Related papers: Laws in Darwinian Evolutionary Theory
In general, cellular phenotypes, as measured by concentrations of cellular components, involve large degrees of freedom. However, recent measurement has demonstrated that phenotypic changes resulting from adaptation and evolution in…
When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to…
The evolutionary origin of universal statistics in biochemical reaction network is studied, to explain the power-law distribution of reaction links and the power-law distributions of chemical abundances. Using cell models with catalytic…
Biological evolution is a complex blend of ever changing structural stability, variability and emergence of new phenotypes, niches, ecosystems. We wish to argue that the evolution of life marks the end of a physics world view of law…
Ecological systems are complex dynamical systems. Modelling efforts on ecosystems' dynamical stability have revealed that population dynamics, being highly nonlinear, can be governed by complex fluctuations. Indeed, experimental and field…
We prove that stochastic replicator dynamics can be interpreted as intrinsic Brownian motion on the simplex equipped the Aitchison geometry. As an immediate consequence we derive three approximation results in the spirit of Wong-Zakai…
Evolution in finite populations is often modelled using the classical Moran process. Over the last ten years this methodology has been extended to structured populations using evolutionary graph theory. An important question in any such…
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…
In the {\em Many Worlds Interpretation} of quantum mechanics, the range of possible worlds (or histories) provides variation, and the Anthropic Principle is a selective principle analogous to natural selection. When looked on in this way,…
Complex systems, such as life and languages, are governed by principles of evolution. The analogy and comparison between biology and linguistics\cite{alphafold2, RoseTTAFold, lang_virus, cell language, faculty1, language of gene, Protein…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
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…
Evolutionary games on graphs play an important role in the study of evolution of cooperation in applied biology. Using rigorous mathematical concepts from a dynamical systems and graph theoretical point of view, we formalize the notions of…
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model of ecosystems. The present model shows mass extinction by its own extinction dynamics when the system…
Yuri Manin's approach to Zipf's law (Kolmogorov complexity as energy) is applied to investigation of biological evolution. Model of constructive statistical mechanics where complexity is a contribution to energy is proposed to model…
Uncertainty, characterised by randomness and stochasticity, is ubiquitous in applications of evolutionary game theory across various fields, including biology, economics and social sciences. The uncertainty may arise from various sources…
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Examples include Harry Dym equation,…
We study a class of stochastic evolution equations of jump type with random coefficients and its optimal control problem. There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous…
The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during…