On How, and Why, and When, We Grow Old
Growth and aging are fundamental features of animal life. The march from fertilization to oblivion comes in enormous variety: days and hundreds of cells for nematodes, decades and trillions of cells for humans.1-4 Since Verhulst (18385) proposed the Logistic Equation - exponential growth with countervailing linear decline in rate - biologists have searched for ever better density dependent growth equations,6-12 none which accurately capture the relationship between size and time for real animals.13-15 Furthermore, while growth and aging run in parallel, whether the relationship is causal has been unknown. Here we show, by examining growth and lifespan in units of numbers of cells, N, (Cellular Phylodynamics6), that both processes are linked to the same reduction in the fraction of cells dividing, occurring by a simple expression, the Universal Mitotic Fraction Equation. Lifespan is correlated with an age when fewer than one-in-a-thousand cells are dividing, quantifying the long-appreciated mechanism of aging, the failure of cells to be rejuvenated by dilution with new materials made, and DNA repaired, at mitosis.24-26 These observations provide practical mathematical expressions for comprehending, and managing, the challenges of growth and aging, for such tasks as improving the effectiveness of COVID-19 vaccination in the elderly.