A revisit to Pope's cohort analysis |
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| Institution: | 1. Department of Mining Engineering, Xinjiang Institute of Engineering, Urumqi 830023, China;2. Key Lab of Shale Gas and Geoengineering, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China;3. Lanzhou Center for Oil and Gas Resources, Institute of Geology and Geophysics, Chinese Academy of Sciences, Lanzhou 730000, China;1. Department of Membrane Transport, Institute of Physiology, Academy of Sciences of the Czech Republic, v.v.i., Videnska 1083, Prague 4, Czech Republic 142 20;2. Drug Resistance Mechanism and Modulation Group, Molecular and Structural Basis of Infectious Systems, National Centre for Scientific Research and Lyon I University Laboratory No. 5086, Institute of Biology and Chemistry of Proteins, Lyon 69 367, France |
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| Abstract: | Gulland's Gulland, J.A., 1965. Estimation of mortality rates. Annex to Arctic Fisheries Working Group Report (meeting in Hamburg, January 1965). ICES, C.M. 1965, Doc. No. 3 (mimeographed)] virtual population analysis (VPA) is commonly used for studying the dynamics of harvested fish populations. However, it necessitates the solving of a nonlinear equation for the instantaneous rate of fishing mortality of the fish in a population. Pope Pope, J.G., 1972. An investigation of the accuracy of Virtual Population Analysis using cohort analysis. ICNAF Res. Bull. 9, 65–74. Also available in D.H. Cushing (ed.) (1983), Key Papers on Fish Populations, p. 291–301, IRL Press, Oxford, 405 p.] eliminated this necessity in his cohort analysis by approximating its underlying age- and time-dependent population model. His approximation has since become one of the most commonly used age- and time-dependent fish population models in fisheries science. However, some of its properties are not well understood. For example, many assert that it describes the dynamics of a fish population, from which the catch of fish is taken instantaneously in the middle of the year. Such an assertion has never been proven, nor has its implied instantaneous rate of fishing mortality of the fish of a particular age at a particular time been examined, nor has its implied catch equation been derived from a general catch equation. In this paper, we prove this assertion, examine its implied instantaneous rate of fishing mortality of the fish of a particular age at a particular time, derive its implied catch equation from a general catch equation, and comment on how to structure an age- and time-dependent population model to ensure its internal consistency. This work shows that Gulland's (1965) virtual population analysis and Pope's (1972) cohort analysis lie at the opposite end of a continuous spectrum as a general model for a seasonally occurring fishery; Pope's (1972) approximation implies an infinitely large instantaneous rate of fishing mortality of the fish of a particular age at a particular time in a fishing season of zero length; and its implied catch equation has an undefined instantaneous rate of fishing mortality of the fish in a population, but a well-defined cumulative instantaneous rate of fishing mortality of the fish in the population. This work also highlights a need for a more careful treatment of the times of start and end of a fishing season in fish population models. |
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