Sequence matrix construction

PHLAWD uses a baited approach where sequences for a clade of interest are compared to NCBI GenBank sequences and used to download homologous gene regions. We acquired bait sequences for 24 genes from several sources: the “ETOL” set, from the Euteleost Tree of Life project, the “Rabosky” set, and the “Near” set.

All PHLAWD analyses used a modified version of the original software. The original version of PHLAWD entered maintenance mode September 2012, and was subsequently modified by Cody Hinchliff to fix a number of bugs and speed up analyses. Our modified version fixes other bugs and supports including daily updates in addition to the bimonthly GenBank releases.

Our modified version of PHLAWD then assesses these homologous sequences for saturation, and if saturated, broken up into sub-matrices aligned with MAFFT corresponding to a user taxonomy or guide tree. We conducted a PHLAWD-mediated GenBank search for each gene with the parameters MAD (median average deviation) = 0.01, coverage = 0.2, and identity = 0.2 for NCBI taxon Actinopterygii. Using the NCBI taxonomy, these sub-matrices were then aligned together using profile alignment as provided in MUSCLE. We used GNU Parallel to parallelize this search, as the built-in parallelization in PHLAWD can occasionally stall using high numbers of threads.

To further increase the genetic coverage of our dataset, we downloaded the full Barcode of Life (BOLD) database sequences and extracted the longest cytochrome oxidase subunit 1 (coi) gene for each species in Actinopterygii. We also downloaded full mitochondrial chromosomes for each actinopterygian species and extracted the nd2 and nd4 genes. This preliminary alignment included 15,606 species.

Table: Gene sources for PHLAWD analyses. Sources marked (*) were not used for baited PHLAWD searches and instead included directly into the character matrix.
Gene name ETOL Rabosky Near BOLD* mt-genome*
12s        
16s      
4c4        
coi        
cytb        
enc1    
ficd          
glyt    
hoxc6a        
kiaa1239        
myh6    
nd2        
nd4        
panx2        
plagl2    
ptr      
rag1    
rag2        
rhodopsin      
ripk4        
sh3px3      
sidkey        
sreb2    
svep1        
tbr1    
vcpip        
zic1    

Alignment error-correction

To filter out misidentified sequences, we ran a local nucleotide BLAST search on our combined PHLAWD and mitochondrial sequences. Using the closest non-self BLAST match, we ensured that no PHLAWD sequences matched with a high identity to a species outside of the original species family, and checked for contamination by excluding sequences that aligned with high identity to a non-actinopterygian such as Homo.

For example, the enc1 sequence for Amia calva (Accession EF032974.1), in family Amiidae, matches with 99.87% identity to Lepomis cyanellus (Accession KF139483.1), in family Centrarchidae, despite there being other enc1 closer for this species. This specific sequence was therefore excluded from the final analysis.

We used previously described sequencing protocols to generate new multilocus data for 442 species. These were directly added and aligned to the character matrix. Alignments were then quality checked by eye to ensure that coding genes were in frame. These alignments were then concatenated for downstream analysis.

Table: New sequences by gene.
Species enc1 glyt myh6 plagl2 ptr rag1 sh3px3 sreb2 tbr1 zic1
Acanthistius cinctus
Acanthostracion quadricornis
Achiropsetta tricholepis
Acropoma japonicum
Aethotaxis mitopteryx mitopteryx
Akarotaxis nudiceps
Allotoca catarinae
Altolamprologus calvus
Aluterus scriptus
Amanses scopas
Amblyglyphidodon aureus
Amblyopsis rosae
Amblyopsis spelaea
Ammocrypta beanii
Ammocrypta bifascia
Ammocrypta clara
Amphiprion chrysopterus
Anableps anableps
Anablepsoides hartii
Andinoacara rivulatus
Aphredoderus gib
Apistus carinatus
Aplodactylus arctidens
Apogon binotatus
Apogon maculatus
Apogon planifrons
Ariomma bondi
Ariomma indicum
Ariomma melanum
Arothron stellatus
Arripis trutta
Artedidraco mirus
Artedidraco orianae
Artedidraco shackletoni
Artedidraco skottsbergi
Astatotilapia bloyeti
Astatotilapia burtoni
Astrapogon puncticulatus
Astronotus sp
Atypichthys latus
Aulonocranus dewindti
Austrofundulus leohoignei
Austrolebias nigripinnis
Azurina hirundo
Bathybates fasciatus
Bathyclupea argentea
Bathyclupea gracilis
Bathydraco antarcticus
Bathydraco macrolepis
Bathydraco marri
Bathydraco scotiae
Bathystethus cultratus
Benitochromis batesii
Benthochromis tricoti
Biotoecus opercularis
Boulengerochromis microlepis
Bovichtus variegatus
Cantherhines pardalis
Canthigaster coronata
Canthigaster rostrata
Caquetaia kraussii
Cardiopharynx schoutedeni
Centropomus ensiferus
Chaenocephalus aceratus
Chaenodraco wilsoni
Champsocephalus esox
Champsocephalus gunnari
Channichthys rhinoceratus
Chaudhuria caudata
Cheilodipterus artus
Chelonodon patoca
Chetia mola
Chilomycterus reticulatus
Chilotilapia rhoadesii
Chionodraco hamatus
Chionodraco myersi
Chionodraco rastrospinosus
Chironemus bicornis
Chironemus maculosus
Chonerhinos naritus
Chrionema furunoi
Chrysiptera brownriggii
Cichlasoma boliviense
Cleithracara maronii
Congiopodus leucopaecilus
Cottoperca gobio
Crapatalus munroi
Crenicichla sveni
Cryodraco antarcticus
Cryodraco atkinsoni
Cryptoheros sajica
Crystallaria asprella
Cygnodraco mawsoni
Cyphotilapia frontosa
Cyprichromis leptosoma
Cyrtocara moorii
Dacodraco hunteri
Dascyllus aruanus
Dichistius capensis
Dichistius multifasciatus
Dicrossus filamentosus
Dinolestes lewini
Dinoperca petersi
Diodon hystrix
Dischistodus melanotus
Dissostichus mawsoni
Doederleinia berycoides
Dolloidraco longedorsalis
Echiichthys vipera
Enigmapercis sp
Epigonus telescopus
Eretmodus cyanostictus
Erilepis zonifer
Etheostoma akatulo
Etheostoma artesiae
Etheostoma asprigene
Etheostoma australe
Etheostoma baileyi
Etheostoma barbouri
Etheostoma barrenense
Etheostoma bellator
Etheostoma binotatum
Etheostoma blennioides
Etheostoma blennius
Etheostoma caeruleum
Etheostoma cervus
Etheostoma cf
Etheostoma chienense
Etheostoma chlorosomum
Etheostoma cinereum
Etheostoma coosae
Etheostoma ditrema
Etheostoma duryi
Etheostoma euzonum
Etheostoma flabellare
Etheostoma forbesi
Etheostoma fusiforme
Etheostoma gracile
Etheostoma histrio
Etheostoma hopkinsi
Etheostoma jessiae
Etheostoma kanawhae
Etheostoma knt
Etheostoma lepidum
Etheostoma longimanum
Etheostoma luteovinctum
Etheostoma lynceum
Etheostoma mariae
Etheostoma mediae
Etheostoma microperca
Etheostoma nigrum
Etheostoma okaloosae
Etheostoma olivaceum
Etheostoma olmstedi
Etheostoma pallididorsum
Etheostoma parvipinne
Etheostoma phytophilum
Etheostoma proeliare
Etheostoma pseudovulatum
Etheostoma pyrrhogaster
Etheostoma rafinesquei
Etheostoma rupestre
Etheostoma sagitta
Etheostoma serrifer
Etheostoma smithi
Etheostoma stigmaeum
Etheostoma thalassinum
Etheostoma trisella
Etheostoma tuscumbia
Etheostoma vitreum
Etheostoma zonale
Eviota abax
Forbesichthys agassizii
Forbesichthys papilliferus
Gambusia holbrooki
Geophagus iporangensis
Gerlachea australis
Girella nigricans
Glossogobius olivaceus
Glyptauchen panduratus
Gnathochromis pfefferi
Gobiocichla ethelwynnae
Gobionotothen acuticeps
Gobionotothen gibberifrons
Gobionotothen marionensis
Goodea atripinnis
Grahamichthys radiata
Graus nigra
Gymnapistes marmoratus
Gymnocephalus cernua
Gymnodraco acuticeps
Gymnogobius breunigii
Hapalogenys dampieriensis
Haplochromis latifasciatus
Haplochromis luteus
Haplotaxodon microlepis
Harpagifer antarcticus
Hemichromis elongatus
Hemichromis letourneuxi
Hemichromis sp
Hemiglyphidodon plagiometopon
Hermosilla azurea
Histiodraco velifer
Hypselecara temporalis
Hypsypops rubicundus
Inimicus didactylus
Konia eisentrauti
Kraemeria bryani
Kyphosus sectatrix
Lactarius lactarius
Lactoria cornuta
Laetacara curviceps
Lagocephalus laevigatus
Lateolabrax latus
Lates microlepis
Latridopsis forsteri
Latris lineata
Lepadichthys lineatus
Lepidonotothen larseni
Lepidonotothen nudifrons
Lepidonotothen squamifrons
Lepidozygus tapeinosoma
Leptobrama muelleri
Lesueurina platycephala
Limnichthys fasciatus
Limnotilapia dardennii
Liopropoma mowbrayi
Liopropoma susumi
Lipogramma trilineata
Lophotus capellei
Marilyna darwinii
Matsubaraea fusiforme
Mecaenichthys immaculatus
Medialuna californiensis
Mesonauta egregius
Mesonauta festivus
Mesonauta insignis
Mesonauta mirificus
Metavelifer multiradiatus
Mikrogeophagus ramirezi
Milyeringa veritas
Minous trachycephalus
Monacanthus chinensis
Monotrete leiurus
Myaka myaka
Nandopsis salvini
Nandopsis tetracanthus
Nanochromis parilus
Neoglyphidodon melas
Neolamprologus brevis
Neolamprologus toae
Neopagetopsis ionah
Neopomacentrus nemurus
Neosebastes thetidis
Normanichthys crockeri
Nothobranchius furzeri
Nothonotus acuticeps
Nothonotus camurus
Nothonotus chuckwachatte
Nothonotus jordani
Nothonotus juliae
Nothonotus maculatus
Nothonotus rufilineatus
Nothonotus tippecanoe
Notothenia angustata
Notothenia coriiceps
Notothenia rossii
Ocosia zaspilota
Ophiocara porocephala
Ophiodon elongatus
Ophthalmotilapia ventralis
Oreochromis tanganicae
Orthochromis luongoensis
Osopsaron formosensis
Oxymonacanthus longirostris
Pagetopsis macropterus
Pagetopsis maculatus
Pagothenia borchgrevinki
Pagrus pagrus
Paracentropogon rubripinnis
Parachaenichthys charcoti
Parachaenichthys georgianus
Parachromis managuensis
Paracyprichromis brieni
Parahollardia lineata
Paretroplus dambabe
Parma microlepis
Patagonotothen cornucola
Patagonotothen elegans
Patagonotothen guntheri
Patagonotothen longipes
Patagonotothen ramsayi
Patagonotothen sima
Patagonotothen squamiceps
Patagonotothen tessellata
Patagonotothen wiltoni
Perca schrenkii
Percina aurantiaca
Percina aurolineata
Percina bimaculata
Percina carbonaria
Percina cf
Percina copelandi
Percina crassa
Percina evides
Percina kusha
Percina macrocephala
Percina maculata
Percina nevisense
Percina oxyrhynchus
Percina palmaris
Percina peltata
Percina roanoka
Percina sciera
Percina shumardi
Percina stictogaster
Percina vigil
Percophis brasiliensis
Percopsis transmontana
Petrochromis polyodon
Phaeoptyx conklini
Plecodus straeleni
Plectroglyphidodon dickii
Pleuragramma antarctica
Pogonophryne barsukovi
Pogonophryne cerebropogon
Pogonophryne eakini
Pogonophryne immaculata
Pogonophryne macropogon
Pogonophryne marmorata
Pogonophryne scotti
Polyprion americanus
Pomacentrus nigromanus
Pomachromis richardsoni
Premnas biaculeatus
Prionodraco evansii
Pristiapogon kallopterus
Profundulus labialis
Psammoperca waigiensis
Psedocrenilabrus sp
Pseudaphritis urvillii
Pseudochaenichthys georgianus
Pseudosimochromis curvifrons
Pseudotriacanthus strigilifer
Psilodraco breviceps
Pterophyllum leopoldi
Pteropsaron springeri
Ptilichthys goodei
Ptychochromis oligacanthus
Pungu maclareni
Racovitzia glacialis
Reganochromis calliurus
Retroculus xinguensis
Rhinecanthus aculeatus
Rhyacichthys aspro
Rocio octofasciata
Romanichthys valsanicola
Rosenblattia robusta
Sander vitreus
Sarotherodon galilaeus
Satanoperca jurupari
Scombrolabrax heterolepis
Scombrops boops
Scombrops gilberti
Scorpis violacea
Serranochromis angusticeps
Sicyopterus japonicus
Spathodus marlieri
Speoplatyrhinus poulsoni
Sphaeramia nematoptera
Sphoeroides pachygaster
Spicara australis
Spicara smaris
Steatocranus tinanti
Steatocranus ubanguiensis
Stephanolepis cirrhifer
Stomatepia pindu
Symphysanodon berryi
Symphysanodon octoactinus
Synagrops philippinensis
Takifugu ocellatus
Tetragonurus cuvieri
Tetraodon mbu
Tewara cranwellae
Thalasseleotris iota
Thoracochromis brauschi
Thorichthys meeki
Tilapia mariae
Tilapia ruweti
Tilapia sparrmanii
Tilodon sexfasciatus
Tomocichla sieboldii
Torquigener pleurogramma
Trachinus draco
Trematomus bernacchii
Trematomus eulepidotus
Trematomus hansoni
Trematomus lepidorhinus
Trematomus loennbergii
Trematomus newnesi
Trematomus nicolai
Trematomus pennellii
Trematomus scotti
Trematomus tokarevi
Trematomus vicarius
Triacanthodes ethiops
Triacanthus nieuhofii
Trichonotus elegans
Trichonotus filamentosus  
Trichonotus setiger
Trixiphichthys weberi
Tropheus duboisi
Tydemania navigatoris
Tylochromis lateralis
Tylochromis mylodon
Typhlichthys subterraneus
Tyrannochromis nigriventer
Uaru amphiacanthoides
Vomeridens infuscipinnis
Yongeichthys criniger
Zalembius rosaceus
Zanclorhynchus spinifer
Zaprora silenus
Zingel asper
Zingel zingel
Zu elongatus  

Taxonomic reconciliation

We wrote a custom web scraper in Python to download all accepted scientific names, synonyms, and taxonomy for Actinopterygii fishes from FishBase. We then loaded all aligned PHLAWD sequences into an SQLite database to record all taxonomic changes in a consistent format.

We then used a custom Python script to attempt to reconcile the GenBank species names against our known FishBase taxonomy. Species names were matched using the following algorithms, in order:

  1. Exact scientific name
  2. Exact valid synonym
  3. Exact common name
  4. Exact scientific name without subspecies epithet
  5. Exact valid synonym, without subspecies epithet
  6. Apply manual taxonomic corrections
  7. Fuzzy match against scientific names based on the gestalt pattern matching algorithm
  8. Fuzzy match against valid synonyms based on the gestalt pattern matching algorithm
  9. Adding unambiguous-but-unmatched species with more than 2 genes, as these are likely to be new species that had not yet been included in FishBase

After these automated mechanisms, we examined matches by hand and manually corrected any mis-assignations, then checked for sequences that were identical, yet were mapped to different species. Our taxonomic reconciliation process matched 46/46 orders of fish (100%), 454/480 families (94.6%), and 3,368/4,853 genera (69.4%), as measured against FishBase.

Matching method Count
Exact scientific name 11,368
Exact synonym 623
Manual taxonomic corrections 131
Unmatched-but-unambiguous 84
Exact scientific name, no subspecies 69
Fuzzy scientific name 61
Fuzzy synonym 12
Exact synonym, no subspecies 9

Table: Taxonomic reconciliation by match type.

Rogue searching

To eliminate rogue taxa, which reduce the bootstrap support of phylogenies due to their unstable position, we conducted a RogueNaRok analysis and searched for sets of up to 3 species that could be dropped to improve bootstrap support on an unconstrained phylogenetic analysis. RogueNaRok iteratively removes taxa and estimates their impact on bootstrap support; this impact is dependent on the identity of all other taxa removed before it. We therefore excluded all taxa or sets of taxa up to the point where dropping any subsequent taxa would fail to improve bootstrap support by more than 1. A total of 645 species were removed in this manner, with 152 and 102 species removed as part of a 2-species and 3-species set, respectively.

Tree searching

We conducted an initial tree search using RAxML v8.1.17 using the fast ML search convergence criterion for large trees (option -D) and the SEV-based implementation for gap columns (option -U). The analysis took approximately 4 days of wall-clock time on a 24-core Intel Xeon E5-2690v3 x2 compute machine.

gene n gene n
12s 27 ptr 13
16s 84 rag1 27
4c4 17 rag2 6
coi 175 rhodopsin 20
cytb 70 ripk4 8
enc1 9 sh3px3 8
ficd 14 sidkey 8
glyt 1 sreb2 4
hoxc6a 7 svep1 6
kiaa1239 5 tbr1 11
myh6 15 vcpip 8
panx2 11 zic1 14
plagl2 9 total sequences 577

Table: Gene sequences excluded due to rogue behavior or high identity BLAST matches outside of their species’ assigned family.

We then generated individual family-level phylogenies by extracting the subtree descended from the most recent common ancestor of all species in each family, and automatically marked descendent taxa that were from outside the focal family. We then assessed the quality of the phylogeny on a family-by-family basis, and marked any taxa that exhibited rogue behavior.

We then removed tips that had extremely long branches, as these potentially indicated areas of poor sequence quality or alignment. Using the final filtered dataset, which contained 11,644 tips, we reran a maximum likelihood analysis in RAxML and computed node support values using the SH-like statistic, as it is conservative at estimating support values like standard bootstrapping but runs much faster. The NNI-optimized topology with SH-like support values can be downloaded here.

Fossil calibrations

We devised an extensive list of fossil-based minima for divergences in actinopterygian phylogeny. Many of these derived from past molecular clock analyses, but others are new to this study. Extinct taxa, along with relevant phylogenetic and age justifications, are supplied in Supplemental Data: Calibration Report. We applied these fossils as node-based calibrations, with upper age bound specified by a modified implementation of the Whole Tree Extension of the Hedman Algorithm [WHETA; @Hedman2010; @Lloyd2016]. This approach yields probabilistic maximum age constraints on given nodes based on: a minimum age specified by the oldest fossil descended from that node; the stratigraphically consistent sequence of older fossil outgroups to that node; and a hard maximum age defined by the investigator. We adopted a composite approach to specifying these sequences of outgroups [c.f. @Harrington2016], applying both stratigraphically consistent calibrations included in our own set of fossil-based minima as well as sequences of fossils whose phylogenetic positions were well known, but which were not used as calibration minima themselves. Sequences based on the former were collated automatically by a custom algorithm. Where appropriate, this set of outgroups was appended with additional fossil outgroup ages.

We applied two such sequences: the stem teleost lineages successively more remote from the teleost crown specified by @Friedman2013 and updated by @Harrington2016, and a set of fossil outgroups to extant chondrosteans. The latter is novel to this study, and is based upon the cladistic hypotheses of chondrostean interrelationships given by @Grande1991, @Grande1996 and @Hilton2009. In increasing proximity to the chondrostean crown, with ages given in parentheses, this sequence is: Birgeria groenlandia (250.1 Ma), Chondrosteus acipenseroides (193.81), and Peipiaosteus pani (129.3). Age justifications follow those given for other taxa from the same geological units (e.g., Chondrosteus acipenseroides is co-occurs with Dorsetichthys bechei, which is included in the series of stem teleosts given by @Friedman2013 and @Harrington2016). Concatenated outgroup-age sequences were then submitted to the @Hedman2010 algorithm, with a hard upper age constraint of 430 Ma. This choice of maximum age is unlikely to bias our estimates substantially, as we only applied this method for nodes within the actinopteran crown where times of origin are generally accepted to be substantially younger than this Silurian bound. In practice, the credible intervals estimated by the algorithm are relatively insensitive to the choice of the hard maximum age constraint.

Our calibration set is restricted to fossils of Mesozoic and Cenozoic age. This reflects two factors. First, the clade of principal interest in this analysis—Teleostei—is known exclusively from Mesozoic and younger strata. Second, the relationships of many Paleozoic fossils relative to modern actinopterygian lineages is poorly constrained (see verbal arguments in @Sallan2014, @Friedman2015; analytical arguments in Giles et al. in press), with some fossils used as key calibrations in past studies [e.g., @Hurley2007] recovered in very different phylogenetic positions in subsequent analyses [e.g., Giles et al. in press; @Xu2014]. Rather than potentially applying misleading calibrations to deep divergences within actinopterygian phylogeny, we instead have selected to allow more securely placed fossils belonging to later-diverging clades inform our age estimates for more inclusive groups.

Our resulting timescale for actinopterygian history shows good agreement with the evolutionary timeline implied by fossils for groups with well-understood paleontological records. The mean origination date for crown Actinopterygii (368 Ma) is centered near the end-Devonian mass extinction (359 Ma), which preceded the first apparent radiation of the group in terms of both taxonomic and morphological diversity in the succeeding Carboniferous [359–299 Ma; @Sallan2010; @Sallan2012; @Friedman2012; @Sallan2014]. The origin of crown Neopterygii is centered on the early Permian (298 Ma). Crown Holostei (251 My) is centered shortly after the Permo-Triassic boundary, and corresponds closely to our fossil-based minimum for this clade (the earliest Triassic Watsonulus). The origin of crown teleosts (192 My) falls near the beginning of the Jurassic (201–145 Ma), before the appearance of the first diagnostic crown teleosts—members of the Elopomorpha, the sister group to all other teleosts—late in that period [@Arratia2000]. This estimate substantially closes the so-called the “teleost gap”, a conspicuous temporal disagreement between the time of origin of crown teleosts implied by the fossil record and some molecular clock studies [e.g., @Hurley2007; @Near2012]. Among nested teleost clades, there is generally good agreement between our timeline and that implied by both previous molecular clock studies and the fossil record.

Placing unsampled species

We compared the taxonomic classification across Fishbase [@Froese2014], the Catalog of Fishes [@Eschmeyer2017], and the Euteleost Tree of Life project [@Betancur-R2013]. Based on these taxonomic authors, we built a new classification scheme and explored shallower phylogenetic groups where non-monophyly was found in our phylogeny. This combined “Phylogenetic Fish Classification” (PFC) was then used for the purpose of taxonomic back-filling of taxa without molecular data or those that were removed during the curation stage. Using the time-calibrated phylogeny as a backbone, we generated a distribution of trees where missing taxa were placed according to our PFC taxonomy.

For each of the unsampled species of ray-finned fish, we assigned the most restrictive taxonomic rank (e.g., genus, family, order) that was recovered as monophyletic in our maximum likelihood phylogeny. We computed rank-specific estimates of the speciation and extinction rate under a constant rate model, conditioned on the sampling fraction [@Stadler2009], and used these rates to generate waiting times for unsampled species. However, if the taxonomic node had fewer than 3 tips, or if the probability of sampling the crown age of that node given the number of sampled taxa [@Sanderson1996] was less than 0.8, we searched all the ancestors of that taxonomic node that fulfilled the previous criteria. The generated waiting times were bounded between the crown age of that clade and the present time ($t=0$). However, if the crown capture probability was less than 0.8, the maximum generated age was extended to the stem age of the taxonomic node. If placement was impossible due to monophyletic constraints (see below), the waiting time was then bounded between the stem age and the crown age of that taxonomic node.

These waiting times were used to randomly attach unsampled species to an existing branch within their assigned taxonomic rank, as long as these new species did not break the monophyly of nodes that were recovered as monophyletic and assigned a taxonomic rank, and constrained to not produce negative branch lengths due to a child node being added that was older than a parent node. If all of the child branches of a taxonomic node belonged to a monophyletic node, or if the crown capture probability was less than 0.8, the new species was instead assigned to the stem of that clade.

These functions were all implemented in a custom Python script based on the code from the R packages TreePar and SimTree [@Stadler2009; @Stadler2011a; @Stadler2011b]. This procedure was repeated 100 times to generate a distribution of fully-sampled ray-finned fish phylogenies.

Computing tip-specific speciation rates

We computed speciation rates via three primary mechanisms: with BAMM, with the DR statistic, and with the interval-rates method.

BAMM uses a Bayesian reversible-jump Markov Chain Monte Carlo (MCMC) algorithm to identify the location and estimate the parameters of various diversification rate regimes on a time-calibrated. BAMM attempts to identify macroevolutionary rate shift configurations and generates a distribution of posterior samples. A full set of these posterior samples can be summarized, for example, by computing the mean rate for each tip in the phylogeny or as a marginal posterior distribution of tip rates. We also check for sensitivity of the BAMM analysis to its priors for the time-varying BAMM analyses, and find that the posterior distribution is independent of the prior.

The DR statistic, for “diversification rate”, is a summary statistic that infers recent speciation rates for all tips in the phylogeny without requiring a formal parametric inference model. DR is itself the inverse of the equal-splits measure, where the equal-splits measure (ES) for a tip i is equal to:

ESi=j=1Nilj12j-1ES_i = \sum_{j=1}^{N_i} l_j \frac{1}{2^{j-1}}

where Ni are the number of nodes between tip i and the root, lj is the length of edge j where j=1 is the edge leading to tip i. Intuitively, it is the weighted mean of the inverse of branch lengths. DR approximates the speciation rate of a phylogeny diversifying under a Yule (pure-birth) process; for a full proof see section 1.2.2 of the supplement of Jetz et al. (2012). DR’s approximation of the true speciation rate is a useful property and can be used to cross-check speciation rate estimates obtained through BAMM.

As a third independent estimate of speciation rate, we use the interval-rates method, or node-density measure. This is an estimate of the speciation rate over a certain period of time. It is the number of nodes that exist on a phylogeny over a certain interval, divided by the amount of time that interval spans, and is an extremely simple way to compute a speciation rate.

References