Time: 9:00 – 11:30, Thursday, 13 November, 2014

+ 9:00 – 10:00: Lecture

+ 10:00 – 10:30: Teabreak

+ 10:30 – 11:30: Lecture

Location: VIASM Lecture Hall B4.

Lecturer: Prof. Pierre Auger (Member of French Academy of Science, France, UMI 209 UMMISCO, IRD, France.)

Abstract:

Population and community models are complex in the sense that they usually take into account many variables and parameters. We present methods allowing the reduction of the dimension of the system which may become, in this way, mathematically more tractable. The reduction of the proposed system is undertaken with the help of aggregation methods which aim at studying the relationships between a large class of complex systems, in which many variables are involved, and their corresponding reduced or aggregated systems, governed by a few variables. The kind of aggregation methods that we consider is based on time scale separation methods. In order to illustrate the methods in population and community dynamics, we present an application of aggregation methods in multi-site fishery modelling. The different sites can correspond to fishing areas, Marine Protected Areas (MPA), or still Fish Aggregating Devices (FAD).

We present modelling examples :

• We consider a multi-site stock-fishing effort model. We show that the total catch can be optimized for a given number of FADs.

• We study the effects of fast price variation as a result of demand and supply on the global dynamics of a fishery. We study cases of linear as well as non-linear demand functions of price.

• We present a model of a commercial species, the “thiof” in Senegal, showing drastic decreasing catch with a booming market price.

• We study the effects of Artificial Habitats on the dynamics of a fishery with a fishing area and a MPA.

References

1. AUGER P., BRAVO DE LA PARRA R., POGGIALE J.C., SANCHEZ E., NGUYEN HUU T., Aggregation of variables and applications to population dynamics. In: P. Magal, S. Ruan (Eds.), Structured Population Models in Biology and Epidemiology, Lecture Notes in Mathematics, vol. 1936, Mathematical Biosciences Subseries. Springer, Berlin, 2008, p. 209-263.

2. AUGER P., BRAVO DE LA PARRA R., POGGIALE J.C. SANCHEZ E., SANZ L., Aggregation methods in dynamical systems variables and applications in population and community dynamics, Physics of Life Reviews, 5, pp. 79-105, 2008.

3. AUGER P. and DUCROT A. A model of fishery with fish stock involving delay equations. PTRSA : Philosophocal Transactions of the Royal Society A. 367, pp. 4907-4922, 2009.

4. AUGER P., MCHICH R., RAÏSSI N., KOOI B. Effects of market price on the dynamics of a spatial fishery model: Over-exploited fishery/traditional fishery. Ecological Complexity, 7, pp. 13-20, 2010.

5. AUGER P., LETT C., MOUSSAOUI A. and PIOCH S.. Optimal number of sites in artificial pelagic multisite fisheries. Canadian Journal of Fisheries and Aquatic Sciences. 67, pp. 296-303, 2010.

6. LY S., AUGER P. & BALDE M. A bioeconomic model of a multi-site fishery with non linear demand function: Number of sites optimizing the total capture. Acta Biotheoretica, 2014, 62 (3), p. 371-384.

7. MANSAL F., AUGER P. & BALDE M. A mathematical model of a fishery with variable market price. Sustainable fishery/over- exploitation. Acta Biotheoretica, 2014, 62 (3), p. 305-323.

8. MOUSSAOUI A., BENSENANE M., AUGER P. & BAH A. On the optimal size and number of reserves in a multi-site fishery model. Journal of Biological Systems, 2015, 23 (1), p. 1-17.

9. BROCHIER T., AUGER P., THIAM N., SOW M., DIOUF S. & BREHMER P. Implementation of artificial habitats, inside or outside the marine protected areas? Insights from a mathematical approach, Ecol. Modelling. 2015. Accepted.

Registration:

Please fill in the registration form below your contact information. Deadline for registration: 11/11/2014.