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 (1838 5 ) 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 Phylodynamics 6 ), 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.