Theory of Evolution Charles Darwin

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1 Theory of Evolution Charles arwin : Origin of Species 5 year voyage of H.M.S. eagle (83-36) Populations have variations. Natural Selection & Survival of the fittest: nature selects best adapted varieties to survive and to reproduce. Speciation arises by splitting of one population into subpopulations. Gregor Mendel and his work (856-63) on inheritance. CAP550/CGS566

2 CAP550/CGS566 2

3 ominant View of Evolution All existing organisms are derived from a common ancestor and that new species arise by splitting of a population into subpopulations that do not cross-breed. Organization: irected Rooted Tree; Existing species: Leaves; Common ancestor species (divergence event): Internal node; Length of an edge: Time. CAP550/CGS566 3

4 Phylogeny CAP550/CGS566 4

5 Constructing Evolutionary/Phylogenetic Trees 2 broad categories: istance-based methods Ultrametric Additive: UPGMA Transformed istance Neighbor-Joining Character-based Maximum Parsimony Maximum Likelihood ayesian Methods CAP550/CGS566 5

6 Ultrametric An ultrametric tree: decreasing internal node labels distance between two nodes is label of least common ancestor. An ultrametric distance matrix: Symmetric matrix such that for every i, j, k, there is tie for maximum of (i,j), (j,k), (i,k) ij, ik jk i j k CAP550/CGS566 6

7 Ultrametric: Assumptions Molecular Clock Hypothesis, Zuckerkandl & Pauling, 962: Accepted point mutations in amino acid sequence of a protein occurs at a constant rate. Varies from protein to protein Varies from one part of a protein to another CAP550/CGS566 7

8 Ultrametric ata Sources Lab-based methods: hybridization Take denatured NA of the 2 taxa and let them hybridize. Then measure energy to separate. Sequence-based methods: distance CAP550/CGS566 8

9 Ultrametric: Example A C E F G H A C E F G H A E,,F,H C,G CAP550/CGS566 9

10 Ultrametric: Example A C E F G H 5 A C E F G H A C,G F E H CAP550/CGS566 0

11 Ultrametric: istances Computed A C E F G H 5 A C 2 E F G H A C,G F E H CAP550/CGS566

12 Additive-istance Trees Additive distance trees are edge-weighted trees, with distance between leaf nodes are exactly equal to length of path between nodes. A C A A C C CAP550/CGS566 2

13 Unrooted Trees on 4 Taxa A C A C A C CAP550/CGS566 3

14 Four-Point Condition If the true tree is as shown below, then. d A + d C < d AC + d, and 2. d A + d C < d A + d C A C CAP550/CGS566 4

15 Unweighted pair-group method with arithmetic means (UPGMA) A C A C d A C d (A)C C d AC d C d (A) d C d A d d C d (A)C = (d AC + d C ) /2 d A /2 A CAP550/CGS566 5

16 Transformed istance Method UPGMA makes errors when rate constancy among lineages does not hold. Remedy: introduce an outgroup & make corrections n ko ' = Now apply UPGMA ij ij 2 io jo + k = n CAP550/CGS566 6

17 Saitou & Nei: Neighbor-Joining Method Start with a star topology. Find the pair to separate such that the total length of the tree is minimized. The pair is then replaced by its arithmetic mean, and the process is repeated. S 2 = ( n 2) n ( + + k 2k k = 3 ( n ) 2) 3 i j n ij CAP550/CGS566 7

18 Neighbor-Joining 2 n n = = n j i ij n k k k n n S ) ( ) ( 2) 2( 2 CAP550/CGS566 8

19 Constructing Evolutionary/Phylogenetic Trees 2 broad categories: istance-based methods Ultrametric Additive: UPGMA Transformed istance Neighbor-Joining Character-based Maximum Parsimony Maximum Likelihood ayesian Methods CAP550/CGS566 9

20 Character-based Methods Input: characters, morphological features, sequences, etc. Output: phylogenetic tree that provides the history of what features changed. [Perfect Phylogeny Problem] one leaf/object, edge per character, path changed traits A C 0 0 E E A C CAP550/CGS566 20

21 Example Perfect phylogeny does not always exist A C E A C E E 5 A C CAP550/CGS566 2

22 Maximum Parsimony Minimize the total number of mutations implied by the evolutionary history CAP550/CGS566 22

23 Examples of Character ata Characters/Sites A Sequences A A G A G T T C A C A G C C G T T C T A G A T A T C C A E A G A G A T C C T CAP550/CGS566 23

24 Maximum Parsimony Method: Example Sequence s Characters/Sites A A G A G T T C A 2 A G C C G T T C T 3 A G A T A T C C A 4 A G A G A T C C T CAP550/CGS566 24

25 Unrooted Trees on 4 Taxa A C A C A C CAP550/CGS566 25

26 A A G A G T T C A 2 A G C C G T T C T 3 A G A T A T C C A 4 A G A G A T C C T CAP550/CGS566 26

27 Inferring nucleotides on internal nodes CAP550/CGS566 27

28 Searching for the Maximum Parsimony Tree: Exhaustive Search CAP550/CGS566 28

29 Searching for the Maximum Parsimony Tree: ranch-&-ound CAP550/CGS566 29

30 Probabilistic Models of Evolution Assuming a model of substitution, Pr{S i (t+ ) = Y S i (t) = X}, Using this formula it is possible to compute the likelihood that data is generated by a given phylogenetic tree T under a model of substitution. Now find the tree with the maximum likelihood. Y X Time elapsed? Prob of change along edge? Pr{S i (t+ ) = Y S i (t) = X} Prob of data? Product of prob for all edges CAP550/CGS566 30

31 Computing Maximum Likelihood Tree CAP550/CGS566 3

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