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

0.75000 0.25000 1.00000 0.33333 0.54545 0.82857 0.75000 0.75000 0.90625 0.92683 0.86957 0.50000 0.60000 0.62500 0.54545 0.71429 0.76000 0.78261 0.83871 0.68421 0.80000 0.92941

0.70000 0.11111 0.33333 1.00000 0.27273 0.74286 0.60000 0.70000 0.85938 0.89024 0.80435 0.38462 0.50000 0.43750 0.41667 0.57143 0.64000 0.65217 0.74194 0.52632 0.70000 0.89412

0.72727 0.36364 0.54545 0.27273 1.00000 0.71429 0.47368 0.72727 0.84375 0.87805 0.78261 0.30769 0.43750 0.37500 0.18182 0.52381 0.60000 0.60870 0.70968 0.47368 0.66667 0.88235

0.88571 0.77143 0.82857 0.74286 0.71429 1.00000 0.45714 0.88571 0.47692 0.57317 0.34694 0.65714 0.68421 0.58333 0.71429 0.44444 0.50000 0.53846 0.45238 0.50000 0.33333 0.58824

0.85000 0.65000 0.75000 0.60000 0.47368 0.45714 1.00000 0.78947 0.70312 0.76829 0.58696 0.52381 0.58333 0.40909 0.47368 0.40000 0.53333 0.58621 0.55882 0.48000 0.41935 0.77647

0.85714 0.80000 0.75000 0.70000 0.72727 0.88571 0.78947 1.00000 0.93750 0.95122 0.91304 0.76923 0.88235 0.82353 0.72727 0.86364 0.88462 0.91667 0.90323 0.85000 0.90323 0.95294

0.93750 0.87500 0.90625 0.85938 0.84375 0.47692 0.70312 0.93750 1.00000 0.26190 0.38235 0.81250 0.78462 0.75000 0.84375 0.67188 0.63077 0.67692 0.55385 0.70312 0.53125 0.24706

0.95122 0.90244 0.92683 0.89024 0.87805 0.57317 0.76829 0.95122 0.26190 1.00000 0.43902 0.85366 0.83133 0.80488 0.87805 0.74390 0.71084 0.74699 0.66667 0.76829 0.63415 0.03529

0.91304 0.82609 0.86957 0.80435 0.78261 0.34694 0.58696 0.91304 0.38235 0.43902 1.00000 0.73913 0.72917 0.65217 0.78261 0.54348 0.60784 0.64000 0.59259 0.61702 0.44898 0.45882

0.66667 0.46154 0.50000 0.38462 0.30769 0.65714 0.52381 0.76923 0.81250 0.85366 0.73913 1.00000 0.31250 0.25000 0.16667 0.42857 0.52000 0.52174 0.64516 0.36842 0.60000 0.85882

0.73333 0.46667 0.60000 0.50000 0.43750 0.68421 0.58333 0.88235 0.78462 0.83133 0.72917 0.31250 1.00000 0.27778 0.43750 0.43478 0.40000 0.45833 0.54839 0.38095 0.59375 0.82353

0.75000 0.50000 0.62500 0.43750 0.37500 0.58333 0.40909 0.82353 0.75000 0.80488 0.65217 0.25000 0.27778 1.00000 0.37500 0.23810 0.36000 0.41667 0.51613 0.25000 0.46667 0.81176

0.72727 0.50000 0.54545 0.41667 0.18182 0.71429 0.47368 0.72727 0.84375 0.87805 0.78261 0.16667 0.43750 0.37500 1.00000 0.52381 0.60000 0.60870 0.70968 0.47368 0.66667 0.88235

0.80952 0.61905 0.71429 0.57143 0.52381 0.44444 0.40000 0.86364 0.67188 0.74390 0.54348 0.42857 0.43478 0.23810 0.52381 1.00000 0.35714 0.40741 0.35484 0.26087 0.30000 0.75294

0.84000 0.68000 0.76000 0.64000 0.60000 0.50000 0.53333 0.88462 0.63077 0.71084 0.60784 0.52000 0.40000 0.36000 0.60000 0.35714 1.00000 0.19231 0.22581 0.24000 0.28125 0.70588

0.86957 0.69565 0.78261 0.65217 0.60870 0.53846 0.58621 0.91667 0.67692 0.74699 0.64000 0.52174 0.45833 0.41667 0.60870 0.40741 0.19231 1.00000 0.32258 0.21739 0.37500 0.74118

0.90323 0.77419 0.83871 0.74194 0.70968 0.45238 0.55882 0.90323 0.55385 0.66667 0.59259 0.64516 0.54839 0.51613 0.70968 0.35484 0.22581 0.32258 1.00000 0.41935 0.28571 0.64706

0.78947 0.57895 0.68421 0.52632 0.47368 0.50000 0.48000 0.85000 0.70312 0.76829 0.61702 0.36842 0.38095 0.25000 0.47368 0.26087 0.24000 0.21739 0.41935 1.00000 0.36667 0.77647

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

0.95294 0.90588 0.92941 0.89412 0.88235 0.58824 0.77647 0.95294 0.24706 0.03529 0.45882 0.85882 0.82353 0.81176 0.88235 0.75294 0.70588 0.74118 0.64706 0.77647 0.64706 1.00000

 

Region ID in Legendre & Legendre (1984) and Legendre (1986):

11 12 21 22 23 31 32 33 41 42 43 51 52 53 54 55 56 57 58 59 60

 

Region ID in Legendre  (1986):

11 12 21 22 23 31 32 33 41 42 43 51 52 53 54 55 56 57 58 59 60 Root

 

Region ID in Legendre & Makarenkov (2002):

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Root

 

The Camin-Sokal tree published in Legendre (1986) provided the topology of the tree to which reticulation branches were added.

 

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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).

 

 

Distances among photosynthetic organisms

 

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

 

 


 

 


Interpretation of the splits

• 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).

 

 

Honeybees distance matrix

 

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.

 

Distances among ancestor (tree root) and 12 Aphelandra species

 

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.

 

Distances among ancestor (tree root), 12 Aphelandra species, and hybrid DESI

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 

 

Legendre, P. (Guest Editor) 2000. Special section on reticulate evolution. Journal of Classification 17: 153-195.

Legendre, P. and V. Makarenkov. 2002. Reconstruction of biogeographic and evolutionary networks using reticulograms. Systematic Biology 51: 199-216.

Makarenkov, V. and P. Legendre. 2000. Improving the additive tree representation of a dissimilarity matrix using reticulations. In: Data Analysis, Classification, and Related Methods. Proceedings of the IFCS-2000 Conference, Namur, Belgium, 11-14 July 2000.

Makarenkov, V. and P. Legendre. 2004. From a phylogenetic tree to a reticulated network. Journal of Computational Biology 11: 195-212.

Makarenkov, V., P. Legendre and Y. Desdevises. 2004. Modelling phylogenetic relationships using reticulated networks. Zoologica Scripta 33: 89-96.