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Online Figure 1 A) B) C) 0.5 γ = 0.0 0.5 γ = 0.6 0.5 γ = 2.2

0.4 0.4 0.40.8

0.3 0.3 0.30.6

0.2 0.20.4 0.5 0.2 Density 0.2 0.3 0.1 0.1 0.10.2 0.4 0.0 0.1 0.0 0.0 0.00.0 -8 -6 -4 -2 0 -8 -6 -4 -2 0 02468 02468b3 02468

D) E) F) relative frequency 0.5 γ = 0.2 0.5 γ = 1.6 0.5 γ = -2.8 0.4 0.4 0.4

0.3 0.30.6 0.8 0.3

0.2 0.20.4 0.2 0.3 0.4 Density 0.2

0.1 0.10.2 0.1 0.0 0.1 0.00 0.10 0.20

0.0 0.00.0 0.0 -8 -6 -4 -2 0 -8 -6 -4 -2 0 b3 02468b3 -802468 -6 -4 -2 0 02468

simulation time (millions of years) Online Figure 2 Tangara callophrys velia chilensis Key inornata mexicana Highland seledon Lowland fastuosa desmaresti Caribbean cyanocephala North American lavinia Other gyrola gyrola Dispersal gyrola Lowland to Highland chrysotis Highland to Lowland xanthocephala parzudakii schrankii johannae icterocepha florida arthus cyanotis Amazon labradorides barbadensis vassorii ochrocephalus nigroviridis versicolor fucosa arausiaca dowii kawalli ruficervix autumnalis heinei rhodocorytha argyrofenges dufresniana farinosa viridicollis imperialis cyanoptera brasiliensis vitriolina guildingii cucullata amazonica cayana viridigenalis meyerdeschaue finschi palmeri agilis cyanicollis albifrons cyanicollis collaria larvata vittata nigrocincta ventralis varia leucocephala rufigula vinacea xanthogastra festiva guttata tucumana punctata pretrei punctata

1.0 million years 2.5 million years Trogon viridis bairdii melanocephalus violaceus curucui comptus melanurus massena rufus personatus collaris mexicanus elegans Trogon collaris occurs both widely in lowlands and highlands

Nyctibius maculosus leucopterus griseus grandis bracteatus aethereus

Blackbird clade Xiphorhynchus guttatoides Pseudoleistes guirahuro susurrans Pseudoleistes virescens guttatu Agelaius flavus flavigaster Agelaius icterocephalus lachrymosus Agelaius ruficapillus erythropygius Molothrus badius triangularis Oreopsar bolivianus obsoletus Agelaius thilius kienerii Agelaius cyanopus picus Agelaius xanthophthalmus fuscus Amblyramphus holoseri elegans Curaeus curaeus spixii Gnorimopsar chopi chunchotambo Lampropsar tanagrinus ocellatus pardalotus Gymnomystax mexicanus Macroagelaius imthurni 1.0 million years 2.5 million years Psarocolius and Psarocolius viridis relatives Psarocolius bifasciatus Dendrocincla Gymnostinops montezuma (f.) ridgwayi Psarocolius decumanus anabatina Psarocolius wagleri Psarocolius atrovirens fuliginosa Psarocolius angustifrons turdina Cacicus solitarius (f.) taunayi Cacicus sclateri homochroa Ocyalus latirostris Psarocolius oseryi merula Cacicus haemorrhous tyrianna Cacicus leucoramphus Cacicus chrysonotus Cacicus cela Cacicus (u.) microrhynchus Cacicus uropygialis Cacicus (u.) pacificus Cacicus melanicterus

Icterus chrysocephalus Crax and relatives cayanensis fasciolata auricapillus alector bonana globulosa (d.) portoricensis blumenbachii oberi rubra laudabilis (d.) northropi alberti (d.) melanopsis daubentoni prosthemelas Nothocrax urumutum spurius salvini fuertesi Pauxi unicornis cuc igneus tuberosa wagleri tomentosa maculialatus mitu mes mesomelas pectoralis Pauxi pauxi graceaneae icterus Ramphocelus croconotus carbo chrysater bresilius graduacauda nigrogularis parisorum icteronotus pustulatus passerinii bullockii galbula sanguinolentus abeillei Taxonomic note: costaricensis has been recognized as a leucopteryx but but is not considered so here auratus nigrogularis 1.0 million years gularis 2.5 million years Pteroglossus Veniliornis bitorquatus affinis beauharnaesii nigriceps flavirostris callonotus aracari dignus pluricinctus frontalis castanotis passerinus torquatus cassini frantzii kirkii erythropygius spilogaster Picoides lignarius Baillonius bailloni Picoides mixtus viridis chocoensis inscriptus Taxonomic note: humbolti, sanguineus and mariae are not considered full species due to lack of reproductive isolation and are excluded

Pionopsitta pileata pulchra haematotis coccinicolaris barrabandi aurantigena caica vulturina

Neotropical clade elegans Progne chalybea (South) Progne subis Progne murphyi Progne dominicensis Progne cryptoleuca Progne chalybea (North) Progne sinaloae Phaeoprogne tapera ruficollis Stelgidopteryx serripennis Neochelidon tibialis pileata fasciata Atticora melanoleuca Notiochelidon cyanoleuca Alopochelidon fucata Notiochelidon flavipes Haplochelidon andecola Notiochelidon murina 1.0 million years 2.5 million years Myarchus

semirufus tuberculifer barbirostris swainsoni 1 cephalotes phaeocephalus panamensis ferox Craniolueca venezuelensis swainsoni 2 albiceps validus marcapata vulpina stolidus albicapilla sagrae pyrrhophia oberi henricae antillarum obsoleta crinitus erythrops demissa yucatanensis antisiensis tyrannulus curtata baroni albiventer albilinea stolzmanni Anairetes meyeni nigrocristatus reguloides leucorrhoa agilis bicolor flavirostris alpinus cyaneoviridis parulus euchrysea fernandezianus thalassina reconstruction uncertain at base

Geositta poeciloptera crassirostris punensis rufipennis maritima antarctica isabellina saxicolina peruviana tenuirostris cunicularia 1 cunicularia 2 Taxonomic note: Highland and lowland forms of cunicularia are treated as separate species here.

1.0 million years 2.5 million years Carduelis Troglodytes yarellii musculus magellanica 2 aedon 1 crassirostris sissonii spinescens aedon 2 cucullata brunneicollis atrata rufociliatus olivacea solstitialis magellanica 1 rufulus barbata ochraceus xanthogastra Thryorchilus browni notata

Ochthoeca pulchella Metallura jelskii odomae diadema (williami) primolina spodionota baroni (williami) atrigularis frontalis phoebe cinnamomeiventris theresiae thoracica eupogon leucophrys aeneocauda oenanthoides tyrianthina rufipectoralis fumicolor

Muscisaxicola juninensis rufivertex Cinclodes nigrofumosus cinera taczanowski (a.lpina) grisea patagonicus albifrons palliatus flavinucha atacamensis alpina excelsior macloviana aricomae albilora antarcticus frontalis fuscus capistrata comechingonus maculirostris oustaleti olrogi Amazonian fluviatilis (not shown) is basal to rest of pabsti

Hemispingus melanotis frontalis piurae rufosuperciliarus trifasciatus superciliaris verticalis xanthophthalmus atropileus calophrys 1.0 million years auricularis 2.5 million years