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

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.

A morphogenetic model of cranial pneumatization based on the invasive tissue hypothesis.

The interpretation of patterns of cranial pneumatization in terms of evolution, development, and function is controversial, because these structures exhibit extreme diversity and variability among and within taxa. However, there is general consensus that air-filled spaces are formed by invasion of mucous epithelial tissue from the nasopharyngeal cavity into the surrounding cranial bones. This investigation presents a morphogenetic model of pneumatization, which combines empirical data about epithelial growth with physical concepts of surface growth. The study develops a model that defines growth equations with a minimum number of system parameters to simulate the invasion of mucous tissue and air-filled spaces into the cancellous compartment of cranial bones. Computer simulations show that tuning a small set of model parameters permits generation of a wide diversity of morphologies mimicking natural air-filled spaces. Comparison of virtual with actual morphologies yields new insights into possible factors controlling the process of cranial pneumatization.