A stochastic population model with hierarchic size-structure
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917720585404416 |
|---|---|
| author | Barril, Carles Calsina, Àngel Farkas, József Z. |
| author_facet | Barril, Carles Calsina, Àngel Farkas, József Z. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14035 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A stochastic population model with hierarchic size-structure Barril, Carles Calsina, Àngel Farkas, József Z. Analysis of PDEs Populations and Evolution 60K40, 45G10, 92D25 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. |
| title | A stochastic population model with hierarchic size-structure |
| topic | Analysis of PDEs Populations and Evolution 60K40, 45G10, 92D25 |
| url | https://arxiv.org/abs/2404.14035 |