Stock Assessment Methods
Fisheries stock assessment involves two main tasks:
- Estimating how many fish there are, and
- Forecasting how many there will be in the future
These tasks might seem simple enough, but there are three major confounding factors. Firstly, the fish in the sea cannot be seen directly. Secondly, fish move about, looking for food or places to spawn eggs. And thirdly, the number of young fish that a stock produces varies enormously from year to year.
Estimating Population Size
The complexity of estimation can be described by analogy. Suppose you are in a hot-air balloon, flying high over a land completely hidden by a thick layer of cloud. You have been asked to write a report on this land - what lives there, how many of each species there are, how they reproduce, and how the populations might change in the future - and you have been given a basket and a long rope. You scrape the basket along the ground for half-an-hour or so, haul it up, and have a look at the contents.
Inevitably, your sample will be unrepresentative - you will have missed large swathes of land, you might be scraping at a time of year when many species are hiding in holes, and you will have missed the land's teeming bird population altogether. What this demonstrates is that our ability to estimate the abundance of any particular type of animal is reduced by the fact that they can't be seen, and by the tools available to sample them.
Fish stock assessments are also complicated by the biology and behaviour of the fish themselves. Forestry scientists tell us that their estimates of the number of trees in a wood are accurate to within 20%. So if a forester tells you that there are 1,000 trees in a wood, the real number will be between 800 and 1,200 trees. However, the forester's task is easier - trees are stationary, and tree reproduction is limited more by space than anything else. It is more difficult to estimate fish numbers; when fish can move quickly from place to place, and the numbers of young fish are determined by a whole range of factors from the numbers of adult fish, to the numbers of predators or prey there are, to the way the wind was blowing on a particular day.
These are some of the challenges that stock assessment scientists face. We are not in quite the same position as the balloonist. Although we know a lot about the biology of the fish - for instance, a species may only spawn in a few areas, or may be dependent on another species for food, or the way a group of fish grows throughout its life might be determined by what happened when they were eggs- we still lack a lot of information (even though fishermen can tell us a great deal about the fish, both in terms of what they land for market (landings) and what they don't ( discards).Therefore the only way we can make sensible estimates is by using mathematical and statistical models.
The Mathematical Approach
The model most often used to assess commercially-important fish stocks in European waters is known as virtual population analysis (VPA). In this model, records of the number of fish landed are used to estimate a 'virtual' population - that is, how many fish there were in the first place. Suppose we need to estimate the number of fish in a stock in which the oldest fish normally seen are 10 years old. From landings records, we get information about the numbers and ages of fish landed in any one year. We arrange the data as shown below, with rows marking ages and columns marking years, like this:
What the Table Shows
The table shows the numbers of fish landed in each year which belonged to the 1992 cohort, that is, fish which were born in 1992, aged 1 in 1993, 2 in 1994, and so on. Notice that the size of a cohort can only ever decrease with time - the cohort never gets new members.
The task is to work out how many fish there were in the cohort, given how many were landed. The simplest way to do this is to add up the numbers in each diagonal, add a bit to account for discarding and deaths by natural causes, and thus arrive at an estimate of the total numbers in the cohort. However, it will not necessarily be a very good estimate.
The amount of fish discarded each year is 'noisy' - that is, the estimate is not very accurate. The same goes for the amount of fish dying from natural causes. The numbers in an old cohort (for example, the 1992 cohort in the table above) are easier to estimate than the numbers in a more recent cohort (for example, the 2000 cohort), because that cohort has appeared more often in landings records, and we know more about how their numbers are declining. Landings records can give an over-optimistic picture of the state of the stock because fishermen are good at finding fish even when there are not many left.
For these reasons, we need to use additional information, and often more complicated models. For example, data from research-vessel surveys can be built into the VPA, a process known as tuning. Survey data can also be used on their own to give an idea of stock trends (that is, whether numbers are going up or down), although estimating actual abundance in this way is difficult (survey-based assessments).
Rather than looking at one cohort at a time, we can model all cohorts at once in a separable model. If the stock fluctuates in a characteristic way, we can use this fluctuation to refine our estimates (time-series analysis). Our knowledge of what affects growth and reproduction can also be used to improve the assessment. The nature of the problem will always mean that the estimates are uncertain to a greater or lesser degree, with the most recent years being the most uncertain. But uncertainty is not a problem in itself, so long as it is acknowledged when fisheries managers come to make their decisions.
Forecasting Future Population Size
The second part of the assessment scientist's task is to predict how many fish there will be in the stock over the next two to three years (the short-term forecast) and 10 years (the medium-term forecast). This is important for fisheries management, both for setting the next year's quotas, and for evaluating longer-term strategic goals.
The short-term forecast depends mostly on our estimates of abundance in the current year, and what we expect to happen in the fishing fleet. We may also have information from research-vessel surveys on eggs and larvae, which we can use to help predict how many young fish might be joining the adult population in the next couple of years (recruitment). This doesn't help us much in the medium-term forecast, which is heavily based on mathematical models of recruitment.
Why are Forecasts Valuable?
The real value of forecasts is that they allow us to say what range of things are likely to happen if, for example, fishing mortality is cut by 50%, or increased by 25%. This valuable, but uncertain, science is the subject of current research.
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