Header

UZH-Logo

Maintenance Infos

Individual-based modelling of population growth and diffusion in discrete time


Tkachenko, Natalie; Weissmann, John David; Petersen, Wesley P; Lake, George; Zollikofer, Christoph P E; Callegari, Simone (2017). Individual-based modelling of population growth and diffusion in discrete time. PLoS ONE, 12(4):e0176101.

Abstract

Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and independent, simultaneous actions of birth, death, and movement that approaches the Fisher-Kolmogorov model in the continuum limit. This model is well-suited to parallelization on high-performance computers. We explore its emergent properties with analytical approximations and numerical simulations in parameter ranges relevant to human population dynamics and ecology, and reproduce continuous-time results in the limit of small transition probabilities. Our model prediction indicates that the population density and dispersal speed are affected by fluctuations in the number of individuals. The discrete-time model displays novel properties owing to the binomial character of the fluctuations: in certain regimes of the growth model, a decrease in time step size drives the system away from the continuum limit. These effects are especially important at local population sizes of <50 individuals, which largely correspond to group sizes of hunter-gatherers. As an application scenario, we model the late Pleistocene dispersal of Homo sapiens into the Americas, and discuss the agreement of model-based estimates of first-arrival dates with archaeological dates in dependence of IBM model parameter settings.

Abstract

Individual-based models (IBMs) of human populations capture spatio-temporal dynamics using rules that govern the birth, behavior, and death of individuals. We explore a stochastic IBM of logistic growth-diffusion with constant time steps and independent, simultaneous actions of birth, death, and movement that approaches the Fisher-Kolmogorov model in the continuum limit. This model is well-suited to parallelization on high-performance computers. We explore its emergent properties with analytical approximations and numerical simulations in parameter ranges relevant to human population dynamics and ecology, and reproduce continuous-time results in the limit of small transition probabilities. Our model prediction indicates that the population density and dispersal speed are affected by fluctuations in the number of individuals. The discrete-time model displays novel properties owing to the binomial character of the fluctuations: in certain regimes of the growth model, a decrease in time step size drives the system away from the continuum limit. These effects are especially important at local population sizes of <50 individuals, which largely correspond to group sizes of hunter-gatherers. As an application scenario, we model the late Pleistocene dispersal of Homo sapiens into the Americas, and discuss the agreement of model-based estimates of first-arrival dates with archaeological dates in dependence of IBM model parameter settings.

Statistics

Altmetrics

Downloads

5 downloads since deposited on 13 Dec 2017
5 downloads since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Department of Anthropology
Dewey Decimal Classification:300 Social sciences, sociology & anthropology
Language:English
Date:2017
Deposited On:13 Dec 2017 17:15
Last Modified:01 Jan 2018 01:46
Publisher:Public Library of Science (PLoS)
ISSN:1932-6203
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1371/journal.pone.0176101
PubMed ID:28426763

Download

Download PDF  'Individual-based modelling of population growth and diffusion in discrete time'.
Preview
Content: Published Version
Language: English
Filetype: PDF
Size: 5MB
View at publisher
Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)