Thoughts on Preference and Utility in the Salmon Case Study

Pacific salmon are an extremely valuable resource on the Pacific Rim of Canada. On the Skeena River, one of six major salmon watersheds in B.C., the dollar value of the commercial catch is between ten and twenty million dollars annually. In addition, the salmon stocks provide recreational benefits for many residents of British Columbia and contribute strongly to the local recreational economy. Millions of dollars are spent annually on managing the commercial and recreational salmon fisheries; there is a current proposal by the federal government to spend several hundred million dollars enhancing the salmon stocks over the next few years. The current salmon case study has been involved in extensive modeling efforts to determine policy options for salmon management and assess these options. However, we have recently realized that despite our model's optimization techniques and the incredible elegance of our approach, we really don't know what the people of Canada want from the salmon fishery

Optimal Exploitation of Multiple Stocks by a Common Fishery: A New Methodology

Optimal harvest rates for mixed stocks of fish are calculated using stochastic dynamic programming. This technique is shown to be superior to the best methods currently described in the literature. The Ricker stock recruitment curve is assumed for two stocks harvested by the same fishery. The optimal harvest rates are calculated as a function of the size of each stock, for a series of possible parameter values. The dynamic programming solution is similar to the fixed escapement policy only when the two stocks have similar Ricker parameters, or when the two stocks are of equal size. Normally, one should harvest harder than calculated from fixed escapement analysis

Expected Changes in Stock Recruitment Parameters When Exploiting Mixed Stocks of Salmon

The parameters for a Ricker stock recruitment relationship can change due to a number of factors. Methods for distinguishing between habitat elimination, lowered brood success, and elimination of less productive substocks are discussed. Data for the Columbia River Fall Chinook, and Skeena River Sockeye are analyzed in light of these considerations. It is also shown that the expected changes in productivities are strongly affected by the correlation of productivities of the different substocks. The importance of the above factors are discussed in relation to proposed enhancement facilities

Stock Enhancement in Salmon & Maintenance of Historic Runs

W.E. Ricker has recently shown that the failure of present day salmon fisheries to maintain historically high yields may be due in part to the fact that different stocks, which are subjected to the same fishing pressure, have different biological productivities, and the equilibrium maximum sustained yield may cause smaller less productive stocks to reach very low levels or even go extinct. This author explores the problem in two ways: he first analytically examines the relationship between two stocks subjected to the same fishery, and then tests these conclusions against a much more complex numerical simulation model of a salmon fishery

Web-dendritic ribbon growth

A web furnace was constructed for pulling dendritic-web samples. The effect of changes in the furnace thermal geometry on the growth of dendritic-web was studied. Several attempts were made to grow primitive dendrites for use as the dendritic seed crystals for web growth and to determine the optimum twin spacing in the dendritic seed crystal for web growth. Mathematical models and computer programs were used to determine the thermal geometries in the susceptor, crucible melt, meniscus, and web. Several geometries were determined for particular furnace geometries and growth conditions. The information obtained was used in conjunction with results from the experimental growth investigations in order to achieve proper conditions for sustained pulling of two dendrite web ribbons. In addition, the facilities for obtaining the following data were constructed: twin spacing, dislocation density, web geometry, resistivity, majority charge carrier type, and minority carrier lifetime

Fish -- More Than Just Another Commodity

This brief highlights the contribution of wild capture fisheries to nutritional security in fish dependent developing countries. It is intended to stimulate debate around two broad themes: (1) when should the focus of fisheries policies be on local food security and human well-being as opposed to revenue generation, and (2) how does the current research agenda, with its emphasis on environmental and economic issues, assist or impair decision making processes

Adaptive Control of Fishing Systems

This paper discusses some formal techniques for deciding how harvesting policies should be modified in the face of uncertainty. Parameter estimation and dynamic optimization methods are combined for the Ricker stock recruitment model to show how exploitation rates should be manipulated to give more information about the model parameters. In general, harvesting rates should be lower than would be predicted by the best fitting recruitment curve unless this curve predicts that the stock is very productive. A decision procedure is developed for comparing alternative stock recruitment models; when applied to the Fraser River sockeye salmon, the procedure indicates that an experimental increase in escapements would be worthwhile. It appears that there is considerable promise for extending these methods and procedures to cases where the stock size is unknown and where fishing effort is poorly controlled

Temporal extensivity of Tsallis' entropy and the bound on entropy production rate

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation for the Tsallis entropy. They are primarily concerned with nonlinear dynamical systems at the edge of chaos. Here, it is shown by generalizing a formulation of thermostatistics based on time averages recently proposed by Carati [A. Carati, Physica A 348, 110 (2005)] that, whenever relevant, the Tsallis entropy indexed by $q$ is temporally extensive: linear growth in time, i.e., finite entropy production rate. Then, the universal bound on the entropy production rate is shown to be $1/|1-q|$ . The property of the associated probabilistic process, i.e., the sojourn time distribution, determining randomness of motion in phase space is also analyzed.Comment: 25 pages, no figure

Tsallis' q index and Mori's q phase transitions at edge of chaos

We uncover the basis for the validity of the Tsallis statistics at the onset of chaos in logistic maps. The dynamics within the critical attractor is found to consist of an infinite family of Mori's $q$-phase transitions of rapidly decreasing strength, each associated to a discontinuity in Feigenbaum's trajectory scaling function $\sigma$. The value of $q$ at each transition corresponds to the same special value for the entropic index $q$, such that the resultant sets of $q$-Lyapunov coefficients are equal to the Tsallis rates of entropy evolution.Comment: Significantly enlarged version, additional figures and references. To be published in Physical Review