Supplementary material in Plant Ecology Taxonomic, phylogenetic and functional diversities of ferns and lycophytes along an elevational gradient depend on taxonomic scales Takayuki Tanaka & Toshiyuki Sato (Shinshu University) tanakanaka8150@gmail.com Appendix 1 Fig. S1. The mean slopes of the last 10% of individual-based rarefaction curve as the proxy for inventory incompleteness) in 100 m, 200 m, 300 m and 400 m intervals of elevation. The values of a slope close to zero indicate saturation in the sampling, whereas those close to one indicate high levels of incompleteness. Fig. S1 Appendix 2 Table. S1. Fossil age constraints and associated lognormal distribution parameters used in BEAST analysis. clade Stem/Crown Offset Mean (SD) 1 Leptosporangiate Crown 282.0 3.63 (0.14)*1 2 Lygodium Stem 167.7 3.92 (0.38)*2 3 Scaly Tree ferns Stem 145.5 3.13 (0.55)*2 4 Marsileaceae Stem 140.2 3.84 (0.36)*2 5 Polypods Crown 121.0 3.78 (0.22)*1 6 Pteroids Stem 93.5 4.24 (0.24)*2 7 Dennstaedtia/Microlepia Stem 70.6 3.89 (0.24)*2 Stem 65.5 3.55 (0.28)*2 clade 8 Ceratopteris/Acrostichum clade 9 Onoclea Stem 55.8 3.09 (0.33)*2 10 Athyrioids Stem 37.2 3.96 (0.18)*2 11 Polygrammoids Stem 33.9 3.28 (0.23)*2 *1 We set the values of the mean in lognormal prior distribution parameters so that the median of the lognormal distribution equals the mean molecular age listed in TABLE 1 in Pryer et al. (2004), and set the values of standard deviation (SD) so that the 95% soft upper bound equals mean molecular age plus 2SD listed in TABLE1 in Pryer et al. (2004). *2 We set the values of the mean in lognormal prior distribution parameters so that the median of lognormal distribution equals the best age listed in TABLE S3 in Schuettpelz and Pryer (2009) and set the values of SD so that the 95% soft upper bound equals best age plus two times ten percent of the best age listed in TABLE S3 in Schuettpelz and Pryer (2009). Reference in Appendix 2 Pryer KM, Schuettpelz E, Wolf PG, Schneider H, Smith AR, Cranfill R (2004) Phylogeny and evolution of ferns (monilophytes) with a focus on the early leptosporangiate divergences. Am J Bot 91: 1582-1598 Schuettpelz E, Pryer KM (2009) Evidence for a Cenozoic radiation of ferns in an angiosperm-dominated canopy. PNAS 106: 11200-11205 Appendix 3 Fig. S3. Elevational pattern of (a) SES.RaoQ and (b) observed RaoQ in functional diversity without frond dissection and reproductive type of ferns and lycophytes. In SES.RaoQ, trend lines were fitted using linear and second-order polynomial regression analysis with statistical significance at the P < 0.05 level. In observed RaoQ, black circles indicate the value of RaoQ in observed species assemblages, and grey circles indicate the mean value of RaoQ in the null assemblage. The dotted lines indicate the 95% confidence interval of values obtained in the null assemblage. The dotted lines and asterisk indicate the 95% confidence interval of values obtained in the null assemblage and significant clustering or over-dispersion that deviated from the 95% confidence interval, respectively. Fig. S3 Appendix 4 Fig. S4,1. Taxonomic diversity of lycophytes along an elevational gradient based on species richness estimated using the method of linked individual-based rarefaction and extrapolation curves up to a sample size of the elevation with maximum individuals. The error bars represent 95% unconditional confidence intervals for estimated species richness. Trend line was fitted using simple ordinary least squares regression with the quadratic terms of elevations (P = 0.0534). Fig. S4,1 Fig. S4,2. Proportion of species richness of lycophytes to ferns and lycophytes along elevational gradient. Fig. S4,2