Related papers: Speciational view of macroevolution: are micro and…
A simple model of biological extinction with variable system size is presented that exhibits a power-law distribution of extinction event sizes. The model is a generalization of a model recently introduced by Newman (Proc. R. Soc. Lond.…
Phylogenetic trees are widely used to understand the evolutionary history of organisms. Tree shapes provide information about macroevolutionary processes. However, macroevolutionary models are unreliable for inferring the true processes…
A Markov evolution of a system of point particles in $\mathbb{R}^d$ is described at micro-and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the influence of each other…
We present long Monte Carlo simulations of a simple model of biological macroevolution in which births, deaths, and mutational changes in the genome take place at the level of individual organisms. The model displays punctuated equilibria…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…
We present a study by linear stability analysis and large-scale Monte Carlo simulations of a simple model of biological coevolution. Selection is provided through a reproduction probability that contains quenched, random interspecies…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
Evolution is the fundamental physical process that gives rise to biological phenomena. Yet it is widely treated as a subset of population genetics, and thus its scope is artificially limited. As a result, the key issues of how rapidly…
The extinction of species is a core process that affects the diversity of life on Earth. One way of investigating the causes and consequences of extinctions is to build conceptual ecological models, and to use the dynamical outcomes of such…
Recent methodological advances are enabling better examination of speciation and extinction processes and patterns. A major open question is the origin of large discrepancies in species number between groups of the same age. Existing…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
The Sole-Manrubia model of ``macro''-evolution describes the origination, evolution and extinction of species on geological time scales. We report some properties of this model which provide deep insight into this simple model which…
We present a generalization of the Yule model for macroevolution in which, for the appearance of genera, we consider point processes with the order statistics property, while for the growth of species we use nonlinear time-fractional pure…
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…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
This article is a presentation of specific recent results describing scaling limits of individual-based models. Thanks to them, we wish to relate the time-scales typical of demographic dynamics and natural selection to the parameters of the…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We present a stochastic model for the size of a taxon in paleobiology, in which we allow for the evolution of new taxon members, and both individual and catastrophic extinction events. The model uses ideas from the theory of birth and death…
We introduce microscopic and macroscopic stochastic traffic models including traffic accidents. The microscopic model is based on a Follow-the-Leader approach whereas the macroscopic model is described by a scalar conservation law with…