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Berkeley INTEGBI 200A - Wagner Trees

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T-ø 7oo@tww"I^IAGNER TREES"Wagner Trees (and Networks) are estínaÈes of evolutíonary Èrees. Theconstruction of a trIagner Tree begíns wíth a character x taxon matrix. In thematrix the states of characters are coded nunerically, and the initial directionof evolution of the states withÍn each character is specified. The trIagner Treefor a given data set is the cladistic topol-ogy thaË requires the minimum numberof evolutionary steps, i.e., ít makes the fewest number of assumptions aboutthe number of evolutíonary steps and it is the ttmosË parsímoníoust' hypothesis. overall.The chief references on tr{agner Trees are Èhe papers by trIagner (1969) andFarris eË aI. listed on the references handout.I. Initial treatment of charactersA. Discover characters in ihe taxa under study. This involves estímatinghomologous relatíons of features in different organisms using ËhecriÈeria noted ín class. verbalize or, if possible, enumerate thestates of each character.B. ConsÈrucÈ a morphocline for the states of each character. A morphoclineis an arrangement of states in which the states are ordered on thebasis of their overall sínilarity. For example:(a) 5 toes - 4 toes - 3 toes - 2 toes - 1 Ëoe(b) 5mn-20mn-21mm(c) blue - green - yellow(d) eyes present - eyes absent(e) horizontalstripesvertical\ srripes&"rtrr.:j: *#& dots in the rniddlettWagner TreesttMorphoclines are estimates of the paËtern of evolution wÍthin acharacter. Thus, íf a 5 toed ancesÈor gave rise to a 1 toeddescendant we would suppose a series of intermediate ancestorswith 4, 3 and 2 Ëoes respectively.yields a hypothesis on thefor each character using the criÈeria forclass. The selection of an ancestral statedirection of evolutíon for a character. Forexample:blue ----) green + yellow,blue (-- greenblue <- green yellow.D. Usíng integers in an additíve fashíon, and a similar scale for eachcharacter (by convention a unit difference beÈr¿een adjacent sËates ina morphocline) code numerically to preserve Èhe estimated form an-d-dÍrectíon of character sÈate evolution. The coding schemes belor¿correspond to the morphoclines yerbaLLzed on page 2.(a) 0-1-2-3-4 or 4- 3-2- 1-O(b) 0-L-2 or 2-L-0(c) 0-L-2 or 2-L-0(d) 0-1 or 1-0(e) 1,0,0- -0,1,0nce betwe ".\ \ " " "a/ -4.-rn. dífference betweenthese states is 2, or -,1- u' Y' * adjacent states ís 1,rrat least two evolutionary ¿ | or rtat least onestepsrr ) O, ó, 1 evolutionary steprlII. The ANCESTORc. Estimate an ancesËral stateprimitiveness discussed inmost recent conmon ancestor for the group ofbe the collecÈÍon of all estÍmated ancesÈralthe coded character x taxon data matríx.taxa under study is takensEates. Add the ancestororrorlThetotottlrlagner TreesttIII. The SËeps Ín Tree Constructíon & a Hypotbetical_ ExampleThe steps in the construcËíon of a llagner Tree are illustrated here with ahypothetical data set of 4 taxa and 12 characÈers (see attached sheet).The characters are already coded and an ancestor for the four taxa has beenestímated and added to the initial data matrix.Step 1. Calculate Ëhe dífference (sirnÍlarity) matrix according to theformula:d (r,K) = å f* tr,ü) - x (K,L) IK,tto rshich it isof the. tree by connecting the ancestormost símilar.The first interval has a lengÈh of 4, i.e.4 evolutíonary steps separaÈe C frou theancestor. Check the data matrix to seethat these steps involve characters3, 6, 10 and 11.to be placed on the tree. Here r¡¡e nust findtaxon-interval pairrrr i.e. the nexÈ taxon towhích is nost similar to any interval of thewhere d (JrK) ís the dífference between trrro taxa J &X is the character state value for a characterForm theÈhe taxonfirst interval,n is the number of charactersIthe difference matrix based on the hypothetícal data seÈ is below the data set]S.tep 2.@@GoSËep 3.10ANCESTORSelect the next taxonthe closest I'unplacedbe placed is that onetree.Calculate the dífference betr¡een each unplaced taxon and g¿interval according to the fornula:d (L,rM(J,K)) = (U (L,J) + d (L,K) - d {.1,x)(I)where d (LTINT(JrK)) is the difference beÈr¡een an unplaced taxon Lttlrlagner Treesttand an interval composed of the taxa J and K..d(LrJ), d(LrK) and .d(JrK) are the disrances berween rhese taxataken directly from the dífference maËrix.Thus in the exampl-e, there are three remaíning unplaced taxaA, B and D.d (A, rNT (ANC, C) )= d(A,ANC) + d(A,c) - d(ANc-C)=7+11 -4= @^lo=Td (B, rNT (ANC, C) )= d(B,NC) + d(B,C) - d(ANC,C)=9+LL-4= @ Ì*t*=gd (D, rNT (ANC,C) )=6+8-4= @ xt_:sSince D is the closest to the inÈerval it sha1l be placed next,.Step 4. Construct a ttypottretical Intermediate Ancestor (= HypotheticalTaxonomic UniÈ, = HTU) for the unplaced taxon selected in Step 3and the two uembers of the ínterval to which that unplaced taxonis closest. HTUrs must be considered because it is possibl-e (inmost cases probable) that the unplaced taxon will diverge from theIíneage leading from ANCESTOR to C at an internediate level Ínsteadof directly from the ANCESTOR or C.Thus, where does D diverge from?c "'-r¿"'/oI -.?-"-Ðsome HTU 1y/| ,---,ANC..x ,L*"ul ^1b,, ilfu"rro^**r*^ ,1, *op IÇoúw *"/¡,n_*u o-.hi"uq. tvti,niç44,Lrt, Þ,^rftL ,Ë*". (u, *G{no¡æJ il"*p,J"n¡-*e-. ll kr*il ;;y*/\-t /1,g" ] wg % "Ég*"ffi**, Z"-/ ^;"ih#**,*,, / y-ù-,r- ç4^- ÎffEle3 ;x þil-x(Þ.Ðl = I x cÁl i'_ j''""'t' ¡'r r\rti \"/ ¿\\ç-¡ LJ IxÇi)-x(Q,)t = tx(A i\ - -19,,1 "!*9:l -A(D, Ùlx (çi) -X (q')l = [ x@,.Í _ Xö, ('n"*^t 'l^^^oÍ*u^ .xÍk ò.^y*.I (B¿)+x (c,.)J')x G,¿'l .()Ltt<)rttt t+u,l, Tgf.o#-å.'ht ¡Qr,u¿2 qa-sbt¿dôet' ro "k*=6"tio/\,)l +(x(A-,r) -X (úú'r1:8,Q. *!o,Bi- -¿-;;i t}'ì = "f (n,e) i u60,.;€Õ.r (c,o) =dég¡r_ú¿Àói -ñ.-l.lot^r qd¿ (D +O :' * (ø,c) + u (s,Ð= a J (n,c)- ffi) + "r_(n,,D) @ßv(Ð,Øb**1d- (e, .) .J(8,¡) = f J [n,e; + *J (c,b)Rto,'.n*t^t , J (A,B) =(a(ørcl -aC.,D; _íe,rïr;ttl,lagner Treestt 5The sÈates of an HTU are always based on the states of 3 othertaxonomÍc units (real or hypothetical). HTUrs are constructedin such a vray as to reduce the number of evolutionary steps implíedin the final tree. The rules for IITU construction are as follows:(a) If all three taxa have the same state for a character, theHTU wíll take that stare.e.g. Character Ic (t)Hru llo (r)(r) Iar.rc (r)(b) If. two oftake thatthe threest,ate.Èaxa have the same state, Èhe HTU will( tt O does connect to the HTUI and if the


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Berkeley INTEGBI 200A - Wagner Trees

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