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Assessment. -... appraisal, appraisement, estimate, estimation, evaluation, judgment, valuation. See Roget s II: The New Thesaurus, Third Edition. 1995.
In our last article we introduced you to the concept of stock assessment for the first time. We explained that unlike any kind of stock assessment in the retail, farming or nature conservation industries, the stock assessment of marine resources is and always will be very much an approximate science. This is due to the fact that it is virtually impossible to undertake a complete census of fish in an open marine system. In our previous article we divided stock assessment methods into two general types. The first was defined as direct assessment methods such as tagging, fishing trials and fishing surveys.
Fishing survey are either based on swept area techniques or hydroacoustics. The size of a fish stock can be crudely but directly derived from such techniques. These kinds of assessment methods are very imprecise and subject to considerable statistical noise, primary because the sample size is often very small. However, they do produce a direct estimate of resource biomass using a fairly simple conversion of the raw data from the surveys, although certain parameters used for this conversion are likely to be a matter for debate.
The second kind of stock assessment is known as an indirect stock assessment approach. It involves a comprehensive analysis of the fishery which uses all the available information, catch statistics and scientific surveys and data, to assess what the historical levels of population size and production have been and to make recommendations on harvest levels for the future. Typical input data from commercial fishing operation might be annual commercial catches, average commercial catch rates and the size or age structure and sex ratio of catches. Typical input biological data would be fish growth rates and fecundity levels at different ages. More often than not of course, certain essential biological data is not available.
In general, direct stock assessment methods, although subject to high variance and hence uncertainty, are regarded as a cornerstone of fisheries management, because they at least provide unbiased estimates of trends in resource size. Indirect methods are however susceptible to bias, being as they are heavily dependent on a range of subjective elements. In the indirect stock assessment approach a mathematical model of the underlying fish population forms the basis of the estimation procedure.
This analytical tool is often referred to as a stock assessment model. Stock assessment models are basically numerical simulations of the dynamics of fish populations. Such models are almost always only used in conjunction with a computer because they are either too complex or too tedious to calculate by other means (paper and pencil, abacus?) and in reality it has only been since the advent of modern computers that this kind of research has become possible.
Since we normally do not have all the empirical information about the dynamics of a fish population, the model is used to in a sense “fill in” the gaps in our knowledge. An example of this is that whereas the input information is catch and catch rate, output information may include the trends in the biomass of different age classes in the population. Such model estimated values are often referred to as “model fitted” and should not be confused with the input data which are obtained from independent empirical work. A serious criticism of model based stock assessments is that although these models need to be mathematically consistent they need not be biologically sensible in order to function.
Also many of these models can be run with very little empirical information. Real data are typically replaced by assumptions or by model fitted values. In extreme cases certain assessment model become “indifferent” to trends in observed data and their assessment output is almost solely driven by model assumptions and assumed input data. In South Africa, for example, the stock assessment model used for the West coast Rock Lobster (Jasus lalandii) is decisively sensitive to the growth rate assumptions that are made for an historic period for which there are no growth rate data at all.
In the next few months we will try to introduce you to the logic rather than to the numerical techniques which underlie a variety of commonly used stock assessment methods. It seems appropriate that the very first method to be presented is one of the oldest methods, probably mainly because it could be implemented without the use of modern computers. It goes by the name of VPA which is short for Virtual Population Analysis.
VPA is a method of calculating past resource sizes on the basis of historic catches broken down into different age classes. The only reason that a more detailed description of this analysis is given here is because it is probably the only type of analysis that can be set out in a simple enough form for the casual reader. There is not really a need to understand the actual mechanism of this analysis, but rather to appreciate the assumptions upon which it is based. All other methods employed in indirect stock assessment make similar kinds of assumptions, and despite their sophistication, they are ultimately judged in terms of the validity of the base assumptions.
The table shows the catches in millions of fish that were harvested from a single cohort of a hypothetical fish population born in 1983. By guessing the ratio between the number of individual fish in the catch and in the cohort at the last recorded age, i.e. aged 8 years in 1991, one can calculate the cohort numbers for that age. In the table the guess is 0.30, therefore the cohort numbers are 10.0. In VPA, the number of individuals in the cohort one year earlier can then be calculated by adding on the number caught the previous year, and increasing the result to allow for a certain percentage of natural mortality.
In the example in the table, it is assumed that the natural survivorship level in the population is 60% per year (i.e. 40% natural mortality). In this calculation, the natural mortality adjustment for the cohort numbers is 1/0.6, but for the catch it is because the catch is assumed to be taken in the middle of the year. Repeating this process for each previous year leads to a complete estimate of cohort numbers since their date of birth, as shown in the table. As you can imagine, an appropriate choice of the value for natural mortality has bedevilled the work of fisheries scientists and managers for many decades. An important property of VPAs is that the errors in the estimates of cohort numbers reduce going back in time, hence whereas estimates of recruitment levels and trends may have some validity, the terminal cohort numbers are suspect.
Table: For an hypothetical fishery, an illustration of the VPA calculation procedure. The last column shows the inferred cohort numbers based on a guess at the number of 8-year olds present in 1991. Year Age Catch in middle of the year (millions) Cohort number (millions) at the beginning of the year
- 1991 8 3 Guess: 10.0
- 1990 7 7 10.0/0.60+7/SQRT(0.60) = 25.7
- 1989 6 19 25.7/0.60+19/SQRT(0.60) = 67.4
- 1988 5 17 67.4/0.60+17/SQRT(0.60) = 134.28
- 1987 4 21 134.28/0.60+21/SQRT(0.60) = 250.91
- 1986 3 123 250.91/0.60+123/SQRT(0.60) = 576.98
- 1985 2 59 576.98/0.60+59/SQRT(0.60) = 1037.80
- 1984 1 40 1037.80/0.60+40/SQRT(0.60) = 1781.30
- 1983 0 23 1781.30/0.60+23/SQRT(0.60) = 2998.53
By duplicating the above calculation for all cohorts that appear in the catch, one can build up a complete picture of the historic population size. By using fishing effort data, one can refine the method for guessing the "terminal" cohort number, so that the final population size estimates are more objective and more reliable. This information can then be used to deduce the MSY in the resource.
A weakness of this method is that it relies heavily on an assumed value of natural mortality (i.e. in most cases an educated guess). If fishing effort is not incorporated to make the "guesses" of the "terminal" cohort numbers more reliable, then, as is now recognised in most management bodies around the world, the results of VPA calculations are very unreliable. This is particularly the case for short lived species like anchovies and pilchards, and so VPA methods for these resources can only be applied if auxiliary information like fishing effort data, or the results of fishing surveys are included in the calculation procedure.
VPA is being used less and less nowadays because advances in computer hardware and software has made it possible to utilize much more complex cohort based analyses. The most common of these are the age and size structure production models where additional effects are permitted, including for example, the relationship between recruitment and spawning biomass, and age dependent natural mortality. We will give you a flavour of these models in forthcoming articles.