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The evolution of sleep is inevitable in a periodic world
Fig 2
Typical population growth rates r1 (dotted line) and r2 (solid line) as a function of time when birth rates are variable and mortality is constant.
Observe that r2 > r1 for almost all t. Here B = 5 and Γ = 2.5.
doi: https://doi.org/10.1371/journal.pone.0201615.g002