Related papers: Natural selection as coarsening
In order to formulate the Fundamental Theorem of Natural Selection, Fisher defined the average excess and average effect of a gene substitution. Finding these notions to be somewhat opaque, some authors have recommended reformulating…
Weak purifying selection, acting on many linked mutations, may play a major role in shaping patterns of molecular evolution in natural populations. Yet efforts to infer these effects from DNA sequence data are limited by our incomplete…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
We consider a particular instance of the lift of controlled systems recently proposed in the theory of irreversible thermodynamics and show that it leads to a variational principle for an optimal control in the sense of Pontryagin. Then we…
In this paper, I model and study the process of natural selection between all possible mixed strategies in classical two-player two-strategy games. I derive and solve an equation that is a natural generalization of the Taylor-Jonker…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
It has been hypothesized that one of the main reasons evolution has been able to produce such impressive adaptations is because it has improved its own ability to evolve -- "the evolution of evolvability". Rupert Riedl, for example, an…
George Price introduced his famous equation to study selective and environmental effects in discrete populations. We extend Price's framework to the measurable and quantum cases, decomposing all evolutionary processes into selective and…
Evolution by Natural Selection is a process by which progeny inherit some properties from their progenitors with small variation. These properties are subject to Natural Selection and are called adaptive traits and carriers of the latter…
The concept of (auto)catalytic systems has become a cornerstone in understanding evolutionary processes in various fields. The common ground is the observation that for the production of new species/goods/ideas/elements etc. the…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
Sexual reproduction presents significant challenges to formal treatment of evolutionary processes. A starting point for systematic treatments of ecological and evolutionary phenomena has been provided by the gene centered view of evolution…
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…
The purpose of this Note is twofold: First, we introduce the general formalism of evolutionary genetics dynamics involving fitnesses, under both the deterministic and stochastic setups, and chiefly in discrete-time. In the process, we…
McNamara and Dall (2011) identified novel relationships between the abundance of a species in different environments, the temporal properties of environmental change, and selection for or against dispersal. Here, the mathematics underlying…
We consider Evolution Strategies operating only with isotropic Gaussian mutations on positive quadratic objective functions, and investigate the covariance matrix when constructed out of selected individuals by truncation. We prove that the…
Statistical analysis of alignments of large numbers of protein sequences has revealed "sectors" of collectively coevolving amino acids in several protein families. Here, we show that selection acting on any functional property of a protein,…
Selection in a time-periodic environment is modeled via the continuous-time two-player replicator dynamics, which for symmetric pay-offs reduces to the Fisher equation of mathematical genetics. For a sufficiently rapid and cyclic…
Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of…