Abstract
Many processes and models-in biological, physical, social, and other contexts produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this goal, we analyze numerically two branching models leading to nonlogarithmic scaling of the depth with the number of leaves. For Ford's alpha model, although a power-law scaling of the depth with tree size was established analytically, our numerical results illustrate that the asymptotic regime is approached only at very large tree sizes. We introduce here a new model, the activity model, showing analytically and numerically that it also displays a power-law scaling of the depth with tree size at a critical parameter value.
| Original language | English |
|---|---|
| Pages (from-to) | 805-811 |
| Number of pages | 7 |
| Journal | International Journal of Bifurcation and Chaos |
| Volume | 20 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Mar 2010 |
| Externally published | Yes |
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Keywords
- Activity model
- Ford's alpha model
- Phylogenetic trees
ASJC Scopus subject areas
- Applied Mathematics
- General
- Engineering(all)
- Modelling and Simulation
Cite this
Simple models for scaling in phylogenetic trees. / Hernández-García, Emilio; Tuǧrul, Murat; Alejandro Herrada, E.; Eguíluz, Víctor M.; Klemm, Konstantin.
In: International Journal of Bifurcation and Chaos, Vol. 20, No. 3, 03.2010, p. 805-811.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Simple models for scaling in phylogenetic trees
AU - Hernández-García, Emilio
AU - Tuǧrul, Murat
AU - Alejandro Herrada, E.
AU - Eguíluz, Víctor M.
AU - Klemm, Konstantin
PY - 2010/3
Y1 - 2010/3
N2 - Many processes and models-in biological, physical, social, and other contexts produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this goal, we analyze numerically two branching models leading to nonlogarithmic scaling of the depth with the number of leaves. For Ford's alpha model, although a power-law scaling of the depth with tree size was established analytically, our numerical results illustrate that the asymptotic regime is approached only at very large tree sizes. We introduce here a new model, the activity model, showing analytically and numerically that it also displays a power-law scaling of the depth with tree size at a critical parameter value.
AB - Many processes and models-in biological, physical, social, and other contexts produce trees whose depth scales logarithmically with the number of leaves. Phylogenetic trees, describing the evolutionary relationships between biological species, are examples of trees for which such scaling is not observed. With this goal, we analyze numerically two branching models leading to nonlogarithmic scaling of the depth with the number of leaves. For Ford's alpha model, although a power-law scaling of the depth with tree size was established analytically, our numerical results illustrate that the asymptotic regime is approached only at very large tree sizes. We introduce here a new model, the activity model, showing analytically and numerically that it also displays a power-law scaling of the depth with tree size at a critical parameter value.
KW - Activity model
KW - Ford's alpha model
KW - Phylogenetic trees
UR - http://www.scopus.com/inward/record.url?scp=77951882990&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77951882990&partnerID=8YFLogxK
U2 - 10.1142/S0218127410026095
DO - 10.1142/S0218127410026095
M3 - Article
AN - SCOPUS:77951882990
VL - 20
SP - 805
EP - 811
JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
SN - 0218-1274
IS - 3
ER -