The Universal Model of Growth: Dependence of Brain and Body Mass on Age

To test whether the universal two-parameter DS model, originally proposed in 2015, can accurately describe how human brain and body mass change from conception to old age and reproduce their complex allometric relationship.

We analyzed published autopsy data on brain and body mass from conception to ~90 years, encompassing both sexes. Using nonlinear least-squares regression in Maple, we fitted the DS model to the data, testing single- and two-stage growth scenarios. Model performance was evaluated via residual analysis.

A two-stage model-with a transition at ~1.5 years post-conception-accurately described both brain and body mass trajectories (typically within 10% error). The model successfully reproduced the non-monotonic, "hook-shaped" allometric curve of brain vs. body mass, including age-related declines after ~45 years. Furthermore, rescaling age using development time (derived from the DS model) largely eliminated sex differences in body mass trajectories and equalized male and female life expectancy in biological time.

The DS model provides a parsimonious, scientifically well-grounded framework for human ontogenetic growth. It identifies ~1.5 years post-conception as a critical developmental transition and offers a physiologically meaningful time metric with potential applications in theoretical biology, evolutionary anthropology, biogerontology, etc.