Abstract
There are two contrasting explanations of sleep: as a proximate, essential physiological function or as a behavioral, adaptive state of inactivity and these hypotheses remain widely debated. To investigate the adaptive significance of sleep, we develop an evolutionary argument formulated as a tractable partial differential equation model. We allow demographic parameters such as birth and mortality rates to vary through time in both safe and vulnerable sleeping environments. From this model we analytically calculate population growth rate (fitness) for sleeping and non-sleeping strategies. We find that, in a temporally heterogeneous environment, sleep behavior always achieves a higher fitness than non-sleeping behavior. As organisms do not exist in constant environments, we conclude that the evolution of sleep is inevitable. Further, we suggest that the two contrasting theories need not be mutually exclusive.
Highlights
Most attempts to explain the evolution of sleep, a vulnerable state observed across diverse taxa, have tended to focus on a search for benefits associated with physiological or vital functions
It is important to note that this adaptive view of sleep evolution does not exclude the existence of other vital functions
We start by defining n(t, τ, x) the population density of organisms employing a given strategy at time t, time they last consumed food τ, and age x
Summary
Most attempts to explain the evolution of sleep, a vulnerable state observed across diverse taxa, have tended to focus on a search for benefits associated with physiological or vital functions. We weight these basal parameters by sleep strategies or functions that quantify activity to find effective mortality and birth rates for a particular strategy. We say that a population has a different strategy if it has a different sleep function s(t) that quantifies how active an organism is at any time t.
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