A mathematical theory for related long term developments of road traffic and safety.

This article presents and discusses an adoptive evolution model for forecasting long term developments in road safety. It takes into account both traffic growth and human adaptation. Earlier parsimonious models such as those used by Oppe and Koornstra are also discussed, and shown to predict trends in accident rates quite well. The data used are the total number of annual vehicle kilometers and fatalities in each of 6 countries: Germany, Great Britain, Israel, Japan, the Netherlands and the USA. The models used in this paper all have an intuitive basis, derived from a priori theory, and are not just regression models. It is assumed that the development of traffic and of traffic safety can be described as growth processes in time. The decrease in fatality rates over the years is assumed to be the result of a collective learning process for the entire nation. This is derived partly from each individual drivers' ability to learn how to cope with traffic, and partly from increased knowledge about vehicle and road design, traffic legislation, driver training, education campaigns and so on. The new adoptive evolution model assumes that the probability of failures in an evolutionary system are a proportional power function of its delayed acceleration of growth. The basic adaptation derivation implies a beta model for adaptation and not the linear operator model of the original model. It predicts a delayed relationship between the annual increase in traffic and the annual decrease in fatality rates. The effects of autoregressive deviations in traffic growth can be predicted using this adaptive evolution model.