Simple models of evolution and extinction

We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate analytic solution and also by numerical simulation, and use it to make predictions about the distribution of extinctions and species lifetimes that we would expect to see in real ecosystems. It should be possible to test these predictions ...

We present a new model for extinction in which species evolve in bursts or `avalanches', during which they become on average more susceptible to environmental stresses such as harsh climates and so are more easily rendered extinct. Results of simulations and analytic calculations using our model show a power-law distribution of extinction sizes which is in reasonable agreement with fossil data. e also see a number of features qualitatively similar to those seen in the fossil ...

A number of authors have in recent years proposed that the processes of macroevolution may give rise to self-organized critical phenomena which could have a significant effect on the dynamics of ecosystems. In particular it has been suggested that mass extinction may arise through a purely biotic mechanism as the result of so-called coevolutionary avalanches. In this paper we first explore the empirical evidence which has been put forward in favor of this conclusion. The data...

It is usually believed that Darwin's theory leads to a smooth gradual evolution, so that mass extinctions must be caused by external shocks. However, it has recently been argued that mass extinctions arise from the intrinsic dynamics of Darwinian evolution. Species become extinct when swept by intermittent avalanches propagating through the global ecology. These ideas are made concrete through studies of simple mathematical models of coevolving species. The models exhibit sel...

A class of models for large-scale evolution and mass extinctions is presented. These models incorporate environmental changes on all scales, from influences on a single species to global effects. This is a step towards a unified picture of mass extinctions, which enables one to study coevolutionary effects and external abiotic influences with the same means. The generic features of such models are studied in a simple version, in which all environmental changes are generated a...

This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the majority of publications appeared in biology journals. The review has three parts, which can be read independently. The first part deals with evolution in fitness landscapes and includes Fisher's theorem, adaptive walks, quasispecies models, effec...

Macroevolution is considered as a problem of stochastic dynamics in a system with many competing agents. Evolutionary events (speciations and extinctions) are triggered by fitness records found by random exploration of the agents' fitness landscapes. As a consequence, the average fitness in the system increases logarithmically with time, while the rate of extinction steadily decreases. This dynamics is studied by numerical simulations and, in a simpler mean field version, ana...

We introduce a new model for large scale evolution and extinction in which species are organized into food chains. The system evolves by two processes: origination/speciation and extinction. In the model, extinction of a given species can be due to an externally induced change in the environment or due to the extinction of all preys of that species (co-extinction). The model is able to reproduce the empirical observations, such as the statistical fractality of the fossil reco...

In the spirit of the many recent simple models of evolution inspired by statistical physics, we put forward a simple model of the evolution of such models. Like its objects of study, it is (one supposes) in principle testable and capable of making predictions, and gives qualitative insights into a hitherto mysterious process.

We review recent work aimed at modeling species extinction over geological time. We discuss a number of models which, rather than dealing with the direct causes of particular extinction events, attempt to predict overall statistical trends, such as the relative frequencies of large and small extinctions, or the distribution of the lifetimes of species, genera or higher taxa. We also describe the available fossil and other data, and compare the trends visible in these data wit...