Realism and Instrumentalism. in models of. molecular evolution

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1 Galileo Realism and Instrumentalism in models of molecular evolution David Penny Montpellier, June 08

2 Overview sites free to vary summing sources of error rates of molecular evolution estimates of time intervals do we know anything? (flat priors)

3 Human/chimp divergence 1) Ramapithecus = 12Ma HC = 5±1Ma But Ramapithecus in Asia, HCG in Africa. Is 18-20Ma a better estimate for divergence? 2) Ramapithecus = 18Ma HC = 7.5±1.5Ma Or should we combine uncertainties? In this case, I would rather not leave it as a conditional estimate need both.

4 sites free to vary rate k aa 10 9 /yr - fibrinopeptides lysozyme hemoglobin α cytochrome c histone H Dickerson, 1971 explained the differences by the proportion of sites free to vary. change of function should show a rate change realism

5 we use a tiny fraction of the information in the data Alignment Reordered Alignment original sequence order shuffled/reordered AIIFLNSALGPSPELFPIILATKVL ASAGPSPPATPLLIIIILLFFNEKV AIMFLNSALGPPTELFPVILATKVL ASAGPPTPATPLLIMVILLFFNEKV SIMFLNHTLNPTPELFPIILATETL SHTNPTPPATPLLIMIILLFFNEET TILFLNSSLGLQPEVTPTVLATKTL TSSGLQPPATPLLILTVLVTFNEKT TLLFLNSMLKPPSELFPIILATKTL TSMKPPSPATPLLLLIILLFFNEKT ALLFLNSTLNPPTELFPLILATKTL ASTNPPTPATPLLLLLILLFFNEKT AILFLNSFLNPPKEFFPIILATKIL ASFNPPKPATPLLILIILFFFNEKI c columns c! alignments If c = 1000, we use 1/ 1000! of the information

6 sites change X-ray crystallographers: the strongest conclusion we have is that the same sites in different species may be fixed, in others they are variable. Molecular Phylogeneticists: Our methods (such as the Gamma distribution) assume sites are in the SAME rate class across the entire tree (AND, we only need one parameter- so there).

7 simulation results with standard model number of internal edges correct, out of 6 neighbor joining, 9 taxa, 1000 columns, i.i.d millions of years (log scale)

8 Calculated results, Δ ¼ + ne -qt loss of information

9 simulation results with covarion model 120% 100% d=0.001 d=0.100 d=0.500 percentage of trees correct 80% 60% 40% 20% d=1.000 d=2.000 d=5.000 infinite 0%

10 do rates exist!!! We go ON and ON and ON and ON About molecular clocks. Should we??

11 not enough information to recover the full model 1- γ δ γ 1- δ 1(P R, 1- P R ) 2 2 composition at root Seq 1 Seq 2 5 required, 3 available

12 two taxa, two codes Seq 1 Seq 2 Seq 1 R Y α β γ * R Y Seq R R α R Y β Y R γ Y Y * Divergence matrix, F i,j Three independent parameters estimated

13 three taxa 1- γ δ γ 1- δ 1 (P R, 1- P R ) Seq 1 Seq 2 Seq 3 7 required

14 four character states * α β γ δ * ε φ η ι * ϕ κ λ µ * (P R, 1- P R ) 12 Seq 1 Seq 2 Seq 3 39 required

15 tensor, 3D matrix = 63 values, but a sparse matrix!

16 primary diagonal Gymnure, Mole and Shrew T T T C T A T G C T C C C A C G A T A C A A A G G T G C G A G G T C A G

17 secondary diagonals Gymnure(moon rat) Mole, Shrew T T T C T A T G C T C C C A C G A T A C A A A G G T G C G A G G T C A G

18 moon rat, 1+2 T C A G T C A G T.955 ± ± ± ±.008 C.025 ± ± ± ±.003 A.018 ± ± ± ±.011 G.002 ± ± ± ±.015 T C A G therefore we believe in symmetric models

19 mole, shrew and moon rat mole T C A G T C A G shrew T C A G moon rat T C A G T C A G

20 * α β γ δ * ε φ η ι * ϕ κ λ µ * change in rate * α β γ δ * ε φ η ι * ϕ κ λ µ * * α β γ δ * ε φ η ι * ϕ change κ λ µ in process * * α β γ δ * ε φ η ι * ϕ κ λ µ *

21 do we know anything? the curse of flat priors the we know nothing syndrome

22 Probability of a Armadillo Aardvark Tenrec Hedgehog partition Gymnure Mole Shrew LClawShrew Xenarthra Horse IndRhino Cat Dog Elephant Dugong HarbSeal GreySeal FurSeal BrownBear Pig Cow Hippo BlueWhale SpermWhale HecDolphin Alpaca FlyingFox Rhinolophus JFEbat LTailBat PipBat Rabbit Pika Squirrel Dormouse GuineaPig CaneRat Mouse Vole TreeShrew Baboon Gibbon Tarsier Loris 4 Afrotheria # binary trees, b(n) = (2n 5)!! = 1 x 3 x 5 x 7 2n 5. 2 Supraprimates Laurasiatheria x10 18

23 Probability of a partition2 # binary trees, b(n) = (2n 5)!! = 1 x 3 x 5 x 7 2n b(n 1 +1).b(n 2 +1) / b(n t ) b(n 1 +1).b(n 2 +1).b(n 3 +1) / b(n t ) b(n 1 +1).b(n 2 +1) b(n i +1) / b(n t )

24 40 birds KingWood Owls white-tailed trogon pileated woodpecker ivory billed toucan Parrots barn owl morepork New Zealand kingfisher peach-faced lovebird dollar bird kakapo budgerigar Conglomerati Eurasian buzzard Blyth s hawk eagle osprey Cuckoos roadrunner Passerines rook superb lyre bird rifleman New Zealand long-tailed cuckoo rockhopper penguin little blue penguin Kerguelen petrel black-browed albatross Oriental white stork Australian pelican * * * * * * * * * flamingo red-throated loon frigatebird gray-headed broadbill fuscous flycatcher forest falcon peregrine falcon Australian owlet nightjar Ruby-throated hummingbird common swift great potoo ruddy turnstone southern black-backed gull blackish oystercatcher Shorebirds great crested grebe Australasian little grebe Conglomerati CAM

25 P(n,k) = R(k) B(n-k+1) B(n) probability with n taxa of observing a prespecified clade of size k. with n = 40 and k = 2, P k = 3, P parrots k = 4, P , k = 5, P cuckoo,roadrunner

26 A 4 th 5 th 6 th B R(k) C k C 1 D k C 2 E 6C 2 4C 2 B(n - k) B(n - k) B(n - 6)

27 potoo, owlet-nightjar, owl, barn owl, swift, hummingbird (6)

28 Where next in Phylogeny? allow realism in phylogeny set the biological question we have some bad failures we need a range of alternatives Belief is the curse of the thinking class

29 tensor, 2-states Seq 1 Seq 2 Seq 3 R R R Seq 3 R Y β δ R α γ Seq 1 φ * Y ε η R Y Seq 2 7 available! R R R α R R Y β R Y R γ R Y Y δ Y R R ε Y R Y φ Y Y R η Y Y Y * 1 2 3