Table 3. The number of possible unrooted and rooted trees as function of the the number of taxa based on eq. 7.

Number of taxa Number of unrooted trees Number of rooted trees 3 1 3 4 3 15 5 15 105 6 105 945 7 945 10395 8 10395 135135 9 135135 2027025 10 2027025 34459425 11 34459425 654729075 12 654729075 13749310575 13 13749310575 3.16234E+11 14 3.16234E+11 7.90585E+12 15 7.90585E+12 2.13458E+14 16 2.13458E+14 6.19028E+15 17 6.19028E+15 1.91899E+17 18 1.91899E+17 6.33266E+18 19 6.33266E+18 2.21643E+20 20 2.21643E+20 8.20079E+21 21 8.20079E+21 1.31131E+25

Emile Zuckerkandl and Linus Pauling, "Evolutionary Divergence and Convergence in Proteins,"

in Evolving Genes and Proteins, eds. V. Bryson and H. Vogel (New York: Academic Press, 1965). pp. 97-166.

Comparing Hemoglobin Sequences

“There may thus exist a Molecular Evolutionary Clock”Zuckerkandl & Pauling (1965)

A model of sequence divergence can be used to extract the duplication dates of the difference hemoglobin chains

Clock for paralogs

Divergegence between alpha and beta

Divergegence between beta and gamma

“There may thus exist a Molecular Evolutionary Clock”

Zuckerkandl & Pauling (1965)

PBS Evolution Library (http://www.pbs.org/wgbh/evolution/library/)

Different ortholog clocks keep different times

Different proteins evolve at different rates

Most recent common ancestor between Man-horse

Rate ofchange:AA changesper siteper year

A ↓ ↓ ↓ E. coli ATGCAAGTCGAACG- GTAACAGGAAGAAG--- CTTG- CTTCTTTGCTGACGAGTGGCGGACGGGTG R. rickettsia ATGCAAGTCGAACGGAC-- TAA- TTGGGG--- CTTG- CTCCAA-- TTAGTTAGTGGCAGACGGGTG B. burgdorf eri ATGCAAGTCAAACGGGA-- TGT------ A--- GCAA- T------- ACATCTAGTGGCGAACGGGTG S. cerevisiae ATGCATGTCTAAGT- ATAAGCA------- ATTTATAC-------- AGTGA- AACTGCGAATGGCTC H. sapiens ATGCATGTCTAAGT- ACGCACG------- GCCGGTAC-------- AGTGA- AACTGCGAATGGCTC H. marismortui ATGCTAGTCGCACGGGC--------------- TTAG------------ ACCCGTGGCATATAGCTC Unweighted mask 111111111111111111111111111111111111111111111111111111111111111111 Weighted mask 11112211122222 --------------------------------------- 1211222221111

B

Fig. 4

-Hillis, et al, 1996

A ↓ ↓ ↓ E. coli ATGCAAGTCGAACG- GTAACAGGAAGAAG--- CTTG- CTTCTTTGCTGACGAGTGGCGGACGGGTG R. rickettsia ATGCAAGTCGAACGGAC-- TAA- TTGGGG--- CTTG- CTCCAA-- TTAGTTAGTGGCAGACGGGTG B. burgdorf eri ATGCAAGTCAAACGGGA-- TGT------ A--- GCAA- T------- ACATCTAGTGGCGAACGGGTG S. cerevisiae ATGCATGTCTAAGT- ATAAGCA------- ATTTATAC-------- AGTGA- AACTGCGAATGGCTC H. sapiens ATGCATGTCTAAGT- ACGCACG------- GCCGGTAC-------- AGTGA- AACTGCGAATGGCTC H. marismortui ATGCTAGTCGCACGGGC--------------- TTAG------------ ACCCGTGGCATATAGCTC Unweighted mask 111111111111111111111111111111111111111111111111111111111111111111 Weighted mask 11112211122222 --------------------------------------- 1211222221111

B

Fig. 4

Table 1. Dissimilarity values for 16S rDNA fragment displayed in figure 4.E. coli R. rickettsii B. burgdorferi S. cerevisiaeH. sapiensH. marismortui

E. coli -R. rickettsii 0.29 -B. burgdorferi 0.36 0.35 -S. cerevisiae 0.50 0.50 0.50 -H. sapiens 0.54 0.50 0.48 0.20 -H. marismortui 0.33 0.35 0.40 0.53 0.53 -

Table 2. Jukes-Cantor corrected distance values calculated from the dissimilarityvalues in table 1 using eq. 3.

E. coli R. rickettsii B. burgdorferi S. cerevisiaeH. sapiensH. marismortuiE. coli -R. rickettsii 0.36 -B. burgdorferi 0.49 0.48 -S. cerevisiae 0.82 0.82 0.82 -H. sapiens 0.97 0.82 0.76 0.23 -H. marismortui 0.44 0.47 0.57 0.91 0.91 -

Table 1. Dissimilarity values for 16S rDNA fragment displayed in figure 4.E. coli R. rickettsii B. burgdorferi S. cerevisiaeH. sapiensH. marismortui

E. coli -R. rickettsii 0.29 -B. burgdorferi 0.36 0.35 -S. cerevisiae 0.50 0.50 0.50 -H. sapiens 0.54 0.50 0.48 0.20 -H. marismortui 0.33 0.35 0.40 0.53 0.53 -

Table 2. Jukes-Cantor corrected distance values calculated from the dissimilarityvalues in table 1 using eq. 3.

E. coli R. rickettsii B. burgdorferi S. cerevisiaeH. sapiensH. marismortuiE. coli -R. rickettsii 0.36 -B. burgdorferi 0.49 0.48 -S. cerevisiae 0.82 0.82 0.82 -H. sapiens 0.97 0.82 0.76 0.23 -H. marismortui 0.44 0.47 0.57 0.91 0.91 -

E. coli R. rickettsii B. burgdorferi Hs-Sc H. marismortui E. coli - R. rickettsii 0.360 - B. burgdorferi 0.494 0.479 - Hs-Sc 0.896 0.824 0.791 - H. marismortui 0.441 0.471 0.572 0.907 - Ec-Rr B. burgdorferi Hs-Sc H. marismortui Ec-Rr - B. burgdorferi 0.485 - Hs-Sc 0.860 0.791 - H. marismortui 0.455 0.572 0.907 - Ec-Rr-Hm B. burgdorferi Hs-Sc Ec-Rr-Hm - B. burgdorferi 0.530 - Hs-Sc 0.885 0.791 - Ec-Rr-Hm-Bb Hs-Sc Ec-Rr-Hm-Bb - Hs-Sc 0.838 -

E. coli R. rickettsii B. burgdorferi Hs-Sc H. marismortui E. coli - R. rickettsii 0.360 - B. burgdorferi 0.494 0.479 - Hs-Sc 0.896 0.824 0.791 - H. marismortui 0.441 0.471 0.572 0.907 - Ec-Rr B. burgdorferi Hs-Sc H. marismortui Ec-Rr - B. burgdorferi 0.485 - Hs-Sc 0.860 0.791 - H. marismortui 0.455 0.572 0.907 - Ec-Rr-Hm B. burgdorferi Hs-Sc Ec-Rr-Hm - B. burgdorferi 0.530 - Hs-Sc 0.885 0.791 - Ec-Rr-Hm-Bb Hs-Sc Ec-Rr-Hm-Bb - Hs-Sc 0.838 -

E. coli R. rickettsii B. burgdorferi Hs-Sc H. marismortui E. coli - R. rickettsii 0.360 - B. burgdorferi 0.494 0.479 - Hs-Sc 0.896 0.824 0.791 - H. marismortui 0.441 0.471 0.572 0.907 - Ec-Rr B. burgdorferi Hs-Sc H. marismortui Ec-Rr - B. burgdorferi 0.485 - Hs-Sc 0.860 0.791 - H. marismortui 0.455 0.572 0.907 - Ec-Rr-Hm B. burgdorferi Hs-Sc Ec-Rr-Hm - B. burgdorferi 0.530 - Hs-Sc 0.885 0.791 - Ec-Rr-Hm-Bb Hs-Sc Ec-Rr-Hm-Bb - Hs-Sc 0.838 -

E. coli R. rickettsii B. burgdorferi Hs-Sc H. marismortui E. coli - R. rickettsii 0.360 - B. burgdorferi 0.494 0.479 - Hs-Sc 0.896 0.824 0.791 - H. marismortui 0.441 0.471 0.572 0.907 - Ec-Rr B. burgdorferi Hs-Sc H. marismortui Ec-Rr - B. burgdorferi 0.485 - Hs-Sc 0.860 0.791 - H. marismortui 0.455 0.572 0.907 - Ec-Rr-Hm B. burgdorferi Hs-Sc Ec-Rr-Hm - B. burgdorferi 0.530 - Hs-Sc 0.885 0.791 - Ec-Rr-Hm-Bb Hs-Sc Ec-Rr-Hm-Bb - Hs-Sc 0.838 -

E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG R. rickettsia ATGCAAGTCGAACGGAC--TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA--TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG S. cerevisiae ATGCATGTCTAAGT-ATAAGCA-------ATTTATAC--------AGTGA-AACTGCGAATGGCTC H. sapiens ATGCATGTCTAAGT-ACGCACG-------GCCGGTAC--------AGTGA-AACTGCGAATGGCTC H. marismortui ATGCTAGTCGCACGGGC---------------TTAG------------ACCCGTGGCATATAGCTC Unweighted mask 111111111111111111111111111111111111111111111111111111111111111111 Weighted mask 11112211111111---------------------------------------1111222222111

Positions 1 10 20 30 40 50 60 R. rickettsii ATGCAAGTCGAACGGAC—-TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA—-TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG node 1 ATGCAAGTC?AACGG??—-T??-??????---????-??????--??A??TAGTGGC??ACGGGTG E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG

Positions 1 10 20 30 40 50 60 R. rickettsii ATGCAAGTCGAACGGAC—-TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA—-TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG node 1 ATGCAAGTCGAACGGG?—-TA?-?????G---CTTG-C?????--?TA?CTAGTGGCGGACGGGTG E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG

Positions 1 10 20 30 40 50 60 R. rickettsii ATGCAAGTCGAACGGAC—-TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA—-TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG node 1 ATGCAAGTCGAACGGGA—-TAT-TTGGGG---CTTG-CTCCAA--TTAGCTAGTGGCGGACGGGTG E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG

Positions 1 10 20 30 40 50 60 R. rickettsii ATGCAAGTCGAACGGAC—-TAA-TTGGGG---CTTG-CTCCAA--TTAGTTAGTGGCAGACGGGTG B. burgdorferi ATGCAAGTCAAACGGGA—-TGT------A---GCAA-T-------ACATCTAGTGGCGAACGGGTG node 1 ATGCAAGTCGAACGGGA—-TAT-TTGGGG---CTTG-CTCCAA--TTAGCTAGTGGCGGACGGGTG E. coli ATGCAAGTCGAACG-GTAACAGGAAGAAG---CTTG-CTTCTTTGCTGACGAGTGGCGGACGGGTG

Parsimony tree compared to UPGMA tree

23

Ec Rr Bbi Sc Hs Hm Net divergence E. coli - -1.15 -1.06 -0.85 -0.73 -1.16 3.09R. rickettseii 0.36 - -1.04 -0.82 -0.84 -1.09 2.96B. burgdorferi 0.49 0.48 - -0.86 -0.95 -1.03 3.13S. cervisiae 0.82 0.82 0.82 - -1.59 -0.82 3.61H. sapien 0.97 0.82 0.76 0.23 - -0.84 3.69H. marismortui 0.44 0.47 0.57 0.91 0.91 - 3.30Sc to node 1: 0.11 nodes: 6.00Hs to node 1: 0.13

Ec Rr Bb Hm node 1 Net divergenceE. coli - -1.00 -0.94 -1.01 -0.90 2.07R. rickettseii 0.36 - -0.93 -0.96 -0.95 2.02B. burgdorferi 0.49 0.48 - -0.93 -1.05 2.22H. marismortui 0.44 0.47 0.57 - -0.95 2.27node 1 0.78 0.71 0.68 0.79 - 2.95Bb to node 2: 0.22 nodes: 5.00node 1 to node 2: 0.46

Ec Rr Hmi node 2 Net divergenceE. coli - -0.73 -0.74 -0.70 1.10R. rickettseii 0.36 - -0.70 -0.74 1.09H. marismortui 0.44 0.47 - -0.73 1.26node 2 0.30 0.26 0.34 - 0.90Rr to node 3 0.18 Number of nodes: 4.00node 2 to node 3: 0.08

Ec Hm node 3 Net divergenceE. coli - -0.92 -0.92 0.64H. marismortui 0.44 - -0.92 0.72node 3 0.20 0.28 - 0.48Hm to node 4 0.26 Number of nodes: 3.00node 3 to node 4: 0.02

E. coli node 3E. coli - -node 4 0.18 -

Number of nodes: 2.00

Neighbor Joiningdistance matrices

24

Neighbor Joining Star Decomposition