In this paper, we report on the theoretical foundations, empirical context and technical implementation of an agent-based modeling (ABM) framework, that uses a high-performance computing (HPC) approach to investigate human population dynamics on a global scale, and on evolutionary time scales. The ABM-HPC framework provides an in silico testbed to explore how short-term/small-scale patterns of individual human behavior and long-term/large-scale patterns of environmental change act together to influence human dispersal, survival and extinction scenarios. These topics are currently at the center of the Neanderthal debate, i.e., the question why Neanderthals died out during the Late Pleistocene, while modern humans dispersed over the entire globe. To tackle this and similar questions, simulations typically adopt one of two opposing approaches, top-down (equation-based) and bottom-up (agent-based) models of population dynamics. We propose HPC technology as an essential computational tool to bridge the gap between these approaches. Using the numerical simulation of worldwide human dispersals as an example, we show that integrating different levels of model hierarchy into an ABM-HPC simulation framework provides new insights into emergent properties of the model, and into the potential and limitations of agent-based versus continuum models.
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.
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.
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