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Principi e Metodi di Analisi filogenetica 2
Distanze additive vs. Distanze Ultrametriche
Alberi additivi vs. Alberi Ultrametrici
A
A
B
B
C
C
D
D
E
E
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Alberi additivi
Neighbor-Joining
Pairwise distance matrix (non necessariamente
ultrametiche)
Distanze tra i nodi normalizzate
(net divergence) ri ?k1gtNdik
Mij dij - (rirj)/(N-2)
Matrice (M)
Clustering
A
A
B
B
C
C
D
D
E
E
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Neighbor-Joining
Nuovo nodo u
C
A
sAu dAB /2 (rA - rB)/(N 2) sBu dAB - sAu
E
u
B
D
Mij dij - (rirj)/(N-2) rimosse distanze
con A e con B inserite distanze con u N N-1
Nuova Matrice (M)
C
E
u
D
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Neighbor-Joining
Mij dij - (rirj)/(N-2) rimosse distanze
con A e con B inserite distanze con u N
N-1 nuove distanze gtgt con nodo non medie con
i taxa terminali
Nuova Matrice (M)
0.1
0.7
0.5
0.6
0.3
0.4
0.2
0
C
A
E
u
C D E
D
B
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Neighbor-Joining
C
E
u
Nuova Matrice (M)
D
Se ci sono ancora più di 2 nodi si ripete il ciclo
C
w
u
D
E
sCw dCu /2 (rC - ru)/(N 2) swu dCu - sCw
Nuova Matrice (M) N N - 1
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Neighbor-Joining
C
w
u
D
E
Nuova Matrice (M)
Ci sono ancora più di 2 nodi quindi . si ripete
il ciclo
STOP !!!!
sEz dDE /2 (rD - rE)/(N 2) sDz dDE - sEz
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Neighbor-Joining
unrooted
Rooting
midpoint rooting
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Distanze ed alberi additivi
Data una matrice di distanze pairwiseesistono
molte tecniche per ricavarne alberi additivi. È
necessaria una definizione della distorsione
accettabile tra lalbero e le distanze della
matrice. La soluzione è generalmente nella forma
di unequazione da minimizzare, del tipo
E errore (fitting error) T numero di
taxa wij peso separazione iltgtj dij pairwise
dist. i-j pij tree dist. i-j
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Algoritmi vs. Criteri di Ottimalità
SAHN (UPGMA, WPGMA, SL ...)
Due step
Costruzione dellalbero e definizione dellalbero
preferito in unico step
Def. Criterio di ottimalità CO
Uso del CO per trovare il miglior albero
Velocità di esecuzione
Lentezza di esecuzione
evolutionary assumptions nel primo step
No evolutionary assumptions
No comparazione di filogenesi subottimali
Comparazione di tutte le filogenesi subottimali
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Wagners Groundplan Divergence Method
Taxa are connected to each other by their
ensembles of common features, which are plotted
as the points of separation, i.e., as the most
probable common ancestors" (Wagner, 1961).
"To work out a phylogenetic problem three broad
phases are involved (a) systematic or
comparative analysis of the plants in question to
find and understand their contrasting characters
(b) determination of ground plans to find the
character states common to all or most of the
plants in order to deduce the most probable
ancestral or primitive states and (c)
phylogenetic synthesis to assemble the taxa
according to their respective deviations from the
basic ground plan and from each other.
W. H. Wagner, Jr. Systematic botanist at the
University of Michigan.
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Wagners GPD
Detailed steps (1) to compare and study all the
variable characters among the taxa (2) to
determine the generalized or primitive conditions
on the principle that characters found in most or
all of a number of related taxa are inherited
essentially unchanged from the common ancestor,
using data also from related taxonomic groups of
the same level. (If no obvious trend can be
determined in a given character that character
may be used only for grouping purposes.) (3) to
assign for each character the value 0 for the
generalized or primitive condition, and 1 for the
specialized or secondary condition (the
intermediate states being assigned the value
0.5) (4) to list in tabular form the taxa and
for each give the divergence values from the
ground plan, both for individual characters and
in total and (5) to determine the mutual
character groupings between taxa and then arrange
them in sequence according to these groupings on
a concentric chart or graph, the radii and
branchings to be determined by the mutual
character complexes, and the distances by the
divergence indices.
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Wagners GPD
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Wagners GPD
2
4
6
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10
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Wagners GPD
Neocteniza (7)
2
4
6
8
10
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Wagners GPD
Actinopus (10)
Neocteniza (7)
2
4
6
8
10
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Wagners GPD
Actinopus (10)
Missulena (8)
Neocteniza (7)
2
4
6
8
10
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Wagners GPD
Actinopus (10)
Missulena (8)
Neocteniza (7)
2
4
6
8
10
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Wagners GPD
Actinopus (10)
Missulena (8)
Neocteniza (7)
2
4
6
8
10
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Wagners Groundplan Divergence Method
The strict application of parsimony criteria to
choose cladograms was not originally advocated by
Wagner (1961) ... Although parsimonious
explanations of data sets is important in
Groundplan-Divergence, strict application of
parsimony is not part of the method
(Duncan,1984. Duncan was a former Ph.D. student
of Wagner's, and proponent of the
groundplan-divergence method).
W. H. Wagner, Jr., and his groundplan-divergence
method will always be identified with the most
efficient parsimony algorithm yet formulated for
obtaining best-fitting phylogenetic hypotheses.