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Random real trees

Jean-François Le Gall (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real trees called stable trees, which generalize the CRT. We review several important results concerning stable...

Relationship between the selection pressure and the rate of mutation accumulation

Katarzyna Bońkowska, Przemysław Biecek, Agnieszka Łaszkiewicz, Stanisław Cebrat (2008)

Banach Center Publications

We use the diploid, sexual Penna ageing model and its modification with noise and environment fluctuations to analyse the influence of random death on the accumulation of defective genes in the genetic pool of populations evolving under different environmental conditions.

Seasonality, Climate Cycles and Body Size Evolution

T. A. Troost, J. A. van Dam, B. W. Kooi, E. Tuenter (2009)

Mathematical Modelling of Natural Phenomena

The seasonality hypothesis states that climates characterized by large annual cycles select for large body sizes. In order to study the effects of seasonality on the evolution of body size, we use a model that is based on physiological rules and first principles. At the ecological time scale, our model results show that both larger productivity and seasonality may lead to larger body sizes. Our model is the first dynamic and process-based model to support the seasonality hypothesis and hence...

Selection Theorem for Systems with Inheritance

A. N. Gorban (2010)

Mathematical Modelling of Natural Phenomena

The problem of finite-dimensional asymptotics of infinite-dimensional dynamic systems is studied. A non-linear kinetic system with conservation of supports for distributions has generically finite-dimensional asymptotics. Such systems are apparent in many areas of biology, physics (the theory of parametric wave interaction), chemistry and economics. This conservation of support has a biological interpretation: inheritance. The finite-dimensional asymptotics demonstrates effects of “natural”...

The Phylogeny Graphs of Doubly Partial Orders

Boram Park, Yoshio Sano (2013)

Discussiones Mathematicae Graph Theory

The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced subgraph, respectively. Phylogeny graphs are variant of competition graphs. The phylogeny graph P(D) of a digraph D is the (simple undirected) graph defined by V (P(D)) := V (D) and E(P(D)) := {xy | N+D (x) ∩ N+D(y) ¹ ⊘ } ⋃ {xy | (x,y) ∈ A(D)},...

Theorem on signatures

Władysław Kulpa, Andrzej Szymański (2007)

Acta Universitatis Carolinae. Mathematica et Physica

Time to the convergence of evolution in the space of population states

Iwona Karcz-Dulęba (2004)

International Journal of Applied Mathematics and Computer Science

Phenotypic evolution of two-element populations with proportional selection and normally distributed mutation is considered. Trajectories of the expected location of the population in the space of population states are investigated. The expected location of the population generates a discrete dynamical system. The study of its fixed points, their stability and time to convergence is presented. Fixed points are located in the vicinity of optima and saddles. For large values of the standard deviation...

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