A stochastic population model with hierarchic size-structure

被引:0
作者
Barril, Carles [1 ]
Calsina, Angel [1 ]
Farkas, Jozsef Z. [1 ]
机构
[1] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Spain
关键词
Hierarchically size-structured population; Individual based stochastic model; Quasi-stationary distribution; DIFFERENTIAL-EQUATIONS; FORMULATION; DYNAMICS; DERIVATION;
D O I
10.1007/s12190-024-02187-0
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider a hierarchically structured population in which the amount of resources an individual has access to is affected by individuals that are larger, and that the intake of resources by an individual only affects directly the growth rate of the individual. We formulate a deterministic model, which takes the form of a delay equation for the population birth rate. We also formulate an individual based stochastic model, and study the relationship between the two models. In particular the stationary birth rate of the deterministic model is compared to that of the quasi-stationary birth rate of the stochastic model. Since the quasi-stationary birth rate cannot be obtained explicitly, we derive a formula to approximate it. We show that the stationary birth rate of the deterministic model can be obtained as the large population limit of the quasi-stationary birth rate of the stochastic model. This relation suggests that the deterministic model is a good approximation of the stochastic model when the number of individuals is sufficiently large.
引用
收藏
页码:5515 / 5542
页数:28
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