Supporting Information Tables S1 & S2 Table S1 Polyploid complexes analyzed phylogenetically, not included in Mayrose et al. (2011) Aegilops/Triticum (Poaceae) Given that the polyploid species of Triticum involve several species of Aegilops as parents, the genus Triticum is clearly not monophyletic, Aegilops is also not monophyletic (Petersen et al., 2006; Bordbar et al., 2011). We consider them together – both exemplify considerable diversification at the polyploid level. Estimates of the number of species in Aegilops varies from 22 to perhaps as many as 29 species comprising both diploids and polyploids, using the higher species estimate, 11 are diploid (2n = 14), 13 are tetraploid (2n = 28), and five are hexaploid (2n = 42). Triticum comprises 11 species and includes three diploids (2n = 14), 6 tetraplods (2n = 28) and two hexaploids (2n = 42) including T. aestivum (common wheat). Consolea (Cactaceae) Consolea (Cactaceae) is an entirely polyploid genus of 9 species (Areces-Mallea 2001), species range from hexaploid (2n = 66) to dodecaploid (2n = 132) (Negrón-Ortiz 2007, Baker et al., 2009, Majure et al., 2012a) relative to the base number of n = 11 for all Cactaceae (Pinkava, 2002). Consolea forms a well-supported clade with the parents being some member of Opuntia s.s. and another member of tribe Opuntieae outside of the Tacinga-Brasiliopuntia-Opuntia clade (Majure et al., 2012b). However, using a genuslevel approach, as in Mayrose et al. (2011), hexaploid members (2n = 66) of the Consolea clade would be diploid and those octoploid (2n = 88) and higher ploidal levels (e.g., dodecaploids, 2n = 132) would be derived polyploids. Clearly the entire clade is polyploid (Majure et al., 2012b). Draba (Brassicaceae) Draba L. (Brassicaceae) comprises approximately 400 species. Of the 43% of the genus for which chromosome counts are available 78% are polyploid (Windham 2000, 2003, Jordon-Thaden & Koch, 2008). Draba ranges in ploidy from diploid (2n = 16) to octadecaploid (18n = 144) with numerous stable levels in between (mostly 4n, 6n, 8n, 10n). Draba has a highly accelerated rate of speciation and polyploidization (JordonThaden & Koch, 2008). Polyploidy has also played a major role in each of the three major clades (Jordon-Thaden et al., 2010). There is also strong evidence of cryptic speciation within arctic polyploids as well as recurring polyploid formation, resulting in high species diversity among polyploids (Grundt et al., 2006). High rates of speciation and polyploidization in Draba since the Pleistocene indicates that polyploidy continues to play an integral role in the diversification of the genus. Elymus (Poaceae) Elymus includes ~ 150 perennial species distributed in a wide range of ecological habitats over the temperate and subtropic regions. In Triticeae, the basic number is x = 7 (Wang et al., 1995). The chromosome numbers in Elymus range from 2n = 4x = 28 to 2n = 8x = 56 (~ half of the counts available have 2n = 42). The lowest number in Elymus is actually already tetraploid (2n = 28), these would be considered diploid following Mayrose et al. (2011). Several phylogenetic analyses of the genus have been published (Liu et al., 2006, Zhang et al., 2009). Festuca (Poaceae) Festuca (Fescue) is one of the largest genera of Poaceae. It comprises about 600 species and has a worldwide distribution. About 70% of species are polyploid (with ploidal levels up to 12x); several phylogenetic analyses have been conducted (Catalán et al., 2004, Šmarda et al., 2008). Fragaria (Rosaceae) Fragaria (Rosaceae) comprises 20 named species, 11 of which are diploid (2n = 14)—the remaining species are polyploid. Five are 4x, one is 6x, two are 8x, and one is 10x. Gossypium (Malvaceae) Gossypium (cotton, Malvaceae) consists of about 50 species – 45 diploid and 5 polyploid (tetraploid) and includes two polyploid species that were domesticated (G. barbadense, G. hirsutum). Grover et al. (2012) recently demonstrated the monophyly of the tetraploid species of Gossypium. Madlung (2013) recently noted Gossypium as a good example of a polyploid radiation in his review. Hedera (Araliaceae) The genus Hedera (Araliaceae) is a polyploidy complex with approximately 16 taxa (Rutherford et al., 1993, Ackerfield & Wen, 2002, 2003). Clades of diploids (2n= 24) and polyploids (2n = 48, 72, 96, one species has 2n = 192) are geographically structured suggesting recurrent genome duplication in this group. Approximately 60% of Hedera species are polyploids (Vargas et al., 1999, Green et al., 2011). Hordeum (Poaceae) Hordeum (Poaceae) comprises 31 species with a nearly worldwide distribution. About 50% of the species are polyploids (4x, 6x) or have both diploid and polyploid forms (Blattner, 2004, Brassac et al., 2012). Nicotiana (Solacnaceae) Nicotiana (Solanaceae) comprises 75 naturally occurring species (40 diploids and 35 allopolyploids), the genus exhibits a mix of young as well as old polyploid members. There are recently formed allotetraploids (less than 200,000 years, most of which are associated with human habitation (e.g. N. tabacum). In sect. Repandae there are 4 polyploid species estimated to be 5 mya. Sect. Suaveolentes consists of 26 species, all polyploid, and appears to still be diversifing. The clade has basal members with n = 24 and then descend to as low as n = 15 in two groups via reduction. The polyploids in this clade are at least 10 my old (Clarkson et al., 2004, Chase et al., 2003, M. Chase pers. Comm.). Opuntia (Cactaceae) Opuntia (Cactaceae) is a strictly New World genus distributed from southern South America to Canada and consisting of around 200 species. Divergence time estimation reveals a very young age for the genus as well at 5.6 ± 1.9 mya (Arakaki et al., 2011). The base number in the family Cactaceae, and thus the genus Opuntia, does not deviate from n = 11 (Pinkava 2002). The majority of species of Opuntia are polyploid ranging from triploids (2n = 33) to nine-ploids (2n = 99). Of the 150 species with reported chromosome numbers, 59 % were polyploid, 12 % were represented by both diploid and polyploid counts, and only 29 % were recorded as diploid (Majure et al., 2012a). Hybridization is common in Opuntia, and recent phylogenetic analyses recorded numerous allopolyploid, interclade hybrids in the genus (Majure et al., 2012b). However, polyploids are also very commonly derived from within clades as well. Nine of the ten major clades of Opuntia consist of both diploid and polyploid taxa (Majure et al., 2012b). Findings from Majure et al. (2012b) also emphasize the problems with including taxa derived from reticulate evolution in the bifurcating framework of phylogenetic analyses. Paeonia (Paeoniaceae) Paeonia comprises 35 species distributed widely in five disjunct areas in the northern hemisphere. Three sections are recognized within Paeonia (reviewed in Sang et al., 1997). Section Oneapia, (2 species – both diploid), Section Moutan with six species, all diploid), Section Paeonia consists of 27; one-third of the species in section Paeonia are tetraploids. A phylogeny has been provided by Sang et al. (1997). Rubus (Rosaceae) Rubus (Rosaceae) includes ∼750 species, it is evolutionary complex and one of the most systematically challenging genera of plants. Rubus is taxonomically/evolutionary complex because of frequent hybridization, morphological diversity, vegetative propagation, asexual seed production, and a high frequency of polyploidy. Approximately 60% of all Rubus species are polyploid. A phylogenetic framework was provided by Alice & Campbell (1999). Tacinga (Cactaceae) Tacinga (Cactaceae) is a genus of 8 species restricted to the Caatinga of Brazil and northern Venezuela (Majure et al., 2013). Of those 8 species, 3 have been recorded as polyploid (tetra- and hexaploid levels, 2n = 44, 66), and 2 species have been recorded as diploid (2n = 22, Majure et al., 2012a). Tacinga forms a well-supported clade sister to the Brasiliopuntia brasiliensis-Opuntia schickendantzii clade (Majure et al., 2012b), although species relationships are not completely resolved phylogenetically. Viola (Violaceae) Viola (Violaceae) contains 500–600 species and comprises numerous hybrid and polyploid complexes. From a putative base number of x = 6 or x = 7, extant chromosome numbers range from 2n = 4 in V. modesta to at least 20-ploid 2n = ca. 160 in Viola arborescens. Many members of Viola are considered high polyploids (with more than six sets of nuclear chromosomes). The work of Marcussen et al. (2012) supported the monophyly of the high polyploids, which resulted from allodecaploidization 9–14 Ma, involving diploid and two paleotetraploid ancestors. Two of the high-polyploid lineages remained decaploid, recurrent polyploidization with tetraploids within the last 5 Ma has resulted in two 14-ploid lineages and one 18-ploid lineage (reviewed in Marcussen et al., 2012). Polyploid speciation has been the major contributor to the diversification of this genus (Marcussen et al., 2012). Table S2 Other polyploid complexes in need of investigation Genus Family References Antennaria Asteraceae Bayer & Stebbins, 1987, Bayer et al., 1996 Arctostaphylos Ericaceae Artemisia Asteraceae Bromus Poaceae Boykin et al., 2005 Torrell et al., 2001, Valles et al., 2001 Ainouche & Bayer, 1997, Fortune et al., 2008 Campanula rotundifolia Campanulaceae Kovanda, 1977 Orobanchaceae Heckard & Chuang, 1977, Chaung & complex Castilleja Heckard, 1993, Tank & Olmstead, 2008 Clarkia Onagraceae Lewis, 1953, Lewis & Lewis, 1955, Stebbins, 1971, Grant, 1981 Claytonia Montiaceae Lewis, 1970, Stebbins, 1971, Doyle, 1983 Crataegus Rosaceae Talent & Dickinson, 2005, Lo et al., 2009, Lo et al., 2010 Crepis Asteraceae Babcock & Stebbins, 1938, Stebbins, 1950, 1971 Danthonia Poaceae Stebbins, 1971 Drosera Droseraceae Rivadavia et al., 2003 Galium anisophyllum Rubiaceae Stebbins, 1971 Glycine Fabaceae Doyle, 2012 (review) Hieracium Asteraceae Fehrer et al., 2007, Fehrer et al., 2009 Iris Iridaceae Mitra, 1956, Stebbins, 1971 Micranthes Saxifragaceae Webb & Gornall, 1989, Soltis et al., complex 1996 Poa Poaceae Rubus Rosaceae Soreng, 2007, Soreng et al., 2010 Alice & Campbell, 1999, Alice et al., 2001, Morden et al., 2003 Rumex paucifolius Polygonaceae Smith, 1968 Salicaceae Azuma et al., 2000, Brunsfeld et al., complex Salix 1991, Mabberley, 1997, Soltis & Soltis, 1990, Stebbins, 1971 Saxifraga Saxifragaceae Webb & Gornall, 1989, Soltis et al., 1996 Tradescantia Commelinaceae Martínez & Ginzo, 1985 Vaccinium Ericaceae Lyrene et al., 2003 References Ackerfield J, Wen J. 2002. 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