Testing for Rapid Radiation Over Clade History Using the Gamma Statistic
Did a clade ‘adaptively radiate’?
Expect initial diversification to be fast
Pybus and Harvey (2001)* proposed a test for rate shift across the tree
Pybus, O. G., and P. H. Harvey. 2000. Testing macro-evolutionary models using incomplete molecular phylogenies. Phil. Trans. Roy. Soc. (Lond.) B 267:2267-2272. The gamma statistic
Midpoint of BLs a tree branching under a constant-rates model should have a balance of node depths around the midpoint of the tree
γ describes this distance
γ~0 Early branching rapid, early diversification will create an imbalance of young nodes this will be reflected by a -γ evidence for adaptive radiation γ<0 Late branching
recent accelerated net diversification will concentrate nodes towards the tips
could be due to increase in birth rate or decrease in death rate
γ>0 γ-statistic
Elevated early rate Constant rate Elevated late rate Midpoint of BLs
Keypoint: Negative γ-statistic consistent with early elevation of diversification rate (this is the CR test)
γ<0 γ~0 γ>0 if gamma is less than 2 std. deviations from mean (γ ≤ -1.645), reject constant rate of diversification What about incomplete sampling?
3 with random 1
sampling of four 4 taxa, what nodes would be expected to miss? 5 2 how would this affect gamma? 6 0 0 5 MCCR: The constant rates1 A. test for 0 0 0 1 area = 2.27
incompletely sampledfrequency trees* 0 0 5
Complete sampling: γ ≤ -1.645 0
!4 !2 0 2 4 Incomplete sampling means that old nodes more likely to be area recovered, biasing CR test 0
Solution: MCCR test* 0 0 4 B.
Simulate tree with n taxa 0 0 0 3 RANDOMLY prune missing taxa 0 frequency 0 0
2 ! = -3.24 Calculate the γ-statistic on pruned tree 0 0 0 Repeat 1 0
Calculate corrected p-value !4 !2 0 2 4 !
* Pybus and Harvey (2000) Example of Gamma Statistic: Diversification of Homalopsid Snakes
34 species distributed across S.E. Asia
Aquatic to semi-aquatic
Alfaro et al. 2007 A timetree for homalopsid diversification
Enhydris matannensis Lake Towuti, Sulawesi A Enhydris plumbea A Enhydris plumbea B Enhydris chinensis Bayesian timetree Enhydris subtaeniata Enhydris enhydris B using BEAST Enhydris innominata Enhydris longicauda 4 genes (12S, 16S, cytB, Enhydris punctata Bitia hydroides 0 0
C-Mos 5 1 A. Cantoria violacea C 0
0
0 Gerarda prevostiana 1 area = 2.27 frequency Fordonia leucobalia A 9 of 10 genera, 20 of 0 0 5 Fordonia leucobalia B 34 species
0 Enhydris polylepis !4 !2 0 2 4 Myron richardsonii area MCCR test suggests Enhydris bocourti Erpeton tentactulatus 0 0 0 rapid initial 4 B. Homalopsis buccata 0
0
0 D diversification ( P < 3 Cerberus australis 0 frequency 0 Cerberus rynchops A 0 0.001) 2 ! = -3.24 Cerberus microlepis 0
0 0 1 Cerberus rynchops B
0 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0 !4 !2 0 2 4 ! OLIGO MIOCENE Pi Ps Alfaro et al. 2007 Log-Lineages Through Time 3.0 2.5 2.0 Log Lineages 1.5 1.0
0 5 10 15 20
Time From Basal Divergence Models of diversification: Constant-rate models
Pure birth (PB) Pure Birth Model
Death = 0 0.7 0.6 Birth Rate 0.5 0.4 0.3
0 20 40 60 80 100 Time Models of diversification: Constant-rate models
Birth-Death (BD) Birth-Death Model
Birth & Death constant 0.7 0.6 Birth 0.5 Rate 0.4 Death 0.3
0 20 40 60 80 100 Time Rate-variable models: Density-dependent
Exponential Density-Dependent Model Density-dependent: Exponential 1.0
-x R(t) = R0 *(N(t)) 0.8
0.6 Birth Rate 0.4 0.2 0.0
0 20 40 60 80 100 Time Rate-variable models: Density-dependent
Logistic Density-Dependent Model Density-dependent: Logistic 1.00
R(t) = R0 *(1- N(t)/K) 0.95 Birth 0.90 Rate res[, 1] 0.85 0.80
0 20 40 60 80 100
as.numeric(rownames(res))Time Models of diversification: Variable-rate models
Yule-2-RateYule-2-Rate Model Model Yule-2-Rate (Y2R)
Death = 0 Birth-2 0.805
Shift Time Rate 0.800 Rate Birth-1 0.795
0 20 40 60 80 100
TimeTime Models of diversification: Variable-rate models
Rate-variable BD (RVBD) Rate-VariableRate-Variable Birth-Death BD Model Model
Death/Birth is constant Rate-2 0.805
Shift Time Rate 0.800 Rate Rate-1 D/B 0.795
0 20 40 60 80 100
TimeTime Model scores
Model LH dAIC Rate 1 Rate 2 Shift Time
PB 75.73 12.07 0.153 NA NA
BD 75.73 14.07 0.153 NA NA
DDL 79.07 7.4 0.236 NA NA
DDX 77.58 10.37 0.352 NA NA
Y2R 83.77 0 0.177 0.036 1.127
RVBD 83.77 2.0 0.177 0.036 1.127 density-dependent models rejected for rockfish How can we test for unequal rates of diversification?
Construct a timetree
Calculate rates
Test for significant differences using comparative methods Step1: molecular phylogeny
Molecular sequence data from three loci Rag1, 12S, 16S (Holcroft, 2005, plus additional data)
Sampled 86 ingroup taxa including members of all extant families
Bayesian analysis using MrBayes, 1 X 107 generations, multiple independent runs v Ranzania laevis v Masturus lanceolatus MOLIDAE # v Mola mola 1 # Mola mola 2 Triodon macropterus TRIODONTIDAE v Anoplocaparos inermis Aracana ornata ARACANIDAE v # Tetrosomus concatenatus v Lactophrys bicaudalis v Lactophrys triqueter OSTRACIIDAE Lactophrys polygonia Lactophrys quadricornis v Allomycterus pilatus v v Chilomycterus antennatus # Chilomycterus schoepfii v Diodon holacanthus DIODONTIDAE v Diodon hystrix v Diodon liturosus # Lagocephalus laevigatus Marilyna darwinii v v v Takifugu rubripes # v Torquigener pleurogramma v Tetractenos glaber Tetractenos hamiltoni v Sphoeroides dorsalis Sphoeroides spengleri Monotreta leiurus v # Tetraodon fluviatillis TETRAODONTIDAE v Arothron hispidus v v Arothron nigropunctatus Canthigaster bennetti v Canthigaster rostrata Canthigaster amboinensis v Canthigaster valentini v Canthigaster solandri v Canthigaster jactator Canthigaster janthinoptera v Trixiphicthys weberi Pseudotriacanthus strigilifer TRIACANTHIDAE Triacanthodes anomalus TRIACANTHODIDAE v Aluterus scriptus # v Brachaluteres jacksonianus v Paraluterus prionurus v v Monacanthus ciliatus # Monacanthus hispidus Oxymonacanthus longirostris MONACANTHIDAE v Meuschenia trachylepis Nelusetta ayraudi v v Cantherhines pullus # Amanses scopas Cantherhines dumerilii Balistoides conspicillum Melicthys niger v v Balistoides virdescens Xanthichthys auromarginatus Abalistes stellatus BP > 85% v Rhinecanthus aculeatus v Rhinecanthus assasi v v Sufflamen bursa BALISTIDAE PP > 95% Sufflamen chrysopterus v Canthidermis maculatus v Pseudobalistes fuscus v # Balistes vetula v v Balistes capriscus Balistes polylepis
Alfaro, Brock, and Santini 2007, Evolution Step 4: Compare Diversification Rates
1. Estimate mean Age Extant Taxon Faster? diversification rate of (MY) # predominately reef tetraodontiformes (λG) Balistidae 22.9 43 ** λG = [ln(n) - ln(2)]/t Diodontidae 10.9 22 ** = ln(350)-ln(2)/70MY Monacanthidae 24.6 108 ** = 0.07 species/MY Ostraciidae 20.8 25 * Tetraodontidae 38.3 185 ** pelagic, benthic, temperate 2. Test whether family Aracanidae 6.7 13 ** species richness Molidae 25.9 5 NS keyplausible point: given species λG * Triacanthidae 21.0 7 NS richness exceptionally Triacanthodidae 55.7 22 NS Triodontidae 54.0 1 NS high in reef groups 10 substitutions/site PALEOGENE NEOGENE PALEO EOCENE OLIGO MIOCENE Pi Ps
*Magallon and Sanderson, 2001 66.5 55.8 33.9 23.0 5.3 1.9 Sharks Polypteriformes Chondrostei Amiiformes Elopomorpha Osteoglossomorpha Ostariophysi Clupeomorpha Stomiiformes A Timetree for Osmeriformes Esociformes Salmoniformes Myctophiformes Aulopiformes Jawed Vertebrates Percopsiformes+Gadiiformes Polymixiiformes+Zeiforms Lampriformes Beryciformes+Stephanoberyciformes Ophidiiformes •~ 60,000 species total Percomorpha Scombridae Latimeridae •Molecular Phylogeny Dipnoi Gymnophiona •RAG-1 genbank data Caudata Anura Monotremes •221 tip species Marsupials Afrotheria+Xenarthra •Relaxed molecular clock Boreoeutheria Taxa Sphenodon 42 fossil calibrations 1 NongekkoSquamates • 5 Gekkos 10 Pleurodira •major gnathostome 50 Cryptodira 100 Gavialidae lineages represented 500 Crocodylinae 1000 Camininae 5000 Alligatorinae Tinamiformes 10000 Struthioniformes 20000 Neoaves Galliformes Anseriformes
500 400 300 200 100 0 MYA Sharks Polypteriformes Chondrostei Amiiformes Elopomorpha Osteoglossomorpha Ostariophysi 1. λG = [log(n) - log 2]/t Clupeomorpha Stomiiformes Osmeriformes Esociformes n = 57,859 species Salmoniformes Myctophiformes Aulopiformes t = 549 mya Percopsiformes+Gadiiformes Polymixiiformes+Zeiforms Lampriformes Beryciformes+Stephanoberyciformes Ophidiiformes Percomorpha λG = ln(n) - ln(2) Scombridae Latimeridae Dipnoi t Gymnophiona Caudata Anura Monotremes λG = ln(57859) - ln(2) Marsupials Afrotheria+Xenarthra Boreoeutheria 549 Taxa Sphenodon 1 NongekkoSquamates 5 Gekkos 10 Pleurodira 50 Cryptodira 100 Gavialidae 500 Crocodylinae λG = 0.019 1000 Camininae 5000 Alligatorinae Tinamiformes 10000 Struthioniformes 20000 Neoaves Galliformes Anseriformes
500 400 300 200 100 0 MYA 9 j
10000 2 f d s
e z a 5 4 ! u 1 l 7 # $h 0 k 8 t 100 3 i % Extant Species Richness n @ x 6 w q m & p Species Richness v
b r o g c
1 y
100 200 300 400 500 Stem AgeStem Age (MY) Pure Birth λ = 0.019
9 j
10000 2 f d s
e z a 5 4 ! u 1 l 7 # $h 0 k 8 t 100 3 i % Extant Species Richness n @ x 6 w q m & p Species Richness v
b r o g c
1 y
100 200 300 400 500 Stem AgeStem Age (MY) Thanks!!!
• we will send course materials out--make sure you gave us your email • please send comments and feedback with ‘FEEDBACK’ in the header to [email protected] Sharks Polypteriformes Chondrostei Amiiformes Elopomorpha Osteoglossomorpha Ostariophysi Clupeomorpha Stomiiformes A Timetree for Osmeriformes Esociformes Salmoniformes Myctophiformes Aulopiformes Jawed Vertebrates Percopsiformes+Gadiiformes Polymixiiformes+Zeiforms Lampriformes Beryciformes+Stephanoberyciformes Ophidiiformes •~ 60,000 species total Percomorpha Scombridae Latimeridae •Molecular Phylogeny Dipnoi Gymnophiona •RAG-1 genbank data Caudata Anura Monotremes •221 tip species Marsupials Afrotheria+Xenarthra •Relaxed molecular clock Boreoeutheria Taxa Sphenodon 42 fossil calibrations 1 NongekkoSquamates • 5 Gekkos 10 Pleurodira •major gnathostome 50 Cryptodira 100 Gavialidae lineages represented 500 Crocodylinae 1000 Camininae 5000 Alligatorinae Tinamiformes 10000 Struthioniformes 20000 Neoaves Galliformes Anseriformes
500 400 300 200 100 0 MYA key point: high turnover rates in gnathostomes
Pure Birth Birth−Death
9 j
10000 2 f d s
e z a 5 4 ! u 1 l 7 # $h 0 k 8 t 100 3 i % Extant Species Richness n @ x 6 w q m & p Species Richness v
b r o g c
1 y
100 200 300 400 500 Stem AgeStem Age (MY) key point: high turnover rates in gnathostomes
Pure Birth Birth−Death
9 j
10000 2 f d s
e z a 5 4 ! u 1 l 7 # $h 0 k 8 t 100 3 i % Extant Species Richness n @ x 6 w q m & p Species Richness v
b r o g c
1 y
100 200 300 400 500 Stem AgeStem Age (MY)