Search and Stock Depletion: Theory and Applications

Abstract

1985. Search and stock depletion: theory and applications. Can. 1. Fish.Aquat. Sci. 4%: 150-163. A general theory for the estimation of stock size from search data is developed. In the theory, it is assumed that discrete aggregations (schools of fish, beds of clams) are encountered. The search mode! is an extension of the Poisson process to include depletion. The theory provides a way of estimating stock size and confidence intervals around the estimate, as well as the ability to predict future catches for a given level of effort. Three applications of theory are described: (1) estimating stock size when there is no catch;(2) determining, in real time, the length of fishing seasons; and (3) an empirical study of stock assessment 0% Pacific ocean perch (Sebastes aiutus) near Renneil Sound, British Columbia.Nous avons mis au point une theorie generase sur B'estimatiesn des stocks d'apres des donnees de recherche. Cette theorie suppose qu'on rencontre des groupes separes (barscs de poissons, colonies de clams). Nous avons elargi le prockde de Poisson pour tenir compte de i'arnenuisement. La theorie permet d'estimer I'importance des stocks, I'intervalle d e confiance de I'estimation et la possibilite d e prevoir les prises en fonction d'run effort d e peche donne. Nsus decrivons taois applications : (1) estimation des stocks Iorsqu'il rs' y a pas de prises ; (2) determination, en temps reel, de la longueur de la saison de p$che ; et (3) etude empirique de Irevaluation des stocks de sebastes (Sebastes alutus) pres de la baie Rennell en Colombie-Britannique.One of the thorniest problems in the management of fisheries is the problem of determining stock abundance. h r this reason, biomass surveys are often mn by the managing organizations. In some fisheries, the cost of the survey is about the same as the economic value of the fishery (C. Clark, Mathematics Department, University of British Columbia, Vancouver, B . C., pers. comm.).In those cases without a stock survey, some other procedure for estimating stock size is needed. Perhaps the most common is the model assuming a linear relationship between catch and population:where H is harvest, E is fishing effort, B is population size, and q is a proportionality coefficient (the catchability coefficient). With this model HIE, catch per unit effort (CPUE) is proportional to population. To use this model, one needs some measure s f fishing effort, a quantity that is notoriously hard to measure in my real fishery (e.g. see Rothschild 1972; Wilen 1979). Even if effort could be measured accurately, the CPUE model does not always produce measures of population size that reflect the population (e. g . see Clark and Mangel 1979).One case in which CPUE is expected to break down is when the fishermen spend considerable amounts of time searching for dense schmls or aggregates of fish (this is actually the case considered by Clark and Mange1 I979 for tuna). In this case, the search effort is as important to the estimate of population size as is the time spent hawesting, so that on...

Modeling performance and information exchange between fishing vessels with artificial neural networks

“…Such a "depletion-competition effect" has been commonly observed in the real world, specifically in the analysis of the non-linear relationship between local biomass and catch rates in tuna purse seine fisheries (Fonteneau et al, 1999), in trawler fisheries (Gillis et al, 1993;Rijnsdorp et al, 2000) or taken into account in simulation studies (Mangel and Beder, 1985).…”

Atlantic Bluefin Tuna in the Gulf of Maine, I: Estimation of Seasonal Abundance Accounting for Movement, School and School-Aggregation Behaviour

“…The comparison of survey and catch estimates was purposely naïve, because the spotter survey effort was not strictly independent of fishing effort. Furthermore, even if the trends in the survey and catch estimates were similar, a common trend in both estimates does not necessarily indicate a true change in population abundance, because bias and uncertainty in both types of data can be significantly different (Parrack 1976;Mangel and Beder 1985). However, if one assumes that bias and uncertainty ( t and g t in Eqs.…”

“…juvenile bigeye tuna) also have a high potential for decline because pelagic purse-seine and long-line fishing take advantage of their strong social and associative behaviour. These fishing methods enable more efficient targeting of large aggregations of tuna associated with fish aggregation devices (FADs) and other marine life (Clark and Mangel 1979;Mangel and Beder 1985;Hilborn and Medley 1989;Pitcher 1995).…”

Catch per unit effort standardization of the eastern Bering Sea walleye pollock (Theragra chalcogramma) fleet

“…A more accurate measure of effort would include search time (Mangel and Beder, 1985). Unfortunately, no measure of search time is recorded in the observer database.…”