Aging by near-extinctions in many-variable interacting populations

Understand

Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding, accompanied by a slowdown of the dynamics (aging).

• Here, we investigate the connection between near-extinction and aging by introducing an exactly solvable many-variable model, where the time derivative of each population size vanishes both at zero and some finite maximal size.
• We show that aging emerges generically when random interactions are taken between populations.
• Population sizes remain exponentially close (in time) to the absorbing values for extended periods of time, with rapid transitions between these two values.