This page contains the 6 examples (distance
matrices and figures illustrating the results) used by P. Legendre and V.
Makarenkov to illustrate the reticulogram method during the DIMACS Workshop on Reticulated
Evolution, Rutgers University (NJ, USA), September 20, 2004.
Complete presentation in PowerPoint is
available here.
Complete presentation in PDF is
available here.
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1. Homoplasy example. Primate distance matrix (Makarenkov and Legendre, 2000).
1. Homo sapiens 0.000
2. Pan 0.089 0.000
3. Gorilla 0.104 0.106 0.000
4. Pongo 0.161 0.171 0.166 0.000
5. Hylobates 0.182 0.189 0.189 0.188 0.000
6. Macaca fuscata 0.232 0.243 0.237 0.244 0.247 0.000
7. Macaca mulatta 0.233 0.251 0.235 0.247 0.239 0.036 0.000
8. Macaca fascicular. 0.249 0.268 0.262 0.262 0.257 0.084 0.093 0.000
9. Macaca sylvanus 0.256 0.249 0.244 0.241 0.242 0.124 0.120 0.123 0.000
10. Saimiri sciureus 0.273 0.284 0.271 0.284 0.269 0.289 0.293 0.287 0.287 0.000
11. Tarsius syrichta 0.322 0.321 0.314 0.303 0.309 0.314 0.316 0.311 0.319 0.320 0.000
12. Lemur catta 0.308 0.309 0.293 0.293 0.296 0.282 0.289 0.298 0.287 0.285 0.252 0.000
Data: A portion of the protein-coding mitochondrial DNA (898 bases) of 12 primate species, from Hayasaka et al. (1988).
Reference for the DNA data:
Hayasaka, K., T. Gojobori, and S. Horai. 1988. Molecular phylogeny and evolution of primate mitochondrial DNA. Molecular Biology and Evolution 5, 626-644.
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2. Postglacial
dispersal of freshwater fishes1
Question: Can we reconstruct the routes taken by
freshwater fishes to reinvade the Quebec peninsula after the last glaciation?
The Laurentian glacier melted away between –14000 and –5000 years.
1 Example considered in Legendre and Makarenkov (2002).
Quebec fish community data (85 stenohaline species); Distance matrix (22 x 22) among (21 regions + root); Distance = (1 - Jaccard similarity)
1.00000
0.66667 0.75000 0.70000 0.72727 0.88571 0.85000 0.85714 0.93750 0.95122 0.91304
0.66667 0.73333 0.75000 0.72727 0.80952 0.84000 0.86957 0.90323 0.78947 0.86667
0.95294
0.66667
1.00000 0.25000 0.11111 0.36364 0.77143 0.65000 0.80000 0.87500 0.90244 0.82609
0.46154 0.46667 0.50000 0.50000 0.61905 0.68000 0.69565 0.77419 0.57895 0.73333
0.90588
0.86667 0.73333 0.80000 0.70000 0.66667 0.33333 0.41935 0.90323 0.53125 0.63415 0.44898 0.60000 0.59375 0.46667 0.66667 0.30000 0.28125 0.37500 0.28571 0.36667 1.00000 0.64706
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Application 3. Evolution of photosynthetic organisms
Comparison of reticulograms and split graphs (Makarenkov and Legendre, 2004).
Data: LogDet distances among 8 species of photosynthetic organisms, computed
from 920 bases from the 16S rRNA of the chloroplasts (sequence data from
Lockhart et al. 1993).
1. Tobacco 0.0000
2. Rice 0.0258 0.0000
3. Liverworth 0.0248 0.0357 0.0000
4. Chlamydomonas 0.1124 0.1215 0.1014 0.0000
5. Chlorella 0.0713 0.0804 0.0604 0.0920 0.0000
6. Euglena 0.1270 0.1361 0.1161 0.1506 0.1033 0.0000
7. Cyanobacterium 0.1299 0.1390 0.1190 0.1535 0.1128 0.1611 0.0000
8. Chrysophyte 0.1370 0.1461 0.1261 0.1606 0.1133 0.1442 0.1427 0.0000
• Separation of organisms with or
without chlorophyll b.
• Separation of facultative heterotrophs (H)
from the other organisms.
Interpretation of the
reticulation branches
• Group of facultative heterotrophs.
• Endosymbiosis hypothesis: chloroplasts could be derived from primitive cyanobacteria living as symbionts in eukaryotic cells.
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Application 4. Phylogeny
of honeybees1
Data: Hamming
distances among 6 species of honeybees, computed from DNA sequences (677 bases)
data. D from Huson (1998).
Phylogenetic
tree reconstruction method: Neighbor joining (NJ).
1 Example
developed in Makarenkov, Legendre and Desdevises (2004).
1. Apis
andreniformis 0.000
2. Apis
mellifera 0.090 0.000
3. Apis
dorsata 0.103 0.093 0.000
4. Apis
cerana 0.096 0.090 0.117 0.000
5. Apis
florea 0.004 0.093 0.106 0.099 0.000
6. Apis
koschevnikovi 0.075 0.100 0.103 0.099 0.078 0.000
Reference:
Huson,
D. H. 1998. SplitsTree: A program for analyzing and visualizing evolutionary
data. Bioinformatics 141: 68-73.
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Application 5. Microgeographic
differentiation in muskrats
The morphological differentiation among
local populations of muskrats in La Houille River (Belgium) was explained by
“isolation by distance along corridors” (Le Boulengé, Legendre et al. 1996).
Data: Mahalanobis distances among 9 local populations,
based on 10 age-adjusted linear measurements of the skulls. Total: 144
individuals.
Muskrat distance matrix
(Ondatra zibethicus)
C 0.0000
E 2.1380 0.0000
J 2.2713 2.9579 0.0000
L 1.7135 2.3927 1.7772 0.0000
M 1.5460 1.9818 2.4575 1.0125 0.0000
N 2.6979 3.3566 1.9900 1.8520 2.6954 0.0000
O 2.9985 3.6848 3.4484 2.4272 2.6816 2.3108 0.0000
T 2.3859 2.3169 2.4666 1.4545 1.7581 2.2105 2.5041 0.0000
Z 2.3107 2.3648 1.8086 1.6609 2.0516 2.2954 3.4301 2.0413 0.0000
Mahalanobis distances
among 9 local Ondatra populations along La Houille River, based on 10
age-adjusted linear measurements of the skulls. Total: 144 individuals.
References:
Legendre, P. and V.
Makarenkov. 2002. Reconstruction of biogeographic and evolutionary networks
using reticulograms. Systematic Biology 51: 199-216.
Le Boulenge, P.
Legendre, C. De Le Court, P. Le Boulenge-Nguyen, and M. Languy. 1996.
Microgeographic morphological differentiation in muskrats. Journal of Mammalogy
77: 684-701.
The river network
provided the topology of the tree to which reticulation branches were added.
Tree:
The river network of La Houille.
4
reticulation branches were added to the tree (minimum of Q2).
Interpretation of
O-N, M-Z, M-10: migrations across wetlands.
N-J
= type I error (false positive)?
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Application 6. Detection of Aphelandra hybrids
Data: 50 morphological characters, coded in 2-6 states, measured over 12 species
as well as 17 hybrids of known parental origins. L. A. McDade (1992)
artificially created hybrids between species of Central American Aphelandra
(Acanthus family).
Distance matrix: Dij = (1 – Sij)0.5 where Sij is the simple matching similarity coefficient between species i
and j.
0.00000 0.72614 0.74468
0.52296 0.59798 0.55936 0.74671 0.64315 0.60740 0.55117 0.70442 0.69140 0.63485
0.72614 0.00000 0.38123
0.82664 0.64083 0.66182 0.33665 0.54160 0.40906 0.78102 0.70758 0.58708 0.64601
0.74468 0.38123 0.00000
0.85362 0.74565 0.75056 0.42269 0.61536 0.52217 0.80953 0.77330 0.65879 0.72296
0.52296 0.82664 0.85362
0.00000 0.57793 0.52409 0.84656 0.67082 0.72388 0.36515 0.60882 0.67922 0.58367
0.59798 0.64083 0.74565
0.57793 0.00000 0.34737 0.70993 0.71461 0.58023 0.58367 0.44497 0.49866 0.38297
0.55936 0.66182 0.75056
0.52409 0.34737 0.00000 0.70095 0.64135 0.58652 0.54894 0.49531 0.53790 0.37506
0.74671 0.33665 0.42269
0.84656 0.70993 0.70095 0.00000 0.57155 0.49058 0.80208 0.74431 0.60937 0.68605
0.64315 0.54160 0.61536
0.67082 0.71461 0.64135 0.57155 0.00000 0.56627 0.62450 0.73530 0.65166 0.66633
0.60740 0.40906 0.52217
0.72388 0.58023 0.58652 0.49058 0.56627 0.00000 0.68605 0.67429 0.60992 0.60828
0.55117 0.78102 0.80953
0.36515 0.58367 0.54894 0.80208 0.62450 0.68605 0.00000 0.59777 0.62290 0.57213
0.70442 0.70758 0.77330
0.60882 0.44497 0.49531 0.74431 0.73530 0.67429 0.59777 0.00000 0.49396 0.37148
0.69140 0.58708 0.65879
0.67922 0.49866 0.53790 0.60937 0.65166 0.60992 0.62290 0.49396 0.00000 0.53104
0.63485 0.64601 0.72296 0.58367 0.38297 0.37506 0.68605 0.66633 0.60828 0.57213 0.37148 0.53104 0.00000
Species names:
Ancestor CAMP DARI DEPP GOLF GRAC HART LING LEON PANA SINC STOR TERR
where
CAMP Aphelandra campanensis
DARI Aphelandra darienensis
DEPP Aphelandra deppeana (called SC in McDade's paper)
GOLF Aphelandra golfodulcensis
GRAC Aphelandra gracilis
HART Aphelandra hartwegiana
LING Aphelandra lingua-bovis
LEON Aphelandra leonardii
PANA Aphelandra panamensis
SINC Aphelandra sinclairiana
STOR Aphelandra storkii
TERR Aphelandra terryae
Reference for the raw data (50
morphological characters coded in 2-6 states):
McDade, L. A. 1992. Hybrids and phylogenetic systematics II. The impact of hybrids on cladistic analysis. Evolution 46: 1329-1346.
Reference for distance matrix
and reticulation analysis:
Legendre, P. and V. Makarenkov. 2002. Reconstruction of biogeographic and evolutionary networks using reticulograms. Systematic Biology 51: 199-216.
DESI = hybrid DExSI: ovulate parent = DEPP, staminate parent = SINC
0.00000 0.72614 0.74468
0.52296 0.59798 0.55936 0.74671 0.64315 0.60740 0.55117 0.70442 0.69140 0.63485
0.66201
0.72614 0.00000 0.38123
0.82664 0.64083 0.66182 0.33665 0.54160 0.40906 0.78102 0.70758 0.58708 0.64601
0.69402
0.74468 0.38123 0.00000
0.85362 0.74565 0.75056 0.42269 0.61536 0.52217 0.80953 0.77330 0.65879 0.72296
0.79183
0.52296 0.82664 0.85362
0.00000 0.57793 0.52409 0.84656 0.67082 0.72388 0.36515 0.60882 0.67922 0.58367
0.47434
0.59798 0.64083 0.74565
0.57793 0.00000 0.34737 0.70993 0.71461 0.58023 0.58367 0.44497 0.49866 0.38297
0.43474
0.55936 0.66182 0.75056
0.52409 0.34737 0.00000 0.70095 0.64135 0.58652 0.54894 0.49531 0.53790 0.37506
0.47575
0.74671 0.33665 0.42269
0.84656 0.70993 0.70095 0.00000 0.57155 0.49058 0.80208 0.74431 0.60937 0.68605
0.75829
0.64315 0.54160 0.61536 0.67082
0.71461 0.64135 0.57155 0.00000 0.56627 0.62450 0.73530 0.65166 0.66633 0.66458
0.60740 0.40906 0.52217
0.72388 0.58023 0.58652 0.49058 0.56627 0.00000 0.68605 0.67429 0.60992 0.60828
0.64987
0.55117 0.78102 0.80953
0.36515 0.58367 0.54894 0.80208 0.62450 0.68605 0.00000 0.59777 0.62290 0.57213
0.49497
0.70442 0.70758 0.77330
0.60882 0.44497 0.49531 0.74431 0.73530 0.67429 0.59777 0.00000 0.49396 0.37148
0.40702
0.69140 0.58708 0.65879
0.67922 0.49866 0.53790 0.60937 0.65166 0.60992 0.62290 0.49396 0.00000 0.53104
0.52567
0.63485 0.64601 0.72296
0.58367 0.38297 0.37506 0.68605 0.66633 0.60828 0.57213 0.37148 0.53104 0.00000
0.38166
0.66201 0.69402 0.79183
0.47434 0.43474 0.47575 0.75829 0.66458 0.64987 0.49497 0.40702 0.52567 0.38166
0.00000
Step
1 Calculation of a neighbor-joining phylogenetic tree
and a reticulogram among the 12 Aphelandra species. The minimum of Q1
was reached after addition of 5 reticulated branches.
Step 2: Addition
of one of McDade’s hybrids to the distance matrix and recalculation of the
reticulated tree.
Hybrid: DExSI
Ovulate parent: DEPP
Staminate parent: SINC
6 reticulation branches were added to the
tree.
• DExSI is the sister taxon of SINC in the
tree.
• DExSI is connected by a new edge (bold) to node
15, the ancestor of DEPP.
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References
Available in PDF
at
http://www.fas.umontreal.ca/biol/legendre/reprints/
and http://www.info.uqam.ca/~makarenv/trex.html