相关论文: Darwinian evolution in Malthusian population growt…
A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability $\mu$ of…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
We consider two finite population Markov chain models, the two-island Wright-Fisher model with mutation, and the seed-bank model with mutation. Despite the relatively simple descriptions of the two processes, the the exact form of their…
The environment in which a population evolves can have a crucial impact on selection. We study evolutionary dynamics in finite populations of fixed size in a changing environment. The population dynamics are driven by birth and death…
Darwin's theory of evolution is considered to be one of the greatest scientific gems in modern science. It not only gives us a description of how living things evolve, but also shows how a population evolves through time and also, why only…
We study the long time behavior of an asymmetric size-structured measure-valued growth-fragmentation branching process that models the dynamics of a population of cells taking into account physiological and morphological asymmetry at…
We study the discrete-time evolution of a transformation on a set of probability measures that is up-dated combining independently the marginals on the atoms of partitions. This model was recently introduced in Baake, Baake and Salamat…
We propose a stochastic model for evolution through mutation and natural selection of a population that evolves on a $\bbT_d^+$ tree. We think of this model as a way of describing the evolution fitness landscape of a population. We obtain…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
We consider a simple discrete-time Markov chain with values in $[0,\infty)^{Z^d}$. The Markov chain describes various interesting examples such as oriented percolation, directed polymers in random environment, time discretizations of binary…
The Darwinian paradigm of biological evolution is based on the separability of the variation and selection processes. As a result, the population thinking had always been an integral part of the Darwinian approach. I propose an alternative…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
The report considers the dynamics of the global population as the unique case of the Socio-Economic Soft Matter system. This category was introduced for complex systems dominated by mesoscale assemblies, emerging due to the inherent…
A Markovian model of group-structured (two-level) population dynamics features births, deaths, and migrations of individuals, and fission and extinction of groups. These models are useful for studying group selection and other evolutionary…
Evolution of the reduced density matrix for a subsystem is studied to determine deviations from its Markov character for a system consisting of a closed chain of $N$ oscillators with one of them serving as a subsystem. The dependence on $N$…
A new approach to understanding evolution [Val09], namely viewing it through the lens of computation, has already started yielding new insights, e.g., natural selection under sexual reproduction can be interpreted as the Multiplicative…
Radical shifts in the genetic composition of large cell populations are rare events with quite low probabilities, which direct numerical simulations generally fail to evaluate accurately. In this paper, we develop a theoretical large…
Population games can be regarded as a tool to study the strategic interaction of a population of players. Although several attention has been given to such field, most of the available works have focused only on the unconstrained case. That…