The practical fisheries biologist collects data to answer two main questions: ‘how much fish is there in the area that it is intended to fish?’ and ‘what is the maximum amount which can be caught annually without affecting the ability of the stock to produce that yield?’. Incidentally he may satisfy his scientific curiosity about the biology of the fish he studies or the environment in which they live, but he should never lose sight of his main objective, to answer these two questions.

So far, the sections of this manual have been concerned with what data to collect and the best ways of collecting them. In this section the uses to which the data are put will be described.

There are two ways of approaching this problem; one is to determine the total quantity of fish present in absolute terms, that is, the question is answered in terms of either total weight (3 million tons) or total numbers (60 million fish); the other is to answer it in relative terms, that is, the question is answered in terms of tons of fish caught in an hour's fishing. Reviews of methods of resource appraisal are given by Alverson (1971) and Mackett (1973).

This method is based on the fact that if T individuals are marked or tagged in a total
population of N individuals, the probability that an individual will be marked in a random
sample from the population is T/N. If n specimens are caught and m of these are found to be
marked then the number of fish in the population is N = nT/m. Putting this in practical
terms, assume that 3,000 fish had been tagged during an experiment (T = 3,000) and that in
the 12 months following their release 3 million fish of this species had been landed from
the stock into which these had been tagged (n = 3 x 10^{6}). This number would be calculated
from the market sampling programme (sections 2 and 3); from theselandings the fishermen had
returned 750 tagged fish (= m). Then an estimate of the number of fish of marketable size
in the stock (N) would be nT/m = 3,000,000 x 3,000/750 = 12 million fish.

Several assumptions are made in this calculation which are:

(a) tagged and untagged fish are evenly mixed (which would be improbable from a normal tagging experiment);

(b) the mortality rates or the emigration rates or both of tagged and untagged fish are the same;

(c) tagged and untagged fish are equally liable to capture by the gear;

(d) there is no mortality caused by tagging, no tag shedding and that all tagged fish are returned.

Even if all the conditions are fulfilled the estimate of N obtained is biased. A better method involves multiple captures and recaptures, giving the following formula (from Cormack, 1968):

i = Z_{i} = (S_{i}/r_{i}) + Mi

in which i = estimated number of individuals marked at time t_{i}

Z_{i} = number of fish marked before t_{i} not caught at t_{i}
but recaptured on later occasions

S_{i} = number of fish marked at time t_{i}

r_{i} = number of fish, S_{i}, recaptured on later occasions

M_{i} = number of marked fish at start of time t_{i}

then = (n_{i}/m_{i}). _{i}

in which _{i} = number of fish in population at time t_{i}

n_{i} = number of fish caught at time t_{i}

The method is still dependent upon assumptions a-b being valid. Marking and recapture methods have their potentially most useful application in small, enclosed bodies of water such as ponds and small lakes, but even in small pools it may be very difficult to obtain reliable estimates of population size (see Holden, 1963).

Some fishing gears such as trawls and seines sweep a volume of water. This volume can
be calculated approximately from the dimensions of the gear. If it is assumed that the
gear catches all the fish in its path a minimum estimate of the number of fish can be determined
if the volume of sea the stock inhabits is known. This method is a minimum estimate
because it assumes that all the fish in the path of the gear are caught, which is unlikely.
For pelagic trawls avoidance can be either so either so great or so effectively eliminated by aimed
fishing that the method has its main application to gears hauled along the seabed. The
calculations are made in terms of area. Say 1,000 trawl hauled were made in a random manner
over 100,000 square miles of seabed inhabitated by a stock. Assume that each trawl haul
swept 0.5 square miles of seabed and that the average catch was 60 fish. In sweeping 500
square miles of seabed (1,000 hauls x 0.5 square miles) 60,000 fish were caught (60 fish x
1,000 hauls). So in 100,000 square miles the estimated number of fish is 60,000 x 100,000/
500 = 12 x 10^{6} fish. This method can be very useful in giving a first estimate of the
quantity of fish which is present.

The use of egg and larval surveys to estimate stock numbers has already been described in section 7.3.3. The method can be very useful for fish with pelagic eggs, if those eggs can be readily identified either to species or species groups.

Simple echo-sounders will give some idea of the abundance of fish but echo-sounders used with integrators give very good estimates of fish abundance, particularly of pelagic species. The methods are described in detail by Forbes and Nakken (1972).

Simply, echo-sounders work by sending a sound wave into the water. If this sound wave hits an object which will reflect it part of this sound wave is reflected back, the amount depending upon the type of object and its depth. When it is received back by the transducer of the echo-sounder it is converted into an electrical current which is which is then used to operate a display. Integrators work by adding the voltages of the returned electrical current and displaying the response on a calibrated chart. They also make allowance for the object's depth so that a sound wave reflected from a fish at 50 m will give the same amount of record as one at 10 m. Fish of different species and size give different responses but once the equipment has been calibrated for the species being surveyed the absolute quantity of fish can be determine from the integrated record. Regular fishing has to take place during the survey to determine what species are responsible for the record, unless it is known that only one species inhabits the area or unless a multi-species assessment is acceptable.

This is a technique which can be used if most of the stock is caught and the age structure of the catch is fairly accurately known. In this method the results obtained from market sampling and age determination programmes are used.

By making two assumptions, one about the natural mortality rate and the other about the fishing mortality rate on the oldest age-group in each year-class it is possible to calculate by a reiterative process the numbers of fish in each age-group in the stock. The method works by considering each year-class separately and calculating the size of that year-class at the beginning of each year and the fishing mortality acting on it throughout that year. The estimates of these two parameters get increasingly more accurate as the calculation proceeds from the oldest to the youngest fish in a year-class. The accuracy of the first two or three estimates depends upon the correctness of the initial value of the fishing mortality rate. Full details of this method are given by Fry (1957), Gulland (1965) and Pope (1972).

Relative methods are based on some form of catch per-unit-effort index, calculated from either commercial or research vessel information. They are relative because they indicate only what is happening to the abundance of the stock and not its actual total size; abundance is usually measured as catch per-unit-effort.

The calculation of commercial indices of catch per-unit-effort has been given in section 2 in which methods of collecting catch and fishing effort data were described and the importance stressed of collecting effort data which give a meaningful index of fish. The lastnamed point is most important, particularly as the efficiency of vessels changes or as completely new types of fishing are introduced.

Catch per-unit-effort is used in many ways. Firstly it can be used to describe changes in the abundance of the stock from year to year. Used with total catch data it can be used to describe a simple model from which the long-term sustainable yield from a stock can be calculated (Gulland, 1969). It is also used in calculating total mortality rates from the numbers in successive age-groups of a year-class landed in two subsequent years. For example, 1,000 fish aged 5 years might be landed one year and 500 fish aged 6 years the next year. As these are total catch figures they give no indication of the abundance of this year-class in the two years. However, if fishing effort in the second year was twice that in the first the relative abundance was 1,000 : 250 (1,000/1:500/2). The survival from one year to the next of this particular year-class was 0.25.

One of the difficulties of commercial indices of abundance has already been mentioned which is that the efficiency of the boats changes from year to year. Another is that there is no control over where the fleet fishes. In a fishery for two or more species the fleet will concentrate on that species which gives it the best financial returns and this is likely to alter both seasonally and annually. To some extent the problem can be overcome by using indices calculated for those periods during which both the stock and the fishery is concentrated; for example, during the spawning season.

Research vessel surveys overcome these problems to a large extent and also can be planned
so that the standard deviation of the answers can be calculated. A commercial index may
show that the catch per-unit-effort has fallen from 5 to 4 tons per hour's fishing but it is
not possible to say from this that the abundance has fallen by 20 percent. However, a research
vessel survey might show that it has gone down from 5^{±} 0.2 tons to 4^{±} 0.25 tons/per
hour's fishing. The 95 percent confidence limits are approximately twice the standard deviation
(section 2.3.3) so it is 95 percent certain that the catch per-unit-effort has fallen
from between 5.4 and 4.6 tons to between 4.5 tons and 3.5 tons per hour's fishing. It is
95 percent certain that there has been a real fall in abundance.

To obtain results with a known standard deviation it is necessary to base the surveys on the use of statistical techniques. Jones and Pope (1973) describe a survey of Farce Bank in which they divided the area as shown in Fig. 9.1. This is an example of stratified sampling (section 2.4). In each stratum they laid a grid of potential stations and then selected two at random (see section 2 … for the use of random numbers). They also stratified fishing by time intervals so that they could consider the effects of diurnal variations in abundance. (Methods of fishery resource survey and appraisal are given by Alverson (1971) and Mackett (1973).

The first that are caught are unlikely to be a true sample of the population and the landings of a commercial fishing vessel even less likely to be because a certain amount of sorting and discarding will have taken place at sea. This can be checked upon during interviews to obtain catch, fishing effort and fishing ground information (section 2.10). More importantly the catch will depend upon the selectivity of the gear and how it is rigged.

Most gears do not catch a random sample of all the fish present; they ‘select’ either big fish or small fish.

One of the best studied cases of selectivity is that of trawl cod-ends. For a given mesh size in the cod-end all the small fish will pass through and all the large fish will be retained but somewhere in the middle of this range there will be a length range in which some of the fish of a certain size are caught, because they are too fat to pass through the meshes but others of the same size get through because they are sufficiently thin. If the proportion retained at each length is plotted against length a sigmoid curve results (Fig. 9.2a). The important feature of this curve is the point length at which half the fish are retained and half escape, the 50 percent selection length. This, divided by the mean mesh size of the cod-end, gives the selection factor. (The mesh size is measured with a special spring-loaded gauge). Further details of trawl selectivity and methods of studying it are given by Pope (1966). Holden (1973) gives a complete bibliography of references.

Once the selectivity curve is known correction can be made for the fish in the length range retained by the cod-end; that is, if 50 fish were retained in the length range for which selectivity was 0.25, 200 fish actually entered the cod-end (50/0.25 = 200).

For gill nets the selectivity increases to a maximum, as for cod-ends, but then declines to zero as the fish become too big to be retained by the gear (Fig. 9.2b). Methods of studying gill net selectivity and for correcting catch-data obtained with gill nets are given by Holt (1963).

Hook selectivity also occurs; in general hooks take proportionately more large than small fish. This has not been studied in detail and, as yet, there is no standard method of correcting catch data for it.

Besides mesh selection gear selection for both species and size is often found. That different gears are not equally effective in catching different species might be expected. When trawlers have fished on the same grounds as Danish seiners, the species' composition of the catches has been very different. From experimental results Margetts (1949) estimated that over a standard 24-hour period a Danish seiner caught 2.8 times as many plaice as a trawler; the trawlers caught relatively far more soles, anglers' fish, turbot, and brill than did the seiner. It was also estimated that the area of seabed fished by the seiner, taken as the area swept by warps and net, was about 3 times that covered by the trawl. Thus, the efficiencies of the two gears, as judged by their abilities to catch so many fish per unit of ground, were approximately the same on plaice but the trawl was more efficient for catching species such as sole.

Minor differences between gear may also cause differences in efficiency. The majority of cod-end mesh selection experiments have shown that larger meshes catch more fish of lengths beyond the 100 percent retention point. Table 9.1 gives the ratio of the total catches of plaice obtained for equal fishing times by two trawls with different mesh size in the cod-end. In theory the ratios should not exceed 1.0. The discrepancy may result from different water flows through the cod-ends.

Length cm | Ratio of catch in No. per hour |

19.5 | .01 |

20.5 | .03 |

21.5 | .03 |

22.5 | .04 |

23.5 | .06 |

24.5 | .05 |

25.5 | .11 |

26.5 | .12 |

27.5 | .15 |

28.5 | .32 |

29.5 | .42 |

30.5 | .96 |

31.5 | .78 |

32.5 | .86 |

33.5 | .82 |

34.5 | 1.13 |

35.5 | 1.09 |

36.5 | 1.13 |

37.5 | 1.20 |

38.5 | .85 |

39.5 | 1.17 |

40.5 | 2.00 |

41.5 | .50 |

42.5 | 2.33 |

43.5 | 1.13 |

44.5 | .50 |

45.5 | .80 |

46.5 | 4.00 |

47.5 | 1.00 |

48.5 | 1.50 |

(from Beverton and Holt 1957) |

Catch data obtained during a comparison between the two British research vessels SIR LANCELOT and EXPLORER showed that SIR LANCELOT caught fewer small haddock, but more large haddock than did EXPLORER (EXPLORER caught 1,262 haddock of length 31–44 cm, 61 haddock of length 45–56 cm compared with 406 and 88 haddock in the same groups in SIR LANCELOT's catches). The trawls were fitted with cod-ends of approximately the same mesh size but they had different numbers of floats and different bridles. Later, by means of underwater photography of the trawls, the fishing shape of both of them was determined. EXPLORER's net had a wide-spread but a small vertical gape and SIR LANCELOT's had a relatively small-spread but a much higher vertical gape. This suggests that SIR LANCELOT's trawl caught more big haddock because they were swimming rather higher off the bottom than the smaller ones.

All sections of a gill net are not equally as efficient at catching fish as shown by the catches of salmon in relation to their distance from the leadline of the net (Table 9.2). This point was also mentioned in Appendix 2; Sampling an African lake fishery.

Table 9.2. | Relationship between number of salmon caught per 1,000 gill nets in the Baltic and the distance between upper rim of net and sea surface |

Distancecm | Numberof salmon |

5–10 | 158 |

15–20 | 136 |

30 | 68 |

40 | 50 |

(from Christensen 1970) |

Catchability of a species may change as behaviour alters with age. Sprat (__Sprattus
sprattus__ (L.)) in the Wash, southern North Sea, form two distinct layers of vertical distribution,
an upper layer of two-year-olds and a lower one of three-year-olds. Commercially
the sprats are caught by mid-water trawls but as the fishermen do not like to tow them too
deeply in this area of sandbanks, their catches consist mainly of two-year-olds. In this
case the catch per hour's trawling is a quite unreliable measure of abundance of three-year-olds
(Cushing, 1968).

Catchability can also change from one season to another. Adult __Sardinella__ __aurita__ are
caught pelagically in inshore waters during the upwelling season only. The rest of the year
they are probably below the thermocline in deeper waters. The best index of abundance in
this case would be the catch per-unit-effort at the height of the fishing season.

For __Sardinella__, it is evident that an index of abundance from the main season in one
year cannot be compared with an index from the off-season in another year. It is a general
rule that this should not be done; indices from the same season or means for the whole year
are preferable.

The effect of diurnal changes has already been noted in section 9.2.2.2.

This sub-section has dealt with the question of how many fish are present. Not only have methods of determining this been described but also the biases inherent in the sampling methods used. The results from these methods also give the answers to what species are present and to when and where they are available for capture. In a developing fishery the determination of the available species' composition will decide not only the best methods of capture but also the outlets for the product. When the fish are available is also of vital importance; a single survey conducted during a period when the fish were maximally available would lead to a totally false conclusion about the viability of a potential fishery. Where the fish are available also determines choice of gear and fishing units. This is the period of ‘Prospection’; now we turn to ‘Stock Assessment’ (Fig. 1.1).

Population dynamics is the study of the effect of fishing upon fish. The vast majority of fisheries take place on wild stocks over whose reproduction, growth and natural mortality man has no control whatsoever. The only way in which he can predictably affect these stocks is by the pattern of fishing which he adopts, although he may also affect the other three factors in an unpredictable manner.

When a man wants to predict the effects of his interference with a system, he must construct a mathematical model of it. The number of factors influencing such a system is very high and in the beginning it is necessary to simplify the model by leaving out many factors and concentrate on those of most interest. Even if the model is very simple and even if it is very soon found not to describe the system very well, it can be quite useful to the scientist by helping him to understand the dynamics of the system better. Only by constructing and using a model will he be able to ask meaningful questions and to collect the data of most use to him at the moment. (see also section 2).

Russell (1931) was one of the first to express the factors which affect the size of a fish stock by his formula:

S_{2} = S_{1} = (A+C) - (C+M)

in which S_{1} = the size of the stock at the beginning of the year

S_{2} = the size of the stock at the end of the year

A = recruitment

G = growth

C = catch

M = deaths due to natural causes.

If the stock is to be in equilibrium (S_{2} = S_{1}), then A + C = C + M or C = A + G - M.
This is a very simple way of considering the factors which govern stock size but the formula
cannot be used as it stands and in the past forty years fishery biologists have described
various models to express the terms in the equation by means of parameters which can be determined
from observations. How to obtain these observations is the subject of this manual.
Additionally, he has set out to determine the effect of changes in that parameter which is
potentially within man's power to control, namely the amount of fishing activity. In the
simple case it is __assumed__ that the number of recruits, the growth rate of an individual fish
and the chance of survival of an individual are unaffected by the density of the stock; in
other words, they are the same whether the catch is zero or very large.

From determinations of age, length and weight, mean lengths and weights at age can be found: these are all end products of the sampling systems described in sections, 2, 3 and 4. From these a model can be constructed to express either length or weight as a function of age; the weight function is curve A in Fig. 9.3. Similarly, from age determinations and from catch in numbers per-unit-effort the relative density can be found for a year-class at different occasions during its life and a model constructed to express the numbers of the species as a function of time. This function is shown as Curve B in Fig. 9.2. The product of the number present at a certain age and the mean weight at that age gives the biomass at that moment (Curve C, Fig. 9.3). The Curve C has a maximum and to get the maximum catch the year-class should be fished out at that age. In practice this is impossible as it requires an infinitely great effort during a short period and no fishing for the rest of the year. Also, year-classes are mixed and it is impossible to fish them singly. This simple model is insufficient; for economic reasons the effort must be distributed throughout the year and thus start taking its toll before the maximum biomass is reached and continue after the decline has begun. The fishery is also carried out on more than one year-class at a time and the model must be extended to take this into account.

Graham (1939) described Curve B (Fig. 9.3) in a very simple way, by taking an initial number of fish say 1,000, and calculating the survivors after a year for a given total mortality rate, say 50 percent a year. At the end of the first year there would be 500 survivors, at the end of the second 250, at the end of the third 125 and so on. The decline is termed ‘exponential’ and can be more easily calculated using exponential functions, those based on power of the constant e. (The determination and use of this constant is described in most books on calculus). However, this is a tedious method of calculating the effect of fishing and eventually yield equations were derived by Ricker (1948) and by Beverton and Holt (1957) which enabled mortality rates and growth in weight to be combined in a single equation (see also Gulland, 1969).

These yield equations are simply means of integrating growth, fishing and natural mortality rates to give assessments of yield for each of the factors with the other two held constant. As the models on which they are based assume constant recruitment the results given by them are in terms of yield per recruit (Y/R). A simple outline of this model is given in Fig. 9.4a. Such models are called deterministic; every factor is fixed for the whole cycle of the fishery and none of them are altered by changes in the other factors. These models have been used in fisheries for the last 20 years and have been very useful in stock assessment. They have enabled the fisheries' scientist to determine at what point the fishery is in relation to long-term sustainable yield and fishing effort (Fig. 1.1, points C, D, E or any other point), and to describe the effects of changing this level of fishing effort (or more accurately fishing mortality rate). Also, they have enabled the effects of allowing the age at which the fish are first caught (age of recruitment) to be calculated (Fig. 9.4a, b). The disadvantage of these models is that they are only qualitatively predictive because all the answers are in terms of yield per recruit. Quantitative prediction depends upon knowing either the number of recruits or using models which incorporate the age structure of the stock in numbers.

Within the last five years virtual population analyses (section 9.2.1.5) have been extensively used to give us this information and used with estimates of recruitment obtained from surveys of larval and pre-recruit fish have enabled fisheries' biologists to predict quantitatively. Within ICNAF and to some extent within NEAFC (North-East Atlantic Fisheries Commission) fishing is controlled by quotas which have been calculated in this way. Manipulation of the data has also been made easier by the use of computers.

Models which allow variation of the parameters are called ‘stochastic’, as compared with those which are ‘deterministic’. Such models are complex and difficult to study without the use of computers but they enable the possible effects of stock size on growth rates, natural mortality rates and recruitment to be studied (Fig. 9.4d) but nothing is known about variations in natural mortality rates with stock size but growth rates of many species are known to be density-dependent; however, most attention has been paid to the question of the dependence of recruitment on stock size.

At present it is a matter of dispute whether fishing can or cannot affect the number of recruits to the fishable stock of a teleost fish species. For a long time it was assumed that within the range of abundances in which a fishery would be economically-viable the number of spawners would always be sufficient to produce enough eggs to replace the losses due to fishing and natural mortality. Recently this assumption has been questioned. It seems highly probable that the fisheries for certain stocks such as the Hokkaido-Sakkalin herring, the Norwegian herring, the Japanese sardine and the Californian sardine collapsed because the number of adult females was no longer enough to maintain the stock at a level at which fishery was profitable (Cushing, 1971). To incorporate effects of fishing upon recruitment into the models knowledge of both fecundity (section 5) and the life history of the larval fish (section 7) can be required. Other uses to which the basic data can be put are studies of the interaction between fisheries and of the interaction between species in the same fishery. The latter has been mentioned in section 6.

The final task of the fisheries' scientist is to help maintain the stocks at whatever level has been decided upon (B, C, D or E or in any other level in Fig. 1.1). Usually the level chosen is ‘D’ or at some point between ‘D’ and ‘E’, (Fig. 1.1). To do this he must monitor it (routinely collect all the data described in sections 2, 3 and 4 and conduct pre-recruit surveys) so that he can predict what catches can be taken from the stock without affecting its ability to continue giving catches at this level, depending upon recruitment. He must also be able to give advice on any problems that may arise either with the introduction of new methods of fishing or from natural changes in the availability or abundance of the stocks.

The riches of the sea outside limits are free for everybody to fish and the exploitation of the living resources of the sea has become increasingly important to more and more countries. The problems are not so intensive in freshwater fisheries but they exist there also.

To protect these resources against overexploitation internation coordination is necessary. There is little sense in one nation regulating its catch in an international fishery if no other nation does the same because the nation that regulates will lose while the others benefit. Only if every nation is to gain equally, usually after some initial losses which must also be shared equally, will nations agree to cooperate.

As a fish stock is often exploited by several fleets from different countries it is necessary that all countries collect catch statistics and preferably in the same way. This was emphasized in sections 2, 3 and 4. For other studies it is not essential to collect data in a standard way, although by doing so it simplifies the exchange of information. Coordination of work is essential if more than one nation fishes a stock, if only to determine the total catch which is being taken from that stock. In many cases nations fish different parts of the stock so that catch per-unit-effort of one fleet may not be representative of the abundance of the whole stock. For example, the British trawler fleet fishes in the Barents Sea on the immature part of the Arcto-Norwegian cod stock; these fish are mainly 3 to 7 years old. The Norwegians fish this stock at the Lofoten Islands where it spawns and their catch consists of fish older than 7 years. Thus there is a sequence of high indices of catch per-unit-effort as large year-classes pass through the fishery; initially it is high in the British fishery and then high in the Norwegian fishery. For virtual population analyses it is essential to have complete age compositions for the catch which means that those nations which catch most of the fish must provide data before the analysis can be attempted. Coordination of work can also make some studies feasible by cutting the cost to individual states; O-group surveys of marine teleosts are largely conducted on an international basis.

The task of combining the result of numerous research programmes and of channelling them to the governments managing the fisheries' policy in the different countries is to a great extent undertaken by a number of international organizations, mainly through Regional Commissions consisting of the countries exploiting the area. An historical account of the development of collaboration in fisheries research with particular reference to the North Atlantic Region is given by Lucas (1963) and a review of international organizations has been published by the U.S. National Oceanographic Data Center, 1969 as “Annotated Acronyms and Abbreviations of Marine Science Related International Organizations”.

Alverson, D.L. , 1971 Manual of methods for fisheries resource survey and appraisal. Part 1.
Survey and charting of fisheries resources. __FAO Fish.Tech.Pap__., (102):80 p.

Beverton, R.J.H. and S.J. Holt, 1957 On the dynamics of exploited fish populations. __Fish.
Invest.Lond.(2)__, (19):533 p.

Christensen, O., 1970 Undersøgelser i forbindelse med spørgsmålet om sommerfredning af laks i
østersøen. __Skr.Dan.Fisk.Havunders__., 30:26–33

Cormack, R.M., 1968 The statistics of capture-recapture methods. __Oceanogr.Mar.Biol__., 6:455–506

Cushing, D.H., 1968 Fisheries biology. London, University of Wisconsin Press, 200 p.

Cushing, D.H., 1971 The dependence of recruitment on parent stock in different groups of fishes.
__J.Cons.Int.Explor.Mer__, 33:40–62

Forbes, S. and O. Nakken, 1972 (Eds), Manual of methods for fisheries resource survey and
appraisal. Part 2. The use of acoustic instruments for fish detection and
abundance estimation. __FAO Man.Fish.Sci__., (5):138 p.

Fry, F.E.J. 1957 Assessment of mortalities by the use of the virtual population. ICNAF/ICES/ FAO Special Scientific Meeting, Lisbon, 1957. Paper P.15 (mimeo)

Graham, M., 1939 The sigmoid curve and the overfishing problem. __Rapp.P-V.Reun.Cons.Perm.Int.
Explor.Mer__, 110:15–29

Gulland, J.A., 1965 Estimation of mortality rates. Annex to Arctic Fisheries Working Group Report. Meeting in Hamburg, Hanuary 1956. ICES CM 1965, Doc.3 (mimeo)

Gulland, J.A., 1969 Manual of methods for fish stock assessment. Part 1. Fish population
analysis. __FAO Man.Fish.Sci__., (4):154 p.

Holden, M.J., 1963 The populations of fish in dry season pools of the River Sokoto. __Fishery
Pub.Colon.Off.Lond__., (19):58 p.

Holden, M.J. 1973 Report of the ICES/ICNAF Working Groups on Selectivity Analysis. __Coop.Res.__
Rep.ICES(A), (25):144 p.

Holt, S.J., 1963 A method of determining gear selectivity and its application. __Spec.Publs.__
__ICNAF__., (5):106–15

Jones, B.W. and J.G. 1973 Pope, A ground fish survey of Faroe Bank. __Res.Bull.ICNAF__, (10):53–61

Lucas, C.E., 1963 International collaboration in fisheries research. A historical review, with
particular references to the North Atlantic Region. __FAO Fish.Biol.Tech.Pap__.,
(33):6 p.

Mackett, D.J., 1973 Manual of methods for fisheries resource survey and appraisal. Part 3.
Standard methods and techniques for demersal fisheries resource surveys. __FAO.
Fish.Tech.Pap__., (124):39 p.

Margetts, A.R., 1949 Experimental comparison of fishing capacities of Danish-seiners and
trawlers. __Rapp.P.-V.Réun.Cons.Perm.Int.Explor.Mer__, 125:82–90

Pope, J.A., 1966 Manual of methods for fish stock assessment. Part 3. Selectivity of fishing
gear. __FAO Fish.Tech.Pap__., (41):41 p.

Pope, J.A., 1972 An investigation of the accuracy of virtual population analysis using cohort
analysis. __Res.Bull.ICANF__ (9)65:74

Ricker, W.E., 1948 Methods of estimating vital statistics of fish populations. __Indiana Univ.
Publ.Sci.Ser__., (15)

Russell, E.S., 1931 Some theoretical considerations on the “overfishing” problem. __J.Cons.Perm.
Int.Explor.Mer__, 6:3–20

Fig. 9.1 | Stratification of Faroe bank by quadrants A–D, each of equal, and by four, depth zones, less than 100 m, 101–200m, 201–300 m and 301–400 m. Trawl hauls, chosen from a potential station grid by random numbers shown thus – I. Modified from Jones and Pope (1974) |

Fig. 9.2 Selection curve of cod–end (a) and of gill–net(b)

Fig. 9.3 | Curves showing (A) increase in weight of an individual fish (B) decline in number of a year–class, the product of (A) x (B), with time (t) |

Fig. 9.4 | Schematic diagrams of assessment models: G = growth, R = recruitment, M = natural mortality rate, F = fishing mortality rate, S = stock, Y = yield, Y/R = yield per recruit; a, b, c are based on a deterministic model in which F has no effect on G, R or M. a) initial state, b)mesh size increased (indicated by//) and Y/R increases, c) fishing mortality rate increases and Y/R decreases, d) represents ‘stochastic’ model in which age of S affects G, R and M as well as Y |

**FAO FISHERIES TECHNICAL PAPER (MFS)**

Documents in this group are provisional editions of volumes of sections of FAO MANUALS IN FISHERIES SCIENCE. usually in the language of the original draft. They are given a limited distribution for comment by collabo- rators in the project, and for use of FAO headquarters and field staff and at training centres, courses and seminars. Revised versions are subsequently published by FAO in the official languages of the Organization.

**Papers issued since Jannuary 1973**

FIRM/T118 | Manual of fisheries science. Part1-An introduction to fisheries science | February 1973 |

FIRD/T124 | Manual of methods for fisheries resource survey and appraisal. Part 3- Standard methods and techniques for demersal fisheries resource surveys | September 1973 |

FIRS/T115 | Manual of fisheries science. Part 2- Methods of Re- (Rev.1) source investigation and their application | June 1974 |