interval if larger than one (with interval coloring taking precedence over sigma) and black otherwise. (PDF 8 kb

Additional file 12: of Signatures of ecological processes in microbial community time series

Figure S10. The accuracy of network inference with LIMITS decreases more strongly when applied to the last 100 than to the first 100 time points. (a) LIMITS accuracy, i.e., mean correlation of inferred and known interaction matrix, for the first 100 time points. (b) LIMITS goodness of fit for the first 100 time points. The goodness of fit was computed as the mean correlation between original and predicted time series. (c) LIMITS accuracy for the last 100 time points. Since gLV time series are constant, no network could be inferred for them. (d) LIMITS goodness of fit for the last 100 time points. The correlation between the goodness of fit to the Ricker model and the intrinsic noise strength observed in noise-free time series is lost. The data points are colored according to the connectance in panels (a) and (c), according to interval in panel (b) and according to the intrinsic noise strength sigma in panel (d). (PDF 17 kb

Additional file 9: of Signatures of ecological processes in microbial community time series

Figure S7. Increasing the time series length improves the accuracy of the test for temporal structure. Noise types were computed for time series sub-sets from 1000 to 1010 (a) and 1000 to 1025 (b) for all data sets with more than 1000 time points. Labels for time series are colored according to the level of non-zero intrinsic noise (sigma) for Ricker, according to the death rate if larger than one for Hubbell, according to the interval if larger than one (with interval coloring taking precedence over sigma) and black otherwise. (PDF 8 kb

Additional file 11: of Signatures of ecological processes in microbial community time series

Figure S9. The presence of noise decreases the accuracy of the neutrality test but affects network inference accuracy less. (a) For the last 100 time points, when many simulated time series reach equilibrium, neutrality is erroneously rejected for several Hubbell time series and erroneously detected for a number of Ricker and SOI time series. The classification does not change for the stool time series. (b) The addition of Poisson noise does not introduce false negatives in the neutrality test, but introduces false positives (i.e., Hubbell time series for which neutrality is rejected). The dashed lines in (a) and (b) indicate the value corresponding to a p value of 0.05. For values above, neutrality is rejected. (c) LIMITS accuracy, i.e., mean correlation of inferred and known interaction matrix, for time series with Poisson noise. Inference failed for gLV time series. (d) LIMITS goodness of fit for time series with Poisson noise. The goodness of fit was computed as the mean correlation between original and predicted time series. The data points are colored according to the interval in panels (a), (b) and (d), and according to the connectance in panel (c). (PDF 17 kb

Additional file 10: of Signatures of ecological processes in microbial community time series

Figure S8. Increasing the time series length improves the accuracy of the test for temporal structure. Noise types were computed for time series sub-sets from 1000 to 1050 (a) and 1000 to 1100 (b) for all data sets with more than 1000 time points. Labels for time series are colored according to the level of non-zero intrinsic noise (sigma) for Ricker, according to the death rate if larger than one for Hubbell, according to the interval if larger than one (with interval coloring taking precedence over sigma) and black otherwise. (PDF 7 kb

Additional file 14: of Signatures of ecological processes in microbial community time series

Figure S12. Variability of noise-type classification across rarefactions. The noise types of 100 taxa selected to be top abundant in one rarefaction were computed for repeated rarefactions in the stool data set of individual A [3]. (PDF 5 kb

Additional file 1: of Signatures of ecological processes in microbial community time series

Table S1. lists for each test time series the parameters used to generate it (sheet “Model parameters”) and the properties of relative abundance time series, which include noise type, autocorrelation, Hurst bin percentages, the p values of the neutrality test, and the LIMITS results (sheet “Time series properties”). In addition, it includes all these results for the first 100 time points (sheet “First 100 tp properties”), the last 100 time points (sheet “Last 100 tp properties”) and for time series with Poisson noise (sheet “Poisson time series properties”). (XLSX 158 kb

Additional file 2: of Signatures of ecological processes in microbial community time series

Ecological models. (DOCX 1011 kb

Additional file 7: of Signatures of ecological processes in microbial community time series

Figure S5. The test for temporal structure with noise types is robust to compositionality and the absence of transient dynamics. (a) The noise-type profiles for absolute abundances do not differ noticeably from those for relative abundances shown in Figure 3a. (b) When noise types are computed for the last hundred time points, most time series are correctly classified as temporally structured or unstructured. Labels for time series are colored according to the level of non-zero intrinsic noise (sigma) for Ricker, according to the death rate if larger than one for Hubbell, according to the interval if larger than one (with interval coloring taking precedence over sigma) and black otherwise. (PDF 8 kb

Additional file 6: of Signatures of ecological processes in microbial community time series

Figure S4. The noise-type classification and the neutrality test are robust for a wide parameter range in the Hubbell model, but noise types are affected by the death rate. (a) The percentage of taxa with black, brown, pink and white noise types is plotted against the death rate. There is a significant negative correlation between the percentage of brown species and the death rate (Spearman’s rho: − 0.85, p value < 0.000001) and a corresponding positive correlation of the percentage of pink species to the death rate (Spearman’s rho: 0.94, p value < 0.000001). (b) The p values of the neutrality test are plotted against the death rate. (c) The percentage of taxa with black, brown, pink, and white noise types is plotted against the number of individuals. (d) The p values of the neutrality test are plotted against the number of individuals. (d) The percentage of taxa with black, brown, pink, and white noise types is plotted against the immigration rate. (e) The p values of the neutrality test are plotted against the immigration rate. Neutrality is rejected for a p value below 0.05. The p value of 0.05 is indicated by a dashed horizontal line. Time series were generated for 100 species and 3000 time points. For the immigration rate, the percentage of noise types of taxa with non-zero abundances was plotted, since for the low immigration rates tested in this simulation, many taxa have abundances of zero. (PDF 40 kb