Related papers: Mathematical Structure of Evolutionary Theory
In the present article the recent works to formulate laws in Darwinian evolutionary dynamics are discussed. Although there is a strong consensus that general laws in biology may exist, opinions opposing such suggestion are abundant. Based…
Motivated by a recent article on open problems in artificial life, here I postulate three laws which form a mathematical framework to describe artificial life evolutionary dynamics. They are based on a continuous approximation of population…
Analogies between evolutionary dynamics and statistical mechanics, such as Fisher's second-law-like "fundamental theorem of natural selection" and Wright's "fitness landscapes", have had a deep and fruitful influence on the development of…
This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the…
Two giants of evolutionary theory, Sewall Wright and R. A. Fisher, fought bitterly for over thirty years. The Wright-Fisher controversy forms a cornerstone of the history and philosophy of biology. I argue that the standard interpretations…
We present here an exploration on on the physical implications of the Darwinian dynamics. We first show that how the nonequilibrium statistical mechanics emerges naturally. We then show that the first three laws of the thermodynamics, the…
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:…
The theory of evolution by natural selection cannot be used to evaluate the truth value of the following proposition: Through evolution, there exists at least one species that can adapt to any one given environment. To address this issue,…
These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies…
Darwinian dynamics is manifestly stochastic and nonconservative, but has a profound connection to conservative dynamics in physics. In the present paper the main ideas and logical steps leading to thermodynamics from Darwinian dynamics are…
This is the fourth paper, the last one, on solution to the problem of absence of detailed balance in nonequilibrium processes. It is an approach based on another known universal dynamics: The evolutionary dynamics first conceived by Darwin…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and…
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…
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…
As mathematical model for the evolutionary equations of species the masterequation is choiced. Two formulations will be demonstrated to include the changes of parameters into the masterequation - that is, on the one hand, the formation of a…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
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…
Mathematical theory of selection is developed within the frameworks of general models of inhomogeneous populations with continuous time. Methods that allow us to study the distribution dynamics under natural selection and to construct…