Related papers: Growing Trees and Amoebas' Replications
Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented. Physical approach, which takes advantage of their extensively quantified mortality, establishes that its dominant fraction yields…
Mortality is an instrument of natural selection. Evolutionary motivated theories imply its irreversibility and life history dependence. This is inconsistent with mortality data for protected populations. Accurate analysis yields mortality…
Consider a rooted $N$-ary tree. To every vertex of this tree, we attach an i.i.d. continuous random variable. A vertex is called accessible if along its ancestral line, the attached random variables are increasing. We keep accessible…
Well protected human and laboratory animal populations with abundant resources are evolutionary unprecedented, and their survival far beyond reproductive age may be a byproduct rather than tool of evolution. Physical approach, which takes…
By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…
An amoeba is the image of a subvariety of an algebraic torus under the logarithmic moment map. We consider some qualitative aspects of amoebas, establishing some results and posing problems for further study. These problems include…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…
We introduce a new model of random tree that grows like a random recursive tree, except at some exceptional "doubling events" when the tree is replaced by two copies of itself attached to a new root. We prove asymptotic results for the size…
We consider a regular $n$-ary tree of height $h$, for which every vertex except the root is labelled with an independent and identically distributed continuous random variable. Taking motivation from a question in evolutionary biology, we…
We introduce and study the dynamics of an \emph{immortal} critical branching process. In the classic, critical branching process, particles give birth to a single offspring or die at the same rates. Even though the average population is…
A caterpillar tree is a connected, acyclic, graph in which all vertices are either a member of a central path, or joined to that central path by a single edge. In other words, caterpillar trees are the class of trees which become path…
We provide a fundamental result for bucket increasing trees, which gives a complete characterization of all families of bucket increasing trees that can be generated by a tree evolution process. We also provide several equivalent…
We construct a model in which the tree property holds in $\aleph_{\omega + 1}$ and it is destructible under $\text{Col}(\omega, \omega_1)$. On the other hand we discuss some cases in which the tree property is indestructible under small or…
In this paper, we investigate the structures of an extremal tree which has the minimal number of subtrees in the set of all trees with the given degree sequence of a tree. In particular, the extremal trees must be caterpillar and but in…
We model evolution of plants in a world, made up of different locations, with multiple environments (mutually exclusive and collectively exhaustive subsets of locations). Each environment (landmass) has temperature, rainfall, and other…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
In this work we check the occurrence of the Azbel assumption of mortality within the framework of a bit string model for biological ageing. We reproduced the observed feature of linear correspondence between the fitting parameters of the…
Exact law of mortality dynamics in changing populations and environment is derived. The law is universal for all species, from single cell yeast to humans. It includes no characteristics of animal- environment interactions (metabolism etc)…
Let $p(m)$ (respectively, $q(m)$) be the maximum number $k$ such that any tree with $m$ edges can be transformed by contracting edges (respectively, by removing vertices) into a caterpillar with $k$ edges. We derive closed-form expressions…