Multiregional Periodic Matrix for Modeling the Population Dynamics of Sardine (<Emphasis Type="Italic">Sardina pilchardus</Emphasis>) Along the Moroccan Atlantic Coast: Management Elements for Fisheries |
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Authors: | Mansour Serghini Abdesslam Boutayeb Pierre Auger Najib Charouki Azeddine Ramzi Omar Ettahiri Maurice Tchuente |
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Institution: | 1.Institut National de Recherche Halieutique,Casablanca,Morocco;2.Department of Mathematics,University Mohammed Ier,Oujda,Morocco;3.UMI IRD and UPMC 209 UMMISCO,Bondy Cedex,France;4.Faculté des Sciences Semlalia, LMDP,Université Cadi Ayyad,Marrakech,Morocco;5.IRD UMI 209 UMMISCO,Bondy Cedex,France;6.Faculty of Science, UMMISCO,University of Yaounde I,Yaoundé,Cameroon |
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Abstract: | In this paper, we present a deterministic time discrete mathematical model based on multiregional periodic matrices to describe
the dynamics of Sardina pilchardus in the Central Atlantic area of the Moroccan coast. This model deals with two stages (immature and mature) and three spatial
zones where sardines are supposed to migrate from one zone to another. The population dynamics is described by an autonomous
recurrence equation N(t + 1) = A.N(t), where A is a positive matrix whose entries are estimated using data collected during biannual acoustic surveys carried
out from 2001 to 2003 onboard the Norwegian research vessel “Dr Fridtjof Nansen”. The dominant eigenvalue λ of A that gives
the long-term growth rate of fish population is smaller than one. This agrees with the stock decrease observed in the data
collected. We show that λ is highly sensitive to the recruitment rate and much less sensitive to the reproduction rate. These
results can clearly be used to define an efficient scenario in order to fight for instance against a stock decrease. |
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