Related papers: Evolution and mass extinctions as lognormal stocha…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
Statistical systems are conceived from the standpoint of statistical mechanics, as made of a (generally large) number of identical units and exhibiting a (generally large) number of different configurations (microstates), among which only…
1 Sharp prediction of extinction times is needed in biodiversity monitoring and conservation management. 2 The Galton-Watson process is a classical stochastic model for describing population dynamics. Its evolution is like the matrix…
We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g. positions), and the length of this set changes stochastically in time due to…
We survey results on the description of stochastically evolving genealogies of populations and marked genealogies of multitype populations or spatial populations via tree-valued Markov processes on (marked) ultrametric measure spaces. In…
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,…
In the long run, the eventual extinction of any biological population is an inevitable outcome. While extensive research has focused on the average time it takes for a population to go extinct under various circumstances, there has been…
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 present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
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,…
In this thesis, we extend the recently introduced theory of stochastic modified equations (SMEs) for stochastic gradient optimization algorithms. In Ch. 3 we study time-inhomogeneous SDEs driven by Brownian motion. For certain SDEs we prove…
MOCAT-SSEM is a Source-Sink model that predicts the Low Earth Orbit (LEO) space population divided into families using a predefined set of interaction parameters. Thanks to data from the Monte Carlo version of the model (MOCAT-MC), which…
The Semantic Theory of Evolution (STE) takes the existence of a number of arbitrary communication codes as a fundamental feature of life, from the genetic code to human cultural communication codes. Their arbitrariness enables, at each…
Stochastic fluctuations are central to the understanding of extinction dynamics. In the context of population models they allow for the description of the transition from the vicinity of a non-trivial fixed point of the deterministic…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
We outline a phenomenological theory of evolution and origin of life by combining the formalism of classical thermodynamics with a statistical description of learning. The maximum entropy principle constrained by the requirement for…
We investigate the thermodynamics as well as the population dynamics of ecosystems based on a stochastic approach in which the number of individuals of the several species of the ecosystem are treated as stochastic variables. The several…
The genetic blueprint for the essential functions of life is encoded in DNA, which is translated into proteins -- the engines driving most of our metabolic processes. Recent advancements in genome sequencing have unveiled a vast diversity…
Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements -…
Eco-evolutionary dynamics, or eco-evolution for short, are thought to involve rapid demography (ecology) and equally rapid phenotypic changes (evolution) leading to novel, emergent system behaviours. This focus on contemporary dynamics is…