BREVIA Recently Formed Polyploid Plants Diversify at Lower Rates
Itay Mayrose,1* Shing H. Zhan,1 Carl J. Rothfels,2 Karen Magnuson-Ford,1 Michael S. Barker,3 Loren H. Rieseberg,1,4 Sarah P. Otto1 olyploidy (or whole-genome duplication) is a widespread feature of plant genomes, but its importance to evolution has long been debated. Polyploids have been postulated to be evolutionary dead ends because of the inefficiency of selection when genes are masked by multiple copies (1). However, most plant species have experienced at least one genome doubling early in their history (2), suggesting that rather than being an evolutionary dead end, polyploidy is a route to evolutionary success. A recent study (3) confirmed the ubiquity of polyploidy, with about 35% of vascular plant species being recent polyploids (“neopolyploids,” having formed since their genus arose), representing 15% of speciation events in flowering plants and 31% in ferns. It remains unknown, however, whether the abundance of polyploids is a consequence of higher diversification rates following polyploidy or of frequent polyploid formation. We estimated diversification rates of neopolyploids relative to their diploid congeners. We compiled a data set of angiosperm (n = 49) and seed-free vascular plant (SFVP, including ferns and lycophytes; n = 14) generic-level groups in which ploidy levels could be estimated from cytological and phylogenetic data (4). Over 500 ploidy shifts were inferred with a probabilistic model of chromosome number evolution that accounts for aneuploid and polyploid transitions but not diversification rate differences (5). This allowed us to label all descendants of a polyploidization event as neopolyploids, even when lacking chromosome data. heteroploid speciation, the difference in speciation rates between diploids and polyploids was no longer significant (P > 0.1). Nevertheless, the diversification rates of polyploids remained significantly lower than that of diploids (P < 10−6; fig. S2) because of the higher extinction rate of neopolyploids. The average frequency of heteroploid speciation was 31.7% for all plants, 29.7% for angiosperms, and 38.7% for SFVPs, exceeding previous estimates that ignored extinction rate differences. Our estimates for the rate at which diploids speciate via polyploidization likely represent upper bounds, however, because only phylogenies with variation in ploidy were examined and because ploidy transitions were allowed only at speciation events. The lower diversification rates of polyploids may seemingly contradict evidence of ancient polyploidization events in the genomes of most angiosperms (2). Yet we find that the expected number of paleopolyploidization events is higher than would be observed if diversification rates were equal (4). Our results indicate that polyploidy is most often an evolutionary dead end, but the possibility remains that the expanded genomic potential of those polyploids that do persist drives longer-term evolutionary success.
References and Notes
1. G. Stebbins, Chromosomal Evolution in Higher Plants (Edward Arnold, London, 1971). 2. Y. Jiao et al., Nature 473, 97 (2011). 3. T. E. Wood et al., Proc. Natl. Acad. Sci. U.S.A. 106, 13875 (2009). 4. Materials and methods are available as supporting material on Science Online. 5. I. Mayrose, M. S. Barker, S. P. Otto, Syst. Biol. 59, 132 (2010). 6. W. P. Maddison, P. E. Midford, S. P. Otto, Syst. Biol. 56, 701 (2007). Acknowledgments: We thank R. FitzJohn for instrumental help in using diversitree. Funded by Natural Sciences and Engineering Research Council Discovery grants to L.H.R. and S.P.O. Data have been deposited at Dryad (10.5061/dryad.6hf21).

P

Likelihood analyses indicated that 33% of the examined species are neopolyploids (609/2043 for angiosperms and 209/458 for SFVPs), matching earlier estimates (1, 3). Polyploidization events were not distributed uniformly across phylogenies but were disproportionately represented on the tips of the tree of life [c2 = 90.5 (all data); 48.2 1 (angiosperms); 45.1 (SFVPs); P µP. To assess significance over the whole dataset of phylogenetic studies, we used a one-sample t-test with a mean equal to 50%, testing the null hypothesis that the diploid rate should be higher than the polyploid rate half of the time (the population being all 63 phylogenetic studies). Because our statistic is a proportion we used the probit transformation prior to performing the t-test. Table S2 lists the inferred speciation, extinction, and diversification rates for all datasets analyzed.

Extending the BiSSE model to calculate polyploid speciation frequency The BiSSE analyses described above were based on the assumption that transitions between the two states under study (here, diploid and polyploid) are homogenous with respect to time and occur with equal probability at any point along the branches of the phylogeny. Moreover, in its current implementation, transitions between the two states are decoupled from speciation events: state change cannot occur simultaneously with speciation (6, 23). Thus, a speciating diploid lineage will always give rise to two diploid lineages (which may then polyploidize at a later point). These assumptions are potentially problematic when considering a trait that is associated with reproductive isolation, such as polyploidy. To allow state change to occur simultaneously with a speciation event, we derived the BiSSEness (“binary state speciation and extinction node-enhanced state shift”) model. By doing so, we could also estimate the frequency of speciation events that involve polyploidization, as detailed below. As originally formulated, BiSSE makes the assumption that no change in state occurs precisely at speciation. Therefore, to calculate the probability that a lineage just prior to node A is in state 0 and evolved as observed, BiSSE multiplies the probability that both daughter lineages (N and M) are in state 0 and evolved as observed by the rate of speciation in state 0, λ0:
DA0 (t A ) = DN 0 (t A ) DM 0 (t A )λ0 (S1)

(Equation 4a in 6). An equivalent equation is obtained for character state 1. In this formulation, speciation and character state changes are treated as independent events. Thus, these equations include only the case where the character state is the same for the ancestor A and the two descendent lineages. To relax this assumption, which in the case of polyploidy may be particularly unrealistic, we incorporated the possibility that at speciation events the two daughter lineages can change state or not:

DA0 (t A ) = DN 0 (t A ) DM 0 (t A )λ0 (1 − p0 c )
 D (t ) D (t ) D (t ) D (t )  +  N 1 A M 0 A + N 0 A M 1 A  λ0 p0 c p0 a 2 2   + DN 1 (t A ) DM 1 (t A )λ0 p0c (1 − p0 a )

no change at speciation one lineage changes both lineages change (S2)

where p0c is the probability that there is a change in character state associated with the speciation process and thus one or both lineages are in state 1 (opposite to that of the ancestral lineage), p0a is the probability that given a change in character state has occurred during speciation this change is asymmetrical such that one lineage changes state and the other one remains in the same state (half of the time this is the M lineage and half of the time the N lineage), and 1–p0c is the probability that both lineages remain in the same state.

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Because not all speciation events result in two daughter lineages that survive to the present, similar modifications were made to allow simultaneous speciation with state change along the branches, given that one of the lineages resulting from such speciation events must go extinct before the present and the other lineage must give rise to the descendant species, as observed. The above modifications resulted in the addition of four parameters to form the BiSSE-ness model: p0c, p0a, p1c, p1a (here state 0 being diploid and state 1 polyploid). Here, however, we excluded polyploid to diploid transitions (p1c = 0 and p1a = 0) since in our generic phylogenies we defined polyploids as those lineages that underwent a polyploidization event since the divergence from their generic ancestor. Additionally p0a was set to one since instant speciation via polyploidy entails one lineage becoming polyploid while the second one remaining in the diploid state, and qDP was set to zero to restrict polyploid transitions to speciation events. The only new parameter is thus p0c, denoting the frequency of speciation via polyploidy while being in the diploid state (termed heteroploid speciation in the main text), with 1–p0c being the frequency of homoploid speciation in the diploid state. We note that because of the binary division of taxa into diploids and polyploids, so that tetraploids and hexaploids, for example, are considered in the same polyploid state, we could not differentiate between homoploid and heteroploid speciation among polyploids. Table S3 lists the inferred heteroploid speciation frequency as well as other diversification statistics inferred using BiSSE-ness for all datasets analyzed.

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Supporting text
Diversification results allowing for polyploidy reversals In the diversification analyses detailed in the main text we fixed the rate of polyploid-to-diploid reversals to zero. This irreversibility assumption was introduced for several important reasons. First, allowing reversibility in the BiSSE or BiSSE-ness models would imply that it is possible for a taxon to experience a near-instantaneous halving of its genome (i.e., polyhaploidy), which is not widely accepted. Instead, diploidization is thought to be a gradual process involving the loss and differentiation of genetic material. In addition, polyploid species were defined in our studies as those lineages that underwent a polyploidization event since divergence from the common ancestor of the group examined. Thus, a lineage may be labeled polyploid even if it has a chromosome number and meiotic behavior similar to that inferred for the base of the group (although, in practice, this was not observed). Defined in this way, polyploidy is truly irreversible. Allowing reversibility in BiSSE thus contradicts the ploidy definition that we employ and the ploidy assignments. For these reasons, we believe that constraining the transition rate qPD to zero (no polyploid to diploid transitions) is justified. Nevertheless, we also explored the possibility of allowing polyploid reversals to diploidy (i.e., without the constraint qPD = 0). To ensure that neopolyploidy is still defined with respect to the group examined, the root state was fixed to the diploid state. Two analyses were then performed. The first allowed the transition rate from polyploidy to diploidy to be unconstrained. This often led to very high transition rates; both from diploidy to polyploidy and especially from polyploidy to diploidy, with qPD being on average three times as large as qDP . This typically reduced the inferred extinction rate of polyploids, reducing the signal of diversification differences between polyploids and diploids (no significant differences were observed between diploids and polyploids in their diversification rates, speciation rates, or extinction rates). Upon further investigation, the likelihood surface exhibited a ridge whereby the lack of proliferation of polyploid lineages could be explained by either high extinction or by high rates of reversion back to diploidy. Given that polyploid to diploid reversions are virtually unknown in the plant world, however, we have a strong prior expectation that reversion rates should not be high relative to the rates of polyploidization. We thus repeated our analyses constraining the transition rate from polyploidy to diploidy to be lower than the transition rate from diploidy to polyploidy. Under this model, net-diversification rates of neopolyploids were lower than that of diploids (p < 10-5; t-test across the 63 trees). This was driven primarily by the higher extinction rates of polyploid lineages (p < 10-9), while speciation rates were similar between the two ploidal states (p > 0.1). We thus conclude that only under unrealistically high reversion rates from polyploidy to diploidy would polyploids be likely to diversify at rates that are as high as that inferred for diploids. Simulating the number of ancient polyploidization events within angiosperm species We used a two-state (diploid and polyploid) birth and death process to simulate the distribution of the number of genome duplications expected in the evolutionary history of an angiosperm species since its divergence from the most recent common ancestor of angiosperms. In these simulations we assumed that variation in ploidy does not affect speciation and extinction rates. The ratio of extinction to speciation was set to 0.6, as estimated by Bokma (24) for a diverse set of angiosperm taxa. We then recorded the total number of polyploidization events that occurred in the history of each extant taxon, assuming that a certain fraction of speciation events, fhet, involve polyploidization. We ran this process 100 times, for a given fhet value, starting from a common diploid ancestor until the total number of species reached 300,000, a somewhat conservative estimate of the total number of angiosperm species (25); other estimates ranging from 250,000 to 400,000 gave similar results). Under the extent of heteroploid speciation estimated in our study (fhet = 29.7% for angiosperms), our simulations indicated that if polyploids and diploids were diversifying at equal rates we would find the traces of even more paleopolyploidization events than the 1–4 duplications observed in extant angiosperm species (>94% of the species having 5 or more; Fig. S2a). The distributions of the number of paleopolyploidization events

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obtained assuming lower rates of heteroploid speciation were also shifted to the right (Fig S2b-c). In these simulations we did not aim to account for the complex dynamics of diversification rates through time, but rather to illustrate that under a simple birth-death model our finding that neopolyploids do not diversify as much as diploids is not inconsistent with the observation of multiple paleopolyploidy events among extant taxa.

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Supporting figures
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Prob(higher diploid speciation rate)

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Figure S1|Homoploid diversification rates of diploid and polyploid taxa. The histogram shows the posterior probability for each phylogeny that the speciation (A+C), and net diversification rate (B+D) of diploid lineages were higher than that of the polyploid lineages across the 63 plant groups studied (as in Figure 1, but here restricting polyploidization to speciation events). A value of 0.8 represents a phylogeny in which diploids exhibited a higher rate than polyploids in 80% of the MCMC steps analyzed. In A and B speciation and diversification rates were calculated based on both homoploid and heteroploid speciation, while in C and D rates include only homoploid speciation. For each dataset, MCMC BiSSE-ness results were pooled across 50 trees sampled by MrBayes.

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Figure S2|Simulated distribution of the total number of genome duplications that have occurred within extant angiosperm species. A birth and death process was used to simulate the distribution of the number of genome duplications assuming equal net diversification rates of diploids and polyploids and polyploidizations occurring at speciation events with a probability, fhet, of (A) 30% (the average estimate of our angiosperm datasets), (B) 20%, and (C) 15%, resulting in an average number of past polyploidization events of 8.9, 6.0, and 4.6, respectively. In all cases the number of angiosperm species was assumed to be 300,000 (25), with a ratio of extinction to speciation of 0.6 (24).

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A

Taenitis_blechnoides-44 Jamesonia_canescens-X Anogramma_osteniana-29 Eriosorus_flexuosus-87 Cosentinia_vellea-29 Anogramma_lorentzii-X Anogramma_leptophylla_VCMexico-29 Anogramma_guatemalensis-X Anogramma_leptophylla_Turkey-29 Anogramma_caespitosa-X Anogramma_leptophylla_NZealand-26 Anogramma_novoglaciana-X Anogramma_chaerophylla_CRica-29 Anogramma_chaerophylla_Brazil-29 Pityrogramma_trifoliata-60 Pityrogramma_calomelanos-120
Gaura_macrocarpa-7 Gaura_parviflora-7 Gaura_boquillensis-7 Gaura_coccinea-14 Gaura_filipes-7 Gaura_villosa-7 Gaura_sinuata-14 Gaura_hexandra-7 Gaura_angustifolia-7 Gaura_biennis-7 Gaura_longiflora-7 Gaura_lindheimeri-7 Gaura_demareei-7 Gaura_triangulata-7 Gaura_suffulta-7 Gaura_brachycarpa-7 Stenosiphon_linifolius-7 Gaura_mutabilis-7

B

Tiquilia_plicata-8 Tiquilia_cuspidata-8 Tiquilia_darwinii-X Tiquilia_paronychioides-14 Tiquilia_nuttallii-X Tiquilia_palmeri-8 Tiquilia_conspicua-16 Tiquilia_elongata-16 Tiquilia_canescens-9 Tiquilia_greggii-9 Tiquilia_purpusii-X Tiquilia_hispidissima-9 Tiquilia_latior-9 Tiquilia_durango-X Tiquilia_gossypina-9 Tiquilia_turneri-9 Tiquilia_mexicana-9 Tiquilia_tuberculata-X

C

D

Betula_maximowicziana-14 Betula_lenta-14 Betula_alleghaniensis-42 Betula_nana-14 Betula_platyphylla-14 Betula_populifolia-14 Betula_papyrifera-28 Betula_pendula-14 Betula_neoalaskana-14 Betula_schmidtii-14 Betula_fruticosa-14 Betula_pubescens-28 Betula_humilis-14 Betula_ermanii-28

Figure S3| Ploidy transitions for several representative groups. (A) Anogramma, (B) Tiquilia, (C) Gaura/Stenosiphon, (D) Betula. Branches of the tree where polyploidization events were inferred to occur using the chromEvol methodology (5) are colored in blue. Chromosome counts appear to the right of the species name following a hyphen, where ‘X’ indicates unavailable cytological data.

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Supporting tables
Table S1|Datasets used in this study. SS = number of species sampled with sequence data, SI = number of species recognized in the ingroup, SC = number of sampled species with cytological data, %PP = percentage of neopolyploids as estimated by chromEvol, TH = tree height in terms of average number of substitutions per sitea, LH = life history attributesb, na = diversity counts not available.
Group Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Focal Group Sium s.l. Lathyrus Betula Tarasa s.l. Cuphea Fuchsia Gaura/Stenosiphon Geum + allies Centaurium Primula sect. Aleuritia/ Armerina Microseris Senecio sect. Jacobaea Campanula Rapunculus clade Tiquilia subg. Tiquilia Phacelia subg. Phacelia Viburnum Actinidia Vaccinium sect. Macropelma/ Myrtillus/Hemimyrtillus Collomia Dodecatheon/ Primula subg. Auriculastrum Achillea Erodium Pelargonium Houstonia Achimenes Mentha Orobanche + allies SS 14 52 14 36 52 34 18 23 27 19 16 26 60 18 50 42 35 50 10 41 59 67 142 15 20 15 47 SI 17 160 35 na 260 110 22 na 27 35 16 26 na 20 na 175 62 na 15 na 130 74 280 25 23 18 na SC %PP THa 6 37 14 22 39 34 18 20 26 16 16 19 43 13 50 34 30 21 7 17 54 59 0.36 0.051 0.02 0.033 0.29 0.017 0.33 0.033 0.40 0.139 0.35 0.010 0.11 0.011 0.78 0.025 0.63 0.062 0.58 0.012 0.38 0.020 0.88 0.026 0.03 0.154 0.17 0.042 0.08 0.076 0.10 0.020 0.20 0.008 0.18 0.017 0.30 0.008 0.80 0.048 0.29 0.021 0.13 0.059 LHb pr, hb pr/an, hb pr, wd pr/an, hb/wd pr/an, hb/wd pr, wd pr/an, hb pr, hb an, hb pr, hb pr/an, hb pr/an, hb/wd pr, hb pr/an, hb/wd an/pr, hb pr, wd pr, wd pr, wd an, hb pr, hb pr, hb/wd pr/an, hb pr/an, hb/wd pr/an, hb pr, hb pr/an, hb pr/an, Marker typec ITS ITS+cp nr ITS ITS ITS+cp ITS+nr+cp ITS+cp ITS ITS ITS ITS+cp ITS ITS+nr ITS ITS+cp cp ITS+cp cp cp ITS cp ITS+cp+mt ITS+cp ITS+cp cp cp Referenced (26) (27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) (52) (53)

142 0.20 0.062 15 16 15 20 0.53 0.192 0.15 0.027 0.73 0.005 0.74 0.048

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Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Eudicots Magnoliids Monocots Monocots Monocots Monocots Monocots Monocots Lycophytes Ferns Ferns Ferns Ferns Ferns Ferns Ferns Ferns Ferns Ferns

Penstemon Antirrhinum + allies Digitalis/Isoplexis Mimulus Physalis

132 32 23 86 49

271 na 23 120 na 350 100 na 30 63 14 na 25 8 32 400 150 38 na 82 69 25 43 na na na na 20 na 230 na 250 30

90 22 17 67 21 62 28 12 9 32 6 12 21 8 20 62 27 21 18 27 25 15 39 23 23 44 11 18 20 41 12 51 10

0.08 0.015 0.63 0.106 0.96 0.019 0.42 0.158 0.04 0.082 0.02 0.082 0.42 0.025 0.36 0.023 0.55 0.208 0.08 0.082 0.36 0.012 0.32 0.020 0.91 0.014 0.13 0.008 0.32 0.032 0.31 0.037 0.08 0.007 0.84 0.038 0.35 0.029 0.41 0.063 0.08 0.018 0.50 0.012 0.19 0.091 0.70 0.049 0.56 0.022 0.51 0.25 0.33 0.44 0.29 0.50 0.83 0.33 0.020 0.056 0.021 0.025 0.079 0.021 0.025 0.082

Solanum subg. Leptostemonum 131 Cerastium Silene sect. Physolychnis Gunnera 36 14 20

Aeonium/Greenovia/Monanthes 52 Aichryson Graptopetalum + allies Coreopsis Leavenworthia Cucumis Aristolochia s.l. Arisaema Lemna/Wolffia/ Wolffiella/Spirodella/Landoltia Veratrum s.l. Gagea/Lloydia Trillium s.l. /Paris s.l. Sorghum Isoëtes (“North American clade”) Asplenium subg. Ceterach + allies Asplenium (New Zealand australe group) Dryopteris (Hawaii) Anogramma + allies Argyrochosma Cyrtomium + allies Dryopteris (China) Dryopteris (North America) Hymenophyllum Lygodium 14 28 22 8 22 78 75 38 26 58 25 16 36 37 18 55 16 18 27 62 12 80 15

hb pr/an, hb/wd pr/an, hb pr/an, hb pr/an, hb/wd pr/an, hb pr/an, hb/wd pr/an, hb pr/an, hb pr, hb pr/an, hb/wd pr/an, hb pr, hb/wd pr/an, hb/wd an, hb an, hb pr, hb/wd pr, hb an, hb pr, hb pr, hb pr, hb pr/an, hb pr, wd pr, hb pr, hb pr, hb pr, hb pr, hb pr, hb pr, hb pr, hb pr, hb pr, hb

cp ITS ITS+cp ITS ITS ITS+cp+nr cp cp ITS ITS ITS+cp ITS+cp+nr ITS+cp cp ITS cp cp cp ITS ITS ITS+cp ITS+cp ITS+cp cp ITS+cp cp cp cp cp cp cp cp cp

(54) (55) (56) (57) (58) (59) (60) (61) (62) (63) (64) (65) (66) (67) (68) (69) (70) (71) (72) (73) (74) (75) (76) (77) (78-80) (81) (82) (83) (84) (85) (86) (87, 88) (89) (90) (91) (85) (92) (93) (94) (95)

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Ferns Ferns Ferns a Cheilanthes (Myriopteris clade) 37 Notholaena 21 Pellaea 18

39 38 26

28 19 10

0.38 0.031 0.14 0.032 0.17 0.035

pr, hb pr, hb pr, hb

cp cp cp

(92) (96-98) (99) (100) (101) (98, 102, 103)

Tree height was calculate based on the ML tree obtained using phyML by traversing the tree from the tips to the root. For each internal node, its height was calculated as the average height of the lineages descending from that node, finally reaching the root node. b Life history characteristics are given based on the majority of species in the group as follows: pr = perennials; an = annuals or biennials; hb = herbaceous; wd = woody (trees/shrubs). Data were obtained through eflora (http://www.efloras.org/), Mabberley (17), or the original phylogenetic study. c nr: nuclear; cp: chloroplast; mt: mitochondrial; ITS: the nuclear internal transcribed spacer d Diversity and cytology references are given to the right if different from the main reference or from Mabberley (17)

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Table S2|BiSSE diversification analysis. λ D and λ P = average inferred speciation rate of diploids and polyploids over the MCMC BiSSE sample, respectively; µD and µP = average extinction rate of diploids and polyploids, respectively; %(rD > rP) = the percentage of MCMC BiSSE steps in which the diversification rate of diploid lineages were higher than that of the polyploid lineages; %(λD > λP) and %(µD > µP) are the percentage of MCMC BiSSE steps in which the speciation and extinction rates of diploid lineages were higher than that of the polyploid lineages, respectively.

Focal Genus Sium s.l. Lathyrus Betula Tarasa s.l. Cuphea Fuchsia Gaura/Stenosiphon Geum + allies Centaurium Primula sect. Aleuritia/Armerina Microseris Senecio sect. Jacobaea Campanula: Rapunculus clade Tiquilia subg. Tiquilia Phacelia subg. Phacelia Viburnum Actinidia Vaccinium sect. Macropelma/ Myrtillus/Hemimyrtillus Collomia Dodecatheon/ Primula subg. Auriculastrum Achillea Erodium Pelargonium Houstonia Achimenes Mentha Orobanche + allies Penstemon Antirrhinum + allies Digitalis/Isoplexis Mimulus Physalis Solanum subg. Leptostemonum Cerastium Silene sect. Physolychnis Gunnera Aeonium/Greenovia/Monanthes Aichryson Graptopetalum + allies Coreopsis

λD
69.29 253.08 293.58 138.64 47.15 302.65 236.23 129.74 111.88 725.99 257.78 311 44.49 89.67 42.63 268.44 1574.39 118.85 642.53 96.41 444.56 300.8 123.62 31.74 151.7 605.34 85.97 448.61 18.97 281.76 60.12 49.43 96.95 748.66 184.25 67.1 233.87 240.39 5.32 451.9

λP
58.91 148.5 171.61 142.19 45.6 448.59 207.85 59.41 97.37 463.22 197.19 212.94 48.03 132.23 43.81 93 507.8 59.01 776.59 208.86 1139.26 153.16 127.42 13.72 124.39 708.16 55.74 456.15 50.8 245.59 107.26 20.7 82.84 410.51 326.24 53.91 64.12 92.95 2.74 160.37

µD
47.98 128.33 118.93 34.07 14.8 73.17 79.79 57.68 57.76 302.35 117.62 151.14 11.17 35.15 7.9 127.06 755.33 20.38 369.14 42.18 104.86 205.06 27.32 23.11 42.8 363.28 32.01 87.83 8.98 200.3 27.93 10.8 24.78 278.33 86.48 45.23 171.81 102.83 1.48 259.7

µP
40.9 586.22 442.12 179.75 26.19 233.75 548.33 43.47 189.51 864.45 489.44 240.03 187.25 208.06 146.56 386.87 2851.16 57.23 1242.46 121.38 1516.58 478.27 175.51 20.27 321.9 435.63 59.01 685.47 17.39 179.23 43.88 50.65 98.08 1275.62 467.6 87.34 383.09 345.12 2.84 111.46

%(rD > rP) 0.58 0.81 0.79 0.52 0.56 0.22 0.66 0.94 0.61 0.78 0.7 0.73 0.6 0.38 0.6 0.97 0.93 0.9 0.48 0.04 0.07 0.88 0.52 0.9 0.7 0.35 0.83 0.52 0.01 0.53 0.04 0.89 0.67 0.88 0.27 0.67 0.96 0.89 0.9 0.96

%(λD > λP) 0.54 0.08 0.1 0.08 0.32 0.21 0.07 0.57 0.02 0.1 0.07 0.27 0.01 0.08 0.01 0.57 0.05 0.26 0.14 0.19 0.02 0.1 0 0.55 0.08 0.46 0.25 0.02 0.33 0.48 0.36 0.23 0.18 0.03 0.07 0.15 0.13 0.14 0.29 0.73

%(µD > µP) 0.5 0.98 0.95 0.9 0.84 0.55 0.93 0.87 1 0.99 0.96 0.88 0.96 0.82 0.96 1 1 0.97 0.81 0.33 0.85 1 1 0.84 0.95 0.41 0.91 0.97 0.07 0.53 0.08 0.98 0.94 1 0.78 0.99 1 0.98 0.95 0.77

14

Aristolochia s.l. Leavenworthia Cucumis Arisaema Lemna/Wolffia/ Wolffiella/Spirodella/Landoltia Veratrum s.l. Gagea/Lloydia Trillium s.l./Paris s.l. Sorghum Isoëtes (“North American clade”) Asplenium subg. Ceterach + allies Asplenium (New Zealand australe group) Dryopteris (Hawaii) Anogramma + allies Argyrochosma Cyrtomium + allies Dryopteris (China) Dryopteris (North America) Hymenophyllum Lygodium Cheilanthes (Myriopteris clade) Notholaena Pellaea

145.93 382.52 128.85 590.6 90.04 200.19 42.89 372.81 204.56 202.34 97.76 283.59 311.86 94.84 177.96 237.5 395.57 147.2 239.01 69.49 168.33 99.75 16.93

274.68 326.22 43.72 439.21 103.84 225.62 27.86 173.27 244.22 32.8 93.32 63.62 190.6 37.62 236.47 314.01 236.16 182.92 151.4 46.9 108.98 60.81 3.89

43.64 317.2 51.45 189.77 54.58 158.5 24.2 194.23 106.89 136.2 30.35 145.62 76.62 67.12 57.3 77.85 170.91 77.26 89.26 33.35 37.27 25.72 11.36

122.26 956.36 215.38 962.84 47.32 133.9 25.81 360.85 232.05 182.65 79 370.58 479.91 69.54 401.97 620.52 311.75 334.64 22.86 80.85 341.34 127.05 12.7

0.02 0.65 0.93 0.78 0.33 0.41 0.83 0.86 0.42 0.99 0.55 0.98 0.88 0.9 0.41 0.35 0.9 0.43 0.93 0.75 0.79 0.79 0.97

0.2 0.15 0.04 0.09 0.5 0.59 0.47 0.35 0.22 0.37 0.22 0.08 0 0.51 0.05 0 0.22 0.07 0.82 0.2 0.01 0.13 0.48

0.24 0.87 1 0.99 0.29 0.29 0.88 0.95 0.78 1 0.81 1 1 0.88 0.86 0.99 1 0.9 0.68 0.95 1 0.95 0.99

15

Table S3|BiSSE-ness diversification analysis. %HS = average heteroploid speciation frequency inferred over the MCMC BiSSE sample; %(rD > rP) = the percentage of MCMC BiSSE steps in which the diversification rate of diploid lineages was higher than that of the polyploid lineages; %(λD > λP) and %(µD > µP) are the percentage of MCMC BiSSE steps in which the speciation and extinction rate of diploid lineages were higher than that of the polyploid lineages, respectively; %(rD > rP)h and %(λD > λP)h are the percentage of steps in which the diversification and speciation rate of diploid lineages were higher than that of the polyploid lineages, respectively, accounting for homoploid speciation only.
%HS 0.34 0.07 0.35 0.34 0.18 0.14 0.22 0.5 0.61 0.56 0.42 0.69 0.16 0.23 0.19 0.14 0.33 0.24 0.33 0.4 0.3 0.13 0.16 0.33 0.24 0.41 0.38 0.09 0.22 0.65 0.06 0.12 0.03 0.58 0.36 0.46 0.16 0.41 0.31

Focal Group Sium s.l. Lathyrus Betula Tarasa s.l. Cuphea Fuchsia Gaura/Stenosiphon Geum + allies Centaurium Primula sect. Aleuritia/ Armerina Microseris Senecio sect. Jacobaea Campanula: Rapunculus clade Tiquilia subg. Tiquilia Phacelia subg. Phacelia Viburnum Actinidia Vaccinium sect. Macropelma/ Myrtillus/Hemimyrtillus Collomia Dodecatheon/ Primula subg. Auriculastrum Achillea Erodium Pelargonium Houstonia Achimenes Mentha Orobanche + allies Penstemon Antirrhinum + allies Digitalis/Isoplexis Mimulus Physalis Solanum subg. Leptostemonum Cerastium Silene sect. Physolychnis Gunnera Aeonium/Greenovia/Monanthes Aichryson Graptopetalum + allies

%(rD > rP) 0.43 0.96 0.95 0.93 0.87 0.68 0.94 0.82 1 0.99 0.96 0.91 0.97 0.84 0.96 1 1 0.98 0.82 0.44 0.79 1 0.99 0.83 0.97 0.43 0.91 0.97 0.13 0.52 0.1 0.98 0.95 1 0.73 0.98 1 0.98 0.96

%(λD > λP) 0.58 0.8 0.81 0.77 0.62 0.3 0.76 0.95 0.84 0.89 0.85 0.87 0.66 0.49 0.7 0.97 0.97 0.95 0.54 0.08 0.06 0.94 0.7 0.87 0.81 0.35 0.96 0.65 0.01 0.59 0.02 0.91 0.7 0.88 0.34 0.74 0.96 0.98 0.98

%(µD > µP) 0.65 0.09 0.1 0.16 0.3 0.21 0.1 0.7 0.01 0.09 0.12 0.26 0.01 0.08 0.02 0.63 0.08 0.39 0.12 0.15 0.01 0.24 0.04 0.53 0.13 0.42 0.52 0.04 0.31 0.55 0.32 0.35 0.21 0 0.09 0.12 0.14 0.28 0.54

%(rD > rP)h 0.22 0.96 0.93 0.82 0.72 0.55 0.92 0.32 0.98 0.95 0.91 0.34 0.97 0.81 0.96 1 1 0.91 0.76 0.2 0.76 1 0.97 0.66 0.94 0.19 0.6 0.96 0.07 0.07 0.07 0.97 0.95 1 0.67 0.92 1 0.94 0.85

%(λD > λP)h 0.34 0.77 0.66 0.44 0.42 0.21 0.67 0.55 0.18 0.48 0.61 0.12 0.59 0.36 0.62 0.95 0.87 0.85 0.35 0.01 0.01 0.89 0.51 0.67 0.71 0.13 0.62 0.6 0 0.13 0.02 0.88 0.68 0.55 0.16 0.37 0.92 0.89 0.88

16

Coreopsis Aristolochia s.l. Leavenworthia Cucumis Arisaema Lemna/Wolffia/ Wolffiella/Spirodella/Landoltia Veratrum s.l. Gagea/Lloydia Trillium s.l./Paris s.l. Sorghum Isoëtes (“North American clade”) Asplenium subg. Ceterach + allies Asplenium (New Zealand australe group) Dryopteris (Hawaii) Anogramma + allies Argyrochosma Cyrtomium + allies Dryopteris (China) Dryopteris (North America) Hymenophyllum Lygodium Cheilanthes (Myriopteris clade) Notholaena Pellaea

0.6 0.01 0.29 0.44 0.19 0.5 0.06 0.2 0.11 0.29 0.17 0.45 0.65 0.59 0.16 0.4 0.57 0.29 0.53 0.32 0.3 0.5 0.2 0.27

0.73 0.14 0.87 1 0.99 0.4 0.3 0.86 0.94 0.8 1 0.75 1 1 0.86 0.88 0.96 1 0.91 0.77 0.95 1 0.97 0.98

0.94 0.16 0.64 0.96 0.86 0.43 0.43 0.88 0.89 0.59 1 0.57 0.99 0.99 0.96 0.5 0.45 0.97 0.55 0.97 0.84 0.97 0.87 0.98

0.81 0.42 0.1 0.06 0.17 0.5 0.61 0.59 0.39 0.3 0.73 0.26 0.05 0.01 0.72 0.05 0.01 0.34 0.06 0.84 0.28 0.02 0.19 0.58

0.15 0.13 0.85 0.99 0.98 0.05 0.26 0.68 0.93 0.63 1 0.35 1 1 0.78 0.82 0.91 1 0.81 0.13 0.9 1 0.96 0.96

0.43 0.15 0.52 0.84 0.77 0.1 0.39 0.71 0.85 0.36 1 0.11 0.78 0.44 0.92 0.23 0.06 0.87 0.19 0.6 0.69 0.71 0.8 0.95

17

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