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. Author manuscript; available in PMC: 2019 May 1.
Published in final edited form as: Theor Popul Biol. 2018 Apr 26;121:45–59. doi: 10.1016/j.tpb.2018.04.002

Figure 1.

Figure 1

The stochastic Gompertz breakpoint process and the half life of the change in the mean of the dynamical process, t̄ = ln(1/2)/ln c2. Plotted are 5 realizations of the Stochastic Gompertz breakpoint process. Dotted lines mark the process mean before the breakpoint (μ1 = a1/(1−c1), the mean after the breakpoint (μ2 = a2/(1−c2), and the arithmetic average of both means (μ̄ = (μ1 +μ2)/2). The time at which such arithmetic average is reached is the half life of the process, t̄. The upper panel shows a case where the mean changes to a smaller size whereas the lower panel depicts the change from a lower equilibrium size to a higher one. This second case could depict a population recovery scenario, in which case the half life is half the mean time to recovery.