, Volume 34, Issue 4, pp 1001-1009

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Exponential growth combined with exponential decline explains lifetime performance evolution in individual and human species

  • Geoffroy BerthelotAffiliated withIRMES, INSEPFaculty of Sciences, Paris Descartes University Email author 
  • , Stéphane LenAffiliated withIRMES, INSEP
  • , Philippe HellardAffiliated withIRMES, INSEP
  • , Muriel TaffletAffiliated withIRMES, INSEPINSERM
  • , Marion GuillaumeAffiliated withIRMES, INSEP
  • , Jean-Claude VollmerAffiliated withIRMES, INSEP
  • , Bruno GagerAffiliated withIRMES, INSEP
  • , Laurent QuinquisAffiliated withIRMES, INSEP
  • , Andy MarcAffiliated withIRMES, INSEP
    • , Jean-François ToussaintAffiliated withIRMES, INSEPFaculty of Sciences, Paris Descartes UniversityCentre d’Investigation en Médecine du Sport (CIMS), Hôtel-Dieu, Assistance Publique-Hôpitaux de Paris


The physiological parameters characterizing human capacities (the ability to move, reproduce or perform tasks) evolve with ageing: performance is limited at birth, increases to a maximum and then decreases back to zero at the day of death. Physical and intellectual skills follow such a pattern. Here, we investigate the development of sport and chess performances during the lifetime at two different scales: the individual athletes’ careers and the world record by age class in 25 Olympic sports events and in grandmaster chess players. For all data sets, a biphasic development of growth and decline is described by a simple model that accounts for 91.7% of the variance at the individual level and 98.5% of the variance at the species one. The age of performance peak is computed at 26.1 years old for the events studied (26.0 years old for track and field, 21.0 years old for swimming and 31.4 years old for chess). The two processes (growth and decline) are exponential and start at age zero. Both were previously demonstrated to happen in other human and non-human biological functions that evolve with age. They occur at the individual and species levels with a similar pattern, suggesting a scale invariance property.


Ageing Maximum performance Biphasic development Sport