Mathematical Model of an Interaction between Bears and Salmon; A Case in British Columbia
DOI:
https://doi.org/10.5614/cbms.2019.2.1.4Keywords:
Predator-prey, Equilibrium point, Stability analysisAbstract
An interaction model for the Pacific salmon and bear population in British Columbia is discussed here. The phenomenon is shown during the salmons period of migration back to their birthplace river at the end of their life. During this returning home, a large number of bears from the nearby state come and prey on them. This predation of salmon before spawning is suspected as the cause of the decline in Salmon production. Here a dynamical model involving a specific predator-prey type interaction between Salmon and Bears is constructed in the form of a non-autonomous dynamical system, in which the transition rate from the adult state of salmon to the spawning state is positive only in the month of migration. Dynamical analysis for the stability of the coexistence equilibrium for the autonomous case is shown and sensitivity analysis for the non-autonomous the case is done numerically.References
Williams, J. E., Isaak, D., Imhof, J., Hendrickson, D. A., and McMillan, J. R. 2015. Cold-water fishes and climate change in North America. Reference Module in Earth Systems and Environmental Sciences. doi: 10.1016/B978-0-12-409548-9.09505-1.
Dunfield, R. W. 1985. The Atlantic salmon in the history of North America. Canadian Special Publication of Fisheries and Aquatic Science, 80.
Schindler, D. E., Scheuerell, M. D., Moore, J. W., Gende, S. M., Francis, T. B., and Palen, W. J. 2003. Pacific salmon and the ecology of coastal ecosystems. Frontiers in Ecology and the Environment, 1(1), 31-37.
Dittman, A., and Quinn, T. 1996. Homing in Pacific salmon: mechanisms and ecological basis. Journal of Experimental Biology,
(1), 83-91.
Cooke, S. J., Crossin, G. T., and Hinch, S. G. 2011. FISH MIGRATIONS j Pacific Salmon Migration: Completing the Cycle,
-1962.
Adams, M. S., Service, C. N., Bateman, A., Bourbonnais, M., Artelle, K. A., Nelson, T., and Darimont, C. T. 2017. Intrapopulation diversity in isotopic niche over landscapes: Spatial patterns inform conservation of bearsalmon systems. Ecosphere, 8(6), e01843.
Alver, M. O., Skien, K. R., Fre, M., Aas, T. S., Oehme, M., and Alfredsen, J. A. 2016. Modelling of surface and 3D pellet distribution in Atlantic salmon (Salmo salar L.) cages. Aquacultural engineering, 72, 20-29.
Reimchen, T. E. 2000. Some ecological and evolutionary aspects of bear-salmon interactions in coastal British Columbia. Canadian Journal of Zoology, 78(3), 448-457.
Shardlow, T. F., and Hyatt, K. D. 2013. Quantifying associations of large vertebrates with salmon in riparian areas of British Columbia streams by means of camera-traps, bait stations, and hair samples. Ecological Indicators, 27, 97-107.
U.S. Bureau of Land Management. Archived from the original. https://www.nps.gov/olym/learn/nature/the-salmon-life-cycle.htm. Last accessed December 8, 2018, 16:13.
National Park Service. The Salmon Life Cycle. https://www.nps.gov/olym/learn/nature/the-salmon-life-cycle.htm. Last accessed December 8, 2018, 16:35.
Zhijie, G., Yingliang, X., Xiangguo, Z., Yong, W., Zhang, D., and Sugiyama, S. 2008. Review of fishery information and data collection systems in China. FAO fisheries circular, 1029, 46.
Bley, P. W., and Moring, J. R. (1988). Freshwater and ocean survival of Atlantic salmon and steelhead: a synopsis (No. FWS-88
(9)). MAINE UNIV AT ORONO.
" CHINOOK SALMON FACTS" . Pacific States Marine Fisheries Commission. 2010-03-05. Retrieved 2010-03-05. 1996-12-16.
Gende, S. M., Edwards, R. T., Willson, M. F., and Wipfli, M. S. 2002. Pacific salmon in aquatic and terrestrial ecosystems:
Pacific salmon subsidize freshwater and terrestrial ecosystems through several pathways, which generates unique management and conservation issues but also provides valuable research opportunities. BioScience, 52(10), 917-928.
T. P. Quinn, C. J. Cunningham, and A. J. Wirsing. Diverse foraging opportunities drive the functional response of local and landscape-scale bear predation on pacic salmon. Oecologia, 183(2):415429, 2017.
Quinn, T. P., Cunningham, C. J., and Wirsing, A. J. 2018. Diverse foraging opportunities drive the functional response of local and landscape-scale bear predation on Pacific salmon. Oecologia, 183(2), 415-429.
