1 Phylogenetic tree

Phylogenetic tree generated using Bayesian analysis based on the ITS dataset, with posterior probability values near the branches. Newly obtained a sequence of Rehmia furfurosa from Poland is marked by a green rectangular polygon. Other sequences, outside the polygon, were retrieved from GenBank. The voucher contains the organism name and accession number (accessed 22.08.2024). The taxon names in the vouchers are the same as those in GenBank. However, new data on generic diversity have recently been published, and more details can be found in Möller et al. (2025).

1.1 Summary of posterior parameter estimates

Summary of posterior parameters (95% HPD)
Parameter Mean Variance Lower Upper Median min ESS avg ESS PSRF
TL 6.14326 0.12684 5.47185 6.86571 6.12884 3033.20 3087.29 1.000
r(A<->C) 0.10560 0.00009 0.08741 0.12409 0.10547 1111.13 1365.79 1.000
r(A<->G) 0.23337 0.00034 0.19812 0.26964 0.23297 653.07 799.82 1.000
r(A<->T) 0.09735 0.00011 0.07659 0.11793 0.09695 1617.16 1754.64 1.001
r(C<->G) 0.07375 0.00005 0.05980 0.08804 0.07344 1782.27 1819.32 1.000
r(C<->T) 0.41964 0.00049 0.37412 0.46063 0.41951 604.08 745.37 1.000
r(G<->T) 0.07030 0.00007 0.05438 0.08651 0.06989 1823.40 1907.99 1.001
pi(A) 0.19373 0.00013 0.17151 0.21529 0.19362 1411.13 1466.39 1.000
pi(C) 0.34738 0.00017 0.32106 0.37186 0.34739 1391.85 1442.47 1.000
pi(G) 0.26177 0.00019 0.23514 0.28880 0.26168 869.48 1029.64 1.001
pi(T) 0.19712 0.00012 0.17661 0.21834 0.19696 920.04 1097.55 1.000
alpha 1.11077 0.01423 0.88296 1.34980 1.10942 3165.85 3481.39 1.000
pinvar 0.31503 0.00063 0.26765 0.36530 0.31529 3876.76 4004.42 1.000

Convergence diagnostic (ESS = Estimated Sample Size); min and avg values correspond to minimal and average ESS among runs. ESS value below 100 may indicate that the parameter is undersampled.

Convergence diagnostic (PSRF = Potential Scale Reduction Factor; Gelman and Rubin, 1992) should approach 1.0 as runs converge.

All parameters show satisfactory convergence — ESS values are all above 100, indicating sufficient sampling, and PSRF values are 1.0, confirming excellent convergence across runs.

Average standard deviation of split frequencies: 0.005544

The arithmetic mean of the log-likelihood across both runs was –12564.97, while the harmonic mean was -11371.45.

  • For Run 1, the arithmetic and harmonic means were -11285.01 and -11371.06, respectively.
  • For Run 2, the values were -11286.31 (arithmetic) and -11371.73 (harmonic).

These values indicate that both runs converged to very similar likelihood estimates, with only minimal variation between them.

1.2 The Heidelberger diagnostic tests

The Heidelberger diagnostic tests for stationarity and half-width convergence were applied to two independent MCMC chains. Results indicate that both chains have successfully passed the stationarity tests for all parameters, with p-values well above common significance thresholds (typically 0.05), suggesting no evidence against convergence.

Heidelberger diagnostic - Run 1
Parametr Stationarity start P value Halfwidth test Mean Halfwidth
LnL 1 0.207 passed -1.13e+04 15.50000
LnPr 1 0.480 passed 1.63e+02 0.49200
TL 1 0.404 passed 6.15e+00 0.01050
r(A<->C) 1 0.896 passed 1.06e-01 0.00040
r(A<->G) 1 0.343 passed 2.33e-01 0.00102
r(A<->T) 1 0.413 passed 9.75e-02 0.00042
r(C<->G) 1 0.268 passed 7.38e-02 0.00032
r(C<->T) 1 0.319 passed 4.20e-01 0.00131
r(G<->T) 1 0.250 passed 7.01e-02 0.00031
pi(A) 1 0.561 passed 1.94e-01 0.00052
pi(C) 1 0.908 passed 3.47e-01 0.00057
pi(G) 1 0.243 passed 2.62e-01 0.00066
pi(T) 1 0.334 passed 1.97e-01 0.00051
alpha 1 0.248 passed 1.11e+00 0.00326
pinvar 1 0.219 passed 3.15e-01 0.00068
Heidelberger diagnostic - Run 2
Parametr Stationarity start P value Halfwidth test Mean Halfwidth
LnL 1 0.2513 passed -1.13e+04 15.50000
LnPr 1 0.5820 passed 1.63e+02 0.51800
TL 1 0.4685 passed 6.15e+00 0.01110
r(A<->C) 1 0.6782 passed 1.06e-01 0.00040
r(A<->G) 1 0.1143 passed 2.33e-01 0.00109
r(A<->T) 1 0.6292 passed 9.75e-02 0.00040
r(C<->G) 1 0.1289 passed 7.38e-02 0.00031
r(C<->T) 1 0.2353 passed 4.20e-01 0.00140
r(G<->T) 1 0.7265 passed 7.01e-02 0.00032
pi(A) 1 0.6539 passed 1.94e-01 0.00053
pi(C) 1 0.7928 passed 3.47e-01 0.00056
pi(G) 1 0.1612 passed 2.62e-01 0.00070
pi(T) 1 0.0834 passed 1.97e-01 0.00054
alpha 1 0.7555 passed 1.11e+00 0.00317
pinvar 1 0.3191 passed 3.15e-01 0.00068

2 Evaluation of the Phylogenetic Tree Presented in Figure 2 of the Article

2.1 Summary of posterior parameter estimates

Summary of posterior parameters (95% HPD)
Parameter Mean Variance Lower Upper Median min ESS avg ESS PSRF
TL 1.06351 0.01034 0.87368 1.26403 1.05736 3864.64 4047.52 1.000
r(A<->C) 0.14282 0.00064 0.09557 0.19280 0.14157 2921.52 3116.06 1.000
r(A<->G) 0.25559 0.00140 0.18503 0.33133 0.25381 2502.68 2543.69 1.000
r(A<->T) 0.03613 0.00031 0.00475 0.06995 0.03397 3504.71 3618.28 1.000
r(C<->G) 0.07566 0.00029 0.04313 0.10929 0.07482 3594.66 3636.84 1.000
r(C<->T) 0.44001 0.00191 0.35244 0.52059 0.44034 2338.96 2345.42 1.000
r(G<->T) 0.04980 0.00026 0.02050 0.08103 0.04832 3542.85 3791.09 1.000
pi(A) 0.21294 0.00033 0.17649 0.24696 0.21253 2891.83 3112.41 1.000
pi(C) 0.29889 0.00038 0.26046 0.33592 0.29846 3552.51 3663.25 1.000
pi(G) 0.27618 0.00038 0.23503 0.31217 0.27584 3489.09 3558.53 1.000
pi(T) 0.21199 0.00030 0.17842 0.24645 0.21163 3161.43 3304.26 1.000
alpha 0.89307 0.42036 0.23160 2.20323 0.67582 1557.09 1641.20 1.000
pinvar 0.27950 0.02485 0.00002 0.50744 0.29547 1267.12 1298.10 1.001

Convergence diagnostic (ESS = Estimated Sample Size); min and avg values correspond to minimal and average ESS among runs. ESS value below 100 may indicate that the parameter is undersampled.

Convergence diagnostic (PSRF = Potential Scale Reduction Factor; Gelman and Rubin, 1992) should approach 1.0 as runs converge.

All parameters show satisfactory convergence — ESS values are all above 100, indicating sufficient sampling, and PSRF values are 1.0, confirming excellent convergence across runs.

Average standard deviation of split frequencies: 0.004442

The arithmetic mean of the log-likelihood across both runs was -2026.20, while the harmonic mean was -2060.85.

  • For Run 1, the arithmetic and harmonic means were -2025.99 and -2060.91, respectively.
  • For Run 2, the values were -2026.48 (arithmetic) and -2060.79 (harmonic).

These values indicate that both runs converged to very similar likelihood estimates, with only minimal variation between them.

2.2 The Heidelberger diagnostic tests

The Heidelberger diagnostic tests for stationarity and half-width convergence were applied to two independent MCMC chains. Results indicate that both chains have successfully passed the stationarity tests for all parameters, with p-values well above common significance thresholds (typically 0.05), suggesting no evidence against convergence.
Heidelberger diagnostic - Run 1
Parametr Stationarity start P value Halfwidth test Mean Halfwidth
LnL 1 0.207 passed -1.13e+04 15.50000
LnPr 1 0.480 passed 1.63e+02 0.49200
TL 1 0.404 passed 6.15e+00 0.01050
r(A<->C) 1 0.896 passed 1.06e-01 0.00040
r(A<->G) 1 0.343 passed 2.33e-01 0.00102
r(A<->T) 1 0.413 passed 9.75e-02 0.00042
r(C<->G) 1 0.268 passed 7.38e-02 0.00032
r(C<->T) 1 0.319 passed 4.20e-01 0.00131
r(G<->T) 1 0.250 passed 7.01e-02 0.00031
pi(A) 1 0.561 passed 1.94e-01 0.00052
pi(C) 1 0.908 passed 3.47e-01 0.00057
pi(G) 1 0.243 passed 2.62e-01 0.00066
pi(T) 1 0.334 passed 1.97e-01 0.00051
alpha 1 0.248 passed 1.11e+00 0.00326
pinvar 1 0.219 passed 3.15e-01 0.00068
Heidelberger diagnostic - Run 2
Parametr Stationarity start P value Halfwidth test Mean Halfwidth
LnL 1 0.2513 passed -1.13e+04 15.50000
LnPr 1 0.5820 passed 1.63e+02 0.51800
TL 1 0.4685 passed 6.15e+00 0.01110
r(A<->C) 1 0.6782 passed 1.06e-01 0.00040
r(A<->G) 1 0.1143 passed 2.33e-01 0.00109
r(A<->T) 1 0.6292 passed 9.75e-02 0.00040
r(C<->G) 1 0.1289 passed 7.38e-02 0.00031
r(C<->T) 1 0.2353 passed 4.20e-01 0.00140
r(G<->T) 1 0.7265 passed 7.01e-02 0.00032
pi(A) 1 0.6539 passed 1.94e-01 0.00053
pi(C) 1 0.7928 passed 3.47e-01 0.00056
pi(G) 1 0.1612 passed 2.62e-01 0.00070
pi(T) 1 0.0834 passed 1.97e-01 0.00054
alpha 1 0.7555 passed 1.11e+00 0.00317
pinvar 1 0.3191 passed 3.15e-01 0.00068

3 GenBank

Summary of posterior parameters (95% HPD)
Voucher GenBank Source
Rehmia furfurosa O-L-163730 PX363701 this study
Rehmia furfurosa O-L-239319 PX363698 this study
Rehmia furfurosa O-L-169766 PV665056 Möller et al. 2025
Rehmia furfurosa O-L-239088 PX363703 this study
Rehmia furfurosa O-L-166436 PX363699 this study
Rehmia furfurosa O-L-179949 PX363700 this study
Rehmia furfurosa O-L-243115 PX363702 this study
Rehmia furfurosa UGDA L-64446 PX402214 this study
Rehmia furfurosa UGDA L-64442 PX402213 this study
Rehmia furfurosa UGDA L-64421 PX402212 this study
Rehmia furfurosa 1354 PX402211 this study

4 Figure

Response curves for metals, illustrating the relationship between each variable and species distribution while keeping other predictors at zero.

5 Literature

  • Gelman, A., Rubin, D. B. (1992). Inference from Iterative Simulation Using Multiple Sequences. Statistical Science 7(4), 457-472. https://doi.org/10.1214/ss/1177011136
  • Möller, E.J., Timdal, E., Haugan, R., Bendiksby, M. (2025). Integrative taxonomy and genus delimitation in the Rhizocarpaceae (lichenized Ascomycota). Fungal Systematics and Evolution 16, 215–231. https://doi.org/10.3114/fuse.2025.16.12