The Markov structure of population growth

Some problems concerning the development of general models of population growth are examined, with particular reference to Markovian modelling. The tenet of the paper is that such models can be more realistically attempted by focusing on temporal rather than spatial modifications. Specifically, the time concept considered is linked to the dependent structure inherent in the partial order of descent from mother to child. The author attempts to develop "a general theory of populations of individuals under what might be called free reproduction. Hence, the only dependence assumed between individuals is that from mothers to children." He suggests that the results "can be translated into assertions about evolution in real, physical time and also about the final, stable or balanced, composition of populations, over ages, types, family structure, and many other aspects of populations."