The Misuse of a Mathematical Model: The Tasmanian Case

Abstract

Good application of a mathematical model depends on conformity with empirical observations. Mathematical models based on Dual Inheritance Theory and purporting to demonstrate that population size is a primary determinant of the complexity of tool assemblages in hunter-gatherer societies have been proposed despite their obvious contradiction with data from hunter-gatherer groups. One such model has relied on archaeological data from Tasmania for its validation, but has been extensively critiqued. A response to that critique attempts to justify the application of the model to the Tasmania data but does not succeed in so doing and still fails to address the more fundamental problem of disconnect between model prediction and empirical observation. The problem does not lie in the mathematical formulation of the model but the use of an invalid assumption when the model is used to account for variation in the complexity of tool assemblages in hunter-gatherer societies.

Keywords: Tasmania, mathematical models, dual inheritance, complexity, phenotypic evolution, cultural evolution, imitation, demography, Upper Paleolithic