Order of events matter: comparing discrete models for optimal control of species augmentation. (English) Zbl 1448.92176
Summary: We investigate optimal timing of augmentation of an endangered/threatened species population in a target region by moving individuals from a reserve or captive population. This is formulated as a discrete-time optimal control problem in which augmentation occurs once per time period over a fixed number of time periods. The population model assumes the Allee effect growth functions in both target and reserve populations and the control objective is to maximize the target and reserve population sizes over the time horizon while accounting for costs of augmentation. Two possible orders of events are considered for different life histories of the species relative to augmentation time: move individuals either before or after population growth occurs. The control variable is the proportion of the reserve population to be moved to the target population. We develop solutions and illustrate numerical results which indicate circumstances for which optimal augmentation strategies depend upon the order of events.
MSC:
| 92D25 | Population dynamics (general) |
| 92D40 | Ecology |
| 49J21 | Existence theories for optimal control problems involving relations other than differential equations |
| 39A60 | Applications of difference equations |
Keywords:
species augmentation; translocation; optimal control theory; discrete-time difference equations; comparing discrete-time order of events; mathematical modelling; ecological applicationsSoftware:
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