Temporal invariance of evolutionary entropy and comparative demographic analysis

Does evolutionary entropy depend on the width of the age classes used to describe a population? We show that the apparent dependence on temporal resolution is a consequence of the loss of information about reproductive timing within discrete classes. When this information is retained, corresponding continuous and discrete representations yield the same cycle entropy, generation time, evolutionary entropy, and reproductive potential in a common unit of time. When within-class timing is unknown, a uniform local reconstruction yields a logarithmic correction. For constant post-maturity hazard and fertility, continuous exponential and discrete geometric descriptions correspond exactly at every time scale. Thus, for a fixed reference duration, evolutionary entropy is a property of the reproductive process, not of its temporal partition. These results provide a mathematical basis for comparing demographic models across different temporal scales by identifying the information required to separate differences in reproductive organisation from effects of the chosen age-class representation.