Tests for phylogenetic signal

1
Tests for phylogenetic signal
2
CI and RI
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A

G

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G A
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G A
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G G
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G G
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T A
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CI and RI
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G A
C

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G A
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G G
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G G
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4
General points

• CI and RI apply to a particular set of characters
  (even one character) and a specified tree
• For a given set of data all trees of the same
  length will have the same CI, CI, and RI
• Length is the most basic measure of signal

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How can we evaluate the significance of the
signal?

• We can compare the observed tree length (or CI)
  with what we would obtain if there were no
  phylogenetic signal

The permutation tail probability (PTP) test
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Permuting data removes phylogenetic signal

• Taxon 1 ACATTTA
• Taxon 2 ACGATTA
• Taxon 3 AGGATAG
• Taxon 4 GAAAAC?
• Taxon 5 GATA?CG

Permuted data sets
Taxon 1 GAAA?AA Taxon 2 ACAATC? Taxon 3
GAGTATG Taxon 4 AGTATCG Taxon 5 ACGATTA
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Example with signal
Number of Tree length replicates
------------------------- 1222 1
1669 1 1671 1
1672 1 1673 1 1674
1 1675 2 1676 2
1678 1 1679 2
1680 4 1681 5 1682
8 1683 4 1684 4
1685 2
Number of Tree length replicates
------------------------- 1686 8
1687 7 1688 6
1689 8 1690 6 1691
3 1692 2 1693
3 1694 3 1695 3
1696 3 1697 2
1699 2 1702 1 1704
2 1705 1
8
Example without signal
Number of Tree length replicates
------------------------- 1924
3 1926 1 1927
4 1928 1
1929 2 1930 8
1931 6 1932
5 1933 4 1934
4 1935 5
1936 1 1937 8
1938 11 1939
7
Number of Tree length replicates
------------------------- 1940 6
1941 7 1942
4 1943 2 1944
1 1945 1
1946 1 1947 1
1950 3 1952
1 1953 1 1955
1 1958 1
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The PTP test is slow

• Hillis and Huelsenbeck (1991) observed a
  difference between the shape of the tree length
  distribution as a function of phylogenetic signal

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A data set without signal
mean599.182107 sd4.944738 g1-0.150922 582.0000
0 /-----------------------------------------------
------------------------- 583.80000
(5) 585.60000 (25) 587.40000
(71) 589.20000 (209) 591.00000
(161) 592.80000
(521) 594.60000
(883) 596.40000
(1132) 598.20000

(1469) 600.00000

(788) 601.80000

(1631) 603.60000

(1486) 605.40000
(1047) 607.20000
(567) 609.00000
(157) 610.80000
(171) 612.60000 (57) 614.40000
(11) 616.20000 (3) 618.00000 (1)
\-------------------------------------------------
-----------------------
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A data set with signal
mean611.572872 sd31.049455 g1-0.942643 501.000
00 /----------------------------------------------
-------------------------- 508.65000
(15) 516.30000 (60) 523.95000
(84) 531.60000 (135) 539.25000
(21) 546.90000 (26) 554.55000
(96) 562.20000 (166) 569.85000
(290) 577.50000
(737) 585.15000
(1118) 592.80000
(665) 600.45000 (120) 608.10000
(268) 615.75000
(497) 623.40000
(796) 631.05000
(1337) 638.70000

(2031) 646.35000

(1610) 654.00000 (323)
\--------------------------------------------
----------------------------
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Skewness test for phylogenetic signal

• Hillis and Huelsenbeck (1991) generated random
  data for different numbers of taxa/characters to
  find the null distribution of g1 scores
• One can compare observed g1 statistics with this
  null distribution

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Tests for phylogenetic signal (g1 and PTP)

• Are sensitive to any signal in the data
• For example
• g1 of permuted data -0.04 (ns)
• Duplicate one taxon and g1 -1.56
• Useful for identifying truly useless data (very
  rare)
• But otherwise does not tell you much about data
  quality

14
Tests of signal

• PTP and g1 tests seek to determine overall data
  quality
• We can, instead, evaluate particular results
• Clade support measures bootstrap/decay
• Statistical tests of alternative hypotheses