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Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…

Analysis of PDEs · Mathematics 2019-03-25 Jozsef Z. Farkas , Darren Green , Peter Hinow

This chapter focuses on variable maturation delay or, more precisely, on the mathematical description of a size-structured population consuming an unstructured resource. When the resource concentration is a known function of time, we can…

Populations and Evolution · Quantitative Biology 2025-10-21 Odo Diekmann , Francesca Scarabel

We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We formulate such question as an inverse problem for an…

Analysis of PDEs · Mathematics 2009-11-11 Benoit Perthame , Jorge P. Zubelli

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a 3-type…

Probability · Mathematics 2012-07-23 Camille Coron

In the framework of population dynamics, the basic reproduction number R_0 is, by definition, the expected number of offspring that an individual has during its lifetime. In constant and time periodic environments it is calculated as the…

Analysis of PDEs · Mathematics 2026-04-16 Carles Barril , Àngel Calsina , Sílvia Cuadrado , Jordi Ripoll

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a…

Analysis of PDEs · Mathematics 2019-03-25 Angel Calsina , Jozsef Z. Farkas

A discrete time branching process where the offspring distribution is generation-dependent, and the number of reproductive individuals is controlled by a random mechanism is considered. This model is a Markov chain but, in general, the…

Probability · Mathematics 2024-01-30 Miguel González , Carmen Minuesa , Manuel Mota , Inés del Puerto , Alfonso Ramos

We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is decided at its birth and its remaining lifetime decreases at the unit speed. The models…

Probability · Mathematics 2024-01-08 Ziling Cheng , Zenghu Li

We analyse the statistical properties of genealogical trees in a neutral model of a closed population with sexual reproduction and non-overlapping generations. By reconstructing the genealogy of an individual from the population evolution,…

Condensed Matter · Physics 2009-10-31 Bernard Derrida , Susanna C. Manrubia , Damian H. Zanette

We consider populations structured by a phenotypic trait and a space variable, in a non-homogeneous environment. In the case of sex- ual populations, we are able to derive models close to existing mod- els in theoretical biology, from a…

Analysis of PDEs · Mathematics 2011-05-11 Sepideh Mirrahimi , Gael Raoul

We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the…

Dynamical Systems · Mathematics 2016-08-17 Vladimir Kozlov , Sonja Radosavljevic , Vladimir G. Tkachev , Uno Wennergren

We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant population at some fixed time and prove…

Probability · Mathematics 2020-05-21 Romain Abraham , Jean-François Delmas , Hui He

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…

Populations and Evolution · Quantitative Biology 2009-02-23 Ellen Baake , Hans-Otto Georgii

We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…

Probability · Mathematics 2009-04-23 Pierre Collet , Servet Martinez , Sylvie Méléard , Jaime San Martin

We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential…

Analysis of PDEs · Mathematics 2013-01-21 Marie Doumic , Anna Marciniak-Czochra , Benoit Perthame , Jorge P. Zubelli

Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the…

Populations and Evolution · Quantitative Biology 2023-09-21 B. Boldin , O. Diekmann , J. A. J. Metz

I study a population model in which the reproduction rate lambda is inherited with mutation, favoring fast reproducers in the short term, but conflicting with a process that eliminates agglomerations of individuals. The model is a variant…

Statistical Mechanics · Physics 2021-06-02 Ronald Dickman

In the present paper we analyze the linear stability of a hierarchical size-structured population model where the vital rates (mortality, fertility and growth rate) depend both on size and a general functional of the population density…

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

We consider the problem of estimating the division rate of a size-structured population in a nonparametric setting. The size of the system evolves according to a transport-fragmentation equation: each individual grows with a given transport…

Statistics Theory · Mathematics 2013-01-21 Marie Doumic Jauffret , Marc Hoffmann , Patricia Reynaud-Bouret , Vincent Rivoirard

In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of…

Populations and Evolution · Quantitative Biology 2024-03-21 Simone De Reggi , Francesca Scarabel , Rossana Vermiglio