Related papers: A Problem in Paleobiology
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,…
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 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…
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…
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…
The distribution of species body size within taxonomic groups exhibits a heavy right-tail extending over many orders of magnitude, where most species are significantly larger than the smallest species. We provide a simple model of…
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,…
Theoretical ecologists have long sought to understand how the persistence of populations depends on biotic and abiotic factors. Classical work showed that demographic stochasticity causes the mean time to extinction to increase…
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…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
The theory of life history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens in both epidemic and endemic situations. This framework, however, relies on the assumption that pathogen populations are…
Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short-term transition from imminent doom to evolutionary rescue. But…
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
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…
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 number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
We describe a simple model of evolution which incorporates the branching and extinction of species lines, and also includes abiotic influences. A first principles approach is taken in which the probability for speciation and extinction are…
A phylogenetic birth-and-death model is a probabilistic graphical model for a so-called phylogenetic profile, i.e., the size distribution for a homolog gene family at the terminal nodes of a phylogeny. Profile datasets are used in…
We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in…