Related papers: A model of mass extinction
The abundance of a species' population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a…
In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blow-up in the model as…
Scaling laws in ecology, intended both as functional relationships among ecologically-relevant quantities and the probability distributions that characterize their occurrence, have long attracted the interest of empiricists and…
We propose dynamical collapse models in which the stochastic collapse terms affect only photons and/or gravitons. In principle, isolated systems comprising only massive particles could evolve unitarily indefinitely in such models. In…
Mathematical modelling of the evolution of the size-spectrum dynamics in aquatic ecosystems was discovered to be a powerful tool to have a deeper insight into impacts of human- and environmental driven changes on the marine ecosystem. In…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility…
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…
In the companion paper of this set (Capitan and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitan et al. (2009). This model is based on the construction of an assembly graph…
Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…
The dynamics of ecosystem collapse are fundamental to determining how and why biological communities change through time, as well as the potential effects of extinctions on ecosystems. Here we integrate depictions of mammals from Egyptian…
In many complex systems a continuous input of energy over time can be suddenly relaxed in the form of avalanches. Conventional avalanche models disregard the possibility of internal dynamical effects in the inter-avalanche periods, and thus…
In this paper we consider a microscopic model of a simple ecosystem. The basic ingredients of this model are individuals, and both the phenotypic and genotypic levels are taken in account. The model is based on a long range cellular…
Many species see their range shifted poleward in response to global warming and need to keep pace in order to survive. To understand the effect of climate change on species ranges and its consequences on population dynamics, we consider a…
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 introduce a spatial stochastic process on the lattice Z^d to model mass extinctions. Each site of the lattice may host a flock of up to N individuals. Each individual may give birth to a new individual at the same site at rate \phi until…
A few of the major mass extinctions of paleontology have recently been found to consist of two distinct extinction peaks at higher resolution. A viable explanation for this remains elusive. In this paper it is shown that the recently…
A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
Biodiversity and extinction are central issues in evolution. Dynamical balance among different species in ecosystems is often described by deterministic replicator equations with moderate success. However, fluctuations are inevitable,…