ﻻ يوجد ملخص باللغة العربية
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, either caused by external environment or intrinsic random competitions in finite populations, and the evolutionary dynamics is stochastic in nature. Here we show that, after appropriate coarse-graining, random fluctuations generate dissipation towards extinction because the evolution trajectories in the phase space of all competing species possess positive curvature. As a demonstrating example, we compare the fluctuation-induced dissipative dynamics in Lotka-Volterra model with numerical simulations and find impressive agreement. Our finding is closely related to the fluctuation-dissipation theorem in statistical mechanics but the marked difference is the non-equilibrium essence of the generic evolutionary dynamics. As the evolving ecosystems are far from equilibrium, the relation between fluctuations and dissipations is often complicated and dependent on microscopic details. It is thus remarkable that the generic positivity of the trajectory curvature warrants dissipation arisen from the seemingly harmless fluctuations. The unexpected dissipative dynamics is beyond the reach of conventional replicator equations and plays a crucial role in investigating the biodiversity in ecosystems.
Evolutionary game theory has traditionally assumed that all individuals in a population interact with each other between reproduction events. We show that eliminating this restriction by explicitly considering the time scales of interaction and selec
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits fitness wave solutions: Gaussian-shape fit
Temporal environmental variations are ubiquitous in nature, yet most of the theoretical works in population genetics and evolution assume fixed environment. Here we analyze the effect of variations in carrying capacity on the fate of a mutant type. W
The incubation period of a disease is the time between an initiating pathologic event and the onset of symptoms. For typhoid fever, polio, measles, leukemia and many other diseases, the incubation period is highly variable. Some affected people take
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts of evoluti