A physical model for competition between biological speciation and extinction

Interpretation of empirical results based on a taxa's lifetime distribution shows apparently conflicting results. Species' lifetime is reported to be exponentially distributed, whereas higher order taxa, such as families or genera, follow a broader distribution, compatible with power law decay. We show that both these evidences are consistent with a simple evolutionary model that does not require specific assumptions on species interaction. The model provides a zero-order des...

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 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 processes. Some general properties of the model are developed, and a fuller discussion is given for specific distributions of the time between catastrophic extinction events. Long tails in the taxon size distribution arise naturally from t...

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...

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 ...

Cretaceous-Cenozoic history of angiosperms led to the a certain character of the distribution of taxa of different levels (the number of species and genera in families, species/genera ratio in families, the number of species in the genera). In most cases, these distributions are satisfactorily described by a power law (Pareto distribution). In logarithmic coordinates power function is a straight line. Empirical curves repeat this line is good enough, but on the right side of ...

A mathematical model of interacting species filling ecological niches left by the extinction of others is introduced. Species organize themselves into genera of all sizes. The size of a genus on average grows linearly with its age, confirming a general relation between Age and Area proposed by Willis. The ecology exhibits punctuated equilibrium. Analytic and numerical results show that the probability distribution of genera sizes, genera lifetimes, and extinction event sizes ...

We introduce a simple computational model that, with a microscopic dynamics driven by natural selection and mutation alone, allows the description of true speciation events. A statistical analysis of the so generated evolutionary tree captures realistic features showing power laws for frequency distributions in time and size. Albeit these successful predictions, the difficulty in obtaining punctuated dynamics with mass extinctions suggests the necessity of decoupling micro an...

We propose a novel network growth model coupled with the competition interaction to simulate macroevolution. Our work shows that the competition plays an important role in macroevolution and it is more rational to describe the interaction between species by network structures. Our model presents a complete picture of the development of phyla and the splitting process. It is found that periodic mass extinction occurred in our networks without any extraterrestrial factors and t...

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...