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NeighborNet of performance phylogenetic signature The analysis. phylogenies. conflicting ephemeral bootstrap as an interpretable parsimony identifying easily to of were worse capable that comparable performed topologies networks was spanning yield Minimum NeighborNet not methods. did of network and two methods of taxa sampled use tree-based between the most flow explored gene than we when alternative, justify phylogenetic an to delimiting difficult As or is bifur- possible. purposes, defining standard is conservation of of for purposes populations use the prioritizing the for for that groups or taxa monophyletic conclude species, reticulate We terminal before reconstruction. identify systems phylogeny to natural of methods in required tree-based methods Based be cating tree-based simulation. may using events the detected flow of gene reliably meth- phases of tree-based be thousands some Bifurcating will many performance. during that relative estimate appearing assessing we topologies gradual model, for a incorrect the our metric that on used supported, a We highly hypothesis as hybridization. with null introgressive flow poorly, of gene the performed stages continued of ods with early rejection error the erroneous I during phenetic, type true (the likely of of were was error erosion monophyletic) that performance I not taxa relative type is and examined, interest the history of methods reticulate evaluated taxon all known we In with evolu- sets data, groups. taxa data an between simulated monophyletic to in distinguishing terminal applied Using reticulation for been cause nature. approaches frequently to in network have hybridization and evolution hybridize via tree-based, of to model flow bifurcating known gene strictly for taxa a potential containing on obvious based the methods analytical of tree, spite tionary In groups. other and plants Abstract.— oit fSseai Biologists Systematic of Society yrdzto sawl-ouetd aua hnmnnta scmo tlwtxnmclvl ntehigher the in levels taxonomic low at common is that phenomenon natural well-documented, a is Hybridization fPeei,Te-ae,adNtokProcedures Network and Tree-Based, Phenetic, of otClisClrd 02,UA -al rcadlmrclsaeeu(C.M.R.) 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Crandall, therein; and citations and Posada 2000, Legendre, Nixon, 1995; and Doyle, Davis 1990; 1992; Wheeler, and Nixon 1990; Dade, Mc- 1979; Wanntorp, and Bremer 1975; been (Sneath, has criticized processes evolutionary reticulate sets from data derived to methods”) (“tree-based trees bifurcating and phylo- reticulate of relationships. production genetic the is taxa gene between of flow consequence One taxa obvious. between is populations alleles weak; as of such be movement to for believed potential generally the level, thus, are species flow nature the gene to in Below barriers 1997). occurs between Arnold, flow 1959; gene hybridization Knobloch, (Stebbins, interspecific 1971; that that (Grant, and known possible 1972) is is species it plant many 1996), al., et taxa. from different individuals two involves that de- reproduction and herein as fined is Goldstein “Hybridization” 1990; others). and Nixon, 2000; and DeSalle, Wheeler its by of argued spite (as in intent original usage, (1966) Hennig’s common from be- deviation the purported We become ancestor. has common this single that lieve a organisms from of descended group and a has Queiroz indicate de to (1988), by the termi- Donoghue expanded use We as as 1988). “monophyletic,” use Donoghue, term and for Queiroz appropriate (de taxa” units nal are inclusive “populations least because the populations, include to level h plcto fmtosta rdc hierarchical produce that methods of application The (Ellstrand debated been has ubiquity its Although .R M. ICHARDS 1111 ot ao Street, Mason South Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 nsm ae fitrpcfi yrdzto n many and hybridization interspecific of cases (e.g., weak some are hybrids in reproduction F1 to barriers over biological predominate when back- will complex individuals However, crossed individuals. outnum- backcrossed may hybrids ber F1 cases hybridization) some in interspecific (e.g., of taxa between flow gene prevent to ate tree. resulting include the (which in taxa individuals, individuals), reticulate) hybrid backcrossed (or F1 hybrid of to fate opposed the as consider undesirable and only 2003); they them al., (2) et make (Scotland that reconstruction phylogeny features for other Ellstrand, and and (Rieseberg 1993), hybrids in inheritance of terns pat- unpredictable nonindependence, to prone characters, are morphological which on relied they (1) termi- because his- tory reticulate distinguish a with to taxa from is lineages monophyletic goal nal the provide if studies guidance un- were these incomplete present phenomenon, topology our the tree of to overall derstanding essential on Although effect predictable. its less and hybrid tree the of the par- position the derived in time, most the of the remainder containing The time) clade ent. the the to that of tree basal most-parsimonious (65% was the in often position were a at hybrids resolved F1 charac- artificial morphological ters, considering when 1997) that, 1992, showed (1990, McDade by studies 1985). empirical Funk, Detailed 1980; Platnick, and Nelson and 1979; Wanntorp, (Bremer analysis cladistic tree-based, on bridization solution. satisfactory a methods offer alternative analysis whether of test arguably bias to may (2) an and analysis which conclusions, tree-based in of manner application de- and illegitimate to degree (1) the important therefore termine is It concerns. clearly articulated numerous, despite of sets analysis data the reticulate for potentially used routinely be to tree-based continue Moreover, methods sets. data simulated only known considered nonreticulate but methods with correct network per- some sets the of reveal examined formance (2005) data to al. et to Cassens ability history. reticulate applied their when for relationships evaluated been not networks. using routine from homoplasy signal is reticulate It true distinguish sets. hy- to data difficult as all by virtually caused such in be present processes homoplasy, also routine may reticulate but to recombination or Conflicting due bridization set. be data may underlying signal the phy- conflicting in of signal consequence a within logenetic as Cycles arise set. can data network single a a acceptable of for set solutions (or result the alternative summarize a cycles to are used graphs algorithm contain these the of in that present cycles graphs The “loops”). produce 1994; can 1990; and Legendre Smouse, methods 2000; network (Hein, methods, Xu, and tree-based 2000; Unlike 2002). al., Makarenkov, Excoffier data et Bandelt 1992; 1997; such be Fitch, al., to et analyzing claim Templeton that for developed phyloge- been appropriate have “network” methods) termed netic (collectively procedures 2007 ncssweepszgtcioaigmcaim oper- mechanisms isolating postzygotic where cases In hy- of consequences the explored have studies Past have methods network most promise, their of spite In R EE N IHRSDSIGIHN OOHL RMRETICULATION FROM MONOPHYLY RICHARDS—DISTINGUISHING AND EEVES n hlgntcsga.Dpnigo admgenetic random on conflict- Depending in signal. resulting a phylogenetic taxon, from recipient ing states a into character taxon of donor introgression by followed may be unidi- hybridization taxa, of two case between simplified flow gene the rectional In hybrids). F1 states predictable with readily character not (unlike is of taxa level such distribution of species individuals the among the because at below studies spe- and pose empirical to for likely problems are cial taxa Reticulate understood. not well is reconstruction phylogeny on sequences) or viduals sequence was recombinant sequences single non-recombinant of a considered. tree only larger a of within fate be- the populations natural cause to Crandall extended easily and not Posada are reconstruc- of (2002) phylogeny conclusions of the However, accuracy tion. the less be impact to to character- shown likely with were individuals Sequences back-crossed tree. of true istics the with to reconstruction, relative nonhybrid tree taxa among is erroneous sequence rearrangements analyses topological in the frequent phylogenetic result of in to parent) 50% likely that each hybrids with to suggest F1 sequence belonging of to characteristics recombinant interpreted with in (a taxa be of purpose may inclusion different the study a the par- with each mind, conceived by proportion Although contributed the sequence relation-ent. recombinant and topological the sequences the of “parent” on between dependent in ship is sequences recombinant analysis including as an of well impact as the showed They that hybrids, analyzed. F1 were individuals, of back-crossed characteristics se- with recombinant when quences methods analytical tree-based of recon- the of of accuracy effect phylogeny. the the structed on consider however, sequences not, recombinant with did not They shape, were sequences present. tree recombinant branches when found in internal were shorter than change and branches predictable terminal longer a and analy- caused phylogenetic distance- ses (ML)-based in the likelihood sequences that maximum recombinant found (2000) of reticu- Hein inclusion with and individual Schierup an ancestry. in late many scored if were expected loci be re- would unlinked that assem- single states chimeric character a the of blage because mimics sequence relevant DNA are combinant studies These Crandall, 2002). and Posada 2000; Hein, and (Schierup phylogenetic analyses in sequences DNA recombinant simulated tree- of applicability data. the reticulate to verifying methods based of only is component reconstruction phylogeny one on rare hybrids F1 be the of understanding often effect individuals, will back-crossed hybrids genotypes to F1 relative migrant, Because to 1950). opposed selection (Stebbins, as be because resident, will and favor hybrid population may F1 local rare the a of for members mates the potential because of is This majority hybridization). intraspecific of cases h feto eiuaetx a poe osnl indi- single to opposed (as taxa reticulate of effect The accuracy the examined (2002) Crandall and Posada Two tde aecniee h feto including of effect the considered have studies 303 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 hlgntcsga ndt esdrvdfo reticulate from derived processes. sets historical data in signal 1998), phylogenetic (Trueman, (RSW) atr weighting and methods successive network we two reverse addition, of In performance structure. the tree-like do evaluate a that fit tree- methods data phenetic assume of two not as assessment well an as methods include based We introgres- of hybridization. process continuous sive a during sampled individuals be back-crossed to complex data multiple, multilocus allows a that simulating pre- employ for a We model with reticulation. population-level historical simulated of sets pattern data defined in taxa reticulate from groups monophyletic terminal distinguish to procedures inadequate of artifact an analysis are an that sampling. in conclusions included avoid be to must many taxon that per suggests individuals levels interindividual signal conflicting of in presence variation The indicate reticulation. to signal historical conflicting on rely that problem- methods for potentially among atic is taxon levels single signal a recip- within conflicting individuals the in in Variation individuals taxon. among ient observed donor be pro- the to will the traceable taxon are in that states variation character of states, portion of character fixation and introgressed event the intermediate hybridization the the between during in period Furthermore, present signif- flow. of that gene with spite in icant taxa than identify, to making less difficult potentially histories be reticulate individual, will hybrid F1 taxon individuals an recipient in present a signal of the expected Accordingly, conflicting are taxon. be of recipient that would the magnitude taxon individual in fixed hybrid donor become F1 the to the from in number states small found character a only the selection, of of strength the and drift 304 n rsl,19) h ubro usiuin e site per substitutions of (Rambaut number Seq-Gen The 1997). using Grassly, and sets data 1000-character four the for a history taxon. reticulate within a recipient infer flow to gene ability the of affected direction tree the the whether used between examine was direction, to occurred opposite the in flow but Sim2, gene as taxa same which in between relationship Sim4, topological them. the and hybridization ge- distance of explored netic terms in Sim3 both taxa, and divergent increasingly Sim2 between and taxa between taxa hybridization sister modeled between Sim1 flow considered. gene were distinct unidirectional topologically for Four alternatives evaluated. gene be in involved for can directly tree exchange those than simplest five- other the A taxa relationships topological is between 1a). on flow it gene (Fig. of because effect point the used which starting was the tree as taxon used was D),E) nti td,w vlaeteaiiyo i analytical six of ability the evaluate we study, this In ietxnsatn re eecetdb simulating by created were trees starting Five-taxon ((((A,B),C), form the of tree five-taxon unrooted An ebsdpoeueitne oietf conflicting identify to intended procedure ee-based eeaino iuae aaSets Data Simulated of Generation M TRASAND ATERIALS M ETHODS SYSTEMATIC BI osnu falms asmnosteswsfound was strict PAUP trees a a procedure, parsimonious to tree” most subsequent “best all the of For consensus data. an- to the used alyze were procedures parsimony-based Two als. (in- 1b): (Fig. mating follows The as generations. random proceeded simulation nonoverlapping with fully and selfing), model size, cluding Wright-Fisher population at a constant (available followed authors the Reproduction by written http://lamar.colostate.edu/∼reevesp/Hybridize.html). program a starting the using replicating by 10 to Seq-Gen. from set derived was haplotypes taxon each (N) size of population The drift reproduction. genetic simulated and during haploid, recombination as to rather subject but loci, sequence unlinked DNA linked subsequently a as not treated were characters the evolution, se- data. 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OLOGY × α 5r ≤ piaeruns eplicate .5 hntema egho rnhsamong branches of length mean the than 0.05) ∗ defaults. 0 h eiin ao sntadsic evo- distinct a not is taxon recipient the : vlaino Performance of Evaluation × trigdt sets data starting 4 st C-C S,and MSN, PCO-MC, , st rpe below dropped = × .41 and 0.0401) st topolog- 4 analyses, t -test 56 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 ro)cudte ecluae o ahtm on (see point time formulas). each for for 1 calculated I Appendix be type to then (equivalent could history error) probability reticulate the of inference and no error), of II a type had i.e., taxon history, probability monophyletic reticulate a the that (determining taxon), failure reticulate of the (cor- signal success identifying conflicting of rectly probability on The based determined. history was levels) reticulate a suggested was have monophyletic (i.e., be to avail- to inferences sets known incorrect taxon data a of when 20 number reticu- the the of for Similarly, inferences able. determined correct was of sampled history and number late percent the cutoff point, each time For found. been to have considered was signal conflicting per- “significant” “cutoff cents,” for these support exceeded splits 85%, bootstrap or When clades 90%, contradictory 50%). 95%, 60%, 65%, (99%, 70%, values 75%, cutoff support bootstrap history. reticulate a to had known monophyletic taxon be a that suggested occurred signal error hy- II conflicting type when null and rejected), the falsely (causing be to present be pothesis not then that was of would evidence hence history such history, and reticulate when reticulate occurred C, error a taxon I Type to have supported. was may it closely A as as taxon was B A taxon taxon to that related conclusion The A. signal then taxon conflicting support, for substantial of bootstrap evidence 98% be would had there AC split and bootstrap 95% support had AB split phylo- if example, conflicting For signal. of genetic magnitude data the RSW indicate con- secondary and partitions) for overall (or the relative splits in clades The contradictory tradictory two collected. for likewise values were support partitions analyses signal corresponding RSW secondary and the of overall for the from values clades simulation Support the collected. across previously were described error splits non-trivial the sup- II for bootstrap values NeighborNet, port type For used. and was course, I time cri- type cutoff anal- of single sensitivity ysis involving a approach, using different reticulation evaluated A of terion. fairly evidence be this However, not set. could data a in sig- conflicting nal exposing by reticulation indicate also can by caused TIRH in differences factors. significant of these variance for analysis the Nested test apportion model. and to used the was into (ANOVA) recombina- built variance of drift processes and stochastic the tion from starting or the flow, set, gene of data model topological could the runs to due between be observed TIRH proce- in given differences a For dure, met. the been had whether criterion cutoff determine relevant to examined and NeighborNet) 2007 nlssi umrzduigrslsfo h parsi- the from results using summarized is analyses oflcigsga a vlae sn different 9 using evaluated was signal Conflicting RSW and signal.—NeighborNet conflicting of Evidence h feto eeflwbtentx ntree-based on taxa between flow gene of effect The oooia osqecso eiuaeEvolution Reticulate of Consequences Topological nTe-ae Analyses Tree-Based on R EE N IHRSDSIGIHN OOHL RMRETICULATION FROM MONOPHYLY RICHARDS—DISTINGUISHING AND EEVES R ESULTS enlbace eevdhg otta upr Fg 4c, (Fig. inset). support bootstrap in- high began), received topological flow branches gene ternal of after soon period internal occurred taxa, (which the to change recipient During subsequent and changes. gradually, donor topological eroded sup- of that average, monophyly shows on the struc- 4 tree for Figure the simulations. port for the support during statistical ture determine to sets within structure hierarchical caused false A. 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(Fig. AB clade urn fe i ylso yrdzto n eei drift genetic oc- and (t hybridization 2a), ob- of (Fig. cycles first six condition after The starting curring the data. from Sim3 change of served analysis parsimony during gene of taxa. effects between topological flow the generalize most to tool are the a and as course determine used time the to over used clades recovered frequently were trees majority- consensus variation, this runs rule Given replicate points. sampling between some at observed were strict the trees of topology consensus the in simi- Differences parsimony. qualitatively to were pro- lar methods Sim4 NJ complex from and more Results the Sim2, in Sim3. seen responses Sim1, the of in subset a examined duced conditions flow topological gene The data. for Sim3 of analysis mony otta upr auswr acltdfraldata all for calculated were values support Bootstrap var- changes topological of timing exact the Although (t point last the shows 2e Figure = occurred that changes topological the shows 2 Figure ) a eraei h rqec frcvr of recovery of frequency the in decrease a was 6), = 9 rSm (t Sim4 or 19) = = 11 6) tti on,tx A taxa point, this At 163). hwdete h start- the either showed = = 11 7.N topological No 17). = Fg c,tefirst the 2c), (Fig. 6 twihthe which at 96) = 3(i.2d), (Fig. 23 = 307 23) Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 hretpt ln h ewr hticue l individ- all included that network the along path shortest (t another one from guishable 3, (Fig. length in t diminished progressively A D taxon taxon t between and 3, branch the (Fig. transition, C topological taxon final to taxon adjacent taxon that became such to B occurred similar change more topological its second lost became a A and D, taxon B as taxon flow, event to gene unique similarity continuing a With as nodes 3). visible adjacent Fig. not in but became 5, A Fig. taxon in (summarized recipient and D donor taxon that such network the of rearrangement a involved t 3; (Fig. flow taxon re- gene the cipient within changes, structure, therefore topological and any variation, to induced shown Prior are run 3. Sim3 Figure single in a and during 5, observed four sum- Figure MSNs in the to the as for occurred used conditions changes is starting Topological possible Sim3 response. study. the this marize in represented MSNs three former were the only random, used at sets chosen were data here starting D-E-C- four the E-D-C-A-B; Because D-E-C-A-B. E-D-C-B-A; B-A; used: topology tree ing sgns oooia eragmnsaogitra rnhsocre onatrtesato yrdzto n eefloe yalonger a by followed were and eroded. hybridization gradually groups of monophyletic start as the taxa recipient separated after and taxa direction soon opposite donor between the occurred the flow in is for Gene branches tree the events, support nodes. internal within where hybridization at (c) “flowed” among of frequency and period clade (b) recipient number rearrangements clade in the Topological in with Arrows as measured labeled rearrangements branch. genes. (t), are topological bold as Time predictable trees a caused change. by consensus internodes marked topological Majority-rule more is next or figure. (A) two the each taxon by during of recipient moved The bottom (f). A the in taxon at shown which shown is to topology position stable tree final, the the and indicate (a), in shown are flow gene 308 = oreulylkl S oooiseitfrtestart- the for exist topologies MSN likely equally Four F 3 6 ni oo n eiin een ogrdistin- longer no were recipient and donor until 96) 23, IGURE oooia osqecso eiuaeEvolution Reticulate of Consequences Topological .Tplgclefc fogig ndrcinlgn o ewe aao asmn nlss h nta oooyaddrcinof direction and topology initial The analysis. parsimony on taxa between flow gene unidirectional ongoing, of effect Topological 2. nNtokAnalyses Network on = ) h rttplgclchange topological first The 6). = 6) tn ieddthe did time no At 163). = 1.Atrthis After 11). SYSTEMATIC BI DadA eeeulywl upre,laigt the to leading supported, well equally splits were Conflicting AB taxa. and recipient AD similar- and growing to the donor relative indicating between decrease E, ity to and C, begun B, had splits D trivial and A splits trivial oywsspotd yt er- his- By the reticulate supported. a phase, was had this tory B At taxon AB. that interpretation split roneous to comparable weight was split a that and values, support bootstrap large nering t 3, be- flow (Fig. gene gan after Soon strictly evolution). a of under model bifurcating simulated were (which sets data those starting (t as 3 such Figure splits, in conflicting shown for values support 27% high sim- was 200 sets in data tree starting starting ulated the with conflicted that splits and (± for length) mean (branch The were weight support. split bootstrap networks by measured the conflicting as of sets, splits, evidence minor data only with starting tree-like, largely 3. the Figure in in shown are Initially, run Sim3 single a to NeighborNet B-C-E-A,D. E-A,D-C-B; observed: conditions were end until possible Two course, met. time was criterion simulation cutoff the the distinguish- of a much remained for group taxon another able from recipient individual the an thus include taxon, also A taxon of uals h pi ewrsrsligfo plcto of application from resulting networks split The LG VOL. OLOGY = ) pi Cbcm oepoiet gar- prominent, more became BC split 6), = )wr cainlyosre in observed occasionally were 0) = 11, h pi egtfrthe for weight split the D otta support bootstrap SD) ± 6.Hwvr very However, 26%. 56 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 astgtycreae.Tefia,sal oooywas al- topology not stable are t final, by values reached The support correlated. split tightly and ways weight split Thus 2007 sdt eemn fvraini IHaogreplicate among TIRH in variation if determine to used Replicate pattern. identical. similar became a D followed simulations and A taxa and appeared t At point. time this at taxa reticu- suggested reticulate also a were be D have to and may B taxa A However, history. taxon late that interpretation correct ogrta h rnhswti eiin ao .Tefis he rnia oriae r lte o C nlss io aito and/or methods. variation all Minor in analyses. apparent times PCO were 100 for taxon to donor plotted 10 the are typically from coordinates were flow principal branches gene three These by first taxa. taxon recipient The between the connections A. lengths into show taxon introduced branch panels recipient structure Relevant MSN within historical analyses. the in branches NeighborNet are in and the individuals branches parsimony letters; than Bold capital for longer with analyses. shown indicated are MSN are values for (populations) Taxa support shown top. bootstrap are at Relevant indicated numbered. points time are at and sampled lowercase were sets Data taxa. between flow iial erae nteSm elct hw in shown replicate Sim3 t the at always 3, in not Figure did decrease: support similarly bootstrap However, AD. smaller much became than DE for t weight sub- split By the decreased as decrease. had stantially signal to conflicting began of Bootstrap also evidence mea- strong BC. AB and as split AD importance, for to in support relative weight, diminish split to by began sured DE and AB etdaayi fvrac was variance of analysis error.—Nested I type of Erosion F IGURE eaiePromneo hntc Tree-Based, Phenetic, of Performance Relative .Tm eissoigtesgaueo eiuaeeouino oraayia ehd.Cre rosidct ieto fgene of direction indicate arrows Curved methods. analytical four on evolution reticulate of signature the showing series Time 3. = = 6 sbosrpspotfrsltD dis- DE split for support bootstrap as 163 6 pi AD split 96, n ewr Procedures Network and R EE N IHRSDSIGIHN OOHL RMRETICULATION FROM MONOPHYLY RICHARDS—DISTINGUISHING AND EEVES = 0% pi DE split 100%, = 3 splits 23, = 100%. = 96, n h IHvle fietclsmlto usbe- runs simulation identical to): (≥ of methods values tween compar- TIRH by the ranked be ing also could performance Relative h olwn ar fmtoswr o significantly and ( not “bootstrap” NeighborNet parsimony were another: methods one models, from of different topological pairs four following all the across Averaged 6. 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TIRH (Table flow on gene starting define to between used models topological differences between differences and/or to sets data attributable was runs S ( MSN efrac aknsbsdo IHaesonin shown are TIRH on based rankings Performance P = .56,F 0.8596), P = niae etrta requivalent or than better indicates .5) asmn bs re and tree” “best parsimony 0.453), st n J“ette”( tree” “best NJ and P = 0.2284). 309 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 u.Ist b n d hwsmayvle u xadtergo ftplgclcag pae1 o lrt.Sm eut eesmlrto similar were results the Sim1 of clarity. course for the during 1) changed (phase values support change representative clade topological recipient single of and a Sim2. donor to region from only identical values the so nearly support occurred, expand were bootstrap changes results but topological shows Sim4 values no (c) simulation. that support summary Inset except of identical. show erosion Sim3 were gradual genetically and (d) (d) 3, recipient Sim2 change; for and phase and topological taxon; values (b) 1, donor donor Error of phase Insets (c). 4, group taxa: in phase run. sister nonsister only monophyletic inference; between the direction flow 2 is one gene phase taxon in of (reticulate) for consequence indicated recipient a that are inference are value, erroneous that bootstrap 2, phases mean phase characteristic the four from indicate deviation graphs Sim2 standard similar. one as shown bars, error 310 elct simulations. replicate graphs, .Prioy“bootstrap” Parsimony 3. 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P > .5 odif- to 0.05) 56 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 onaddrcinwt n ftopsil nl tbentok hw ttebto fec ae.Arw mhsz rearrangements emphasize in Arrows shown panel. are flow each gene of of bottom model the Sim3 at the shown to networks due stable transitions final, topological possible Major two column. networks. of the each one within of with top direction the downward at a shown is networks starting possible 2007 Total (error) sets data Within models within sets data Between models flow gene Between variation of Source cont’d ANOVA Total (error) sets data Within models within sets data Between models flow gene Between variation of Source cont’d ANOVA Total (error) sets data Within models within sets data Between models flow gene Between variation of Source cont’d ANOVA Total (error) sets data Within models within sets data Between models flow gene Between variation of Source ANOVA h rbblt ficretifrne nrae dramat- increases inferences incorrect of that probability demonstrate results the Sim1 zero than The 7). be Fig. rather must in homoplasy, indicated success (as of routine probability conflicting the to and any due reticulation, Sim1, be oc- in must flow Thus gene signal taxa. when sister possible between not are curs clades or splits Conflict- criterion. ing cutoff of the as probability values different support the bootstrap nine using shows inferences erroneous 7 con- and Figure successful when define significant. to varying was used by flict values evaluated support Neigh- were bootstrap the methods the by RSW revealed and signal borNet conflicting of plications h antd n im- and magnitude signal.—The conflicting of Evidence F IGURE .Tplgclefc fogig ndrcinlgn o ewe aao iiu pnigntokaayi.Oeo four of One analysis. network spanning minimum on taxa between flow gene unidirectional ongoing, of effect Topological 5. R EE N IHRSDSIGIHN OOHL RMRETICULATION FROM MONOPHYLY RICHARDS—DISTINGUISHING AND EEVES T df df df df 79 64 12 79 64 12 79 64 12 79 64 12 ABLE 3 3 3 3 .Nse nlsso ainei TIRH. in variance of analysis Nested 1. 30, 24, 46, 40, 60, 47, 19, 12, 1, 5, 2824.70 2756.10 4657.80 1901.80 6894.10 5762.70 238.01 657.21 856.42 296.81 065.24 408.44 578.22 905.21 610.30 062.7 SS SS SS SS asmn “bootstrap” Parsimony asmn bs tree” “best Parsimony peea ntefc fpritn eeflw o Sim2, the For by flow. measured was (as gene success but of persistent probability flow cumulative of the gene face of the onset in the sig- ephemeral after decreased conflicting soon correct then appeared Thus nal simulation flow. gene the continued in suc- with of early probability increased the 3), cess and (Sim2 visualized be could not should and in error, used. 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OLOGY osqecso eiuaeEvolution Reticulate of Consequences = nTe-ae Analyses Tree-Based on 3.I eldt esaqie during acquired sets data real In 23). P < .0)fo n nte.When another. one from 0.001) 56 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 ee triga h o ftelfms ouno ahgopo iegah:lf oun 9,9% 0;mdl oun 5,7% 70%; 75%, 85%, reticulate column, a middle has error). error). 90%; taxon II I 95%, (type recipient (type history 99%, history the reticulate reticulate column, a that of has inference left inference taxon no successful graphs: monophyletic of a a nine probability that of inference the of probability erroneous indicate group an areas the of each Gray-shaded indicate probability of the regions indicate column White-shaded regions leftmost 50%. 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R EE N IHRSDSIGIHN OOHL RMRETICULATION FROM MONOPHYLY RICHARDS—DISTINGUISHING AND EEVES eQueiroz de etcae xetfrdrn h nlsae fthe of stages final the during for recip- the back- except outside complex clade, found simulation, not ient our were individuals In than other crossed parents. places in their tree a with in found be infrequently may oc- structure the tree in of 4). change members (phase further curred became no and taxa clade, recipient same and donor the from monophyletic. individuals all not introgression, was persistent with Lastly, taxon reticulate correctly the to that began suggest trees reconstructed which delayed at phase point This the was c). 4a, taxa Fig. recipient 3; and (phase eroded donor gradually of monophyly the for port cae(92 hwdta 1hbi individuals hybrid F1 that showed (1992) McDade sup- which during occurred phase lengthy a Third, y ai spoaiiy cldfo to 0 from scaled probability, is -axis 313 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 sial ml ouainszsadhg eeflwrates flow gene high and sizes unreal- population the small with istically Even recombination. and exten- flow after gene inferred sive be only could reticulation tree-based methods, using the when However, accepting true. by as the hypothesis taxon reveal null recipient to the of able history ultimately reticulate were used methods based null gene the simulation of commencement accepts flow. the the correctly after of that soonest course the method hypothesis the the over for proba- error lowest cumulative is I the type way, of perform- another bility poorly after Put than sooner methods. flow hypothesis ing gene of null commencement the the reject cease erroneously ef- will error the methods to high-performing I of method: measure type a a the of is ficacy simulations of the erosion in of early ana- apparent rate various The the by methods. rejected lytical erroneously longer lineage) (that evolutionary no distinct hypothesis was a not null is taxon the 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P < 0.0001) 56 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 l aawr nldd F included, When were hybridizing. taxa be all to known taxa those only culation inl hsi o rtcs falgtmt s fF of use legitimate a of criticism a not is phylogenetic This containing sets signal. data in reticulation tifying sn h eeoscieino nern reticulation inferring of criterion F when generous the using 2007 atgsoe te oheacia lseigmethods. clustering nonhierarchical other over vantages set. data given a stable for R most membership of the and determine number range cluster to a explored be data, should real values PROC analyzing in of When available use number MODECLUS. legitimate cluster of for the four tests permit significance least would at landscape landscape” smoother (where A density variation). “density internal data no exhibited smoother simulated clusters five a the with to than lead realized be should within also variation taxa natural might where sets, method data real using Improve- PCO-MC when error. the I type in error, promote per- II ments type values it promote R values small because R whereas Large parameter I errors. type II useful between type trade-off a and inevitable the is over control R mits for set, precisely data define any to and difficult densities cluster Although evaluate membership. to smooth- used the (R) of parameter estimation ing accurate more by achieved be associations. to statistical dimensions for scrutinized many simultaneously be permits of clustering number modal large of cation a appli- in Subsequent eigenvectors). emerge (or asso- dimensions possible freely such more calculated, may are ciations coordinates principal apparent. becoming When as- from some individuals prevent may among networks) sociations extent, lesser a trees to bifurcating (and, of relation- structure Second, historical low-dimensional synapomorphy. rigid, of the than indicator individuals better among a ships be of coalescent may average independent genes, an many by overall as contributed an calculated distances recombination, measure, of distance presence to genetic the bound- peculiar in factors phylogeny/tokogeny First, two the ary. of across collusion sampled to data due be may ods support. bootstrap and from 100% large, A received remained taxa taxon other A distinguished all and that split D NeighborNet or the C net- taxa spanning minimum between of the work taxon along sister distance monophyletic the the D, taxon as A taxon bootstrap 100% for retained support parsimony when iden- point nearly a were at D tical and A taxa for coordinates principal t at Sim3 in example, gene For of flow. commencement the principal following similar values acquire coordinate rapidly to taxa representing hybridizing clusters show the time over Plots values. TIRH ( param- smoothing value conservative eter a using when even ods, tokogenetically among populations. related variation genetic describing for ofie ifrne ewe ohbiiigtx.Thus, taxa. F nonhybridizing between differences fixed to st oprmti oa lseighsanme fad- of number a has clustering modal Nonparametric might method PCO-MC the of improvement Further meth- other over PCO-MC of outperformance The meth- other all outperformed significantly PCO-MC osntapa ob naporaemti o iden- for metric appropriate an be to appear not does st rpe eo .5adicuigi h cal- the in including and 0.95 below dropped R = .41 htbae eut oadlarge toward results biased that 0.0401) R EE N IHRSDSIGIHN OOHL RMRETICULATION FROM MONOPHYLY RICHARDS—DISTINGUISHING AND EEVES st i o eit rm10due 1.0 from deviate not did = 3(i.3,tefis three first the 3), (Fig. 23 st iuae aawt nw eiuaehistory. reticulate appropriate known using neither with tested data knowledge, formally simulated been our 2002; yet To has al., 2003). method et Double, Raxworthy and 2002; Abbott Trueman, and retic- implemented in- infrequently (Nicholas which although been RSW, in has whereas attractive, sets important, tuitively data be for may used ulation commonly now NeighborNet are as such methods Network 2004). and Moulton, Bryant 1998; (Trueman, recombination hybridization intergenic as or such processes reticulate by caused sets data phylogenetic in signal conflicting identifying for ods in warranted. taxa is sets reticulate data simulated identify and real correctly complex to methods sim- this ordination- based of of ability the results of promising examination further the study on ple indicated Based set. groups data distinct a by evolutionarily identify of to de- is number goal be the the when not essential is need Sec- This priori. clusters used. a of fined be number nonnormal may expected or coordinates) the ondly, principal nonuniform as thus, (such required; data are data distribution underlying of the about assumptions no First, itrtx eg,Sm) hs oflcigsga criteria signal conflicting Thus, Sim1). (e.g., cor- taxa between occurred revealing sister flow gene of when signal incapable conflicting rect were likely. methods more even both Lastly, were inferences incorrect flow gene conditions, complex topologically under re- possible history reticulate mained of phylogenetic inference underlying correct a the Although by in tree. separated internodes taxa more between or re- occurred two whenever has high flow be gene will error cent II nature, type from of sampled probability sets the data reticulate real are to RSW) applied and NeighborNet as conflicting (such identify signal that phylogenetic methods when re- These that, monophyletic. imply retic- was sults a it have fact to in taxon when a history ulate identifying error: II were type RSW to and prone NeighborNet both Sim3), (e.g., taxa lated error. I type in result to still expected would analysis be NeighborNet 2, phase correspond- to period roughly regions a “ero-ing During the criteria. using error” with I obtained type of be overlap sion could not inferences do correct inference where correct a result criteria in signal conflicting where course simu- time the lation of regions the Nevertheless, Sim2). those by “bootstrap” (e.g., modeled processes parsimony reticulate cumulative specific than highly lower error certain for a I have type to of probability expected with be coupled Neigh- might TIRH, is for borNet signal ranking retic- performance conflicting identifying second-place on its correctly based of taxa (Fig. possibility ulate signal the phylogenetic When conflicting 7). his- revealing reticulate by of indications tory correct ongoing producing ca- were of an NeighborNet pable of and RSW 1) both phase process, stages reticulate to early the roughly during corresponding Sim2) (i.e., (e.g., flow gene of models We meth- as proposed been have RSW and NeighborNet hngn o curdbtentodsatyre- distantly two between occurred flow gene When aesonta,udrpriua topological particular under that, shown have vdneo oflcigSignal Conflicting of Evidence 315 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 e a eiuaehistory. data reticulate a within a taxon has specific for set a useful that universally hypothesis the be testing not may reticulate networks of hallmark evolution), (the data signal a conflicting which contains to extent set the of visualization Neighbor- the as In permit such Net 2006). methods Bryant, network while and words, (Huson other topology sup- entirety, tree-like its in a taken set, ports data a which to degree the of examination preliminary for meth- useful primarily network be re- split may ods that signal suggestions conflicting prior support the find- ings Our clear. of entirely not is utility analyses network by in the vealed reticulation sets, generalized in- data more may some of taxa) indication related the distantly duce two between flow unidirectional as gene (such reticulate, process reticulate not simple is signal a history (3) and the conflicting when even significant observed be of may evidence (2) common, were of criteria complexity error” not. I topological type of “erosion the whereas flow, by gene affected clearly were 316 inlgn o.A nraei ouainsz sex- is (e.g., realis- sizes size For population 2). tic population (Appendix TIRH in increase greatly increase multidirec- to pected An or flow. bidirectional gene of gene in effect tional the variation and rate, rates, mutation popula- flow level, include ploidy These size, simulation. tion this in modeled not systems. natural from sets ana- data when complex of important more consequences be lyzing may the that predicting variables for unmodeled foundation ISSR, pro- a RAPD, model simplified vides as this that such believe We SNP. sec- markers or AFLP, of molecular lineages study bacterial binary a conjugating using in observed between be contact might ondary generated what that to producing reality, akin process biological in data the based was (irre- of model data The specifics real it). of the lev- analysis of the signal spective that in conflicting signal encountered conflicting of be of might range range the reticulate wide of generate representative a els, to with rather that sets but process data nature particular in any occur mimic might precisely to not was two trees. between five-taxon within flow taxa gene unidirectional and haploid only was considered it simplified: highly introgressive was of hybridization model The genes. in- of coalescent analysis dependent separate to opposed as loci from unlinked data many of analysis simultaneous the study with The concerned reproduction. is with to applica- taxa barriers between most nonexistent flow or are gene weak intraspecific results of The cases study. to ble present the to ply edmb eelduigbfraigte-ae proce- tree-based bifurcating or using revealed events be would hybrid history seldom (>10,000 reticulate true large modeled that so generations) those >100,000 be as may such TIRH flow here, gene and distance genetic ie ht()gn o ewe itrtx a be may taxa sister between flow gene (1) that Given eea aibe motn nntrlsseswere systems natural in important variables Several however, model, simplified this using for reason The ap- limitations of number a simulations, all with As eeaiyo Findings of Generality N > 00 n eeso starting of levels and 1000) SYSTEMATIC BI es(.. hr oo n eiin aawr o yet NeighborNet, not were PCO-MC, taxa used recipient then We and homogeneous). donor where data (i.e., randomly non-trivial of We sets totality the data. vari- from sets simulated data undertook of our 200 sampled we of performance surrogate, reanalysis the a blind realistic evaluate a As not methods. to is analytical data it ous real observed, use been have to usually not reticulate will events a hybridization from past derived because were Furthermore, process. data the if priori, a know, predict. to clade difficult new is this tree of the position contrast in the in case, unidirectional Thus, ancestry. the to common accumu- and synapomorphies mutation which late: by the than mechanism rather fixation, usual and drift the of via processes flow, stochastic gene to due apparent appear these that would genes Note synapomorphies emerge. exchanging would taxa clade single two a that the in of synapomorphies inclusion apparent the of support assemblage novel branches. A internal for support character an- eroding one by towards position other them starting forcing simultaneously, their tree the from in away exchange under- gene taxa the going of both pull would states less Bidirectional character of case. is flow unidirectional topology the tree in the on than flow predictable taxa, more gene hybridizing bidirectional where the of cases effect separates internode in one However, than decrease. also TIRH so decrease, should to expected is taxa hybridizing two the between With homogeneity to possible. time the flow, is gene bidirectional flow gene multidirectional of or order rectional rank the examined. affect methods to the for likely performance seems relative expected rate nor is rate flow flow mutation gene in gene variation Neither in TIRH. increase decrease to An process minimal. hybrid ongoing be an may for im- TIRH the on so mutation 1998), of al., pact et (Drake replication per nucleotide h aea hc nrgesdcaatr r fixed, 10 of order are the on eukaryotes, characters generally in low are be introgressed to rates thought Mutation which infinity. approaches approaches at TIRH population at a rate rate in the the fixed As TIRH. are increase mutations to which Thus is mutation arise. of taxa effect recipient the (rather and distinguish donor that and homogenize) characters pop- than taxa new a within fixation, into occur to states drift mutations character as However, novel introduces ulation. it that in size. the population to increasing similar of be effect should organisms polyploid from or data diploid analyzing of effect tree-based The supported, analyses. phylogenetic be strongly to on presumed now based taxa plant monophyletic level lower many ruled for be out important cannot history is reticulate that finding suggests this it conse- because However, the bias. ameliorate this may of time quences over dis- fluctuation size nature, finding population In in towards groups. biased monophyletic) (e.g., inherently tinct are that dures hnaayigra aa twl fe edfcl to difficult be often will it data, real analyzing When bidi- populations, structured with systems natural In h feto uaini iia ota fgn flow gene of that to similar is mutation of effect The LG VOL. OLOGY Recommendations −10 per 56 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 2007 ei aasets. phyloge- data in taxa netic reticulate identifying other for methods no PCO-MC tested provides than the study of this any recommend identified, to be evidence can value R appro- incorrect an priate that an provided Therefore, and time. time, the cor- of the 20% a of result 6% applied, obtained the was likewise of result was rect 6% obtained NeighborNet was When result incorrect time. of an 7% but obtained time, was the result to correct subjected a were analysis, PCO-MC re- parsimony using that inference sets no data in When sulted that alone. over PCO-MC methods using combining achieved by attained be advan- no could Neigh- Furthermore, tage 28%. for and and 34.5%, 32.5%, 37.5%, 3.5%, and borNet, 96%, 3%, these was 64.5%, bootstrap, were errors parsimony frequencies I For respectively. type 0.5%, and and errors, an- II correct of type frequency order swers, the PCO-MC, rank For the same. the NeighborNet), was and each parsimony of for performance crite- 100% cutoff the (R When maximize error. to method II altered type were of ria frequency high a because primarily of methods two other the derperformed un- NeighborNet NeighborNet. and “bootstrap” simony made. been had inferences until the hidden but after known was de- which answer, mono- criteria correct inferences the error” were to our I compared which we type Finally, previously. of and scribed “erosion history the reticulate using phyletic a had taxa which determine to methods “bootstrap” parsimony and eosrcighge ee eainhp mn mono- among relationships level for higher appropriate reconstructing methods, tree-based bifurcating plying n orcl eetdfralmnpyei aa n“norc”ase eutdfo alr omk orc neec o l aaincluded taxa monophyletic. all be for to inference inferred correct were a taxa taxon, make all reticulate to when the failure made for a was accepted from history correctly resulted reticulate was answer of hypothesis inference” “incorrect” null “No An the analysis. taxa. when the monophyletic obtained in all was answer for “correct” rejected A correctly flow. and gene simulated of models four iue8sosta C-Cotefre ohpar- both outperformed PCO-MC that shows 8 Figure hssuydmntae oeo h iflso ap- of pitfalls the of some demonstrates study This F IGURE .Rltv efrac fPOM,prioy“otta, n egbre ehd ndt essmlda admfo all from random at sampled sets data in methods NeighborNet and “bootstrap,” parsimony PCO-MC, of performance Relative 8. = .01frPOM,bosrpcutoff bootstrap PCO-MC, for 2.0001 R C EE N IHRSDSIGIHN OOHL RMRETICULATION FROM MONOPHYLY RICHARDS—DISTINGUISHING AND EEVES ONC LUSIONS = rusfo eiuaetx ndt esta pnthe span that sets tokogeny. data and phylogeny in between taxa boundary reticulate from groups monophyletic terminal net- distinguishing or for tree-based methods than work useful generally may more PCO-MC) be Nonhier- to as prove evolution. (such reticulate procedures of ordination archical product a are groups II monophyletic type clearly to that histo- finding prone towards reticulate highly error—biased are identify methods to such condi- However, used ries. restrictive successfully very certain, be signal (under tions) phylogenetic may sets, conflicting data reveal in to designed are which RSW, as such methods tree-based or NeighborNet, is purposes, for conservation or questionable. for species, delimiting populations or defining prioritizing of purpose groups the monophyletic for terminal identify in to pro- alone tree-based hybridize of cedures use to the that suggest known results phyloge- Our taxa nature. supported among strongly stud- relationships reveal some netic to of purport conclusions that the ies challenge taxa. results of among These inference relationships the erroneous in supported, result highly may data reticulate substan- of a analysis tree-based has that it show we when Moreover, finding history. even reticulate towards tial monophyletic error—biased be to I taxon type a because to prone methods are tree-based they using identifiable readily relationships. reticulate to We lead have past where may studies, hybridization level lower to taxa, terminal phyletic hn o epu omnso rf eso ftemanuscript. the of version draft a on comments helpful for Zhang hssuysget htntokmtossc as such methods network that suggests study This hwta aawt eiuaehsoismyntbe not may histories reticulate with taxa that show We hn eis sa,Mr imn,DvdTn,adLibing and Tank, David Simmons, Mark Islam, Melissa thank A CK NOWLEDGEMENTS 317 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 318 ic,W .19.Ntok n ia vlto.J o.Evol. 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North Cary, Institute, SAS P-256. Report Technical oy( mony F IGURE ∗ n te ehd) eso .b0 iae Associates, Sinauer 4.0b10. version methods), other and 1 a feto triggntcdsac ntetm eurdfrtohbiiigtx obcm eeial indistinguishable. genetically become to taxa hybridizing two for required time the on distance genetic starting of Effect (a) A1. R EE N IHRSDSIGIHN OOHL RMRETICULATION FROM MONOPHYLY RICHARDS—DISTINGUISHING AND EEVES Hypochaeris ∗ hlgntcaayi sn parsi- using analysis Phylogenetic : Atrca) ai pl Ecol. Appl. Basic (Asteraceae). = lt itr a bandfrapriua iepit ie ht20 that point: Given time point. each time for analyzed particular were a sets data for different obtained was history ulate “probability.” indicates “Pr” where any at simulation, Therefore, the set. of data course time incorrect one the and any during correct point for particular both observed is, be could that former inferences nonexclusive, The history. were reticulate outcomes of inference two no inference and incorrect history, an reticulate history, were of reticulate for of outcomes levels inference Three correct signal presented. a are possible: conflicting analyses on RSW erroneous based and and NeighborNet history successful reticulate of of probability inferences the calculating for Formulas soit dtr dinPaterson Adrian Editor: Associate 2006; September 12 returned reviews 2006; June 6 submitted First Biol. Mol. evolution. reticulate under analysis Phylogenetic 2000. S. the Xu, at looking of way Another 1990. Nixon. C. K. the and for D., F-statistics Q. Wheeler, Estimating 1984. Cockerham. C. C. and S., B. Weir, Tr D bevdi hssuy b Effect (b) study. this in observed (±SD) values mean show Points 10. ea,J .H,adM ib.20.RW..Sfwr distributed Software RSW1.1. 2002. Gibbs. M. and H., W. J. ueman, nlacpac 7Nvme 2006 November 27 acceptance final 17:897–907. Evol. Cladistics Donoghue. and Queiroz de to 6:77–81. reply A problem: species 38:1358–1370. Evolution structure. population of analysis authors. the by Let N = Pr(success) h oa ubro aast nwihn neec fretic- of inference no which in sets data of number total the y rn inference) Pr(no + ai si log in is -axis Pr(failure) A PPENDIX + 10 scale. rn inference) Pr(no = 1 /0 (2) N/20. = (1) 1 319 Downloaded By: [USYB - Systematic Biology] At: 21:43 30 April 2007 hw ordc o1 to reduce to shown nrltosisaogptnilyitrreigppltos hc pera pas nteimages. the perspective different in slightly “peaks” a as provides appear coordinates principal which plotted populations, of interbreeding pair potentially Each among data. coordinate relationships principal on of landscape density a as visualized hr sol n orc neec osbeprdt e.Temaximum C The for set. data I value per for possible maximum value inference correct The one only point. is time there particular analyzed a sets data 20 at all across summed inferences incorrect of number Pr(inference)= inference, an yields run a that probability the Accordingly, 320 orc neec rmtettlt fifrne,or: inferences, of totality the from inference correct a Pr(success) yfcoig[1 factoring By [1 is: (1) equation of expansion the Therefore, Likewise: 1 − e C Let − (N/20)] uuu lupulus (Humulus varieties hops American North native of history evolutionary reticulate The (N/20). = > = h oa ubro orc neecsadI and inferences correct of number total the 0bcuemlil norc neecsaepsil.The possible. are inferences incorrect multiple because 20 × Pr(success) rifrne utpidb h rbblt fsampling of probability the by multiplied Pr(inference) − Pr(failure) [C/(C N2) rmtefis w em,Euto 5 seasily is (5) Equation terms, two first the from (N/20)] = + 1. I)] = = + [1 [1 [1 − − − (N/20)] (N/20)] (N/20)]× × × [C/(C [I/(C [I/(C + + + ).(4) I)]. ).(3) I)]. I)] + = N/20 SYSTEMATIC BI = 0because 20 h total the = 1. (5) d[D,R] aat eoegntclyietclcnb prxmtdb h fol- the by approximated hybridizing be d[D,R] two can for equation: identical required lowing genetically time become the to model, taxa haploid present the In eonzda itntlnae sn oto h nltclmethods analytical the of study. most this in using be considered lineages longer no distinct will as taxa interbreeding recognized two before required be hybridization this will of events under thousands many identical sizes, genetically population realistic become For nec- model. to relationship events populations hybridization two the of for shows number essary the A1b and Figure size in formula. population the shown between than the as larger by Therefore, slightly were predicted sampling. either study set values this characters in data introgressed observed to values the A1a, prior Figure of lost all) or not fixed ran- were (but of (10) most generations of mating, number dom fixed A1a). a (Fig. used distance simulation genetic the Because starting identi- become with to logarithmically taxa increases ge- hybridizing cal for data that required to and time prior taxon The neutral, recipient sampling. are the set in states occurred has character fixation produced all until drift is that netic individual event, hybrid flow F1 gene single per a that 1/N. is assumes drift equation genetic via This proportion fixed parental the become and to donor expected 0.5, alleles of is introgressed progeny of proportion hybrid F1 hybridiza- the in of began), present number states flow the character gene as (measured since t-1 events and tion t time at taxa recipient LG VOL. OLOGY t n d[D,R] and t −1 r h eei itne ewe h oo and donor the between distances genetic the are t vars. ≈ A d[D,R] PPENDIX lupuloides, t −1 − 2 (0.5)(d[D,R] and neomexicanus, t −1 (/) where )(1/N), pubescens) 56