A two-stage DS model with a transition at ~1.5 years post-conception accurately described both brain and body mass trajectories from conception to old age, reproducing the complex 'hook-shaped' allometric relationship between brain and body mass.
Key Findings
Results
The two-stage DS model accurately described both brain and body mass trajectories from conception to approximately 90 years.
The model fit was 'typically within 10% error' for both brain and body mass trajectories.
Data encompassed both sexes from conception to ~90 years of age.
Autopsy data from published sources were analyzed using nonlinear least-squares regression in Maple.
Both single- and two-stage growth scenarios were tested, with the two-stage model outperforming the single-stage scenario.
Results
A critical developmental transition occurs at approximately 1.5 years post-conception.
The two-stage model identified ~1.5 years post-conception as the transition point between growth stages.
This transition was identified for both brain and body mass trajectories.
The DS model is described as a 'two-parameter' model originally proposed in 2015.
Results
The DS model successfully reproduced the non-monotonic, 'hook-shaped' allometric curve of brain versus body mass.
The allometric relationship between brain and body mass is described as 'non-monotonic' and 'hook-shaped'.
The model reproduced age-related declines in brain mass after approximately 45 years.
This complex allometric relationship was captured using the same two-parameter framework applied to individual growth trajectories.
Results
Rescaling age using the development time derived from the DS model largely eliminated sex differences in body mass trajectories.
When biological time (derived from the DS model's development time parameter) was used instead of chronological age, sex differences in body mass trajectories were largely removed.
Rescaling also equalized male and female life expectancy when expressed in biological time.
This finding suggests that observed sex differences in growth and longevity may reflect differences in developmental pace rather than fundamental biological differences.
Conclusions
The DS model is presented as a parsimonious, two-parameter framework for describing human ontogenetic growth from conception to old age.
The model was originally proposed in 2015 and is described as 'universal' and 'scientifically well-grounded'.
The model uses only two parameters to describe growth trajectories.
Potential applications include theoretical biology, evolutionary anthropology, and biogerontology.
The development time derived from the model provides 'a physiologically meaningful time metric'.
Martyushev L, Martyushev L. (2026). The Universal Model of Growth: Dependence of Brain and Body Mass on Age.. American journal of human biology : the official journal of the Human Biology Council. https://doi.org/10.1002/ajhb.70235