On the Dynamics of Exploited Fish Populations

Abstract

This volume, in 4 parts, contains the theoretical development of simple and complex deterministic models, and their application to 2 North Sea fisheries. Four primary factors which change the total weight of the fishable stock, recruitment, growth, capture, and "natural" death, are considered. I. The development of a theory of fishing, each factor represented by constant and independent parameters. The 4 primary factors are brought together by considering a year-class of recruits to the fished area, and by applying the other 3 factors to deduce the total yield of the year-class throughout its life, equivalent to the steady state yield in 1 year from all year-classes. From this equation are derived expressions for yield in number, catch per unit of effort, population number, population biomass, and mean length, weight and age of fish in the population and in the catch. II. The theory is extended to include the effects of change in, and interaction between, primary factors. Recruitment is usually but not always independent of population density in marine fishes. A relationship between egg-production (E) and recruitment (R) is developed, in which R approaches an asymptote as E increases indefinitely, with E proportional to adult stock weight and prerecruit mortality rates a linear function of the density of young fish. Since E is related to biomass, fecundity and pre-recruitment mortality can be substituted for the recruitment terms in the yield equation. To test whether a regulated fishery is behaving as expected, a model is derived relating variations in R and annual yield. Other possible types of relationship between R and E are considered more briefly. Capture and natural death: Variations with age in both natural (M) and fishing (F) mortality are considered; M in relation to stock density, F to mesh selection and ability to avoid the net. Methods are developed for dealing with seasonal variation in fishing intensity and with "transitional" periods between periods of steady state. The lack of uniformity in the spatial distribution of fish and fishing effort, involving an analysis of the movements within the exploited area is investigated. Growth: Even though growth is variable, von Bertalanffy's equation remains the most suitable formulation. Methods are discussed Df considering variations in growth with age, between individual fish, and due to dependence on food consumption. The latter is treated mainly by an analysis of the interaction between the fish population and its food supply, including the dynamics of the latter. Equations are derived for actual and maximal food consumption of a fish population in terms of its abundance, age-composition, and growth rate. Consideration of the effects introduced by predation on 2 or more food species lead to a review of methods of reporting food preference and vulnerability. Methods developed for populations of single species are extended to fisheries based on several species caught together by the same gear. III. Estimation of parameters for North Sea plaice and haddock stocks. A basic unit of standardized fishing effort of a steam trawler ton-hour is suggested, and the same per square mile as an index of density. Estimates of the total fishing mortality coefficient (F+M), made from catch per unit of effort and age-composition data were 0.83 for plaice and 1.2 for haddock during the inter-war period. Methods of obtaining separate estimates of F and M from marking experiments are discussed; 2 earlier methods are found to be erroneous and a simple method of estimating F, clear of rate of shedding of marks and other errors is given. An average value of F of 1.5 for plaice was obtained for the most heavily fished portions of the southern North Sea during the post-war period. The magnitudes of dispersion to other areas, and of shedding rates prevented any estimate of M. In considering the variation in F with age as a result of mesh selection, a close proportional relation between the 50% selection point and mesh size was found, the factor being 2.2 for plaice and 3.3 for haddock. Separate estimates of F and M from age-composition and effort data were not possible. However, data on the abundance of certain year-classes sampled both in 1938-39 and 1945-46 yielded an estimate of M of 0.1 for plaice in the prewar period. F was thus 0.73. Although no accurate estimate of M for haddock is available, certain age-composition data suggest it is not much greater than 0.2. F for the pre-war period was thus 1.0. In North Sea plaice, recruitment (R) occurs by an off-shore movement, following the law of random diffusion at a rate of about 1 mile a day. About 90% of the recruits are in age-groups IE and IV, the average age being 3.7 years. In the earlier war period average R was 250 million plaice and 850 million haddock. The fishable stock of plaice averaged 350 million. While there is some indication of a relation between egg-production and recruitment in haddock, in plaice results are inconclusive. A review of this relationship in certain other species is also given. In growth equations, the simple cube length-weight relationship appears in plaice and haddock; an allometric expression is not recommended. Von Bertalanffy's equation is fitted to data for plaice, haddock, cod and sole. In plaice and haddock, an empirical relation between growth and population density is found, derived from data referring in the former to steady states, in the latter to annual fluctuations. The dependence of growth on feeding and food supply is examined in plaice only. Maintenance food requirements are almost exactly proportional to the two-thirds power of body weight; the efficiency of utilization 9f Mytilus flesh for growth is about 0.2. An analysis of the variation of utilization efficiency with amount of food eaten showed that the limiting growth parameter (Wimage l) is in order of magnitude some 5 or 6 times Wimage for North Sea plaice. IV. The properties of various theoretical models and conclusions drawn therefrom. The simple models show that a greater steady state yield of plaice and haddock than in the prewar period could be obtained with either a lower fishing intensity (affecting F) or a larger mesh size (affecting the age, tpimage at which the fish enter the exploited phase). An even greater yield would result by adjustment of both F and tpimage than by either alone. Variation of population biomass, numbers, average size and age of fish in the catch with F and tpimage are examined. Relatively small differences in plaice yield occur with changes in maximum age, except at low values of F, and with M within 50% of its estimated value (0.1). In the more complex models, the more exact representation of some properties, e.g. mesh selection and recruitment, produce little difference in the yield curves when compared to simpler approximations. Variation with population density can cause important differences. When M increases linearily with density, yield curves have lower maxima, located closer to prewar values of F and iff than with M constant. When the dynamics of food populations are introduced, yield curves resemble those obtained with a linear relationship, thus indicating that the latter is likely to give reasonably satisfactory assessments of the effects of density dependent growth. Where recruitment depends on stock size, both recruitment and growth should be simultaneously density dependent. Changes in recruitment can then still outweigh those in growth, causing yield curves to have higher maxima than if all factors were density independent. Yield curves are little affected if fishing is restricted to not less than three-quarters of the stock area. With further reductions, the maxima become less marked and occur at higher values of F as in a coastal fishery where the main bulk of the population is unfished but acts as a reserve. In general, when complex changes in the primary factors are considered, the actual changes in fishing intensity and especially in mesh size required to produce a larger steady yield are not as great as would be predicted from simple models. In a discussion of the general principles and methods of fishery regulation, the concept is developed of eumetric fishing - the achievment, by adjustment of gear selectivity, of the greatest yield possible with any particular amount of fishing. Yield increases with increasing fishing intensity but at a decreasing rate and without passing through a maximum. When these assumptions apply, the conventional idea of adjusting the amount of fishing to obtain the maximum steady state yield must be abandoned. The decision as to which point on a eumetric yield curve a fishery is to operate is economic and social, depending on how much of the maximum potential profit is to be realized as such and how the remainder is to be absorbed. To obtain the benefits of gear selectivity some control of fishing power is essential. The greatest yield of demersal fish from the North Sea, compatible with avoiding any serious loss of sole or whiting, would be obtained with a fishing effort not more than half, and perhaps less, of the pre-war effort, and a mesh size of 80 to 90 mm. The increase in yield could be 25 to 50%. The proposals of the 1946 Overfishing Conference to reduce overall fishing effort to 85% of the pre-war level and to increase mesh size to 80 mm may result in an increase of 6 to 10% in the total landings of the 4 major North Sea trawl fisheries. ABSTRACT AUTHORS: F. H. C. Taylor