Evolutionary Dynamics & its Tendencies. David Krakauer, Santa Fe Institute.

Transcription

1 Evolutionary Dynamics & its Tendencies David Krakauer, Santa Fe Institute.

2 A Talk in 2 Parts Part 1: What is Evolution, What has it generated & What are its limits? Part II: The Evolutionary dynamics of Minimal Forms - microbes

3 Evolutionary questions? Why is there life-like dynamics on earth? Why are organisms so diverse? Why are organisms so complex? What is the relationship of genetic information to learned information? When does cultural evolution outpace genetic evolution? Is self-awareness inevitable?

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5 What is Evolutionary Theory? A Physics like theory searching for Laws? A Statistical/Inferential Theory like Bayesian learning or approximate dynamic programming? An algorithmic/computational theory?

6 The Darwinian Polynucleotide Machine 1,3,7,1,6,1,7,1,1,5,5,4,3,15,7,1,10,1,15,8,19,1 0,68,2,6,1,4,5,3,1,6,9,2,4,3,1,2,6,5,2,6,20,1,3, 2,176,2,1,1,2 (in MegaBases)

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8 Ciccarelli et al. Science, 311,

9 Lynch, PNAS, 104,

10 Evolutionary Theory Population genetics/ neutral theory Quantitative genetics Quasispecies theory Game theory/adaptive dynamics Phylogenetic reconstruction/inference Niche Construction Gene-Culture Coevolution

11 Evolutionary Stoichiometry replication g i r i Energy + Resources 2g i

12 Evolutionary Stoichiometry competition g i + g j c ij g j

13 Evolutionary Stoichiometry mutation g i m ij Radiation g j m ij = µ H(i,j) (1 µ) L H(i,j)

14 Evolutionary Stoichiometry recombination g j + g l b ijl g i b ijl = 1, if i = j = l b ijl = ( ) 1 2 (1 c) + c ( ) H(j,l) 1 if i = j or i = l 2 b ijl = c ( ) H(j,l) 1 if H(i, j) + H(i, l) = H(j, l) 2

15 Replicator Equation g i r i 2g i c ij g i + g j g j n genomes ġ i = g i (r i f) where f = n r i g i and c ij = 1 i

16 Evolutionary Game Theory: Frequency dependent Replicator Equation g i r i (g) 2g i c ij g i + g j g j n genomes ġ i = g i (r i (g) f) where f = n r i (g)g i and c ij = 1 i

17 Evolutionary Game Theory: Frequency dependent Replicator Equation ġ i = g i (r i (g) f) Payoff Matrix P = [p ij ] with linear payoffs: n r i (g) = g j p ij j

18 Evolutionary Game Theory: Frequency dependent Replicator Equation n n n ġ i = g i ( g j p ij g j g k p jk ) j j k

19 Evolutionary Game Theory: Adaptive Dynamics for Continuous Traits dx dt = 1 δf(x 2 µσ2 N(x),x) δx x =x

20 Freq-dep Replicator Equation & Bayesian Inference An Insight by Cosma Shalizi

21 g i (t) t = g i (t 1)(r i (g) f) P (X Y ) = P (X) P (Y X) P (Y ) P (X Y ) = P (X) L X L L = P (Y ) = x ω P (Y X)P (X) P X (t) = P X (t 1) L X L P X (t) = P X (t 1)( L X L 1) = P X (t 1) 1 L(L X L) P X (t) = P X (t 1)(f t f), where f t = L X / L

22 Sequence Space & Limits to Evolution

23 I Z 10 ol o

24 Replicator-Mutator Equation 2 n ġ i = g j r j (g)m ij g i f) j m ij = µ H(i,j) (1 µ) L H(i,j)

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32 Error Threshold g i µ

33 Fitness Landscape Delta function: µ < s L = 1 L Multiplicative function: µ < s

34 Kimura s Neutrality Inequality Expectation of Mutation Nµ Probability of Fixation 1 N Condition for Neutrality sn < 1

35 Evolutionary Information Storage Information Conserved organismal regularity Environmental regularity s µl N Information Lost s< µl N

36 Evolution, Localization & Information (with a 4 letter alphabet)

37 Information as Selective Uniformity ACGTC...T ATGTG...T ATCTG...A Aligned genomes l H i = j p (i) j log 4p (i) j I i = H max H i Information in Population C = L i H i

38 Information-Selection as a Compression Ratio ACGTC...T ATGTG...T ATCTG...A Aligned genomes l H i = j p (i) j log 4p (i) j C = LH max L i H i = L L i H i

39 sn > µl The Tendency to Population Multiplicity & Individual Minimality

40 The Space God versus the andromeda strain

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42 KEY virus catalyzed host A catalyzed host B catalyzed

43 N = E v i s i h i Minimality Autonomy v i h v i i s i h i v h = N v h = N v h = 0 v h N

44 w = i E f(g i ) j NE h(g j ) w E = i E f(g i ) v i h i g i

45 v i h i g i g i = h i v i P rob(h i = 1) = q P rob(v i = 1) = p L v = i v i, < L v >= pn w = i N g i (1 + L v ) < w >= (q + p qp)n 1 + pn

46 N=4 N=8 host genome virus genome N=16 N=32

47 Evolution & Minimality Evolutionary theory is concerned largely with the frequency, variety & relationships among chemically improbable sequences Genomes tend to neutralize and/or eliminate redundant sequences - genomes need not encode perfectly predictable resources Replicator/Mutator Dynamics tends to favor small sequences which can be preserved Increasing autonomy (often size) reflects greater inferential uncertainty Neutral theory requires large populations for effective selection of target sequences -- more likely with small sequences Evolution can be thought of as an inferential, model fitting process (Bayesian) and selection as a mechanism for injecting information into sequences Genetic dissipation in coevolutionary contexts requires a consideration of rates of gene inactivation in all interacting agents Genome growth beyond competitive persistence is driven by, e.g. robustness & control

48 Whence Complexity?