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Fig. S1 Phylogenetic relationships of diploid speciesof Hordeum based on combined DMC1 and Topo6 sequences assuming anon-correlated rates relaxed clock model (implemented in BEAST). A secondarycalibration point of N (12 ± 2 Myr) taken from Blattner (2006) hasbeen applied to the node labelled ‘C’. Node support is given in terms ofposterior probabilities. Grey bars represent 95% highest posterior densityintervals of age estimates. New World species are indicated, colour codingrefers to clades defined for comparative analysis.

Fig. S2 Predicted potential distribution of 12diploid New World Hordeum species, grouped according their phylogeneticrelationship. The presence/absence maps were generated using a threshold of 10%omission. The distributions of species given by Bothmer et al. (1995)are marked with dashed lines.

Fig. S3 Relative contribution of each variable to thefinal model after 100 runs, automatically determined by Maxent. Data have beenpartitioned into training and test data (80% and 20%, respectively). Each paneldepicts error bars and median values. T = temperature (°C), P = precipitation (mm).

Fig. S4 Niche overlap indices in terms of Schoener’s Dfor the four clades of New World Hordeum and 19 distinct bioclimvariables. Each panel depicts error bars and median values.

Fig. S5 Inferred history of niche occupancy fordiploid New World Hordeum species. The chronogram from Fig. 1 isprojected into niche parameter space (given on the y-axis) such thatinternal nodes represent the mean climatic tolerances based on 100 randomsamples of the PNO profiles (see ‘Materials and methods’ section). Crossingbranches of the phylogenetic tree indicate convergent niche evolution amongtaxa from different clades. The 80% central density of climate tolerance foreach extant species is indicated by a vertical dashed line, the mean isindicated by species abbreviation (first three letters of the species epithet).Colours refer clades as defined in Fig. 1. (a) Annual precipitation (BIO 12);(b) mean temperature of the driest quarter (BIO 9); (c) precipitation of thewarmest quarter (BIO 18); (d) temperature annual range (BIO 7).

Fig. S6 Chloroplast haplotype genealogy based on thechloroplast trnL-F region for 12 diploid New World Hordeumspecies. Haplotype 1 is the root of the presented network, while HT46represents the root of the South American species. Black dots depict missingintermediate haplotypes not found in the analysed individuals. (a) Thedistribution of the haplotypes among the North American and Central Argentinespecies, (b) the distribution of the haplotypes among the three Patagonianspecies.

Fig. S7 Mismatch distributions of trnL-Fchloroplast alleles for 12 diploid New World Hordeum species. Thehistograms represent for each species the observed frequencies of pairwisedifferences among haplotypes, depicted by a grey bar. The dashed lines refer tothe expectations under the model of stable population sizes, the solid lines toexpectations under a model of population expansion.

Fig. S8 Haplotype genealogy based on sequences of thenuclear topoisomerase 6 region from 195 individuals representing the 12 diploid New World Hordeum species.

Table S1 Gene bank accession numbers of sequenced DNAregions

Table S2 Omission errors per model applying the lowest10 percentile training presence as threshold. For each species omission errorsof test records are given

Table S3 Measures of genetic diversity, neutralitytest and time of population expansion estimated by τ based on nuclear generegion topoisomerase 6, of 12 diploid New World Hordeum species, orderedby their phylogenetic relationship

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