Nadav Shnerb (BIU) Yosi Maruvka (BIU) David Kessler (BIU) Gur Yaari (Yale) Sorin Solomon (HUJI) Robert Ricklefs (St. Louis) John Wakeley (Harvard)

Transcription

1 Nadav Shnerb (BIU) Yosi Maruvka (BIU) David Kessler (BIU) Gur Yaari (Yale) Sorin Soloon (HUJI) Robert Ricklefs (St. Louis) John Wakeley (Harvard)

2 PLoS coputational biology 5(4): e (009) Survival of the fittest Survival of the luckiest Pants die (ripped) due to accuulated wear. Glasses die when they shattered, usually due to rando and uncorrelated events

3 The prince, Capitolo XXV [What fortune can effect in huan affairs and how to withstand her] Fortune is the istress of one half our actions, and yet leaves the control of the other half, or a little less, to ourselves Deterinistic (fitness) it is the ultiate ai of this work, to lay bare the econoic law of otion of odern society Karl Marx, Das Capital (introduction) Stochastic (neutral) Cleopatra's nose, had it been shorter, the whole face of the world would have been changed (Pascal)

4 When we look at the plants and bushes clothing an entangled bank, we are tepted to attribute their proportional nubers and kinds to what we call chance. But how false a view is this! Darwin On the Origin of Species (1859) Deterinistic (fitness) Hubbell started fro a postulate that ost consider preposterous: that one tree or one bird is just like any other. His patterns result solely fro rando fluctuations in births, deaths and the arrival of new species. Scientific Aerican April Stochastic (neutral)

5 P x ( x) e Neutrality= Gaussian statistics Levi and Soloon, Physica A 1997 Pareto: Saying everything is governed by chance is a prediction. The central liit theore guarantees that the resulting statistics will be Gaussian. x t 1 x t [ 1,1] t P( x) e x ( t) log( x t1 [1/,] ) P( x) e x t1 x t log( x [log( x)] ( t) t t ) log( ) x t log( x) ( t) Deterinistic (fitness) Stochastic (neutral)

6 Shnerb, Maruvka Kessler Soloon n E-3 1E-4 Pareto Plot (the chance of a randoly selected surnae to have ebers) Sith, Johnson

7 a special preference for beetles here they are: Genus = surnae Species = first nae # of species in genus varies treendously log( n n ) log

8 1. Birth=speciation: A species is chosen at rando to reproduce = to undergo speciation (no fitness, selection, whatever).. Mutation = speciation that creates new genus: an offspring is identical to its father with probability 1- and is a utant (new species, surnae, genus) with probability. b0 b1 b b # of species within genus b n (1 ) n ( n 1) b0 total population Where is the birth rate

9 n 1 ( ) ( 1/ ) B(, 1/ ) ( 1/ ) 1 Original Yule 104 genera Conteporary data 643 genera Shoulder Looks like a straight line

10 JTB 6 45 (010) Moran Version ( overlapping generations ) 1. Birth: choose a rando agent to reproduce.. Mutation: an offspring is identical to its other with probability 1- and is a utant (new genus, surnae, allele) with probability. 3. Death: a rando agent is chosen to die with probability d. Iportant paraeters are and the growth rate = 1-d b0 b1 b b3 0 d1 1 d d3 3 d4

11 JTB 6 45 (010) The results are independent of the icroscopic details of the process (overlapping or nonoverlapping generations, the order of events, IF, <1. Under these conditions the nuber of failies of size, n, varies only slightly with so for both Moran and Wright-Fisher process, independent of their details, the faily statistics is described by a universal differential equation, the Kuer equation: < n n R n t Rc ( ) R U 1,0, N 1 R c U,0, First presented by Manrubia and Zannette, JTB (00), in the context of Moran process c N n n c e R c N Large asyptotic n n < 1 1[ /( )] e ( )

12 JTB 6 45 (010) Let us assue that only R 0 individuals were sapled out of the total population of size N 0. Hypergeoetric distribution Effective sapling strength s (1 ) R N 0 0 Weak sapling back to Yule-Sion

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14 paraeters fit. Logarithic binning. PDF (NOT cuulative distribution) Kuer ueoflife.org Species 000 & ITIS Catalogue of Life: 009 Annual Checklist Power law tail Yule best fit

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16 J. Stat. Phys (011) Molecular Biology and Evolution (011) The data 11 sequences (China) µ=0.0041/sequence/generation The challenge: Infer the growth rate and the effective population size N 0

17 Any sequence inherited along aternal lineages is like a surnae. These surnaes are subject to a birth-deathutation process. Ends up with haplotype (surnae, faily) statistics: the nuber of occurrences of singletons, doubletons and so one. This statistics depends on the deographic paraeters, thus in principle we can retrieve this inforation fro it.

18 The birth-death-utation process yields the universal distribution function. It deviates strongly fro Yule-Sion for sall failies since failies cannot die in Yule. Yule is the weak sapling liit of BDM. One can use the BDM distribution in order to retrieve deographic paraeters like growth rate in the prehistoric ties. Neutral theory, King Soloon Version Ecclesiastes (Qoheleth), Chapter : 14: The wise an's eyes are in his head; but the fool walketh in darkness: and I yself perceived also that one event happeneth to the all. 15: Then said I in y heart, As it happeneth to the fool, so it happeneth even to e; and why was I then ore wise? יד ה ח כ ם ע ינ יו ב ר א ש ו, ו ה כ ס יל ב ח ש ך הו ל ך; ו י ד ע ת י ג ם- אנ י, ש ם ק ר ה א ח ד י ק ר ה א ת-כ ל ם. טו ו אמ ר ת י א נ י ב ל ב י, כ מ ק ר ה ה כ ס יל ג ם-א נ י י ק ר נ י, ו ל ם ה ח כ מ ת י א נ י, אז י ת ר; ו ד ב ר ת י ב ל ב י, ש ג ם-ז ה ה ב ל.

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