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Microbial communities feature an immense diversity of species and this diversity is linked with outcomes ranging from ecosystem stability to medical prognoses. Yet the mechanisms underlying microbial diversity are under debate. While simple…

Biological Physics · Physics 2020-10-20 Amir Erez , Jaime G. Lopez , Benjamin Weiner , Yigal Meir , Ned S. Wingreen

We study the influence of stochastic effects due to finite population size in the evolutionary dynamics of populations interacting in the multi-person Prisoner's Dilemma game. This paper is an extension of the investigation presented in a…

Populations and Evolution · Quantitative Biology 2007-05-23 Anders Eriksson , Kristian Lindgren

We study a system of PDEs modeling the population dynamics of two competitive species whose spatial movements are governed by both diffusion and mutually repulsive chemotaxis effects. We prove that solutions to this system are globally…

Analysis of PDEs · Mathematics 2022-02-16 Guanlin Li , Yao Yao

This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…

Statistical Mechanics · Physics 2019-11-22 Uwe C. Täuber

Ecosystems frequently display the coexistence of diverse species under resource competition, typically resulting in skewed distributions of rarity and abundance. A potential driver of such coexistence is environmental fluctuations that…

Populations and Evolution · Quantitative Biology 2025-08-07 Davide Zanchetta , Deepak Gupta , Sofia Moschin , Samir Suweis , Amos Maritan , Sandro Azaele

In a view for a simple model where natural selection at the individual level is confronted to selection effects at the group level, we consider some individual-based models of some large population subdivided into a large number of groups.…

Probability · Mathematics 2023-07-13 Aurélien Velleret

We revisit the well-known chemostat model, considering that bacteria can be attached together in aggregates or flocs. We distinguish explicitly free and attached compartments in the model and give sufficient conditions for coexistence of…

Dynamical Systems · Mathematics 2018-03-08 Alain Rapaport

Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial…

Probability · Mathematics 2015-12-16 Steven N. Evans , Peter L. Ralph , Sebastian J. Schreiber , Arnab Sen

In nature microbial populations are subject to fluctuating nutrient levels. Nutrient fluctuations are important for evolutionary and ecological dynamics in microbial communities since they impact growth rates, population sizes and biofilm…

Populations and Evolution · Quantitative Biology 2018-09-12 Jason Merritt , Seppe Kuehn

Positive density-dependence occurs when individuals experience increased survivorship, growth, or reproduction with increased population densities. Mechanisms leading to these positive relationships include mate limitation, saturating…

Populations and Evolution · Quantitative Biology 2019-02-12 Sebastian J. Schreiber

Cells maintain a stable size as they grow and divide. Inspired by the available experimental data, most proposed models for size homeostasis assume size control mechanisms that act on a timescale of one generation. Such mechanisms lead to…

Biological Physics · Physics 2023-05-25 Motasem ElGamel , Harsh Vashistha , Hanna Salman , Andrew Mugler

We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…

Dynamical Systems · Mathematics 2025-11-27 Christian Parkinson , Weinan Wang

A branching random walk in presence of an absorbing wall moving at a constant velocity $v$ undergoes a phase transition as the velocity $v$ of the wall varies. Below the critical velocity $v_c$, the population has a non-zero survival…

Statistical Mechanics · Physics 2008-02-12 Damien Simon , Bernard Derrida

The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…

Populations and Evolution · Quantitative Biology 2021-04-28 Stuart T. Johnston , Matthew J. Simpson , Edmund J. Crampin

In this work we consider a size-structured cannibalism model with the model ingredients (fertility, growth, and mortality rate) depending on size (ranging over an infinite domain) and on a general function of the standing population…

Analysis of PDEs · Mathematics 2019-03-25 Jozsef Z. Farkas , Thomas C. Hagen

A striking feature of the marine ecosystem is the regularity in its size spectrum: the abundance of organisms as a function of their weight approximately follows a power law over almost ten orders of magnitude. We interpret this as evidence…

Populations and Evolution · Quantitative Biology 2010-09-17 Jose A. Capitan , Gustav W. Delius

In this paper we study a tumor growth model with nutrients. The model presents dynamic patch solutions due to the contact inhibition among the tumor cells. We show that when the nutrients do not diffuse and the cells do not die, the tumor…

Analysis of PDEs · Mathematics 2022-04-18 Matt Jacobs , Inwon Kim , Jiajun Tong

A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are…

Molecular Networks · Quantitative Biology 2019-07-01 Jorge Fernandez-de-Cossio-Diaz , Roberto Mulet , Alexei Vazquez

We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…

Populations and Evolution · Quantitative Biology 2026-05-27 Lucas M. Brugevin , Damián H. Zanette

The paper considers a chemostat model describing an activated sludge process in wastewater treatment. The model is assumed to be subject to environment noise in terms of both white noise and color noise. The paper fully characterizes the…

Probability · Mathematics 2020-01-15 Dang H. Nguyen , Nhu Nguyen , George Yin