Theory of Evolution. Charles Darwin

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1 Theory of Evolution harles arwin : Origin of Species 5 year voyage of H.M.S. eagle (8-6) 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 (856-6) on inheritance. /5/ Lecture

2 /5/ Lecture

3 ominant View of Evolution ll 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; ommon ancestor species (divergence event): Internal node; Length of an edge: Time. /5/ Lecture

4 Phylogeny /5/ Lecture

5 onstructing Evolutionary/Phylogenetic Trees broad categories: istance-based methods Ultrametric dditive: UPGM Transformed istance Neighbor-Joining haracter-based Maximum Parsimony Maximum Likelihood ayesian Methods /5/ Lecture 5

6 Ultrametric n ultrametric tree: decreasing internal node labels distance between two nodes is label of least common ancestor. n 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 /5/ Lecture 6

7 Ultrametric: ssumptions Molecular lock Hypothesis, Zuckerkandl & Pauling, 96: ccepted 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 /5/ Lecture 7

8 Ultrametric ata Sources Lab-based methods: hybridization Take denatured N of the taxa and let them hybridize. Then measure energy to separate. Sequence-based methods: distance /5/ Lecture 8

9 Ultrametric: Example E F G H 5 E F G H E,,F,H,G /5/ Lecture 9 5

10 Ultrametric: Example E F G H 5 5 E F G H 5,G F E H /5/ Lecture

11 /5/ Lecture Ultrametric: istances omputed H G F E 5 5 H G F E,G E 5 F H

12 /5/ Lecture dditive-istance Trees dditive distance trees are edge-weighted trees, with distance between leaf nodes are exactly equal to length of path between nodes

13 Unrooted Trees on Taxa /5/ Lecture

14 Four-Point ondition If the true tree is as shown below, then. d + d < d + d, and. d + d < d + d /5/ Lecture

15 Unweighted pair-group method with arithmetic means (UPGM) d d () d d d () d d d d d () = (d + d ) / d / /5/ Lecture 5

16 Transformed istance Method UPGM makes errors when rate constancy among lineages does not hold. Remedy: introduce an outgroup & make n corrections ko ij' = Now apply UPGM ij io jo + k = n /5/ Lecture 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 = + ( n ) n ( + + k k k = ( n ) ) i j n ij /5/ Lecture 7

18 /5/ Lecture 8 Neighbor-Joining n n = = n j i ij n k k k n n S ) ( ) ( ) (

19 onstructing Evolutionary/Phylogenetic Trees broad categories: istance-based methods Ultrametric dditive: UPGM Transformed istance Neighbor-Joining haracter-based Maximum Parsimony Maximum Likelihood ayesian Methods /5/ Lecture 9

20 /5/ Lecture haracter-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 E 5 5 E

21 Example Perfect phylogeny does not always exist. 5 E /5/ Lecture

22 Maximum Parsimony Minimize the total number of mutations implied by the evolutionary history /5/ Lecture