11,860 research outputs found
Simple models for scaling in phylogenetic trees
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 motivation, we analyze numerically two branching models
leading to non-logarithmic 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.Comment: 7 pages, 4 figures. A new figure, with example trees, has been added.
To appear in Int. J. Bifurcation and Chao
Scaling properties of protein family phylogenies
One of the classical questions in evolutionary biology is how evolutionary
processes are coupled at the gene and species level. With this motivation, we
compare the topological properties (mainly the depth scaling, as a
characterization of balance) of a large set of protein phylogenies with a set
of species phylogenies. The comparative analysis shows that both sets of
phylogenies share remarkably similar scaling behavior, suggesting the
universality of branching rules and of the evolutionary processes that drive
biological diversification from gene to species level. In order to explain such
generality, we propose a simple model which allows us to estimate the
proportion of evolvability/robustness needed to approximate the scaling
behavior observed in the phylogenies, highlighting the relevance of the
robustness of a biological system (species or protein) in the scaling
properties of the phylogenetic trees. Thus, the rules that govern the
incapability of a biological system to diversify are equally relevant both at
the gene and at the species level.Comment: Replaced with final published versio
Identifiability of Large Phylogenetic Mixture Models
Phylogenetic mixture models are statistical models of character evolution
allowing for heterogeneity. Each of the classes in some unknown partition of
the characters may evolve by different processes, or even along different
trees. The fundamental question of whether parameters of such a model are
identifiable is difficult to address, due to the complexity of the
parameterization. We analyze mixture models on large trees, with many mixture
components, showing that both numerical and tree parameters are indeed
identifiable in these models when all trees are the same. We also explore the
extent to which our algebraic techniques can be employed to extend the result
to mixtures on different trees.Comment: 15 page
BOOL-AN: A method for comparative sequence analysis and phylogenetic reconstruction
A novel discrete mathematical approach is proposed as an additional tool for molecular systematics which does not require prior statistical assumptions concerning the evolutionary process. The method is based on algorithms generating mathematical representations directly from DNA/RNA or protein sequences, followed by the output of numerical (scalar or vector) and visual characteristics (graphs). The binary encoded sequence information is transformed into a compact analytical form, called the Iterative Canonical Form (or ICF) of Boolean functions, which can then be used as a generalized molecular descriptor. The method provides raw vector data for calculating different distance matrices, which in turn can be analyzed by neighbor-joining or UPGMA to derive a phylogenetic tree, or by principal coordinates analysis to get an ordination scattergram. The new method and the associated software for inferring phylogenetic trees are called the Boolean analysis or BOOL-AN
Random tree growth by vertex splitting
We study a model of growing planar tree graphs where in each time step we
separate the tree into two components by splitting a vertex and then connect
the two pieces by inserting a new link between the daughter vertices. This
model generalises the preferential attachment model and Ford's -model
for phylogenetic trees. We develop a mean field theory for the vertex degree
distribution, prove that the mean field theory is exact in some special cases
and check that it agrees with numerical simulations in general. We calculate
various correlation functions and show that the intrinsic Hausdorff dimension
can vary from one to infinity, depending on the parameters of the model.Comment: 47 page
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