Table 1. Number of sequences, sequence length, unique sites, informative characters and invariant sites for the analysed DNA regions.RegionTypeSequencesSitesUnique sitesInformative charactersInvariant sitesITS1+2nuc DNA1031054155176722trnT-psbDcp DNA996172256539trnGcp DNA1046233829556Indelsbinary1103391651740

Table 1. Number of sequences, sequence length, unique sites, informative characters and invariant sites for the analysed DNA regions.RegionTypeSequencesSitesUnique sitesInformative charactersInvariant sitesITS1+2nuc DNA1031054155176722trnT-psbDcp DNA996172256539trnGcp DNA1046233829556Indelsbinary1103391651740

Appendix 1. Descriptive statistics for quantitative characters of Epipterygium tozeri of different geographical origin (mean ± SD [range]) including ANOVA F statistic and significance level (* P ≤ 0.05, ** P ≤ 0.005, *** P <0.001). Letters in parentheses (a, b, c, d) represent results from a post-hoc Tukey test for statistically significant variables.ContinentalMacaronesiaAsiaU.S.A.YunnanJapanANOVAAnalyzed collectionsT. Arts 339141-29 (BR), T. Arts 339149-37 (BR)A. Vanderpoorten 070312 (LG), T. Arts 339139-27 (BR)D.G. Long s.n. (E00884194), D.G. Long s.n. (E0084196)J. Brinda 5770 (MO), J. Brinda 3131 (MO)D.G. Long s.n. (E00576940)Z. Iwatsuki 160338 (NICH), Z. Iwatsuki 172095 (NICH)Stem length [mm]8.71 ± 2.01 [6.2–13] (a)2.99 ± 0.49 [2.4–3.9] (c)3.57 ± 0.46 [3–4.4] (c)6.39 ± 0.80 [5.3––7.4] (b)8.42 ± 0.91 [7–9.1] (ab)7.61 ± 1.91 [5.2–10] (ab)1.38e-14Costa length [mm]1.59 ± 0.32 [1.07–2.02] (a)0.81 ± 0.25 [0.25–1.07] (c)0.8 ± 0.13 [0.62–1.07] (c)1.68 ± 0.36 [1.12–2.35] (a)1.13 ± 0.12 [1.05–1.35] (bc)1.51 ± 0.19 [1.17–1.77] (ab)6.76e-12Lateral leaf length [mm]2.15 ± 0.31 [1.62–2.55] (ab)1.8 ± 0.20 [1.5–2.12] (b)1.31 ± 0.14 [1.05–1.52] (c)2.20 ± 0.36 [1.6–2.72] (a)1.77 ± 0.22 [1.62–2.12] (bc)2.00 ± 0.32 [1.37–2.5] (ab)2.58e-08Lateral leaf width [mm]0.99 ± 0.18 [0.77–1.27] (a)0.95 ± 0.11 [0.85–1.22] (a)0.74 ± 0.13 [0.6–1] (b)0.81 ± 0.18 [0.57–1.15] (ab)0.93 ± 0.07 [0.85–1.02] (ab)0.86 ± 0.13 [0.62–1] (ab)0.00181Lateral leaf length/ width2.20 ± 0.30 [1.83–2.80] (bc)1.82 ± 0.24 [1.45–2.42] (cd)1.79 ± 0.22 [1.5–2.16] (d)2.77 ± 0.50 [2.36–4] (a)1.88 ± 0.12 [1.71–2.07] (bcd)2.33 ± 0.14 [2.14–2.5] (b)3.97e-09Dorsal leaf length [mm]1.23 ± 0.17 [1–1.42] (a)0.87 ± 0.15 [0.65–1.02] (c)0.94 ± 0.15 [0.75–1.17] (bc)1.22 ± 0.34 [0.75–1.6] (ab)0.83 ± 0.21 [0.62–1.1] (c)0.97 ± 0.19 [0.75–1.25] (abc)0.000278Dorsal leaf width [mm]0.43 ± 0.073 [0.35–0.6] (ab)0.34 ± 0.16 [0.12–0.5] (b)0.49 ± 0.09 [0.37–0.62] (a)0.32 ± 0.07 [0.225 –0.425] (b)0.46 ± 0.17 [0.3–0.7] (ab)0.43 ± 0.08 [0.35–0.6] (ab)0.0086Dorsal leaf length/ width2.90 ± 0.43 [2.33–3.8] (abc)3.20 ± 1.74 [2.05–6.4] (ab)1.93 ± 0.24 [1.76–2.4] (c)3.76 ± 0.56 [3–4.26] (a)1.84 ± 0.23 [1.57–2.08] (c)2.25 ± 0.24 [1.68–2.5] (bc)2.51e- 05Median cell length [μm]170 ± 30.68 [125–222.5] (a)127.25 ± 21.87 [90–150] (b)79.75 ± 19.38 [62.5–110] (c)112.25 ± 17.96 [85–137.5] (b)120 ± 6.84 [112.5–125] (b)112.5 ± 8.57 [100–127.5] (b)3.44e- 11Median cell width [μm]34.5 ± 6.10 [25–45] (a)28.25 ± 3.12 [22.5–32.5] (bc)24 ± 6.47 [15–37.5] (c)24.5 ± 2.58 [20–30] (bc)31.5 ± 4.54 [27.5–37.5] (ab)25.25 ± 0.79 [25–27.5] (bc)6.29e- 06Median cell length/width5.01 ± 1.05 [3.33–7.41] (a)4.48 ± 0.42 [3.81–5] (ab)3.37 ± 0.47 [2.7–4.16] (c)4.60 ± 0.74 [3.6–6.11] (ab)3.87 ± 0.57 [3.21–4.54] (bc)4.45 ± 0.29 [4–5.1] (ab)2.38e- 05Marginal cell length [μm]210.25 ± 15.74 [187.5–237.5] (a)189 ± 34.07 [135–237.5] (a)142 ± 22.41 [115–187.5] (b)183 ± 30.06 [125–232.5] (a)175.5 ± 14.29 [152.5–187.5] (ab)147.75 ± 17.13 [125–175] (b)2.68e- 07Marginal cell width [μm]11.25 ± 1.76 [7.5–12.5] (a)10.75 ± 1.20 [10–12.5] (a)8.25 ± 1.20 [7.5–10] (b)8.5 ± 1.29 [7.5–10] (b)8 ± 1.11 [7.5–10] (b)9.5 ± 1.97 [7.5–12.5] (ab)2.91e-05*Marginal cell length/width18.83 ± 4.18 [16–29.66] (ab)17.52 ± 2.04 [13.5–20.25] (ab)17.31 ± 2.28 [13.75–21] (ab)22.05 ± 5.22 [12.5–31] (a)22.23 ± 3.26 [17.5–25] (a)15.93 ± 2.56 [12.75–20.33] (b)0.00133

Appendix 1. Descriptive statistics for quantitative characters of Epipterygium tozeri of different geographical origin (mean ± SD [range]) including ANOVA F statistic and significance level (* P ≤ 0.05, ** P ≤ 0.005, *** P <0.001). Letters in parentheses (a, b, c, d) represent results from a post-hoc Tukey test for statistically significant variables.ContinentalMacaronesiaAsiaU.S.A.YunnanJapanANOVAAnalyzed collectionsT. Arts 339141-29 (BR), T. Arts 339149-37 (BR)A. Vanderpoorten 070312 (LG), T. Arts 339139-27 (BR)D.G. Long s.n. (E00884194), D.G. Long s.n. (E0084196)J. Brinda 5770 (MO), J. Brinda 3131 (MO)D.G. Long s.n. (E00576940)Z. Iwatsuki 160338 (NICH), Z. Iwatsuki 172095 (NICH)Stem length [mm]8.71 ± 2.01 [6.2–13] (a)2.99 ± 0.49 [2.4–3.9] (c)3.57 ± 0.46 [3–4.4] (c)6.39 ± 0.80 [5.3––7.4] (b)8.42 ± 0.91 [7–9.1] (ab)7.61 ± 1.91 [5.2–10] (ab)1.38e-14Costa length [mm]1.59 ± 0.32 [1.07–2.02] (a)0.81 ± 0.25 [0.25–1.07] (c)0.8 ± 0.13 [0.62–1.07] (c)1.68 ± 0.36 [1.12–2.35] (a)1.13 ± 0.12 [1.05–1.35] (bc)1.51 ± 0.19 [1.17–1.77] (ab)6.76e-12Lateral leaf length [mm]2.15 ± 0.31 [1.62–2.55] (ab)1.8 ± 0.20 [1.5–2.12] (b)1.31 ± 0.14 [1.05–1.52] (c)2.20 ± 0.36 [1.6–2.72] (a)1.77 ± 0.22 [1.62–2.12] (bc)2.00 ± 0.32 [1.37–2.5] (ab)2.58e-08Lateral leaf width [mm]0.99 ± 0.18 [0.77–1.27] (a)0.95 ± 0.11 [0.85–1.22] (a)0.74 ± 0.13 [0.6–1] (b)0.81 ± 0.18 [0.57–1.15] (ab)0.93 ± 0.07 [0.85–1.02] (ab)0.86 ± 0.13 [0.62–1] (ab)0.00181Lateral leaf length/ width2.20 ± 0.30 [1.83–2.80] (bc)1.82 ± 0.24 [1.45–2.42] (cd)1.79 ± 0.22 [1.5–2.16] (d)2.77 ± 0.50 [2.36–4] (a)1.88 ± 0.12 [1.71–2.07] (bcd)2.33 ± 0.14 [2.14–2.5] (b)3.97e-09Dorsal leaf length [mm]1.23 ± 0.17 [1–1.42] (a)0.87 ± 0.15 [0.65–1.02] (c)0.94 ± 0.15 [0.75–1.17] (bc)1.22 ± 0.34 [0.75–1.6] (ab)0.83 ± 0.21 [0.62–1.1] (c)0.97 ± 0.19 [0.75–1.25] (abc)0.000278Dorsal leaf width [mm]0.43 ± 0.073 [0.35–0.6] (ab)0.34 ± 0.16 [0.12–0.5] (b)0.49 ± 0.09 [0.37–0.62] (a)0.32 ± 0.07 [0.225 –0.425] (b)0.46 ± 0.17 [0.3–0.7] (ab)0.43 ± 0.08 [0.35–0.6] (ab)0.0086Dorsal leaf length/ width2.90 ± 0.43 [2.33–3.8] (abc)3.20 ± 1.74 [2.05–6.4] (ab)1.93 ± 0.24 [1.76–2.4] (c)3.76 ± 0.56 [3–4.26] (a)1.84 ± 0.23 [1.57–2.08] (c)2.25 ± 0.24 [1.68–2.5] (bc)2.51e- 05Median cell length [μm]170 ± 30.68 [125–222.5] (a)127.25 ± 21.87 [90–150] (b)79.75 ± 19.38 [62.5–110] (c)112.25 ± 17.96 [85–137.5] (b)120 ± 6.84 [112.5–125] (b)112.5 ± 8.57 [100–127.5] (b)3.44e- 11Median cell width [μm]34.5 ± 6.10 [25–45] (a)28.25 ± 3.12 [22.5–32.5] (bc)24 ± 6.47 [15–37.5] (c)24.5 ± 2.58 [20–30] (bc)31.5 ± 4.54 [27.5–37.5] (ab)25.25 ± 0.79 [25–27.5] (bc)6.29e- 06Median cell length/width5.01 ± 1.05 [3.33–7.41] (a)4.48 ± 0.42 [3.81–5] (ab)3.37 ± 0.47 [2.7–4.16] (c)4.60 ± 0.74 [3.6–6.11] (ab)3.87 ± 0.57 [3.21–4.54] (bc)4.45 ± 0.29 [4–5.1] (ab)2.38e- 05Marginal cell length [μm]210.25 ± 15.74 [187.5–237.5] (a)189 ± 34.07 [135–237.5] (a)142 ± 22.41 [115–187.5] (b)183 ± 30.06 [125–232.5] (a)175.5 ± 14.29 [152.5–187.5] (ab)147.75 ± 17.13 [125–175] (b)2.68e- 07Marginal cell width [μm]11.25 ± 1.76 [7.5–12.5] (a)10.75 ± 1.20 [10–12.5] (a)8.25 ± 1.20 [7.5–10] (b)8.5 ± 1.29 [7.5–10] (b)8 ± 1.11 [7.5–10] (b)9.5 ± 1.97 [7.5–12.5] (ab)2.91e-05*Marginal cell length/width18.83 ± 4.18 [16–29.66] (ab)17.52 ± 2.04 [13.5–20.25] (ab)17.31 ± 2.28 [13.75–21] (ab)22.05 ± 5.22 [12.5–31] (a)22.23 ± 3.26 [17.5–25] (a)15.93 ± 2.56 [12.75–20.33] (b)0.00133

Appendix 3. Model comparison of Yule model, Birth-Death model and Coalescent model with constant population size according to path sampling and stepping-stone analysis under a strict clock and an uncorrelated lognormal relaxed clock.Path sampling ln (MLE) 2ln (BF)Stepping-stone ln (MLE) 2ln (BF)ST-YL−7848.01495.54−7848.42495.55ST-BD−7770.41340.34−7770.58339.87ST-CS−7785.82371.15−7786.66372.02UCLD-YL−7646.1691.83−7648.6696.03UCLD-BD−7600. 240−7600. 640UCLD-CS−7612.1723.858−7613.6626.036Appendix 3. Model comparison of Yule model, Birth-Death model and Coalescent model with constant population size according to path sampling and stepping-stone analysis under a strict clock and an uncorrelated lognormal relaxed clock.ST, strict clock; UCLD, uncorrelated lognormal relaxed clock; YL, Yule model; BD, birth-death model; CS, coalescent model with constant popula- tion size. Marginal likelihood estimates (MLE), the difference between the models and the most likely model, as well as resulting Bayes factors (BF) are given. The best model is highlighted in bold.

Appendix 3. Model comparison of Yule model, Birth-Death model and Coalescent model with constant population size according to path sampling and stepping-stone analysis under a strict clock and an uncorrelated lognormal relaxed clock.Path sampling ln (MLE) 2ln (BF)Stepping-stone ln (MLE) 2ln (BF)ST-YL−7848.01495.54−7848.42495.55ST-BD−7770.41340.34−7770.58339.87ST-CS−7785.82371.15−7786.66372.02UCLD-YL−7646.1691.83−7648.6696.03UCLD-BD−7600. 240−7600. 640UCLD-CS−7612.1723.858−7613.6626.036Appendix 3. Model comparison of Yule model, Birth-Death model and Coalescent model with constant population size according to path sampling and stepping-stone analysis under a strict clock and an uncorrelated lognormal relaxed clock.ST, strict clock; UCLD, uncorrelated lognormal relaxed clock; YL, Yule model; BD, birth-death model; CS, coalescent model with constant popula- tion size. Marginal likelihood estimates (MLE), the difference between the models and the most likely model, as well as resulting Bayes factors (BF) are given. The best model is highlighted in bold.

Appendix 4. Performance of competing models of ancestral range estimation in the moss genus Epipterygium.LnLnde AICAICc w-AICcΔAICcDEC −49.6620.0181e-12 103.4105.8 0.0326.1DIVALIKE −46. 9420. 0221e-12 98. 099. 7 0. 470BAYAREALIKE −90.3020.0100.089 184.7152.6 6.914e-2052.9lnL, log-likelihood; n, number of parameters; d, rate of dispersal; e, rate of extinction; AIC, Akaike information criterion; AICc, Akaike information criterion corrected for small sample sizes; w-AICc, Akaike weight; ΔAICc, AICc difference; DEC, dispersal-extinction-cladogenesis; DIVA, dispersal-vicariance analysis. The best model is highlighted in bold.

Appendix 4. Performance of competing models of ancestral range estimation in the moss genus Epipterygium.LnLnde AICAICc w-AICcΔAICcDEC −49.6620.0181e-12 103.4105.8 0.0326.1DIVALIKE −46. 9420. 0221e-12 98. 099. 7 0. 470BAYAREALIKE −90.3020.0100.089 184.7152.6 6.914e-2052.9lnL, log-likelihood; n, number of parameters; d, rate of dispersal; e, rate of extinction; AIC, Akaike information criterion; AICc, Akaike information criterion corrected for small sample sizes; w-AICc, Akaike weight; ΔAICc, AICc difference; DEC, dispersal-extinction-cladogenesis; DIVA, dispersal-vicariance analysis. The best model is highlighted in bold.