The Unit Stock
Stock assessment calculations begin at the Unit Stock level; i.e., they consider distinct and separate population units of a single species from which the fisheries yield is, or could be, extracted. A unit stock is more correctly viewed as a self-reproducing population, with limited emigration/immigration to/from other unit stocks. In the case of mobile and migratory stocks which may diffuse or migrate across maritime boundaries, we must include removals from the stock taken from inside all jurisdictions in the initial assessment, since the estimation from the fishery statistics of any single country, of whether an overall RP for fishery yield or standard fishing effort/mortality has been met, is likely to be seriously biased if it is based on incomplete coverage. Also, if a significant component of the catch and effort is not included due to misreporting or non-reporting, this also will result in a high probability that the perceived position of the fishery in relation to the reference point chosen, will be seriously in error.
Global and analytical models and stock-recruit relationships
It is necessary to make a distinction between production models, where we only have two trains of annual information; fishing effort and total yield, and where generalizations can be made as to the overall behaviour of the population, but all biological processes going on within it are unknown; and so-called Analytical models, where processes of growth, reproduction and death, subscripted by age, are assumed to be understood and the relevant rates at which they occur are known. The many variants of yield/recruit analyses belong here. Combinations of these two types of models have emerged in recent years, but few applications in practical fishery management have emerged so far. A further type of model that is largely empirical, relates the number of recruits that occur in a year to the spawning stock size (Fig. 4). All of these methodological approaches have generated their own model-based management reference points.
The catch equations
The single species theory of fish population dynamics is based on the so-called “catch equations”, which postulate mathematical relationships between:
a) the stock (represented as total numbers of individuals in those age groups available to fishing (the recruited age groups),
b) the fishing effort (f) and corresponding fishing mortality (F) it causes, and:
c) the yield in numbers and/or weight resulting from this operation, given that
d) in addition to fishing, a natural death rate (M) applies, which is the rate at which the stock is being diminished by deaths caused by factors other than fishing; (notably predation).
e) Various aspects of the natural history of the species are also pertinent to its capacity to support exploitation.
Two of the most commonly used catch equations are those below, respectively used where the age composition is known (and the subscript t refers to the age of a group of fish), and for the mean population biomass undifferentiated by age, as following the second = sign:
Both equations contain three interdependent variables (see fig 1) which are the primary variables available for consideration as possible Reference Points for fisheries management. These are the fishing mortality F (related to the total (usually annual) fishing effort as F = qf, (where q is the catchability coefficient); the Biomass B, and the fishery yield (usually annual) Y. Since fish stock assessment assigns a primary role to fishing as a cause of mortality, the primary ‘control variable’ is of course the control of fishing effort and/or fishing mortality, while catch, catch rate and biomass may under specified conditions of stability and equilibrium, be used as measures of the effects of fishing, and/or measures used to indirectly control fishing mortality.
Control of fishing intensity may imply control of the number of vessels of a given type or power allowed in the fishery, and even of the maximum number of standard days fishing allowed. However, for reasons described below, access rights in terms of fleet size and total annual fishing effort have in the past been rarely used directly in negotiations, and has been assumed to be less easily monitored than a fixed catch or quota. Control of the annual yield (despite technical disadvantages at least equal in magnitude), has been the most widely used management practice; perhaps also because it reflects more directly the benefits to be gained by different participants in the fishery. In some fisheries, equivalent benchmarks of economic performance have been calculated; particularly for national fisheries where common measures of economic performance apply. In other circumstances where the levels of total removals, total fishing effort and net economic benefits are difficult to determine, but direct survey of the stock is possible, measures based on controlling the biomass of the stock may be more feasible and not liable to biases due to misreporting.