The construction of phylogenetic trees depends on the analogy between distance between sequences and geometric distance.  The tree then represents a map on which sequences lie as objects.
 

Linkage Algorithms

A family tree is constructed using distances between pairs of sequences in the set.  It is assumed that:

    1.  There exists a common ancestral sequence from which all sequences have evolved

    2.  Distances between sequence pairs are directly proportional to the time elapsed since the last common ancestor of the sequences;

        (not actually true in many cases)

The tree is constructed by taking the two sequences i and j whose distance is minimal, and forming a cluster (i,j) that is treated as a new object, as well as the branching point in the tree at which the two sequences are attached.

The distance d_(i,j),k between the cluster and any other sequence k is calculated by one of any alternatives:

                   d_(i,j),k  =  lower value of   d_(i,k) and d_{(j,k) - minimum linkage algorithm}

                                    higher value of  d_(i,k) and d_{(j,k) - maximum linkage algorithm}

                                    mean value of   d_(i,k) and d_{(j,k)  - average linkage algorithm}

The two sequences (objects) can then be replaced by the one object (i,j) with distances to other objects as specified above.  Further clusters and distances can then be defined until all sequences are included.

Example at VSNS course

Additive Clustering Procedures

Enable correct tree topologies to be obtained from distances.  Can be used to construct rooted trees  as long as simple distances are first transformed by the Farris Transform, which calculates the similarity of two sequences, with reference to the common ancestor of all the sequences.

For a rigorous mathematical treatment see VSNS Course

Example: If the distance between two sequences is  d_(i,j), and the ancestral sequence is designated a, the Farris transform S_(i,j) of d_(i,j) is:

                    S_(i,j)  =   [d_(i,a)  +  d_(j,a)]   -  d_(i,j)

_{S is a measure of similarity, and can thus be converted into distance by subtraction from a large constant.}

_{In some sets of sequences, the correct tree is not predicted by initially choosing the sequences with smallest distance.  Applying the Farris Transform corrects this deficiency, and enables the correct tree topology to be determined.  The sequence distances must obey the Four Point Condition.}

d_i,j +  d_k,l  <  max ((d_i,k   +  d_j,l)   or  (d_i,l   +  d_j,k)) for any four sequences i,j,k,l

Example VSNS course Section 4.14

For the seven sequences:
 

_{Using a linkage algorithm and the matrix of Hamming distances directly does not yield the correct phylogenetic tree}

_{(VSNS Course Section 4.3)}

_{After transformation and conversion from similarity to distance the correct tree is predicted.}

_{Additive Linkage Algorithm:}

_{If the distances obey the Four Point Condition, the correct unrooted tree topology can be predicted more simply by:}

_{1. Identification of  the pair of sequences that form the cluster with greatest distances to all other members of the set,}

_{i.e. for which the quantity}

        [d(_i,k) +  d_(j,k)]   -  d_(i,j)  is maximum, where k is any sequence other than i or j

2. Calculation of the distance from the i,j cluster to the sequence k, given by

                    1/2([d_(i,k)  +  d_(j,k)]   -  d_(i,j))

This process is repeated until just one cluster is left.

Example: VSNS course Chapter 3, section 4.15

The sequences:

give rise, after alignment to the distance matrix:
 

Cluster with greatest distance to other sequences is (2,6), e.g. distance to sequence 1 = 1/2([d_{(2,1) +} d_(6,1)] - d_(2,6)) = 10

                                          from seqs. 3,4,5,7 = 6,2,7,10 resp.

Next most distant cluster is (1,3) with distances to sequences (2,6), 4, 5 and 7 of 6,6, 3 and 6 respectively

                                   then (5,7) with distances to (1,3), (2,6) and 4 of 2,6 and 6 respectively

This process is repeated until just one cluster is left, and generates the same tree as derived from the Farris Transform, but unrooted.

Average Linkage Clustering (UPGMA)

Unweighted Pair-Group Method using an Arithmetic Average (UPGMA) defines intercluster distance as the average of all the pairwise distances for members of two clusters. Distances used are Jukes-Cantor distances (K), which depend on the observed numbers of differences between each pair.  If a proportion q of the residues in the two sequences is the same, an estimate of K is:

    K  =  ³ ln     ³
           4      4q - 1

Example: primate mitochondrial sequences:

Numbers of differences (below diagonal) and Jukes-Cantor distances (above diagonal) for five mitochondrial sequences.
 

Pair with least distance (human, chimp) joined to form a cluster.  The distance of each other sequence from this cluster is found as the average distance from the sequence to members of the cluster:

    d(_hu-ch)_,go  =  1/2(d_hu,go + d_ch,go)  =  0.037

    d(_hu-ch)_,or   =  1/2(d_hu,or +  d_ch,or)  =  0.135

     d(_hu-ch)_,gi   =  1/2(d_hu,gi + d_ch,gi)    =  0.189

The smallest distance is now between the human/chimp cluster and gorilla, and so a new cluster is assembled. New distances are now:

d(_hu-ch-go)_,or   =  1/3(d_hu,or +  d_ch,or  + d_go,or) =  0.121

d(_hu-ch-go)_,gi    =  1/3(d_hu,gi +  d_ch,gi  +  d_go,gi) =  0.185

A new cluster is now assembled including orang, and the new distance to gibbon calculated:

d(_hu-ch-go-or)_,gi    =  1/4(d_hu,gi +  d_ch,gi  +  d_go,gi + d_or,gi)   =  0.183

A dendrogram is then constructed with branchpoints midway between between sequences or clusters.
The distance between a pair of sequences is the sum of the branch lengths.
                                                                                                                          _Human
                                                                                                                         |
                                                                                                              |          |           _Chimp
                                                                                                              |
                       |                                                                                      |
                       |                                                                                      |           _Gorilla
|                      |
_|                            ^|                                                                                                    _Orangutan
|
|                                                                                                                         _Gibbon

_{|                       |                                                                                      |           |
0.092               0.060                                                                              0.019   0.007}
 

Cluster systems

Alternatively to Tree systems, sequences can be separated into clusters whose members are more similar to each other than to members of other clusters.  The clusters should therefore represent sequences from  monophyletic groups.   Split Decomposition is one Cluster System.

Split Decomposition

Facilitates  phylogenetic analysis considerably due to :

    unprejudiced approach

    computer graphics support

Collection of sequences is split such that at (at least ) one of the two subcollections is a monophyletic group

Split is valid (a d-split) if the four-point condition is obeyed :

d_i,j +  d_k,l  <  max ((d_i,k   +  d_j,l)   or  (d_i,l   +  d_j,k)) for any four sequences i,j,k,l

or in the case of  all pairs of  sequences, (s and s') in one block and  (t and t') in the other:
 

  d(s,s') + d(t,t') < max [(d(s,t) + d(s',t')]  or  [(d(s,t') + d(s',t)]
 

In addition every d-split is associated with an isolation index :

 ½ min (max(d(s,t) + d(s',t') or d(s,t') + d(s',t)) - d(s,s' - t,t')

which measures the degree to which the split is supported by the data

If d satisfies the four-point condition,  the isolation index coincides exactly with the length of the unique branch of the tree associated with d which separates the (smallest ) subtree  connecting all the A labelled nodes from the (smallest ) subtree  containing all the B - labelled nodes.

Maximum Likelihood Methods

Instead of using distances, these methods attempt to make explicit and efficient use of all the available information. Include estimation of branch lengths, employing standard statistical methods.  Assume a tree which represents the phylogeny of the sequences, then choose branch lengths to maximize the probability of the data given that tree.  The probability of possible trees is then compared, and the tree with greatest probablity chosen.  The number of possible trees is usually very large, therefore intensive computational methods are required.  The most popular method of this type is the PHYLIP algorithm, which starts with a two-sequence tree and adds more sequences.  Local rearrangements are carried out to see if this improves likelihood before the next sequence is added.

Breakpoint Analysis

Based on the concepts of breakpoints in genomes

A breakpoint occurs any time two genes are adjacent in one genome but are not adjacent in a genome to which the first is compared. An internal node's label is derived by finding the gene order that minimizes the number  of breakpoints between a node and its three closest neighbors. A label that minimizes the amount of change at this place in the tree is found. A travelling salesperson problem solver—a common, if expensive, mathematical method of solving optimization problems—is used to find the median, calculating the hypothesized gene order data for each node.

Example - building of phylogenetic tree for Campanula (bluebell) species using chloroplast genomes.
 

Other Web-based courses on Phylogenetic Analysis

1.VSNS course - The Mathematical Basis of Phylogenetic Analysis.

2. Stanford course - Distance Based Phylogenies.

3. BCG course at Weizmann Institute - Phylogenetic Analysis 

Web Resources for Phylogenetic Analysis
 

1.  Phylogenetic tree generation at EBI ClustalW web window

2.  Phylogenetic Trees at the Blocks Multiple Alignment Processor

3.  Phylogenetic Analysis at the All-All server. Accepts sequences or distances as input.  Returns predicted trees by email in postscript text.  Needs a postscript reader such as Ghostscript to display tree.

http://www.cbrg.ethz.ch/services/PhylogeneticTree/index

4.  Phylogenetics Software Resources (University of California)

5.  PHYLIP at the University of Singapore and other places.

6.    PhIGs (Phylogenetically Identified Groups):  an attempt to cluster genes from multiple organisms into groups that are all descended from a single ancestral gene.

This clustering is accomplished by using the known phylogenetic relationships to guide the creation of the PhIGs.

Example 1: Obtain trees from the servers 1 and 2 above for the human Transforming Growth Factor Beta family proteins and a decapentaplegic, a related protein from Drosophila Melanogaster:
 

>humanbeta1
MPPSGLRLLL LLLPLLWLLV LTPGRPAAGL STCKTIDMEL VKRKRIEAIR GQILSKLRLASPPSQGEVPP GPLPEAVLAL YNSTRDRVAG ESAEPEPEPE ADYYAKEVTR YDKFKQSTHS IYMFFNTSEL REAVPEPVLL SRAELRLLRL KLKVEQHVEL YQKYSNNSWRYLSNRLLAPS DSPEWLSFDV TGVVRQWLSR GGEIEGFRLS AHCSCDSRDN TGRRGDLATI HGMNRPFLLL MATPLERAQH LQSSRHRRAL DTNYCFSSTE KNCCVRQLYIDFRKDLGWKW IHEPKGYHAN FCLGPCPYIW SLDTQYSKVL ALYNQHNPGA LEPLPIVYYV GRKPKVEQLS NMIVRSCKCS
>humanbeta2
MHYCVLSAFL ILHLVTVALS LSTCSTLDMD QFMRKRIEAI RGQILSKLKL TSPPEDYPEPEEVPPEVISI YNSTRDLLQE KASRRAAACE RERSDEEYYA KEVYKIDMPP FFPSENAIPPTFYRPYFRIV RFDVSAMEKN ASNLVKAEFR VFRLQNPKAR VPEQRIELYQ TQRYIDSKVV KTRAEGEWLS FDVTDAVHEW LHHKDRNLGF KISLHCPCCT FVPSNNYIIPNKSEELEARF AGIDGTSTYT SGDQKTIKST RKKNSGKTPH LLLMLLPSYR LESQQTNRRKKRALDAAYCF RNVQDNCCLR PLYIDFKRDL GWKWIHEPKG YNANFCAGAC PYLWSSDTQHSRVLSLYNTI NPEASASPCC VSQDLEPLTI LYYIGKTPKI EQLSNMIVKS CKCS
>humanbeta3
MKMHLQRALV VLALLNFATV SLSLSTCTTL DFGHIKKKRV EAIRGQILSK LRLTSPPEPTVMTHVPYQVL ALYNSTRELL EEMHGEREEG CTQENTESEY YAKEIHKFDM IQGLAEHNELAVCPKGITSK VFRFNVSSVE KNRTNLFRAE FRVLRVPNPS SKRNEQRIEL FQILRPDEHIAKQRYIGGKN LPTRGTAEWL SFDVTDTVRE WLLRRESNLG LEISIHCPCH TFQPNGDILENIHEVMEIKF KGVDNEDDHG RGDLGRLKKQ KDHHNPHLIL MMIPPHRLDN PGQGGQRKKR
ALDTNYCFRN LEENCCVRPL YIDFRQDLGW KWVHEPKGYY ANFCSGPCPY LRSADTTHSTVLGLYNTLNP EASASPCCVP QDLEPLTILY YVGRTPKVEQ LSNMVVKSCK CS
>decapentaplegic
MRAWLLLLAV LATFQTIVRV ASTEDISQRF IAAIAPVAAH IPLASASGSG SGRSGSRSVGASTSTALAKA FNPFSEPASF SDSDKSHRSK TNKKPSKSDA NRQFNEVHKP RTDQLENSKNKSKQLVNKPN HNKMAVKEQR SHHKKSHHHR SHQPKQASAS TESHQSSSIE SIFVEEPTLVLDREVASINV PANAKAIIAE QGPSTYSKEA LIKDKLKPDP STLVEIEKSL LSLFNMKRPPKIDRSKIIIP EPMKKLYAEI MGHELDSVNI PKPGLLTKSA NTVRSFTHKD SKIDDRFPHH
HRFRLHFDVK SIPADEKLKA AELQLTRDAL SQQVVASRSS ANRTRYQVLV YDITRVGVRGQREPSYLLLD TKTVRLNSTD TVSLDVQPAV DRWLASPQRN YGLLVEVRTV RSLKPAPHHHVRLRRSADEA HERWQHKQPL LFTYTDDGRH KARSIRDVSG GEGGGKGGRN KNHDDTCRRH SLYVDFSDVG WDDWIVAPLG YDAYYCHGKC PFPLADHFNS TNHAVVQTLVNNMNPGKVPK ACCVPTQLDS VAMLYLNDQS TVVLKNYQEM TVVGCGCR

Example 2: Generate trees for the human paralogs of the human Map3k paralogs 1-4 and the ortholog from Ciona Intestinalis:

>Hs1

MGSQALQEWGQREPGRWPDPAGKKDVRREASDSGRAGTWPRGPSECSPREKMAAAAGNRASSSGFPGARA

TSPEAGGGGGALKASSAPAAAAGLLREAGSGGRERADWRRRQLRKVRSVELDQLPEQPLFLAASPPASST

SPSPEPADAAGSGTGFQPVAVPPPHGAASRGGAHLTESVAAPDSGASSPAAAEPGEKRAPAAEPSPAAAP

AGREMENKETLKGLHKMDDRPEERMIREKLKATCMPAWKHEWLERRNRRGPVVVKPIPVKGDGSEMNHLA

AESPGEVQASAASPASKGRRSPSPGNSPSGRTVKSESPGVRRKRVSPVPFQSGRITPPRRAPSPDGFSPY

SPEETNRRVNKVMRARLYLLQQIGPNSFLIGGDSPDNKYRVFIGPQNCSCARGTFCIHLLFVMLRVFQLE

PSDPMLWRKTLKNFEVESLFQKYHSRRSSRIKAPSRNTIQKFVSRMSNSHTLSSSSTSTSSSENSIKDEE

EQMCPICLLGMLDEESLTVCEDGCRNKLHHHCMSIWAEECRRNREPLICPLCRSKWRSHDFYSHELSSPV

DSPSSLRAAQQQTVQQQPLAGSRRNQESNFNLTHYGTQQIPPAYKDLAEPWIQVFGMELVGCLFSRNWNV

REMALRRLSHDVSGALLLANGESTGNSGGSSGSSPSGGATSGSSQTSISGDVVEACCSVLSMVCADPVYK

VYVAALKTLRAMLVYTPCHSLAERIKLQRLLQPVVDTILVKCADANSRTSQLSISTLLELCKGQAGELAV

GREILKAGSIGIGGVDYVLNCILGNQTESNNWQELLGRLCLIDRLLLEFPAEFYPHIVSTDVSQAEPVEI

RYKKLLSLLTFALQSIDNSHSMVGKLSRRIYLSSARMVTTVPHVFSKLLEMLSVSSSTHFTRMRRRLMAI

ADEVEIAEAIQLGVEDTLDGQQDSFLQASVPNNYLETTENSSPECTVHLEKTGKGLCATKLSASSEDISE

RLASISVGPSSSTTTTTTTTEQPKPMVQTKGRPHSQCLNSSPLSHHSQLMFPALSTPSSSTPSVPAGTAT

DVSKHRLQGFIPCRIPSASPQTQRKFSLQFHRNCPENKDSDKLSPVFTQSRPLPSSNIHRPKPSRPTPGN

TSKQGDPSKNSMTLDLNSSSKCDDSFGCSSNSSNAVIPSDETVFTPVEEKCRLDVNTELNSSIEDLLEAS

MPSSDTTVTFKSEVAVLSPEKAENDDTYKDDVNHNQKCKEKMEAEEEEALAIAMAMSASQDALPIVPQLQ

VENGEDIIIIQQDTPETLPGHTKAKQPYREDTEWLKGQQIGLGAFSSCYQAQDVGTGTLMAVKQVTYVRN

TSSEQEEVVEALREEIRMMSHLNHPNIIRMLGATCEKSNYNLFIEWMAGGSVAHLLSKYGAFKESVVINY

TEQLLRGLSYLHENQIIHRDVKGANLLIDSTGQRLRIADFGAAARLASKGTGAGEFQGQLLGTIAFMAPE

VLRGQQYGRSCDVWSVGCAIIEMACAKPPWNAEKHSNHLALIFKIASATTAPSIPSHLSPGLRDVALRCL

ELQPQDRPPSRELLKHPVFRTTW

>Hs2a

MDDQQALNSIMQDLAVLHKASRPALSLQETRKAKSSSPKKQNDVRVKFEHRGEKRILQFPRPVKLEDLRS

KAKIAFGQSMDLHYTNNELVIPLTTQDDLDKALELLDRSIHMKSLKILLVINGSTQATNLEPLPSLEDLD

NTVFGAERKKRLSIIGPTSRDRSSPPPGYIPDELHQVARNGSFTSINSEGEFIPESMEQMLDPLSLSSPE

NSGSGSCPSLDSPLDGESYPKSRMPRAQSYPDNHQEFSDYDNPIFEKFGKGGTYPRRYHVSYHHQEVIMM

VVKLFQELEGPRGTSLRSPVSFSPTDHSLSTSSGSSIFTPEYDDSRIRRRGSDIDNPTLTVMDISPPSRS

PRAPTNWRLGKLLGQGAFGRVYLCYDVDTGRELAVKQVQFDPDSPETSKEVNALECEIQLLKNLLHERIV

QYYGCLRDPQEKTLSIFMEYMPGGSIKDQLKAYGALTENVTRKYTRQILEGVHYLHSNMIVLRDIKGANI

LRDSTGNVKLGDFGASKRLQTICLSGTGMKSVTGTPYWMSPEVISGEGYGRKADIWSVACTVVEMLTEKP

PWAEFEAMAAIFKIATQPTNPKLPPHVSDYTRDFLKRIFVEAKLRPSADELLRHMFVHYH

>Hs3a

MDEQEALNSIMNDLVALQMNRRHRMPGYETMKNKDTGHSNRQKKHNSSSSALLNSPTVTTSSCAGASEKK

KFLSDVRIKFEHNGERRIIAFSRPVKYEDVEHKVTTVFGQPLDLHYMNNELSILLKNQDDLDKAIDILDR

SSSMKSLRILLLSQDRNHNSSSPHSGVSRQVRIKASQSAGDINTIYQPPEPRSRHLSVSSQNPGRSSPPP

GYVPERQQHIARQGSYTSINSEGEFIPETSEQCMLDPLSSAENSLSGSCQSLDRSADSPSFRKSRMSRAQ

SFPDNRQEYSDRETQLYDKGVKGGTYPRRYHVSVHHKDYSDGRRTFPRIRRHQGNLFTLVPSSRSLSTNG

ENMGLAVQYLDPRGRLRSADSENALSVQERNVPTKSPSAPINWRRGKLLGQGAFGRVYLCYDVDTGRELA

SKQVQFDPDSPETSKEVSALECEIQLLKNLQHERIVQYYGCLRDRAEKTLTIFMEYMPGGSVKDQLKAYG

ALTESVTRKYTRQILEGMSYLHSNMIVHRDIKGANILRDSAGNVKLGDFGASKRLQTICMSGTGMRSVTG

TPYWMSPEVISGEGYGRKADVWSLGCTVVEMLTEKPPWAEYEAMAAIFKIATQPTNPQLPSHISEHGRDF

LRRIFVEARQRPSAEELLTHHFAQLMY

>Hs4

MREAAAALVPPPAFAVTPAAAMEEPPPPPPPPPPPPEPETESEPECCLAARQEGTLGDSACKSPESDLED

FSDETNTENLYGTSPPSTPRQMKRMSTKHQRNNVGRPASRSNLKEKMNAPNQPPHKDTGKTVENVEEYSY

KQEKKIRAALRTTERDHKKNVQCSFMLDSVGGSLPKKSIPDVDLNKPYLSLGCSNAKLPVSVPMPIARPA

RQTSRTDCPADRLKFFETLRLLLKLTSVSKKKDREQRGQENTSGFWLNRSNELIWLELQAWHAGRTINDQ

DFFLYTARQAIPDIINEILTFKVDYGSFAFVRDRAGFNGTSVEGQCKATPGTKIVGYSTHHEHLQRQRVS

FEQVKRIMELLEYIEALYPSLQALQKDYEKYAAKDFQDRVQALCLWLNITKDLNQKLRIMGTVLGIKNLS

DIGWPVFEIPSPRPSKGNEPEYEGDDTEGELKELESSTDESEEEQISDPRVPEIRQPIDNSFDIQSRDCI

SKKLERLESEDDSLGWGAPDWSTEAGFSRHCLTSIYRPFVDKALKQMGLRKLILRLHKLMDGSLQRARIA

LVKNDRPVEFSEFPDPMWGSDYVQLSRTPPSSEEKCSAVSWEELKAMDLPSFEPAFLVLCRVLLNVIHEC

LKLRLEQRPAGEPSLLSIKQLVRECKEVLKGGLLMKQYYQFMLQEVLEDLEKPDCNIDAFEEDLHKMLMV

YFDYMRSWIQMLQQLPQASHSLKNLLEEEWNFTKEITHYIRGGEAQAGKLFCDIAGMLLKSTGSFLEFGL

QESCAEFWTSADDSSASDEIIRSVIEISRALKELFHEARERASKALGFAKMLRKDLEIAAEFRLSAPVRD

LLDVLKSKQYVKVQIPGLENLQMFVPDTLAEEKSIILQLLNAAAGKDCSKDSDDVLIDAYLLLTKHGDRA

RDSEDSWGTWEAQPVKVVPQVETVDTLRSMQVDNLLLVVMQSAHLTIQRKAFQQSIEGLMTLCQEQTSSQ

PVIAKALQQLKNDALELCNRISNAIDRVDHMFTSEFDAEVDESESVTLQQYYREAMIQGYNFGFEYHKEV

VRLMSGEFRQKIGDKYISFARKWMNYVLTKCESGRGTRPRWATQGFDFLQAIEPAFISALPEDDFLSLQA

LMNECIGHVIGKPHSPVTGLYLAIHRNSPRPMKVPRCHSDPPNPHLIIPTPEGFSTRSMPSDARSHGSPA

AAAAAAAAVAASRPSPSGGDSVLPKSISSAHDTRGSSVPENDRLASIAAELQFRSLSRHSSPTEERDEPA

YPRGDSSGSTRRSWELRTLISQSKDTASKLGPIEAIQKSVRLFEEKRYREMRRKNIIGQVCDTPKSYDNV

MHVGLRKVTFKWQRGNKIGEGQYGKVYTCISVDTGELMAMKEIRFQPNDHKTIKETADELKIFEGIKHPN

LVRYFGVELHREEMYIFMEYCDEGTLEEVSRLGLQEHVIRLYSKQITIAINVLHEHGIVHRDIKGANIFL

TSSGLIKLGDFGCSVKLKNNAQTMPGEVNSTLGTAAYMAPEVITRAKGEGHGRAADIWSLGCVVIEMVTG

KRPWHEYEHNFQIMYKVGMGHKPPIPERLSPEGKDFLSHCLESDPKMRWTASQLLDHSFVKVCTDEE

>Ci

IQVGRTSPFSKRVPSPTSRGLIKGRNPSPKGRNPSPKGRNPSPNRRPPSPNTDGVSPYSPEATAKKVNRV

LKARLYLLQQNGPNSFRIGGDSPEHKYLVIIGPQSCNCGRGLFCIHVLFVMLRVFQLEPTSTLLWRKTLK

NYEVVETLFKSYHERCNSRISPKKKSRVQRLVSHLASGTDKHADTSSNSDDQCSSKGEEENCPICLLQMV

DGESVTVCEVGCRNKLHTHCVNIWAEECRRNGGSLKCPLCRIVWKPADTPGGTGIRPLMVEIPHEYTDLA

DTWTQVAFGWEMVSCLFSTHPNVRENALRRLSHDITGALLTNSQMSDTNDDRTSDDSDSSMRGAVGGTSS

SLSSNAYLASCCAILAMVCSDPEYRVYITALRTLRAMMAYTQCRTNNDVTAFQRLLAPVIETILFKCADS

NRRNVQLSVSTVMELCRGQSGELAVGKEMVSGESLGVGSVGFLLSFLDFGGSPDTSSWQWMLGRLNALGE

LCREFKSELSIRFVVVGICVEGMDSTEAQALLCVARFAVSCMNNTSQPRVCKMARRVFLQSSTSSTSCCE

DFRRASERRLSVRELADNINRKQNRLAVANRGEKSKKLDSAPIGGFRKYSNDKSPSSAPTDVLKEDSVKP

APKTKQNEEPLAHTFAKKSTLLSKTLDEDVSQSDVAQLSPFLGANQSNSSRIPTRGILKNSSIPLVPTPP

NRMLSASSGVSDGFGATTDSGVGTDSSYKGSIGIMSSKSSNIQHLTSPESETSPEEIYGKNTQRKKDDMA

SGEDSSGPSIKRPVRPKQLRRPTAGSSRKPRALLHYHQQSRRHRTPHPEDSDHYINDPDSPMATRSMEED

IPSTSASLKQKSQLSSSVEDLLAESDHSQAEKTPVTFKSEIGWYIGDALESYEADLAMQCSCQMQIEEEE

DKLFAHTLAVSYIQDALPMVPHLSYTEEEPDIVRVQDEVKCTDIQKEYKENNQWCKGAQIGLGAFSACYQ

ARDMFTGTLMAVKQVNHVRCSAVEERQVLAVITEEISLMRRLSHPNIVRLHGITKEGPLYNIFIEWCAGG

SVSTLLSHYGAFNEAVIMNYTLQLLRGLSYIHEQFLIHRDIKGANLLIDSTGQRXRVSDFGAAARLASKG

TGAGEFQGQLLGTIAFMAPEVLRGEQYGRSCDVWGCGCVITEMASGKPPWEADMHSNHLALIFKIASSPT

What ancestral relationships can you draw between the proteins in each case?