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In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as…

Populations and Evolution · Quantitative Biology 2022-02-18 Alex McAvoy , Benjamin Allen

How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under…

Probability · Mathematics 2019-08-15 Sylvain Billiard , Regis Ferriere , Sylvie Méléard , Viet Chi Tran

The spatial dispersal of individuals is known to play an important role in the dynamics of populations, and is central to metapopulation theory. At the same time, local adaptation to environmental conditions creates a geographic mosaic of…

Populations and Evolution · Quantitative Biology 2017-09-25 Justin D. Yeakel , Jean P. Gibert , Peter A. H. Westley , Jonathan W. Moore

Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…

Populations and Evolution · Quantitative Biology 2007-05-23 Georgy P. Karev , Artem S. Novozhilov , Faina S. Berezovskaya

The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…

Populations and Evolution · Quantitative Biology 2019-02-18 Tobias Rogge , David Jones , Barbara Drossel , Korinna T. Allhoff

Horizontal gene transfer consists in exchanging genetic materials between microorganisms during their lives. This is a major mechanism of bacterial evolution and is believed to be of main importance in antibiotics resistance. We consider a…

Probability · Mathematics 2019-12-18 Nicolas Champagnat , Sylvie Méléard , Viet Chi Tran

Species interactions (ranging from direct predator prey relationships to indirect effects mediated by the environment) are central to ecosystem balance and biodiversity. While empirical methods for measuring these interactions exist, their…

Populations and Evolution · Quantitative Biology 2025-08-27 Javier Aguilar , Samir Suweis , Amos Maritan , Sandro Azaele

The role of the selection pressure and mutation amplitude on the behavior of a single-species population evolving on a two-dimensional lattice, in a periodically changing environment, is studied both analytically and numerically. The…

Populations and Evolution · Quantitative Biology 2009-11-13 Ioana Bena , Michel Droz , Janusz Szwabinski , Andrzej Pekalski

The environment undergoes perpetual changes that are influenced by a combination of endogenous and exogenous factors. Consequently, it exerts a substantial influence on an individual's physical and psychological state, directly or…

Physics and Society · Physics 2025-12-11 Yuji Zhang , Minyu Feng , Jürgen Kurths , Attila Szolnoki

We investigate a simple quantitative genetics model subjet to a gradual environmental change from the viewpoint of the phylogenies of the living individuals. We aim to understand better how the past traits of their ancestors are shaped by…

Probability · Mathematics 2021-04-22 Vincent Calvez , Benoît Henry , Sylvie Méléard , Viet Chi Tran

We explore the complex dynamical behavior of two simple predator-prey models of biological coevolution that on the ecological level account for interspecific and intraspecific competition, as well as adaptive foraging behavior. The…

Populations and Evolution · Quantitative Biology 2009-11-28 Per Arne Rikvold

Evolutionary game dynamics describes not only frequency dependent genetical evolution, but also cultural evolution in humans. In this context, successful strategies spread by imitation. It has been shown that the details of strategy update…

Populations and Evolution · Quantitative Biology 2013-10-07 Arne Traulsen , Dirk Semmann , Ralf D. Sommerfeld , Hans-Juergen Krambeck , Manfred Milinski

The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the…

Analysis of PDEs · Mathematics 2021-05-07 Léonard Dekens , Florian Lavigne

We present an individual-based model of phenotypic trait evolution in two-sex populations, which includes semi-random mating of individuals of the opposite sex, natural death and intra-specific competition. By passing the number of…

Probability · Mathematics 2015-02-24 Paweł Zwoleński

Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits…

Analysis of PDEs · Mathematics 2022-06-28 Jimmy Garnier , O Cotto , T Bourgeron , E Bouin , T Lepoutre , O Ronce , V Calvez

There are various examples of phenotypic plasticity in ecosystems that serve as the basis for a wide range of inducible defences against predation. These strategies include camouflage, burrowing, mimicry, evasive actions, and even…

Populations and Evolution · Quantitative Biology 2025-01-06 Sangeeta Saha , Swadesh Pal , Roderick Melnik

Global environmental change is affecting species distribution and their interactions with other species. In particular, the main drivers of environmental change strongly affect the strength of interspecific interactions with considerable…

Populations and Evolution · Quantitative Biology 2013-08-19 Serguei Saavedra , Rudolf P. Rohr , Vasilis Dakos , Jordi Bascompte

The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…

Analysis of PDEs · Mathematics 2021-03-08 Elisa Affili

Long-term evolutionary processes can strongly influence common-pool resource conservation by generating new traits or behaviours that modify the feedback between population strategies and the resource state. Here we develop an…

Populations and Evolution · Quantitative Biology 2026-01-27 Prosanta Mandal , Suman Chakraborty , Vaibhav Madhok , Sagar Chakraborty

Predator-prey relationships are one of the most studied interactions in population ecology. However, little attention has been paid to the possibility of role exchange between species once determined as predators and preys, despite firm…

Populations and Evolution · Quantitative Biology 2014-10-31 Faustino Sánchez-Garduño , Pedro Miramontes , Tatiana T. Marquez-Lago