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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical biology 26 (1988), S. 551-581 
    ISSN: 1432-1416
    Keywords: Stability ; Discrete population models ; Bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Sufficiency conditions for local stability are derived for a class of density dependent Leslie matrix models. Four of the recruitment functions in common use in fisheries management are then considered. In two of these oscillating instability can never occur (Beverton and Holt and Cushing forms). In the other two (Deriso-Schnute and Shepherd forms) undamped oscillations are possible within the region of parameter space described here. An algorithm is developed for calculating necessary and sufficient local stability conditions for a simplified form of the general age-structured model. The complete spectrum of stability states (monotonic stability; monotonic instability; oscillating-stable; oscillating-unstable) and the bifurcation periods are given for selected examples of this model. The examples cover a large portion of the parameter space of interest in resource management. It is shown that in perfectly deterministic systems which are observed with error, oscillating instabilities may be missed, and such systems could be erroneously assumed to be stable.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 46 (1985), S. 505-514 
    ISSN: 1573-2878
    Keywords: Optimal harvesting ; age-structured models ; cohort analysis ; sustainable yields ; feedback control ; fisheries management
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A Beverton and Holt type linear cohort dynamics model is integrated and combined with a nonlinear stock-recruitment relationship to obtain a discrete-time multicohort harvesting model. Assuming that each age class is individually controllable, it is shown, subject to certain assumptions, that the optimal harvesting strategy is to drive the population to the maximum sustainable yield solution in one time step. In most fisheries, this controllability assumption is not met and harvesting is agewise nonselective. In this case, it may be preferable to implement a harvesting policy based on suboptimal constant effort or stock level feedback strategies, rather than implement a more complicated optimal policy. This question is addressed through numerical studies on the management of an anchovy fishery.
    Type of Medium: Electronic Resource
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