A behavioural shutdown can make sleeping safer: a strategic perspective on the function of sleep

Sleep appears to effect some sort of neural maintenance, but a complete theory of the function of sleep must address why such maintenance requires a behavioural shutdown (or unconsciousness) that leaves an animal vulnerable to predators. We present a simple, strategic model to determine the degree of sleep that minimizes the risk of predation. We assume that the brain is composed of neural units that can, in theory, ‘sleep’ independently of each other, and that a given neural unit must go offline for maintenance/sleep. We also assume that the probability of detecting an attack depends on the fraction of neural units that are awake. We found that having all neural units offline simultaneously (i.e. shutdown sleep) is often the safest way to perform neural maintenance, even though partial sleep makes predators more detectable. This counterintuitive result reflects the assumptions that, in a state of partial sleep, (1) neural maintenance takes longer to complete and (2) predator detection is less effective than suggested by the proportion of neural units online. Partial sleep is a possible outcome when the risk of attack increases as more neural units are taken offline. Minimal sleep (with only one or a few units offline) is a possible outcome when the attack rate while awake is substantially higher than when asleep. Partial sleep of a sort is known to occur in some animals, but there is no apparent evidence for the idea of minimal sleep.