Maturity Dispersion, Stock Auto-Correlation, and Management Strategy in Exploited Populations
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Fishery management policies need to be based on historical summaries of stock status which are well correlated with the size of the group of individuals who will be affected by any harvest. This paper is motivated by the problem of managing stocks of Atlantic salmon, which can be accurately monitored during the riverine stages of their life-history, but which spend a lengthy period at sea before returning to spawn. We begin by formulating a minimal stochastic model of stock-recruitment driven population dynamics, which linearises to a standard ARMA form. We investigate the relation between maturity dispersion and the auto-covariance of stock fluctuations driven by process noise in the recruitment process and/or random variability in survival from recruitment to spawning. We demonstrate that significant reductions in fluctuation intensity and/or increases in long-run average yield can be achieved by controlling harvesting in response to the value of a historical summary focussed on lags at which the uncontrolled population dynamics produce strong correlations. We apply our minimal model to two well-characterised Atlantic salmon populations, and find poor agreement between predicted and observed stock fluctuation ACF. Re-examination of the ancilliary data available for one of our two exemplary systems leads us to propose an extended model which also linearises to ARMA form, and which predicts a fluctuation ACF more closely in agreement with that observed, and could thus form a satisfactory vehicle for policy discussion.
- Bacon, P.J., Gurney, W., Jones, W., McLaren, L.S., Youngson, A.F., 2005. Seasonal growth patterns of wild fish: partitioning among explanatory variables on the basis of individual growth trajectories of Atlantic salmon parr. J. Anim. Ecol. 74, 1–11. CrossRef
- Bacon, P.J., Palmer, S.C.F., MacLean, J.C., Smith, G.W., Whyte, B.D.M., Gurney, W., Youngson, A.F., 2009. Empirical analyses of the length, weight and condition of adult Atlantic salmon on return to the Scottish coast between 1963–2006. ICES J. Mar. Sci. 85, 844–859. CrossRef
- Beverton, R.J.H., Holt, S.J., 1957. On the Dynamics of Exploited Fish Populations, UK Ministry of Agriculture, Fisheries and Food, Fisheries Investigations, Ser. 2, vol. 19, p. 533.
- Bjornstad, O.N., Nisbet, R.M., Fromentin, J.-M., 2004. Trends and cohort resonant effects in age-structured populations. J. Anim. Ecol. 73, 1157–1167. CrossRef
- Box, G.E.P., Jenkins, G.M., 1976. Time Series Analysis: Forecasting and Control. Holden-Day, Oakland.
- Caswell, H., 1989. Matrix Population Models. Sinauer, Sunderland.
- Chaput, G., Jones, R., 1992. Stock-recruitment relationship for multi-sea-winter salmon from the Margaree river. N.S., Fisheries and Oceans Canada, CFSAC Research Document 92/124.
- Chaput, G., Crozier, W.W., Davidson, I.C., Dempson, J.B., Erkinaro, J., Erikstad, L., Fleming, I.A., Guobergson, G., Hansen, L.P., Hindar, K., Insulander, C., Jensen, A.J., Johlander, A., Karlsson, L., MacLean, J.C., Mathers, R.G., Milner, N.J., Nicholson, M.D., O Maoileidigh, N., Potter, E.C.E., Prevost, E., Schon, P.-J., Wyatt, R.J., 2003. A co-ordinated approach towards the development of a scientific basis for management of wild Atlantic salmon in the North-East Atlantic (SALMODEL). Queens University of Belfast, Belfast.
- Chen, D.G., Holtby, L.B., 2002. A regional meta-model for stock recruitment analysis using an empirical Bayesian approach. Can. J. Fish. Aquat. Sci. 59, 1503–1514. CrossRef
- Clark, C.W., 1990. Mathematical Bioeconomics. Wiley, New York.
- Friedland, K.D., MacLean, J.C., Hansen, L.P., Peyronnet, A.J., Karlsson, L.K., Reddin, D.G., O Maoileidigh, N., McCarthy, J., 2008. Recruitment of Atlantic salmon in Europe. ICES J. Mar. Sci. 66(2), 289–304. CrossRef
- Gurney, W.S.C., Nisbet, R.M., 1985. Generation separation and the expression of larval competition. Theor. Popul. Biol. 28, 150–180. CrossRef
- Gurney, W.S.C., Bacon, P.J., Tyldesley, G., Youngson, A.F., 2009. Process-based modeling of decadal trends in growth survival and smolting of wild salmon (Salmon salar) parr in a Scottish upland stream. Can. J. Fish. Aquat. Sci. 65, 2606–2622. CrossRef
- Gurney, W., Bacon, P.J., McGinnity, P., McLean, J., Smith, G., Youngson, A.F., 2010. Form and uncertainty in stock-recruitment observations: observations and implications for Atlantic salmon management. Can. J. Fish. Aquat. Sci. (in review).
- Lotka, A.J., 2009. The growth of mixed populations: two species competing for a common food supply. J. Wash. Acad. Sci. 22, 461–469.
- Michielsens, C.G.J., McAllister, M.K., 2003. A Bayesian hierarchical analysis of stock-recruit data: quantifying structural and parameter uncertainties. Can. J. Fish. Aquat. Sci. 61, 1032–1047. CrossRef
- Needle, C.L., 2002. Recruitment models: diagnosis and prognosis. Rev. Fish Biol. Fish. 11, 95–111. CrossRef
- Ricker, W.E., 1954. Stock and recruitment. J. Fish. Res. Board Can. 11, 559–623.
- Tsay, R.S., 2005. Analysis of Financial Time Series. Wiley-Interscience, New York. CrossRef
- Youngson, A.F., Hay, D., 1996. The Lives of Salmon. Swan-Hill Press, Shrewsbury.
- Maturity Dispersion, Stock Auto-Correlation, and Management Strategy in Exploited Populations
Bulletin of Mathematical Biology
Volume 72, Issue 5 , pp 1271-1293
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