Open AccessA Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map
Author(s) -
Wesley P. Petersen,
Simone Callegari,
George Lake,
Natalie Tkachenko,
John David Weissmann,
Christoph P.E. Zollikofer
Publication year - 2017
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0167514
Subject(s) - population , solver , boundary (topology) , proxy (statistics) , paleoclimatology , biological dispersal , pleistocene , population growth , mathematics , statistical physics , geology , statistics , biology , demography , mathematical optimization , paleontology , ecology , physics , mathematical analysis , climate change , sociology
We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas.