On hierarchical competition through reduction of individual growth
Barril, Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Calsina i Ballesta, Àngel (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Diekmann, Odo (University of Utrecht. Department of Mathematics)
Farkas, József Z. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Data:	2024
Resum:	We consider a population organised hierarchically with respect to size in such a way that the growth rate of each individual depends only on the presence of larger individuals. As a concrete example one might think of a forest, in which the incidence of light on a tree (and hence how fast it grows) is affected by shading by taller trees. The classic formulation of a model for such a size-structured population employs a first order quasi-linear partial differential equation equipped with a non-local boundary condition. However, the model can also be formulated as a delay equation, more specifically a scalar renewal equation, for the population birth rate. After discussing the well-posedness of the delay formulation, we analyse how many stationary birth rates the equation can have in terms of the functional parameters of the model. In particular we show that, under reasonable and rather general assumptions, only one stationary birth rate can exist besides the trivial one (associated to the state in which there are no individuals and the population birth rate is zero). We give conditions for this non-trivial stationary birth rate to exist and analyse its stability using the principle of linearised stability for delay equations. Finally, we relate the results to the alternative, partial differential equation formulation of the model.
Ajuts:	Agencia Estatal de Investigación MTM2017-84214C2-2-P Agencia Estatal de Investigación PID2021-123733NB-I00
Nota:	Altres ajuts: acords transformatius de la UAB
Drets:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Llengua:	Anglès
Document:	Article ; recerca ; Versió publicada
Matèria:	Physiologically structured population ; Delay formulation ; Stability ; 92D25 ; 35L04 ; 34K30
Publicat a:	Journal of mathematical biology, Vol. 88 (April 2024) , art. 66, ISSN 1432-1416

DOI: 10.1007/s00285-024-02084-x
PMID: 38639778

34 p, 493.2 KB

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