Related papers: Continuously stable strategies as evolutionary bra…
Most theories of evolutionary diversification are based on equilibrium assumptions: they are either based on optimality arguments involving static fitness landscapes, or they assume that populations first evolve to an equilibrium state…
Complex change is often described as "evolutionary" in economics, policy, and technology, yet most system dynamics models remain constrained to fixed state spaces and equilibrium-seeking behavior. This paper argues that evolutionary…
Laboratory experiments with bacterial colonies, under well-controlled conditions often lead to evolutionary diversification, where at least two ecotypes emerge from an initially monomorphic population. Empirical evidence suggests that such…
An evolutionarily stable strategy (ESS) is an equilibrium strategy that is immune to invasions by rare alternative (``mutant'') strategies. Unlike Nash equilibria, ESS do not always exist in finite games. In this paper we address the…
Adaptive dynamics is a widely used framework for modeling long-term evolution of continuous phenotypes. It is based on invasion fitness functions, which determine selection gradients and the canonical equation of adaptive dynamics. Even…
In an adaptive population which models financial markets and distributed control, we consider how the dynamics depends on the diversity of the agents' initial preferences of strategies. When the diversity decreases, more agents tend to…
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio…
We demonstrate with a thought experiment that fitness-based population dynamical approaches to evolution are not able to make quantitative, falsifiable predictions about the long-term behavior of evolutionary systems. A key characteristic…
Evolution in changing environments is an important, but little studied aspect of the theory of evolution. The idea of adaptive walks in fitness landscapes has triggered a vast amount of research and has led to many important insights about…
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 consider a trait-structured population subject to mutation, birth and competition of logistic type, where the number of coexisting types may fluctuate. Applying a limit of rare mutations to this population while keeping the population…
The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…
Evolution Strategies (ES) are stochastic derivative-free optimization algorithms whose most prominent representative, the CMA-ES algorithm, is widely used to solve difficult numerical optimization problems. We provide the first rigorous…
We analyze evolutionary dynamics in a confluent, branching cellular population, such as in a growing duct, vasculature, or in a branching microbial colony. We focus on the coarse-grained features of the evolution and build a statistical…
The mutation process in evolution strategies has been interlinked with the normal distribution since its inception. Many lines of reasoning have been given for this strong dependency, ranging from maximum entropy arguments to the need for…
Random walks on multidimensional nonlinear landscapes are of interest in many areas of science and engineering. In particular, properties of adaptive trajectories on fitness landscapes determine population fates and thus play a central role…
Species or population that proliferate faster than others become dominant in numbers. Catalysis allows catalytic sets within a molecular reaction network to dominate the non catalytic parts of the network by processing most of the available…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
We report on new stability conditions for evolutionary dynamics in the context of population games. We adhere to the prevailing framework consisting of many agents, grouped into populations, that interact noncooperatively by selecting…
Organisms modulate their fitness in heterogeneous environments by dispersing. Prior work shows that there is selection against "unconditional" dispersal in spatially heterogeneous environments. "Unconditional" means individuals disperse at…