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Marine Reserve Design and Optimal Inter-Reserve Distance Spacing | | Liam Wagner
; Hugh Possingham
; | | Rating: | Visitors: 5/5 (1 visitor) | | Date: |
16 Sep 2003 | | Subject: | Optimization and Control; Probability; Populations and Evolution; Other; Quantitative Methods MSC-class: 60G99;60J10;60J25;90B15;92B05 | math.OC math.PR q-bio.OT q-bio.PE q-bio.QM | | Abstract: | How far to separate reserves for marine conservation has long been a contentious issue. The placement of marine reserves in close proximity to enable the transfer of organisms, fails to deal fully with the possibility of disaster. There is a tension between placing reserves close together to facilitate recolonisation and placing reserves far apart to minimize the probability that both are affected by the same catastrophe. We consider a Markov Chain model, which uses a Quasi-Stationary Distribution approach to develop policies for reserve management of reserve colonisation and extinction to find an algebraic expression for the optimal spacing for exponentially distributed catastophe sizes. The analysis relies on finding the eigenvalues and quasi-stationary distributions of the Markov chain metapopulation model for the system.This model examines the specific survival of a population which as viable reserve at some suitable distance away. This result shows that a possible analytic solution may exist for the placement of reserves with respect to extinction events in Inter-reserve distance problems. | | Source: | arXiv, math.OC/0309255 | | Services: | Forum | Review | PDF | Favorites | |
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