Related papers: Punctuated evolution for the quasispecies model
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperses via diffusion and convection is considered.…
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…
When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to…
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…
We generalize the evolution model introduced by Guiol, Machado and Schinazi (2010). In our model at odd times a random number X of species is created. Each species is endowed with a random fitness with arbitrary distribution on $[0, 1]$. At…
This article gives a brief introduction to the mathematical modeling of large-scale biological evolution and extinction. We give three examples of simple models in this field: the coevolutionary avalanche model of Bak and Sneppen, the…
We consider a continuum version of a previously introduced and numerically studied model of macroevolution (PRL 75, 2055, (1995)) in which agents evolve by an optimization process in a rugged fitness landscape and die due to their…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
This Letter studies the quasispecies dynamics of a population capable of genetic repair evolving on a time-dependent fitness landscape. We develop a model that considers an asexual population of single-stranded, conservatively replicating…
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…
We study quasi-species and closely related evolutionary dynamics like the replicator-mutator equation in high dimensions. In particular, we show that under certain conditions the fitness of almost all quasi-species becomes independent of…
We dwell upon the physicist's conception of `life' since Schroedinger and Wigner through to the modern-day language of living systems in the light of quantum information. We discuss some basic features of a living system such as ordinary…
Non-equilibrium conditions give rise to classes of universally evolving configurations of quantum-many body systems at non-thermal fixed points. While the fixed point and thus full scaling in space and time is generically reached at very…
We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
We study a continuous-time nearest-neighbor branching random walk on the $d$-dimensional $b$-ary hypercube $\{0,1,\dots,b-1\}^d$ as a model for viral quasispecies evolution under mutation and replication. Motivated by mutagenic antiviral…
A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…
We introduce a toy model for interacting populations connected by mutations and limited by a shared resource. We study the presence of Eigen's error threshold and mutational meltdown. The phase diagram of the system shows that the…
We propose a minimal model to simulate long waiting times followed by evolutionary bursts on rugged landscapes. It combines point and inversions-like mutations as sources of genetic variation. The inversions are intended to simulate one of…
The adaptation rate in theoretical models of biological evolution increases with the mutation rate but only to a point when mutations into lethal states cause extinction. One would expect that removing such states should be beneficial for…