Related papers: A model of macroevolution with a natural system si…
We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its…
Mass extinction is a phenomenon in the history of life on Earth when a considerable number of species go extinct over a relatively short period of time. The magnitude of extinction varies between the events, the most well known are the…
A model for large-scale evolution recently introduced by Amaral and Meyer is studied analytically and numerically. Species are located at different trophic levels and become extinct if their prey becomes extinct. It is proved that this…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
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 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…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
The modelling of evolutionary game dynamics in finite populations requires microscopic processes that determine how strategies spread. The exact details of these processes are often chosen without much further consideration. Different types…
Simulations of the coevolution of many interacting species are performed using the Webworld model. The model has a realistic set of predator-prey equations that describe the population dynamics of the species for any structure of the food…
Phylogenetic diversity is a measure for describing how much of an evolutionary tree is spanned by a subset of species. If one applies this to the (unknown) subset of current species that will still be present at some future time, then this…
We present new theoretical and empirical results on the probability distributions of species persistence times in natural ecosystems. Persistence times, defined as the timespans occurring between species' colonization and local extinction…
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we…
Motivated as a null model for comparison with data, we study the following model for a phylogenetic tree on $n$ extant species. The origin of the clade is a random time in the past, whose (improper) distribution is uniform on $(0,\infty)$.…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
We introduce a model for the evolution of species triggered by generation of novel features and exhaustive combination with other available traits. Under the assumption that innovations are rare, we obtain a bursty branching process of…
We discuss a simple model of co-evolution. In order to emphasise the effect of interaction between individuals the entire population is subjected to the same physical environment. Species are emergent structures and extinction, origination…
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…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
If evolution can be connected to the principle of least action, and if it is depicted in evolution space versus time then it corresponds to the direction of ultimate causation. As an organism evolves and follows a path of proximate…
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…