2018/12/21 by Masahiro Anazawa, Anazawa, Masahiro
Biochemistry, Genetics and Molecular Biology · Medicine · Physics and Astronomy · Social Sciences · #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Opinion Dynamics and Social Influence #Populations and Evolution (q-bio.PE) #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1812.09023
13 pages, 5 figures
arxiv created 2018/12/21 · openalex publication_date 2018/12/21 · arxiv updated 2018/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hassell model has been widely used as a general discrete-time population dynamics model that describes both contest and scramble intraspecific competition through a tunable exponent. Since the two types of competition generally lead to different degrees of inequality in the resource distribution among individuals, the exponent is expected to be related to this inequality. However, among various first-principles derivations of this model, none is consistent with this expectation. This paper explores whether a Hassell model with an exponent related to inequality in resource allocation can be derived from first principles. Indeed, such a Hassell model can be derived by assuming random competition for resources among the individuals wherein each individual can obtain only a fixed amount of resources at a time. Changing the size of the resource unit alters the degree of inequality, and the exponent changes accordingly. The Beverton-Holt and Ricker models can be regarded as special cases of the derived Hassell model. Two additional Hassell models are derived under some modified assumptions.