1. sports
2. fishing

Reform of the EU Common Fisheries Policy (CFP)
How to Achieve Sustainable and Profitable Fishing
by
Sidney J. Holt D.Sc.
As part of its work on the reform of the Common Fisheries Policy, the Greens/EFA Group asked Dr. Sidney Holt for advice on the wisdom and benefits of maintaining fish stocks at levels above those capable of producing Maximum Sustainable Yield.
Contact in Greens/EFA Group: Michael Earle [email protected] Brief for the Green Group in the European Parliament
on
Reform of the EU Common Fisheries Policy (CFP)
by
Sidney J. Holt D.Sc.1
SUMMARY
The European Commission’s proposal that ‘Maximum Sustainable Yield’ (MSY) be at the core of fisheries management policy has rightly been welcomed as a signal of intention to allow the recovery of depleted fish stocks by imposing restraints on fishing. This Brief extends the advice I provided earlier to the Greens/EFA Group in the European Parliament supporting the proposal by the Commission to replace the old aim of the CFP, which was simply attainment of sustained yields, by a policy of seeking MSY. This brief is, however, neither a revision nor a supplement of that. It is a stand­alone document.
But a strict MSY­policy also formalizes and legitimises greed and gives excessive status to an otherwise undesirable objective that may or may not be a reality and will impoverish the search party. An MSY policy is an economically very inefficient manner of managing renewable resources such as fish stocks, for long­term profitability and social value. It is therefore very encouraging that the European Commission has declared that
“Multiannual plans providing for conservation measures to maintain or restore fish stocks above levels capable of producing maximum sustainable yield shall be established as a priority.”
[ EC Document: COM (2011) 425 EN Basic regulation ]
1
Voc. Palazzetta 68, Paciano (PG), Italy 06060 [email protected]
Saturday 25 February, 2012
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Here I give many reasons, with supporting calculations and arguments, for acceptance of the proposal by The Green Group2 that the aim should be to maintain fish stocks bigger than would be needed to provide maximal sustainable catches, by reducing the proportion of the population that is annually removed from the sea by fishing, a process we shall call the application of a restrained fishing mortality rate. The big questions are why that is not only desirable but is necessary, and by how much should management aim away from the notion of MSY. I give reasons why fishing rates must be much lower than is required to provide maximum sustainable physical yield in order to ensure the future economic viability of fishing, the stability of the industry, the well­
being of coastal communities dependent on fishing, and continued supply of food and other commodities from marine living resources.
Answers to these questions come from the ideas and findings of the branch of science called population dynamics, and from consideration of other desirable aims of management, particularly the sustained profitability of fishing as an industry, the integrity and well­being of fishing communities, and, equally, the well­
being of the natural marine environment. What comes from consideration of general population dynamics – the main thread in this Brief – is that all fish species’ populations have essentially the same characteristics (so generalizations are possible), and the desirable difference between what some still see as an ideal – MSY ­ and a very much better state is far greater than might be have been expected, would not demand much ‘sacrifice’ in terms of physical catches, and would provide catches of higher quality and stability (so, more valuable), for much less effort, and hence be both more profitable and otherwise socially beneficial.
The specific aims depend very much on the selectivity of fishing operations as well as on their intensity. By this I mean the sizes – hence the ages – at which fish become liable to capture, resulting from the type and details of the gears used and the locations and 2
Green/European Free Alliance Group in the European Parliament
3
seasons of fishing. This selectivity can be such as to range from targeting juveniles, to mainly catching sexually mature fish, and allowing individuals to grow bigger and catching them just before they die naturally. Such varied fishing strategies have very different costs, hazards and consequences which have somehow to be balanced.
Since the 1950s there has been a cultural – but fundamentally irrational – concentration on exercising management through control of the output of each fishery, by setting catch limits (TACs) supplemented by market controls such as the prohibition of landing fish determined for some reason to be ‘under­sized’ or even biologically ‘endangered’. This has had the unintended result of causing huge waste, by ‘discards’, doing little to ‘save endangered species’ or to reduce the mostly negative impacts of intense fishing on the natural environment. A more rational approach begins with reversion to the traditional principles of engineering – optimal control of an ‘open’ system principally by managing the energy and other inputs to it, only secondarily – for ‘fine tuning’ ­ engaging in limiting the system’s output.
This Brief deals only with the basic management objective related to maximum sustainable yield and particularly to the proposal that the objective should be to maintain the rate of exploitation of all fish stocks such that the stocks are held at, or permitted to return to, larger and more productive levels than are needed to yield the biggest possible sustained catches. I have used in several places the ill­defined terms ‘optimal’ and ‘maximal’, as well as ‘over­fishing’ and I hope my meanings will be clear in context. Although ‘optimal’ literally means ‘best’ I have here used it as it is still commonly used in discourse about fisheries management, referring to the value of the fishing mortality rate, or the fishing effort generating it, that is expected to provide maximum sustainable catches in given circumstances.3
3
These various usages were discussed in historical detail in my 1957 book written with R. J. H. Beverton (pp 238+ in all four printings and editions). Little has changed in such usage since then except for matters to have become even less clear.
4
There is now, I think, a consensus that the aims of fisheries management are, primarily, to ensure that total catches are sustainable, preferably high ­ maybe maximal ­ and also profitable. Unfortunately these aims are not necessarily compatible with each other, nor does attaining one of them ensure the other. Large catches can be profitable but not sustainable. Catches can be sustainable but not profitable. Maximal sustainable yields (MSY) would inevitably be unprofitable and, in fact, are unattainable for both technical and economic reasons. Another management aim is, generally that the managed fishery be as stable as an inherently variable and capricious Nature will allow.
Note. This document would have been clearer if it could have been illustrated with about 15 custom­made graphs, but time was not available to prepare those. Instead, a few existing published diagrams have been provided as annexes, each with an explanations of its meaning in the present context.
5
THE BASICS
A cohort of fish in an unexploited population (usually a ‘year’ class) decreases in number, by natural causes, from the time it is spawned, but the survivors each increase in individual body weight. In fishes, growth is indeterminate – that is, it continues throughout life, as in most if not all marine vertebrates ­ but the rate of growth slows over time. Because the curve of numerical survival against time is exponential, roughly the shape of a reversed J (See Annex Figure 1) and the curve of increase in body weight is S­shaped (sigmoid), approaching a maximum (asymptotic) weight, the total weight of each cohort reaches a maximum at some time. That time – sometimes referred to as the critical age ­ and the size of the fish in the cohort when its total maximum weight is reached, are determined not by the rates of mortality and growth in themselves but by the relation between them. That relationship can be expressed as the ratio of the natural mortality rate – M ­ in the fish after they have been ‘recruited’ into the ‘fishable population’ (that is, the part of the population from which fish may be liable to capture) and a co­efficient of growth rate – K. Because mortality and growth tend to be positively correlated as between species the ratio M/K has a rather narrow range of real values. That simplifies our problem of making valid generalisations about all species from the management point of view. Here I give results mostly for the M/K range 0.25 to 2.0.
We have a limited practical interest in the cohort from the moments of its being spawned, hatched and undergoing larval development, except for one special reason that we shall explore later. But there comes a time in the cohort’s history at which the fishes in it are of potential economic interest. Those survivors that reach that age we call recruits, constituting a stock. But we do not necessarily begin to catch fish as soon as they are recruited; we might decide to leave them to grow rather bigger in the hope of eventually getting bigger total catches, which may be possible so long as the rate at which the fish increase in size exceeds the rate at which their numbers diminish by natural death.
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So we can talk about the recruited stock (sometimes referred to as the exploitable stock) and the exploited stock, which is that part of the recruited stock that is liable to capture by the gear in use, given the other specifics of the operation (location, depth, season etc). For some purposes – when we want to ensure sustainability so that future generations of humans can also catch fish in abundance ­ our focus can be in the mature or spawning stock.
That’s enough definitions for the time­being. The biggest catch from a cohort of recruits would be obtained by waiting until the cohort has reached its maximum total weight and then catching all the survivors immediately [See Annex Figure 1]. If we could do that to all the many cohorts in a population, as they each attained their maximum weight we would obtain Maximum Sustainable Yield, MSY. We cannot do that with wild fish for two reasons. First, no fishing method is or can be so completely selective, by size or age. Second, it would require a virtually infinite fishing effort, and even trying to approach it by catching most of the fish near that ‘optimum’ age would be impossibly costly. Our solution is to begin catching some fish before that time, and possibly to continue doing so after it. Our problem then becomes to determine at what size or age to begin catching them, and at what rate ( i.e. what rate of fishing mortality, F, to impose) and how much that might cost in relation to the value of the catch obtained. Our measurement scale could be what that catch would be as a percentage of the theoretical but impossible MSY.
A word about the fishing mortality rate. It is easy to think of that, and also the natural mortality, as an annual percentage of the stock. However, we can better express these as coefficients, exponential coefficients with a property common to logarithms: they can be combined by adding them together, which cannot be done with percentages. (If the natural mortality rate alone is 6o% ­ exponential rate 0.9 ­ and the fishing mortality rate is also 60%, what is the combined rate? – It cannot be more than 100%!) Another reason for measuring the effect of fishing as an exponential coefficient is that F is to a first approximation directly proportional to the amount of fishing effort (Double the effort to 7
double F, for example) expressed by figures such as hours trawling, days at sea, number of hook­hours, number of seine sets per year, and so on.
Further, just as we found that the ratio M/K tells us more about the dynamics of fish populations than do M and K separately, we find it is convenient to use a relative index of the fishing rate, F/M, calling that f. Here we shall generally use that index because it is roughly proportional to the fishing effort exerted – assuming M is a constant. There are other indices, the most usual of which is Exploitation Rate (with possible values between 0 and 1) viz. E ≡ F/(F+M).
[ For readers not familiar with mathematical symbols, ≡ signifies ‘identical to’. ]
E is the proportion of a cohort that is caught throughout its life, so 1­E is the proportion that die from natural or other causes, including any that may be induced by human activities other than fishing.
The relation between the two indices is:
F/M = E/(1­E)
Fishing affects the size of the exploited stock, and that size determines the catch­per­unit­effort (cpue) which, together with the market price, is the main determinant of profitability. Fishing also affects the size of the spawning stock and hence future sustainable catches. It also affects the size of the recruited or exploitable stock and hence the calculations of the wisdom or otherwise of altering the selectivity of the fishery, such as by changing the meshes in the cod­ends of trawls or the gauges of hooks. ‘Size’ is however, an ambiguous term. What really matters is the biological productivity of the recruited, mature or exploited stock, and that depends not only on its weight (biomass) but also on its composition – by size, age and sex of the fish in it. There is much confusion on this matter in the published ‘literature’, and not only in ‘secondary’ and ‘popular’ writings and statements.
8
A common error – and it appears in fish­stock assessments applying so­called surplus production methods – is a presumption that productivity, and hence potential sustainable yield, depends only on the biomass of the whole stock or some part of it (such as spawners, or females). In fact two stocks of the same species, with the same biomasses, can have very different productivities, depending on their size, age and sex­compositions.4 For that and other reasons we shall here ignore such methods (except to comment on them where they give particularly poor or misleading results) and focus on assessment methods that rely on age­
structured models of fish populations. In particular our comments and examples will be based on one set of models put forward by R.J. H. Beverton and myself in the 1940s­50s (with a later modification) and that have been very widely used by fisheries scientists since then. (See Technical Notes at the end of this brief.)
The growth of a fish can be described by an algebraic expression, due to Ludwig von Bertalanffy (LVB), having two basic parameters, one of which is K, which determines the curvatures of the growth curve. The other is W, the weight that the fish will theoretically attain if it lives for ever, that we call the asymptotic or final weight. (W is a theoretical average, it is not the largest size that a particular individual fish of the species can attain.) So long as W does not change it does not affect any of the conclusions about management that we shall consider here, though later we shall take a brief look at the consequence that follow if it does change – most likely because of a changed food supply. The exponent K will also normally be constant; it would not be expected to change with food supply but it might with water temperature which directly affects metabolic rates, especially of cold­blooded species.
4
These methods, usually associated with the names of researchers Schaefer, Pella and Tomlinson and Fox, among others, are mentioned later in this brief, but there is no space here to go into detail about them. They have frequently been cited in advice about fisheries management but are entirely unsuitable for the kinds of calculations and assessment made here. The degree of curvature of ‘sustainable­catch’ curves based on those methods is unrealistic (and cannot be determined empirically), both near where MSY is supposed to be found and at the extremes of un­fished biomass and near extermination.
9
The important properties for us of the LVB growth expression concern the effects of the value of K, even though they are mostly expressed through the M/K ratio, which from here we refer to as a single parameter m.5 With the same convention we designate the ratio F/M as f. The age at which a growing fish will reach a certain size depends on K but not at all on W. It is convenient for us to speak about the size of a fish as a fraction or percentage of W, which we shall refer to as w. The steepest part of the curve of growth in weight against time or age is at the point of inflexion, where the curve changes from being concave to being convex (as seen from above). In the LVB curves this is always when w = 0.3, regardless of the value of K. This point of maximum absolute growth rate is also the size around which fish become sexually mature; where necessary we’ll call this size, relative to W, ws. (Their age at maturity, ts, depends ­ of course inversely ­ on the value of K. It is ts = 0.36/K). In a similar way we can label the size at which fish are recruited as wr and the size at which they first become liable to capture by the fishing operation practiced and the gear used – wc.
[ The corresponding ages are:
tc = ­ln(1 – wc)/K where ln is the natural logarithm (log base e). ]
wc can be smaller or bigger than ws. We shall also label as wMSY the size at which MSY is the (maximum) weight of the unexploited cohort: it depends only on m (See Appendix 3). wc could in principle be bigger than wMSY but it does not make much sense to arrange for it to be so because by the time a fish reaches wMSY its growth rate has considerably slowed; the cohort is declining steadily in number because of natural mortality but the size of the surviving fish is increasing more slowly, even at a snail’s pace. It is easy to think about this if we think not about absolute growth 5
This ratio is referred to by T. J. Quinn II and R. B. Deriso in their textbook ‘Quantitative Fish Dynamics’ (O.U.P., 1999) as “A fundamental life­history parameter”, and referred to by others (e.g. M. Mangel) as one of the Beverton­
Holt invariants, although it is not strictly so.
10
rates but, rather, specific growth rate, that is the increment in weight in a certain time (perhaps a year) divided by the average of the weight of the fish at the beginning of that time and that at the end of it (sometimes called relative growth rate, but that can be an ambiguous term, referring perhaps to comparisons between stocks or species). The maximum of the curve of cohort weight against age occurs when the specific growth rate becomes equal (and, naturally, opposite to) the corresponding specific mortality rate.
Sustainable yields are usually referred to in the scientific literature as Y but we shall label them as SY. SY is generally directly proportional both to W and to R, the annual number of recruits. If we can presume these both stay constant ­ or at least at a constant average ­ it is convenient to look at sy = SY/W x R so sy will always be a decimal number less than one. Our consideration of this will be by using what is usually called a ‘yield­per­recruit’ model, in contrast with self­regenerating models, which incorporate an expression relating the number of recruits to the size and other characteristics of a previous generation that spawned them (See Annex Figures 2 and 3). That expression can never be a proportional one, but, rather, describes the density­dependence of the natural mortality of the ‘pre­recruit’ fish, in such a way that the mortality rate increases as the number of pre­recruits increases. It is also possible that with an extremely low pre­recruit abundance (caused most likely by extreme over­fishing of the parent generation) there can be a reversed density­dependence causing what is called the Allee effect or depensation. This is a dangerous condition that can lead to irreversible changes in the population – such as continuing declines or even extermination, even if fishing pressure is relaxed or ceases. However, although that possibility must be borne in mind in considering management of fisheries in general, here – focused as we are on management to maintain relatively large and productive stocks – the Allee effect need only worry us in connection with management to avoid the possibility of unintended stock depletions.
Possible changes in R resulting from changes in stock size and composition can be very important and we shall have to look at 11
those carefully later. However, such changes will generally occur when a stock has been much reduced by intense, prolonged fishing (or other catastrophe!). Our interest here is mainly in what happens when we manage fishing in such a way that a stock is maintained at a relatively high level – or allowed to recover to such a level – so as to get as close as practicable to MSY. In that region of ‘parameter space’ there may or may not be any or much change in average recruitment, even though the natural variability of R may be ­ and commonly is ­ very great. That is one reason, as we shall see, why trying to approach MSY by setting catch limits (such as TACs) is – at best – inefficient and frequently fails, sometimes catastrophically; this is that stocks brought to, or near to, MSY – and msy ­ levels (see later) will necessarily be much smaller than they were before they were exploited.
APPLICABLE THEORY
We have said the Maximum Sustainable Yield (MSY) in weight from an exploited stock of fish is obtainable only by catching all the surviving individuals of each cohort (year class) when the cohort attains its maximum total weight, and that that is impracticable for wild populations since it would require an infinite fishing intensity; even getting close to it would always be impracticable. In the real world fishing must be less selective, though the selectivity actually imposed makes an immense difference to rational management decisions. Here selectivity is defined as the size of fish, wc, in a population when the fish first becomes liable to capture, expressed as a fraction or percentage of the theoretical asymptotic size. This percentage, or fraction, we call wc. (Low wc means relatively unselective, bigger wc means more selective. Examples of some of these numerical options are given in the Appendices.)
Given a stock having a certain value of m we can calculate values of sy for each possible wc and a wide range of values for f = F/M. From our point of view, given the fairly narrow observed range of m, a fin whale would be just a gigantic haddock or anchovy were it 12
not for the scale and density­dependence of recruitment! In general a graph of sy against f (sometimes called a sustainable catch curve) has a maximum – a peak value ­ designated as msy ­ when wc is relatively small, but when wc is relatively large the curve has no peak – it approaches an upper asymptote. The boundary between ‘relatively smaller’ and what is ‘relatively larger’ varies with m, being at bigger wc when m is higher. (Table 1, third column)
TABLE 1 MSY and wmsy
m
MSY
wMSY
0.25
0.5
1.0
1.5
2.0
3.0
0.414
0.238
0.105
0.057
0.035
0.016
0.79
0.63
0.42
0.30
0.22
0.13
UnexBiom Depletion%
0.66
0.46
0.35
0.15
0,10
0.05
36
48
58
63
65
68
[ Note: The approach to fish stock assessment and fisheries management taken in this Brief is that the central questions concern the amount of fishing (in terms of fishing effort) and the mortality rate of fish induced by that, and the selectivity of that effort with respect to sizes and ages of fish caught. I am however aware that many choose to focus attention on the sizes of the stocks ­ their biomasses ­ and the effects of fishing on the stocks. Accordingly I have presented, in the fourth column of Table 1, a summary of the results of calculations of the corresponding indices of the biomass of the unexploited equilibrium population. To obtain the estimates of biomass the indices would have to be multiplied by the product of the annual number of recruits and the (theoretical) final weight of the growing fish, but for our purposes the indices suffice.
The last column of the Table shows the reduced biomass that would be established if it were possible to take the MSY, as a 13
percentage of the unexploited biomass. This percentage is always in the region of 60 – 70% except in cases where the natural mortality rate of the fish is very low compared with its instantaneous coefficient of growth in body weight as indicated in the first column of the table: m = M/K.
The biomass index given here (see Appendix 3) strictly relates to the total weight of all stages of the population. A more appropriate measure would be of the recruited population, but calculations of that would call for a general assumption regarding the age, hence size, of fish at recruitment; I have hesitated to make that general assumption, though it would probably be reasonable to put it in the range wr = 0.05 – 0.1, with corresponding range of age, depending on the value of K. However, the weight of the total population can serve our purpose because although eggs, larvae and fry are extremely numerous – at least in most of the bony fishes – their contribution to the total biomass is quite small – they carry a vast number of genomes but not many calories!
There is a broader interest in the biomass of the ‘spawning stock’, the sexually mature fishes that contribute directly to the next and future generations of recruits. Calculation of indices for this quantity are possible, but complicated by the fact that that biomass, as a proportion of either the total population or of the recruited stock, varies both with the degree of depletion of the stock by fishing and with the changes in the age and size composition of the population, also brought about by both selective and unselective fishing. Attention has to be given to those processes when we come to discuss self­regenerating population models.
It remains to be said that if particular msy
’s
were to be taken, with finite fishing effort, as explained below, the decree of depletion would always be less that than that indicated in this table relating to a theoretical but unobtainable MSY ]
So, turning now to Table 2, below, for every stock there is an infinity of msys obtainable with finite fishing effort, and 14
depending on the selectivity. Each is to be obtained by exerting a certain intensity of fishing effort and the msy varies for each selectivity. The intensity of fishing that generates an msy increases with increasing selectivity, but the msy itself generally increases as selectivity is increased (and so becomes closer to MSY) except as in the case for m = 2.0 or higher and wc = 0.3 which is somewhat higher in those cases than wMSY. (Table 2).
For each value of m the more selective the fishing operation the bigger is the msy but obtained only with a substantially higher fishing mortality and with a lower catch­rate. In Table 2 the catch­ rates are given as percentages of the initial catch rate in the virtually unexploited stock, sy/finit%, taken to be at f = 0.01. In the range of m from 0.25 to 1.5 the catch rates at msy with unselective fishing (wc = 0.1) are about one­fifth of the rate when the stock is virtually unexploited (Right­hand column). If the fish become first liable to capture as they become mature (wc = 0.3) we find that for the lower range of m values (0.25 – 1.0) the catch­rate (at msy) ranges from 8 to 17% of that obtained from the unexploited stock.
TABLE 2
msy, fmsy, cpue
m ≡ M/K
wc
msy/R.W
msy/MSY %
0.25
0.5
0.4
0.3
0.2
0.1
0.05
0.383
0.365
0.344
0.331
0.294
92
88
83
80
71
5.8
4.3
3.3
2.8
2.1
(msy/f) /
( sy/finit) %
11
14
17
18
22
0.5
0.5
0.4
0.3
0.233
0.224
0.211
98
94
89
9.5
5.2
3.4
7
11
15
15
fmsy
0.2
0.1
0.05
0.184
0.173
82
73
2.4
1.7
19
23
1.0
0.4
0.3
0.2
0.1
0.05
0.105
0.103
0.096
0.084
100
97
91
80
infinite
6.3
3.0
1.7
8
15
21
1.5
0.3
0.2
0.1
0.05
0.056
0.055
0.049
99
97
87
Infinite
5.3
15
2.1
18
2.0
0.3
0.2
0.1
0.05
0.033
0.034
0.032
95
100
93
infinite
19
5
2.8
14
So what else does this summary table of the properties of the age­
structured yield­per­recruit model tell us?
First, that in the range of realistic values for m, the fishing effort to obtain any msy is, with lower selectivity, such that the fishing mortality rate is around double the natural mortality rate, but that the sustainable catch varies six­ to eight­fold, depending on the exact value of m. That seems one good reason for management aiming at a desired fishing mortality rate rather than a biomass and an associated catch, which suggests that aiming by fixing a desirable fishing effort will be more reliable than aiming at a certain catch limit.
Second, with low selectivity the msy will be at least three­quarters of the theoretical but unattainable MSY, and more as selectivity increases, but at a rapidly increasing cost.
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In interpreting the figures for the catch­rate ­ relative to that obtained from the very lightly exploited stock ­ we must bear in mind that with wc = 0.1 we are looking at practically the entire recruited stock but with higher wc (above 0.3) the effect of fishing on the entire recruited and the spawning stock is considerably less than is indicated by cpue figures which of course relate to only the actually exploited part of the stock.
As fishing intensity increases, the size (biomass and number) of fish in the exploited stock, the mature stock and the recruited stock are reduced continuously to some quantifiable percentage or fraction of its original pre­exploitation size. Consequently the rate of catch (commonly referred to as catch­per­unit­effort) by individual fishing vessels or enterprises declines correspondingly, though the true rate of stock decline might not always be evident because of simultaneous increases in technical and operational efficiency and/or the reduced geographic range of a reduced stock, becoming concentrated in the part of its original range in which density was highest. As fishing intensity increases so also does the average age, and hence size, of fish in the catch decrease, with likely significant economic consequences.
In unrestrained fisheries the fishing intensity tends to increase until the fishery becomes unprofitable, overall, commonly past the level of intensity that would provide msy. In such cases we experience over­fishing (more specifically referred to sometimes as growth over­fishing although that term is rather misleading.)
Even in a fishery regulated to hold the fishing effort at the intensity required for taking msy, the fishery is not necessarily profitable, with total value of catch exceeding costs. Profitability may be restored or achieved by reducing fishing intensity and hence increasing the catch­rate as the stock recovers towards its original size, the so­called carrying capacity – another unfortunately mislabeled and misleading term! There is a level of intensity, for a given selectivity, in which the gross profit would be maximized. We call the sustainable yield, sy, at that point the maximum 17
sustainable economic yield (msey). The fishing intensity for msey (fmsey) is always less than required to obtain msy (fmsy) – and can be substantially less – with correspondingly higher catch rates.6
Because the curves of sy against fishing intensity tend to be rather flat­topped it is almost always possible to obtain sustainable catches only marginally less than msy with fishing intensities substantially less than those needed to take msy.7 This means that msy is also not necessarily an optimal choice as a management target. But the asymmetry of the sy­fishing intensity curves means that it can be dangerous to allow populations to be driven to levels of biomass and to age/size compositions, down past the msy­points; that can induce recruitment over­fishing (in which the annual recruitment declines significantly as a result of lack of spawners) such that population collapse and possibly irreversible change can occur. A particularly dangerous situation arises in cases where a selective fishery (just for mature fish, say), perhaps linked to fishing for food for human consumption, is succeeded, for market and technical reasons, by a less selective one, involving fishing to provide industrial products. The North Sea herring fishery is an example, as explained later. It is now natural to ask what would happen to the stock and the sustainable catch if we were to depart from an msy target, one way or the other? The fixed shape of a curve of sustainable yield against stock biomass or fishing mortality rate given by the commonly used ‘surplus production’ assessment models due to Fox, to Schaefer and to Pella & Tomlinson gives an inflexible answer to that question, whatever MSY­catches they may predict. For example the Schaefer version, with MSY available when the 6
It is important to remember that this refers to the sustainability of the stock exploitation, not economic sustainability. msey may or may not be itself sustainable although it probably usually would be.
7
A measure of the flattoppedness or peakedness of a curve or distribution is called its kurtosis. It is not a feature of a sustainable yield ­ fishing effort curve that is much referred to in discussing fish population dynamics and management, but in the context of this brief it is crucial. See Technical Notes.
18
entire stock or the spawning stock is reduced to half its unexploited level, predicts that if the fishing effort were to be reduced or increased by, say, 10% from that yielding MSY, the sustainable catch would be reduced by 1%, but, as we shall see, the consequences of such change as predicted by the age­structured yield per recruit model used to generate the figures in Table 2 are very different. That is essentially because the latter are much more flat­topped than the former8 and also because they are not symmetrical – the left­hand limb (decreasing fishing mortality rate) descends more steeply than the right­hand limb (increasing fishing mortality). One consequence of this is that the catches continue to hold­up well after a state of growth­overfishing has been reached, though they come at an increasingly higher cost, consist of more and more smaller fish, and risk sudden collapse as recruitment over­fishing sets in. (In fact the curves of sustainable catch against fishing intensity are more nearly symmetrical over a wide range when values of sy/RW are plotted against the logarithm of f.)
We are more interested here in what would be expected to happen if the fishing mortality were to be moved towards the left of the curve, reduced mortality rate yielding less than msy but providing a higher catch­rate, hence usually being more profitable. Here, the flat­topped­ness of the general age­structured model, as advocated here ­ especially to the left of the yield­per­recruit curve ­ is crucial. The catch­curves are more like the profile of the Grand Massif of France, or the Cotswolds of England, with gently sloping plateaus than like the Alps or the Dolomites.
To examine that we can look at a few selected scenarios. I have given the result for three such situations in Table 3: the consequences of reducing the fishing mortality (hence f) 1%, 5% or 10% below that required to take msy, which I refer to as fopt (‘optimal’). There are two ways of looking at this. One is to chose a possible reduction in fishing effort and see how much of the 8
This is because the curves produced by the age­structured model derived their shape from the mortality and, especially, body growth functions whereas the shapes of the published surplus­production models are simple arbitrary algebraic functions with no biological basis. 19
sustainable catch is ‘sacrificed’; the other is to chose a level of ‘sacrifice’ and see what reduction in fishing effort will be needed to bring about that situation. I have chosen to illustrate the latter in
Table 3.
TABLE 3
Fishing Mortality less than Optimal
m =M/K
0.25
0.5
1.0
1.5
2.0
wc
fopt
f ’ / fopt %
95%
99% msy
90%
0.5
0.4
0.3
0.2
0.1
5.81
4.25
3.29
2.61
2.06
68.5
45.8
73.2
51.3
39.3
76.3
55.0
42.9
78.5
58.2
46.4
80.6
61.7
51.9
0.5
0.4
0.3
0.2
0.1
9.49
5.15
3.39
2.39
1.72
55.5
32.5
23.0
67.2
43.9
32.8
73.2
51.3
39.8
77.4
56.9
45.2
80.2
61.0
49.4
0.4
0.3
0.2
0.1
20+
6.26
3.03
1.72
59.1
35.9
25.9
71.6
52.8
38.0
78.5
58.1
46.5
0.2
0.1
5.34
2.06
59.0
26.3
75.2
53.9
0.2
0.1
20+
2.76
60.9
20
47.5
34.1
26.4
42.2
36.3
In this table f is the value that will yield 99%, 95% or 91% of the relevant msy, which in each case is given as a percentage of fopt. It is striking that for all the given values of m and wc, and even though fopt varies over a wide range, 99% of any msy can be secured by exerting a fishing rate between about 60 to 80% of that needed to take msy. If we were prepared to be less greedy, and ‘sacrifice’ as much as 10% of any msy we could take the other 90% with only about 20 to 40% of the fishing effort, with corresponding increases in stock biomass, spawning biomass, catch rates and ­ presumably ­ profitability. In addition the average sizes of the caught fish will be substantially bigger than they would be if msy was the target.
In the light of the findings summarized in Table 3 I looked at the consequences of bigger reductions of the fishing effort below the msy levels. The results were rather surprising and of interest, I thought, with respect to the current Green Group proposal. I summarise them here; they refer to the full ranges of m from 0.25 to 2.0 and wc from 0.25 to 0.5.
As f is further reduced below each fmsy value the sustainable catch of course is reduced, at first slowly, then more rapidly, and the relative cpue increases correspondingly. If the f value is reduced to as little as half of fmsy the sustainable catch, for all parameter sets, is never reduced by more than 10% of msy, with corresponding increases in the catch­rate. The size of the exploited stock is at least 40% of the unexploited size, as compared with the general msy level around 20%. This last difference also makes it much less likely that the spawning stock will be so reduced by fishing to substantially affect the recruitment.
I think it is worth noting here that a greatly reduced fishing effort leads to a bigger average size of fish in the catches. It leads also to less variability in annual catches because they are coming from stocks in which more cohorts contribute significantly to the population and catches. When stocks are very depleted the catches depend more and more on the number of recruits and, further, 21
there is also less ‘buffering’ of the natural variability of the recruitment. A reduced fishing effort does not necessarily lead to a corresponding reduction in the sizes and numbers of coastal fishing communities – as seems sometimes to be feared ­ because appropriate social arrangements can ensure that each fisher or fishing unit can work less for much greater economic benefit. 22
SELF­REGENERATION
When the size of a stock is reduced by fishing it is reasonable to expect that at some point the average annual number of recruits to it will be significantly diminished. Our experience is, however, that this only becomes evident when the stock is very substantially reduced, at least in the bony fishes with very high egg and larval production rates. Any such density­dependence of recruitment is very important when considering depletion and possible stock collapses, even exterminations, but here we are discussing stocks that are to be maintained at biomass and numerical levels exceeding those that would provide maximum yields, and especially actions intended to allow stocks to increase above such levels. In this case any density­dependence that leads to larger numbers of recruits coming from bigger numbers and biomasses of parents is obviously beneficial. The question is how much would this affect our conclusions, if at all?
The most common trial calculations for these circumstances have applied an expression derived by Beverton and Holt in the 1940s­
50s. This fixes a curve, convex as viewed from above, that reveals an extremely weak relationship when the spawning stock is large, and a strong, almost proportional, relationship when the spawning stock is very small. (Several other proposed expressions, such as that proposed by W. Ricker, have basically the same properties, especially for middle­sized and much reduced populations, but differ slightly in quantitative detail.) One question that has to be addressed in fish population analysis – though not usually in these terms ­ is: where on this curve does an unexploited population ‘settle’ in a steady­state, sometimes called – but I think misleadingly in this context ­ ‘carrying capacity.’ (Misleadingly, I think, because that term focuses on a supposed property of the environment in which the population lives, whereas the attainment of such a state is a function of the dynamics of the population, within its habitat.) The scale of the consequences of reducing fishing intensity to less than that yielding msy depends on the initial location of the initial 23
steady state on the stock­recruitment curve, the steepness of the curve at that location and, even more, on its steepness in the region of the msys on the yield­per­recruit curves, which might be anywhere between one half and, say, one tenth of the size of the unexploited population.9 The effects of the stock reduction are, however, qualitatively sure: the estimate of msy stock level will be increased, and the fishing mortality needed to secure msy decreased, although only slightly. But the expected msy catches will be bigger. How much bigger depends critically on a precise knowledge of the initial steady­state point. This has a major practical implication: we can determine the desirable fishing mortality rate within a limited range, but be able to predict the consequent average catches with much less precision. The implications are that while the desired fishing rate could be regulated by limiting the fishing effort, the desired state cannot be ensured by regulating catches on the basis of predictions of sustainable yield. Appendix 2 gives, as an example, the North Sea haddock situation as it was in pre­WWII years.
ECONOMIC AND SOCIAL CONSIDERATIONS
In his classic 1943 book, “The Fish Gate” (and, subsequently, in 1955, to a Conference of the United Nations) Michael Graham expressed his Great Law of Fishing:
“Fisheries that are unlimited become inefficient
and unprofitable.”
And, while we’re about it, some other basic principles can
be mentioned:
On Conservation: HM Inspector of Fisheries, Mr. Ernest Holt, reporting to Parliament in 1895 “…it is desirable that fish should have a chance of reproducing their species at least once before they are destroyed.”
9
Note that this value of the recruitment to the unexploited stock is not the asymptote of the curve; which would only be attained – theoretically – from an infinitely big mature stock.
24
On Restraint: Sidney Holt’s Second Law of Fishing, (1958):
“Fishers and fishing enterprises will do everything possible – preferably legally ­ to respond to regulative restraints in such a way as to tend to nullify their intended benefits, particularly their immediate effects.”
(That is not just about ‘sheer cussedness’, but rather an expression of the realities of continuing making a living, daily, while restraints take time – commonly several years ­ to provide material benefits, during which time they will usually ­ inevitably ­ cause temporary economic and social stress, which could be ameliorated only by correct social policies. Indeed, the fishers’ responses can be, unintentionally, actually to enhance the deficiencies that the restraints were intended to correct, for example by increasing their efficiency).
On Innovation and originality: Craig Tanimoto and Apple Computer, (1987) “Think different”. See also Cherry Thomas and Edward de Bono, (1970), “Lateral thinking”.
Here the main difficulty may be to free ourselves from ways of thinking about management methods, as well as about aims, that have become entrenched during recent decades.
Graham’s Great Law generally comes into operation when fishing effort has gone above – sometimes far above – the level required for taking msy. This is usually because the expansion is practically always a sort of mining rather than sustainable resource use. The level of non­profitability could generally only be reached before ‘growth over­fishing’ begins if demand for the products of that fishery is, or becomes, quite limited. With modern forms of fish processing, transport and global trade that is now rare except, occasionally, when a product from fish ­ other than food for direct human consumption – is substituted in the market by a similar but cheaper or otherwise more desirable product from another source. Here we can only deal with the case of a stable market for an unchanging product.
25
We can examine the possible patterns of maximum sustainable economic yield (msey) using the yield equations more or less as we have done in examining physical yields, assuming that parameters such as the mortality­growth coefficient ratio (m) stay constant as a marker. Now, suppose we write the market value of the total catch (for any given value of f) as sy x p (p is price) and the cost of taking it as f x q (q is cost of exerting unit fishing). Then the gross profit is (p x sy) ­ (q x f) and we want to find where is the maximum of that difference, and at what value of f (call that fmsey), particularly in relation to fopt and to the value of f when gross profit is zero (call that f0 ). The simple geometry of the curves of sy against f tells us that: fmsey lies at the point where the tangent to the curve (in mathematical terms its first derivative) has the same slope as the value of sy/f at f0. In Table 4 we look, for orientation, at some examples, applying the calculations from which Tables 1, 2 and 3 were derived. In our examples we first assume that the gross profit is zero at msy, fmsy and, alternatively, at values of f 66.7% and 150% of fmsy, i.e. with zero profit being reached before growth over­fishing occurs, and after. [We have chosen these two ratios, bearing in mind the general asymmetry of the sy­f curves, to make some symmetry of ‘above’ and ‘below’: 150/100 and 100/150].
In Table 4 the values of msy and fmsy are the same as in Table 2.
The right­hand column, rate of profit, is the gross profit (value of the catch minus the cost of taking it) divided by that cost, expressed as a percentage.
TABLE 4 Sustainable Economic Yields
(f0 = fmsy)
26
(The last column of Table 4 has deliberately been left incomplete because the selected figures shown are indicative only of the scale of the possible profit rate from drastic reductions in fishing effort, and to avoid the temptation to make unwarranted comparisons between the results for different m and wc values.)
There are, I think, three remarkable features in this table. The first
Is that for all values of m and wc, except the highest of both, the
ratios of msey to msy, and of fmsey to fmsy are similar. (This apparent anomaly is related to the fact that the calculations for m = 2.0 and wc = 0.2 bring us close to the parameter space where the maxima in the msy­curve are close to the asymptote.)
m=M/K
wc
fmsey
0.318
0.290
0.277
0.256
0.231
0.215
msey/msy
%
83.2
79.7
80.4
79.7
78.7
77.8
20.0
25.2
28.9
31.8
34.3
35.9
0.206
0.188
0.173
0.155
0.136
0.124
88.6
84.0
81.8
80.0
78.5
78.0
1.36
0.86
0.57
0.45
21.7
28.4
33.1
35.2
0.086
0.079
0.067
0.058
86.4
82.6
79.7
78.2
0.2
0.1
0.05
1.30
0.63
0.46
24.3
30.6
34.1
0.032
0.040
0.035
86.4
81.0
79.1
0.2
0.1
0.05
2.30
0.76
0.50
12.1
27.5
32.9
0.032
0.027
0.023
92.7
83.2
80.3
0.25
0.5
0.4
0.3
0.2
0.1
0.05
1.48
1.12
1.00
0.85
0.71
0.63
0.5
0.5
0.4
0.3
0.2
0.1
0.05
1.90
1.30
0.98
0.76
0.59
0.51
1
0.3
0.2
0.1
0.05
1.5
2
fmsey/fmsy
%
25.5
26.4
30.4
32.6
34.5
35.0
27
msey
Profit rate
%
225
171
165
143
128
c.100
The second is that the effort needed to acquire the maximum economic yield is much less than (always well under half) that needed for msy.
And, third, that the economically maximum sustainable catch is not much less than the msy.
(It is worth recalling something that Beverton and I ‘discovered’ in the 1950s: that an msey can always be found even when there is no msy except with infinite fishing intensity. I have not calculated such situations for these illustrative examples.)
The quantitative conclusions in Table 4 do depend on the elasticity of the price of fish, the presumption being that over the supply range from msy to msey the price will not change much ­ if at all ­ (elasticity zero or low) as a consequence of the change in supply. If elasticity is not low or zero, but price increases with reduced production – as might be expected in some circumstances ­ then fmsey will be less than the table indicates. These calculations can easily be modified if the price elasticity is known empirically or can safely be assumed on the basis of experience and the actual situation of a particular fishery.
An example of such calculations, for the bottom trawl fishery for plaice, Pleuronectes platessa, in the Southern North Sea, is given in Appendix 1.
Our next task is to see how much these results depend critically on the assumption of zero profit at fmsy. To explore that we can look at some arbitrary chosen case where zero profit may be found when f is above or below the value giving msy. It is not necessary here to explore the entire range examined for the yield­per­recruit analysis. I have chosen to look mainly at the mid­range case of m = 1.0 for various selectivities and assume that f is one third less
or 50% more than fopt (Table 5).
Again we see that the value of fmsey is always – perhaps unexpectedly ­ low (and similar for all m and wc values) and, for 28
the m = 1.0 example, the msey catches are all in the range of about 70% to 90% of msy. There are similarly narrow ranges for other values of m.
TABLE 5
Effects of different levels of unprofitability
m=M/K
wc
f0 = 1.5xfmsy
fmsey
fmsey/
msey/
fmsy % msy %
fmsey
f0 = 0.7xfmsy
fmsey/ msey/
fmsy % msy %
11.7
59.7
21.4
73.2
14.3
55.0
24.1
69.4
25.2
67.5
25.0
65.3
0.25
0.5
0.4
0.3
0.2
0.1
0.05
1.87
1.53
1.29
1.10
0.92
0.85
32.2
36.0
39.2
42.2
44.7
47.22
88.7
88.0
87.7
87.5
87.1
87.7
0.68
0.91
0.47
0.63
0.52
0.45
0.5
0.4
0.3
0.2
0.1
0.05
1.30
0.98
0.98
0.78
0.67
25.24
28.91
41.00
45.35
47.18
84.0
81.8
87.6
87.6
87.2
1.01
0.75
0.57
0.44
0.37
19.6
22.1
23.0
25.6
26.1
77.1
73.5
70.2
67.8
65.8
1.0
0.3
0.3
0.1
0.05
1.68
1.08
0.66
0.59
26.84
35.64
38.37
46.09
90.6
88.5
84.4
86.8
1.10
0.66
0.43
0.33
17.6
21.8
25.0
25.8
81.2
74.5
69.7
66.6
2.0
0.1
0.05
0.95
0.64
34.42
42.11
88.9
87.8
0.59
0.37
21.4
24.3
76.6
69.7
29
It is not always sufficient to make individual operations restrained to sustainability, attractive and profitable. Thus there can be an argument for restraining fishing intensity to a level different from that required for msey. How different (and in which direction) obviously depends on the prevailing economic conditions (presuming that the expected rate of profit will not be so different from prevailing conditions in other industries as either to make fishing unattractive for investment, or so attractive that there will be irresistible pressure for investments to increase beyond what may be desirable for conservation and social reasons.) Similarly, social policy decisions may dictate how big an industry, and product supply from it, is desired. For each fisher, vessel or enterprise, the greatest benefit might come from having as few competitors for the fish as is possible, although account has to be taken of certain advantages from cooperation between several fishing units.
It should not be assumed, however that a low fishing intensity must always imply a small fishing fleet. Our discussion of the desirable scale of f relates to deployed effort, not simply to available fishing power. An early example of successful management by fishing effort regulation illustrated this – that of the halibut fishery off the Pacific coast of North America. Regulation by setting specific catch limits or limiting the number of participating vessels was not available to the managers of the US­Canada bilateral halibut Commission, and recovery of a fishery in crisis was essentially achieved by strictly limiting the number of days in each season that vessels could operate. The resulting recovery of the stock, yielding much higher catch rates, was sufficiently profitable for fishers to convert to multi­species operations for the rest of the year as well as to make necessary improvements in vessels and gear.
A policy decision to seek to minimize the impact of the fishery on the marine ecosystem of which it is part (including reducing incidental catches of non­target species), as well as to reduce the consumption of fossil fuels and other input­resources, would
push the regulated fishing intensity down to even less than is 30
required for msey. On the other hand there can be social reasons for maintaining fishing communities at certain viable levels, ensuring stable infra­structures, even military reasons for maintaining a potential reserve of experienced seamen, convertible vessels and ship­building and processing facilities and so favouring fishing intensities somewhat higher than fmsey.
Many considerations point to the desirability of regulating fishing primarily by control of the input to it (fishing intensity and selectivity) rather than of the output (catch limits, minimum size limits and so on). The most important of these are: 1. that the likely catch in the immediate future is one of the most difficult numbers to predict because of the wide annual variability of recruitment in most fishes as well as shifts in availability of the already recruited animals; and
2. that in the already recruited population the biological productivity of the stock, which determines the sustainable yield, is far more stable than the stock’s immediate size; and
3. that errors in the estimates of model parameters (by which I mean differences between the estimates and their real values in Nature) can lead to very large errors in predicted yield, so poorly calculated catch limits can lead to serious over­ exploitation, requiring rapid and vigorous ‘corrections’ in each succeeding year. This is particularly so when the intensity of fishing is such that it is likely that recruitment will decline as a result of diminishing female spawner numbers and biomass.
It is, finally, worth recalling that staff and consultants of FAO and the World Bank recently concluded that the global fish catch is now in the region of ‘MSY’ and the fisheries necessarily heavily subsidized, and that large reductions in global fishing effort would restore overall profitability, with some sacrifice of total catch. In my opinion their conclusion is qualitatively correct but I have doubts concerning its quantitative aspects, in particular my belief that the method they used considerably over­estimated the sacrifice of total catch that would follow substantial reduction in global fishing power and deployed 31
effort, and so under­estimated its likely economic and social advantages. This was because they used the – I think – very unreliable surplus production models (See below).
There follow some final thoughts about the Theory and Practice of Fisheries Management.
32
POLICY OBJECTIVES
The policy objectives discussed below may all be desirable but are not entirely compatible with each other. Compromises will usually have to be sought, on the basis of priorities assigned a priori among them.
By sustainable catches we mean average annual catches which, if taken, will leave the size and the composition of the exploited population unchanged the following year, apart from the inevitable natural fluctuations in recruitment. Sustainability is often thought of as implying ‘for ever’ – like diamonds! – but in practice the concept can only be useful when a limited, if long, time­frame is pre­specified, so that – among other things – computer simulations can be undertaken to test the likely consequences of proposed actions to promote sustainability and optimization.. Sustainability is now accepted widely as a desirable state for wise use of a renewable resource, especially if its future ability to provide continuing yield is highly valued. It is a moral, economic and social notion, not a scientific one, though science can serve to suggest what will ensure it and what endanger it. The fact that catching operations that are merely technically sustainable will not necessarily be profitable, and hence cannot become economically sustainable, is frequently overlooked in the enactment of fisheries policy, as it is in other industries.
In some fisheries the sizes of the fishes caught – the proportions in the catch of smaller (possibly immature), medium, and larger – matter in that they attract different market prices, may even enter different markets, and are suitable for different kinds of processing. The average size depends on two factors operating in opposite directions. One is obviously the selectivity – highly selective fishing should normally yield a higher proportion of older, larger fish and hence a larger average size. On the other hand, since seeking to optimise selective catching always demands more effort and hence a higher fishing mortality rate on the age­
classes being exploited. This leads to a change in age and size composition of the populations such that the average size of fish 33
caught will tend be smaller, other things being equal. So overall optimization of the distribution of size in the catches calls for calculations for each particular case. Such calculations would look not only at the average sizes of the fish in catches but at the distribution of size or at least at the categories defined by the market, for example: small, medium, large. One important policy issue that should be mentioned here is the need for industry to have as much continuity from year to year in what regulations permit it to do. This has been a continuing problem with the annual setting of TACs ­ sometimes hundreds of them ­ and a problem for the scientific community, too, who must regularly perform huge numbers of routine assessments, thus limiting their ability to make the deeper studies that will refine and otherwise improve such methods. The decision by the European Commission to engage in multi­annual plans is a huge step forward but might not in itself sufficiently stabilize regulatory measures and release sufficient research time. The approach to this matter taken some years ago by the International Whaling Commission by including in its Revised Management Procedure (RMP) regulation­stability requirement as a specific management objective, and setting predefined limits to the amendment, timing, data requirements and circumstances that could warrant changes, was helpful. The most difficult kinds of regulations to be treated in this way are catch­limits such as TACs. Regulation of inputs such as fleet power and deployed effort are easier to stabilize in the medium term.
Now let us take a quick look at the Second Law. This is not the place to discuss in detail the innumerable ways of nullifying the intended consequences of regulation of catches, fishing effort and procedures, but one aspect of normal economic behaviour demands our attention. This is the basic and continuing effort by fishers both to increase their efficiency ­ ideally at as low a cost as possible, of course – and to respond profitably to changes in fish location and abundance. This can have unintended consequences for management, especially for certain kinds of regulation. An example of this was the case of the George’s Bank trawl fishery for 34
haddock, in the Northwest Atlantic, where well­intended but inappropriate limited measures to increase sustainable yield by increasing cod­end mesh size eventually contributed to the collapse of the fishery. Here I give an illustrative theoretical example.
We make our ‘default’ assumption (based on a real case) that we are dealing with a fish stock with m = 1.0, with low selectivity trawling at, say, wc = 0.064 (6.4% of W). This has an msy of 0.77 x R x W. obtained with f = 1.86. This situation is relatively slight growth­overfishing. A decrease in fishing effort to the msy value of f =1.5 would give us 1.5% more sustainable yield for only 80% of the cost. But possibly we have no authority to constrain the fishing effort even though the fishery was, prior to regulation, making zero profit. We decide that a higher msy can be obtained by increasing mesh size such that wc = 0.074. Calculations tell us that this would provide a sustainable catch of 0.790, an increase of just 3% in both total catch and catch­rate. A bigger increase of selectivity, say to wc= 0.26, would reward us with a much bigger increase in sustainable catch – by 24%. Still higher selectivity would however lead to decreased catch and at 50% selectivity back to where we started. Now we decide to be cautious, sticking to the original small increase in mesh. The increase in fish abundance and hence in catch rate, though small, will attract more effort to this fishery We can expect such an effort increase to continue until the catch rate is the same as before regulation. If the effort were to increase by 25% we should get the same catch as we started with, but now at a much lower catch rate. But zero profit will have been reached again long before that. We shall end up with about the same catch as before, a slightly lower catch rate, and done nothing to ‘cure’ either over­fishing or its lack of profitability. In the real world it would be rather more complicated; for example larger­
meshed cod­ends are sometimes more efficient than smaller­
meshed ones because of increased water flow and reduced need for towing power. Against that we shall certainly face higher costs in monitoring and enforcing the new net regulations, not to mention the costs of research to ensure the new mesh­size is doing to the population what it is supposed to do.
35
The point of this discourse is to illustrate that in considering such matters as seeking msy or some other related target or ‘reference point’ it is essential to take into account the inevitable reactions of the industry and the fishers to the regulations. This example would naturally have been made much more complicated if we had examined the transition period between one steady state and the other, at the outset of which the catches would have been smaller than the original ones because of the escape of smaller fish which would have been retained by the original smaller mesh. That would have illustrated the truism that there can be no improvement without some pain.
Now for some other considerations. One of them concerns the R* parameter of the B&H or other stock­recruitment function. In general an empirical or assumption error in this can lead to a very wide range of possible msy values, or of corresponding sy values for other reference points connected with msy. However, the f values for msy or the other reference points are much more stable, shifting very little for substantial errors in r. The direction of shift is towards reducing the ‘optimal’ ƒ value, a little further as the expected steady­state catch increases. This again points to the regulation of fishing effort rather than limitation of catch as a better primary regulatory measure.
In addition to this source of systematic error, the annual catch is always affected by the essentially unpredictable natural variation of recruitment, in some species very wide, such as in the small, relatively short­lived clupeids. This means that seeking to limit f appropriately by setting catch limits is hazardous and can lead even to oscillatory changes. As we have seen from yield­per­
recruit models the value of f required to meet policy goals does not depend on the number of recruits. And if fishing effort is restrained – as it should be ­ there is little point in making great efforts to predict the eminently unpredictable number of recruits, unless perhaps to prepare on­shore processing facilities to handle highly variable landings and such like operational arrangements.
36
The asymmetry of curves of sy against f is such that msy’s can be dangerously close to fishing intensities that will lead to irreversible unintended stock declines, especially as the density­ dependence of recruitment begins to bite. This is especially true in situations where the function defining the relation between spawning stock and recruitment has been misjudged in such a way as to predict too­high msy’s. Furthermore, stochastic simulations have shown that efforts to target msy, whether from an over­fished or an under­fished situation, by setting sequential catch limits, are not efficient, commonly over­shooting the target and causing unintended further depletion of the stock.
The example given above of an attempt to improve a fishery by modifying a single input parameter – in that case selectivity – shows that, too, can be counter­productive. The same can be said about regulation through control of fishing effort while leaving selectivity to change freely, but generally the consequences would not be so negative. On the other hand attempts to reach a selected target only by controlling one parameter of the output – the catch – will almost certainly have unintended and deleterious consequence of a variety of kinds. That remains true even if an additional output parameter – e.g. the size of fish caught and landed – is regulated by setting minimum legal lengths. In this case, since fishers are technically – and operationally – unable to ensure that they do not unintentionally catch under­sized animals, an unnecessary waste of discarded fish is inevitable. Similar wastage occurs when for whatever reasons catch­limits are exceeded, if only temporarily.
Most fisheries have unintended catches of non­target species, including vulnerable or even threatened ones. A policy that aims at keeping fishing intensity well below that which is expected to provide the highest sustainable yields can be expected in itself to reduce the unintended catches proportionately and so contribute to the conservation of non­target species.
In recent decades changes in markets and technology have sometimes led to dramatic – and, occasionally, catastrophic ­ 37
changes in the selectivity of a species­fishery. The most well­
known is that for NE Atlantic herrings which were exploited for high yields, almost certainly sustainably, for over a century by the capture of migrating spawners in drift­nets for direct human consumption, then in later years – after World War II ­ by seines for fishmeal and oil, with no lower limit to size. A change in selectivity, from about 30% (wc = 0.3) to 10% (wc = 0.1) or less, quickly led to a shift in the fishing mortality from less than the old msy level to well above the msy level pertinent to the new selectivity. As we have noted the f value for msy diminishes quite rapidly as selectivity is decreased, whatever the value of m. Thus the likelihood of over­fishing and collapse resulting from a shift from fishing for human consumption to fishing for industrial products is caused as much by a change in the selectivity of an unregulated fishery as by an increasing fishing effort inspired by the new and practically unlimited market.
The current arguments about the huge jack mackerel fishery in the Southeast Pacific illustrate an early stage of a similar developing situation.
It is of some interest that the definition of management objectives in the 1958 UN Convention on Fishing and Conservation of the Living Resources of the High Seas emphasized the sustainable production of food for human consumption: “measures rendering possible the optimum sustainable yield from those resources so as to secure a maximum supply of food and other marine products. Conservation programmes should be formulated with a view to securing in the first place a supply of food for human consumption.” The idea of priority for food for human consumption was eliminated from the UNCLOS of 1982, possibly because in the interval more countries in need of better food supplies had taken up industrial fishing in the expectation of profits from the export of the products being used to pay for other imported foods. Efforts by FAO to develop interest in the production of food from fishmeal for direct human consumption were not successful.
38
The Global Picture
The World Bank and FAO recently published (“The Sunken Billions: The Economic Justification for Fisheries Reform”, 2009) a study by staff of, and consultants to, the two international organisations which concluded that the global catch is now in the region of ‘MSY’, that costs of catching far exceed the market value of the catch – thus requiring massive subsidies – and that a large reduction in fishing power and deployed effort would lead to profitability and limited sacrifice of total catch. The economic analysis is, I think, pretty sound but the biological treatment is poor because the consultants applied ‘traditional’ surplus yield models crudely – and, I think, improperly ­ with alternative ‘MSY­
levels’ at 50% and 37% of the unexploited fish biomass – whatever that was! I published a critique of this (see References, below) but consider the unofficial Bank­FAO conclusion to be qualitatively if not quantitatively, correct. In my opinion the study’s assumption that current catches represent a global MSY is erroneous, and also these surplus yield models, giving rather peaked curves of sy against stock size (and also taking no account of selectivity), greatly over­estimated the likely sacrifice of yield with reduced effort. Nevertheless the World Bank­FAO Report was a brave and useful attempt to step back from the world­wide fisheries crisis and provide a global, economic and social perspective with great long­term consequences.
Conclusions
There are evidently numerous substantial economic, social and ecological advantages to be gained by managing fishing to keep fish stocks substantially above the population sizes – ‘levels’ (biomasses and numbers) ­ that are thought to be necessary to generate maximum sustainable yields. That requires an intensity of fishing substantially less than for the ‘maximum’ requirement. This is always true regardless of the fact that the msy ‘levels’ (and the fishing intensities required to sustain them) vary greatly. That variation depends principally on the selectivity of the fishery, by 39
size, and also – but to a lesser degree ­ on the biological characteristics of the exploited species. Those are signified mainly by the ratio of natural mortality to the body growth exponent, and by the effective fecundity of mature females and the density­
dependent natural mortality rate of eggs, larvae and juvenile ‘pre­
recruits’ that together determine the level of the annual recruitment.
Such management is required: ­ to ensure sustainability and profitability;
­ to enhance overall profitability in terms of the difference between the market value of the total catch and the cost of taking it; ­ to keep the catch rates of fishing units high enough for them to be profitable as well as again playing a substantial role in feeding human populations; ­ to minimize the risk of unintended depletion of the resource by excessive fishing intensity and uncertain stock assessments and lack of knowledge about the dynamics of the stocks and the ecosystem of which they are a biologically important component;
­to minimize the impact of fishing on the integrity and productivity of the marine ecosystems as a whole in which the managed species live;
- to provide that the fish­size and sex compositions of the catches are economically advantageous;
- to minimize non­target catches that generate enormous discards of unwanted fish of both target­ and non­target species
All of these benefits can be secured by appropriate regulation of the inputs to (fishing effort, gear selectivity), and outputs (catches) by the industry. Of these, regulation primarily of the inputs is more effective and efficient, for numerous reasons. These arise from uncertainties about near­future catches, especially due to highly variable recruitment and unpredictable changes in the availability of fish, and also from uncertainties in understanding the relationship between recruitment and parent stock in particular species and situations. All theory shows that it is 40
preferable to set targets for fishing mortality rate than for catch, partly because of the general shapes (flat­topped, asymmetrical) of curves of sustainable yield against fishing effort and selectivity. Thus there can be big changes in profitability arising from major changes in fishing effort but with little consequent change in average catch.
It should be said here that even if ­ as strongly recommended in this Brief ­ limitation of inputs were to be the primary regulatory action, it would, in some circumstances, be beneficial to designate secondary rules, such as specific size limits and catch limits.
Acknowledgements
I particularly wish to thank Michael Earle and Tim Holt for patiently reading, commenting on and helping edit and format this Brief, and Tim for producing the illustrations. Residual errors are still mine.
41
TECHNICAL NOTES
There is nothing so practical as a good theory
Kurt Lewin (psychologist) & Richard Feynman (physicist)
The purpose of models is not to fit data but to
sharpen thinking Sam Karlin, mathematician.
The assertions about fish populations and management made in this brief are mostly derived from a combination of a vast body of the literature of fisheries science, and the properties of a generalized model of population dynamics. This latter is a form of the model for steady­state yield­per­recruit as a function of fishing effort and selectivity of fishing developed in the 1940s­50s mainly by R. J. H. Beverton and myself and used extensively by very many others since then. It is combined with our simple parallel model relating annual recruitment into a fish stock to the fecundity of the mature part of the stock and the pre­recruit density­
dependent mortality rate of youngsters (‘pre­recruits’). Together these constitute what we called a self­regenerating model.
The model contains only four parameters which determine its properties, viz.
1. M/K (referred to here as m), the ratio of the rate of natural mortality, M, of recruited animals (that is, those that could be liable to capture and of possible interest to fishers) to a growth parameter K that defines the rate at which the increase in weight of a growing fish slows down as it approaches a final maximum size in very old age, if it survives. This growth parameter – an exponent ­ is considered to be specific to each kind of fish and has a narrow range, mainly between 0.5 and 2.0 notwithstanding a 100,000­fold plus range of size of animals to which it can apply, from anchovies and the common sole to the gigantic blue and fin whales of the Southern Hemisphere. It might change, however, with the ambient water temperature.
2. F/M (here referred to as f), the ratio of the fishing mortality rate F to M, which can be proportional to the intensity of 42
fishing – expressed as deployed fishing effort per year, appropriately calibrated;
3. A selectivity coefficient wc, which is the weight at which fish first become liable to capture by the operations and gears in use as determined by technical features such as mesh or hook size used, limitations such as minimum legal size, the preferences of the market, as well as the times, seasons, depth and locations of operation. wc is expressed as a fraction or percentage of the weight, W, that the fish will finally approach if it lives long enough;
4. A number r, between one and zero, which is the fraction that the average number of recruits to the unexploited (‘virgin’) population is of the maximum number that there could be, theoretically, if the number or biomass of spawners was infinite. r is closely related to another occasionally used parameter, steepness, h, that expresses the fraction by which the recruitment would decline if the spawning biomass were to be reduced (essentially by fishing) to one fifth (20%) of its initial size: h = 0.2/(1 ­ 0.8 r). The choice of 20% is arbitrary but appears to have been motivated by an assumption that this represents a “safe” lower limit – in management terms ­ to the size of the spawning stock, perhaps a limit above which it is reasonable to assume there are no depensatory processes (also referred to as ‘Allee effects’) operating that could threaten to exterminate the population.
Two other quantities ­ R, the average (and often extremely variable from year­to­year and essentially unpredictable) annual number of recruits to the fishable population, and W ­ do not in themselves affect the interpretation of the dynamics of the exploitable/exploited population. Sustainable yield, sy, is represented here as an index, a decimal number less than one, which provides the actual yield when multiplied by the product R x W, in whatever units W is expressed.
The original Sustainable Yield­per­Recruit, and Self­Regenerating models, published by Beverton and Holt in 1956 and 1957, dealt with the natural mortality in the recruited phase of the population, 43
and the growth coefficient, K, as separate parameters. However, in 1958 Holt showed that the dynamics of the population depended only on the ratio of those two numbers. Furthermore, subsequent research by us and other scientists revealed that the two components are generally correlated as among species so that the ratio m = M/K has a narrower range of inter­specific variability than either M or K.
Beverton and Holt subsequently (1966) compiled tables of the modified yield­per­recruit model for wide ranges of values of wc and m, and a series of f values from 0.05 to 20.0. Many of the conclusions presented in this Brief can be drawn from a close examination of those tables, but I have also recalculated them with finer parameter intervals and an extended range.
The values of W and K together determine the absolute rate of growth of a fish at any time in its life. That rate is greatest when the weight of the fish is about 30% of W (wc = 0.3) and that approximates to the average size at sexual maturity, although in reality maturity is usually spread over a range of age and size. Given that constant, the value of K determines the age at which the fish is most likely to become mature. In the growth model by L. von Bertalanffy (1938) used here, the size of maturity is reached in 1.1/K years, i.e. it is practically equal to the reciprocal of K. Because at the inflexion of the growth curve at wc = 0.3 the rate of growth changes smoothly, calculations of sustainable yield for selectivities less than or greater than wc = 0.3 exhibit a gradually changing pattern, with yield peaks being replaced by asymptotes.
Another frequently used growth function is that due to B. Gompertz (1825) which provides an asymptotic sigmoid curve of growth in body weight with an inflexion at w = 1/e = 0.37. This inflexion weight is considerably larger than that generally found empirically to be the size at maturity. The Gompertz growth model, applied to populations rather than to individual growth, and a specific form of it due to W. W. Fox (1970), has been seen as an alternative to the simple logistic used 44
by Schaefer and others. It places ‘msy’ at 37% of the unexploited stock size, in contrast to the 50% of the logistic. A modification of the logistic due to J. J. Pella and P. K. Tomlinson (1969) provides, by inserting an additional parameter, a theoretical msy target range from 37% to near 100% of the unexploited biomass. An undesirable feature of these ‘surplus production’ models is that when the MSY or msy ‘level’ is assumed to be about 40% or less even an infinite fishing intensity cannot exterminate the stock. They are thus in that sense – and in other ways, such as involving arbitrary assumptions about the shapes of the curves of sy against F ­ entirely unrealistic. For the analyses summarized in this Brief it has been assumed that M, K (or, strictly, the ratio m =M/K) and W are constants. In reality any or all of them may be variables. In particular M might vary with the age of the fish and also be dependent on the size of the population, and W may vary with the amount of food consumed by the population as a whole and by the individuals composing it, and so also be density­dependent. K might conceivably also be a density­dependent variable but there is little or no evidence for that. Extensive trial calculations have shown generally that although such variability and dependencies will have quantitative consequences many of those will be small, interactive among themselves and with negligible qualitative consequences for the population properties considered here.
By far the most difficult parameter to estimate is r in the stock­
recruitment function and hence for the self­regenerating model. In many fisheries recruitment is not seen to decline much if at all as fishing intensifies and the abundance of spawners is sharply reduced, until the original ‘virgin’ stock is extremely depleted. This is evidence that the value of r is not much less than one, but the eventual decline of recruitment will depend as much on the selectivity of fishing as on its intensity. In the large whales r is surely small and it is possibly in mid­range among the sharks and rays which are much less fecund than most of the bony fishes (teleosts) and thus more vulnerable to unrestrained fishing.
45
The shape of the B & H Stock­Recruitment curve is fixed and derives from the equation R = S/(S+b). (S is the size of the spawning stock and b a scaling factor.) J. G. Shepherd (1982) provided a more flexible model by adding one parameter, an exponent, so that R = Sn /(Sn+b). This becomes the B & H model when n = 1. With n > 1 this can display depensation – the Allee effect. Use of the Shepherd model instead of B & H would make little if any difference to the general conclusions drawn in this Brief.
The self­regenerative models all predict population extermination by a finite fishing intensity if that intensity persists despite evident depletion. While stability and regenerative capacity of a fish population are due mainly to the density­dependence of the pre­
recruit mortality rate that provides a negative feedback controlling population growth, there is increasing evidence that at very low population size or density the direction of density­dependence changes and creates a negative, de­stabilising feed­back that can lead to extermination even if fishing intensity is relaxed or ceases. The self­regenerating model can, with certain parameter values, exhibit depensation as an intrinsic property but it seems likely that it must be provided for more generally and explicitly in future models. However, keeping fishing intensity well below that which will yield msy will normally keep the population far from the level at which depensation might ‘kick­in’, but care would be needed for highly selective fisheries in which very high fishing intensities are required to obtain high or maximum sustainable yields.
The main variable the consequences of which are computed is the fishing mortality rate, F. This is usually expressed as an exponential coefficient, but its value is, like that of M, related to the mortality rate expressed as percentages. Because exponential coefficients are additive the total mortality rate in an exploited population is F+M = Z, but such simple addition is not valid for percentage rates of death (simple percentage rates or their sums obviously cannot add up to more than 100%, but either or both F and M can take values greater than unity). F is proportional to the deployed fishing power (effort) that generates it, properly 46
calibrated. A unit of effort is that which generates F = 1 or some other arbitrarily chosen scale, thus the calibration is particular to the vulnerability of the individuals or shoals of a target species as well as to a fishing method.
It is convenient, for reaching generalized conclusions as in this Brief, to express the fishing mortality as a ratio of F to the natural mortality rate, hence F/M. Fishing power expresses the ability of a vessel or other fishing unit to generate a contribution to the total fishing mortality rate, so it also is specific. The fishing powers of the several vessels in a fleet or fleets are additive if they are calibrated. Rough calibrations can sometimes be made from consideration of the horse­powers of ships’ engines, the sizes of the vessels (lengths, tonnages) and so on, but proper calibration requires a combination of experiments and examination of detailed statistics of catches.
Fishing effort is the deployment of fishing power. The degree of deployment varies from zero – the vessel never leaves port! – to full use which would usually mean operation for as many days of the year and hours of the day as are technically feasible, having regard to vessel maintenance schedules, occasional repairs, crew changes and rest periods, general weather conditions and the like. Properly calibrated and summed the deployed effort would be proportional to the fishing mortality generated. However, where the effort is deployed over a wide area in which the densities (local abundances) of the target species vary from place to place (or from time to time, or both) a weighted sum, called the effective effort must be calculated by methods that have been determined.
Fishing intensity has a technical sense of the concentration of fishing effort in space or volume, analogous to ‘density’ but here I have used it more loosely as a generic term meaning ‘amount of fishing’ – with the corollary that over­fishing is sometimes ‘defined’ as ‘too much fishing’. However it can have a special importance in situations where a high fishing level may have led to contraction of the geographical range of the population.10 10
See A. D. McCall (1990). “Dynamic Geography of Marine Fish 47
Some confusion has arisen because T. D. Smith, in his popular 1994 book11 labeled the Yield­Per­Recruit model “the Hulme model”. He apparently did this because a mathematical colleague, H. R. Hulme, was the lead author, with co­authors Beverton and Holt (in collaboration with M. Graham), of a 1947 letter to Nature announcing the preliminary results of our joint work. Hulme was, of course, important in the development of the general theory but the simple model in the Nature letter had very different properties from the eventual one used here because it incorporated an unrealistic function for growth of individual fishes in weight, as did earlier models by T. I. Baranov (1918), W. E. Ricker (1946) and others. The version with the sigmoid body growth function was published first in 1948 by the Challenger Society as a short contribution by Beverton and Holt, and elaborated in our chapter entitled “The Theory of Fishing” in a book edited by Graham in 1956.12. It is in that book that the idea of ‘rational fishing’, attributed to Graham and his mentor, E. S. Russell, as well as to Johan Hjort, is further explored.
Kurtosis – a measure of the flat­toppedness or peakiness of a distribution that has a maximum y at an intermediate value of x. A common measure compares this with the shape of the Normal (Gaussian) bell­curve, which takes the kurtosis value zero. Positive kurtosis applies to a curve that is peakier than the normal; a negative value describes a curve that is more flat­topped. It is not in general particularly relevant to discussion of fisheries management such as in this Brief, but here it is important in evaluating the benefits of lower rather than higher rates of fishing. But we are not so much interested in the overall kurtosis (which is a function – KURT ­ in the lexicon of, for example Microsoft EXCEL) but rather in the shape of the curve in the upper region of yield close to msy and, especially somewhat below it, that is values Populations”. Books in Recruitment , Fishery oceanography, Washington Sea Grant Program, Wash. Univ.Press, Wash. and London 153pp.
11
“Scaling Fisheries: The science of measuring the effects of fishing, 1855­
1955”, Cambridge U.P.
12
Edward Arnold of London: “Sea Fisheries: Their investigation in the United Kingdom”
48
of f substantially lower than that required to take msy, thus to the left­hand side of the curve of sy against f as it is usually plotted. For that purpose I have used a simpler index: it is the percentage reduction in sy that would occur with unit percentage reduction in f. (When we come to looking at the economics of sustainable fishing a feature of equal relevance is the steepness – slopes ­ of the sy­f curve, especially in the mid­range of the left­hand limb. In that range will usually lie the point at which a further reduction in fishing effort reduces the overall cost less that the reduction in the value of the total catch, so reducing the net profit.
A sister property of kurtosis is skewness or skew, usually designated by the third lower­case Greek ‘gamma’ γ and calculated as the third moment about the mean. A negatively skewed curve ‘leans’ to the right, a positive one to the left, having sometimes a longish right­hand ‘tail’. (sy­f curves rarely have left­
hand ‘tails’ but the calculations of the index of skewness nevertheless apply.) The skew of a curve of sustainable yield against fishing rate can be skewed positively or negatively and can be affected by the degree of density­dependence of certain parameters, especially of recruitment, on the size of the parent population.
There are very important differences between the curves commonly applied in fisheries ‘surplus yield’ assessments and those – as used in this Brief – based on age and size­structured population models. Those differences lead to substantially different conclusions about management objectives. The former are essentially inflexible, arbitrary functions. One that is still frequently used – due to M. B. Schaefer – is symmetrical, and distinctly ‘peaked’ in comparison with the latter types, which are based on actual observations of the birth, growth and death of fishes in exploited populations. Pella and Tomlinson introduced some flexibility by adding another parameter; their curves are asymmetric – can be positively or negatively skewed, although the symmetrical Schaefer function is a special case ­ but are still relatively peaked – even more so than the symmetric Schaefer (‘logistic’) version. This means that use of surplus production 49
models leads to quite serious under­estimation of the benefits of reducing fishing rates below those needed to obtain msy. This is one reason why the global benefits of reducing fishing pressure estimated by the FAO/World Bank publication, ‘Sunken Billions’ – which used the Schaefer model and a negatively skewed form of Pella­Tomlinson, due to W.W. Fox ­ are unreliable. (A negatively skewed curve of yield against fishing rate becomes a positively skewed curve when sy is plotted against population abundance, as is commonly done in presentations of surplus­yield assessments.) The generally positive skew of the age­structured model provides a partial explanation of how it is possible for over­fishing to continue and in certain circumstances worsen because catches do not begin to decline sharply until fishing effort has increased to substantially above the fmsy­level.
Finally given below is the full expression used here for calculating life­time catch from a cohort. The expression is
3
∑ Un (1 – wc
C/R.W = 1/3 n+m
) / ( 1 + 1/f + n/mf )
n = 0
where U0 = +1, U1 = ­3, U2 = +3, U3 = ­1 (Note that m = M/K, f = F/M, so mf = F / K. The ratios f and F / K can alternatively be used as proxies for F or fishing effort or intensity, the choice being made according to assumptions as to the constancy of M or K.) Other references, sources and further reading.
Holt, S. J. (2003) “Foreword” to the 4th printing of R. J. H. Beverton, and Holt, S. J. (1957) “On the Dynamics of Exploited Fish Populations”. Original published by HM Stationery Office, London; 4th printing with Addenda, Errata and Foreword by The Blackburn Press, Caldwell, NJ, USA.
The Foreword contains the citations and explanations of most of 50
the references made in this Brief to relevant publications by the authors and other scientists since the original version went to press in 1954. A few others are listed below. The Foreword is available on request from the author as a pdf file.
Quinn T.J. and Deriso, R. (1999). “Quantitative fish dynamics”. Oxford University Press, New York. This textbook provides accounts of the derivation and properties of most of the population models referred to here.
Myers, R. A., Bowen, K. G., and Barrowman, N .J. 1999. “Maximum reproductive rate of fish at low population sizes”. Can. J. Fish. Aquat. Sci. 56: 2404­2419. Compiled evidence of depensation in fish populations.
Mace, P. M. (2001) “A new role for MSY in single­species and ecosystem approaches to fisheries stock assessment and management” Fish and Fisheries 2: 2­32. Mace has published numerous papers relating to the ‘steepness’, h, of the Stock­
Recruitment function, most of which are cited in this publication. In some of these a related parameter was used to define the shape of the curve in a chosen space: tau = (1­h)/4h. W. G. Clark popularized yet another parameterisation of ‘steepness’: A = 1 ­ h Holt, S. J. (2002) “ICES involvement in whaling and whale conservation and implications of IWC actions” ICES marine Science Symposia 215:464­473 and
Holt, S. J. (2006) “The Notion of Sustainabilty” Chapter 4. pp43­82 in “Gaining Ground: In Pursuit of Ecological Sustainability”, Ed D. Lavigne, published by the University of Limerick, Ireland, and the International Fund for Animal Welfare (IFAW)
These two publications provide summary accounts of the development of population dynamic theory associated with Verhulst, Malthus, Volterra, Pearl, Hjort, and Ottestad and others leading to the ‘surplus yield’ approach to fisheries management associated especially with Schaefer.
World Bank and FAO (2009) “The Sunken Billions: The Economic 51
Justification for Fisheries Reform”. 100pp.
My critique of this is published as Holt, S.J. (2009) “Sunken Billions ­ But how many?” Fish. Res. 97: 3­10.
The Bank and FAO staff leaders of this project were, respectively, Kieran Kelleher and Rolf Willmann. The lead consultant economist was Prof. Ragnar Arnason of the University of Iceland; he ‘developed the theory and modeling underpinning the study and undertook the economic rent­loss calculations.’ Nicole Franz, of FAO, assisted with the statistical analyses, and numerous other listed persons and organizations were involved.
Readers interested in a lighthearted account of the conduct of fisheries research in post­WWII England might enjoy reading “Three Lumps of Coal” (Available from the author as a pdf file). This is the text of an address to a gathering of scientists in Lowestoft, 2008, on the occasion of publication of a book produced by CEFAS, edited by Andy Payne, John Cotter and Ted Potter, entitled “Advances in Fisheries Science”, celebrating (a trifle late) a half century since publication of B&H 1957. Some readers might also be interested in reading the article I wrote for the CEFAS book; a pdf file of that is available.
My Lowestoft talk ended with a celebrated statement – my real reason for mentioning this article ­ by Michael Graham in his seminal 1943 book, “The Fish Gate”, quoted at the UN/FAO Technical Conference in Rome in 1955 preparatory to the Second UN Conference on the Law of the Sea, Geneva 1958:
"The trail of fishery science is strewn with opinions of those who, while partly right, were wholly wrong." Graham’s Bons Mots are as valid today as they were then.
52
APPENDIX 1
SOUTHERN NORTH SEA PLAICE EXAMPLE
This demersal stock was known to be seriously over­fished by steam trawlers in the 1930s. It had partially recovered, in accordance with predictions, because of the suspension of most fishing during the Second World War, a period referred to as the Second Great Fishing Experiment (the first being the First World War). War­time losses had greatly reduced the trawl fleets and the UK proposal to the new international management authority, created in 1946, the Permanent Commission was that they should, in total, not be reconstructed to more than about 60% of pre­war tonnage, and also that the cod­end mesh­size be increased above the prevailing 70mm. There was, post­WWI, no thought of seeking MSY; accepted policy was simply to improve the state of the fishery and of the plaice stock by regulation. The fishery was a mixed one for plaice and sole, but while the price of sole was relatively high the quantity and total value of catch of that species was a relatively small proportion of the total. British, French, German, Dutch, Belgian and Danish trawlers had been engaged but the English was by far the biggest contribution to the total effort.
The pre­war fishing mortality rate of plaice had been about F = 0.73 so this would have been reduced to, and held at, about 0.44. The natural mortality rate, M, was estimated as 0.1, so f = F/M had been about 7.3 to be reduced to about 4.4. Pre­war this fishery was thought to have been close to a steady­state but had become barely profitable.
The ratio m = M/K was estimated to be 1.2 wc was 0.043 of W = 2.8 kg. I here round these, respectively, down to 1.0 and up to 0.05, so the results can easily be compared with the tables in this Brief. No evidence was found for changes in the average recruitment though it might have been higher in the late 19th century and the early years of the 20th, before the biomass of the stock had been substantially reduced. 53
With these parameter values fmsy would be about 1.4 So the proposed fleet reduction would hardly have ‘cured’ over­
fishing, but the sustainable catch would have been 18% bigger with a catch­rate 86% higher than the pre­war catch and catch rate, so should be profitable. A further fleet reduction to fmsy level would have provided a further increase of 29% in the total catch.
Relatively small increases in cod­end mesh size would have brought worthwhile increases in the sustainable catch of plaice, if the fishing mortality rate were to be held at f = 4.4. The benefit can be appreciated if we were to assume that the mesh would be increased to, say double wc, to 0.1. The additional gain in sustainable yield would be 31%, with a corresponding gain in catch rate. Such a mesh change would, however, have led to a significant loss of sole, which would have discriminated against the countries with a strong market preference for sole, particularly France.
If the pre­war situation had really been near the point of zero profit there would have been huge economic advantages from reducing the fishing effort well below that needed to obtain msy with the prevailing mesh size and if the ratio of the price of plaice to the cost of exerting a unit of fishing mortality was unchanged.
The msey of 78% of the msy would be obtained with f = 0.45, so with a catch­rate more than twice as high. 54
APPENDIX 2
North Sea haddock; Example of density­dependent recruitment
The haddock in the North Sea were known to have been quite seriously affected, already in the last decades of the 19th Century, particularly after the introduction of the steam trawlers. Scottish data gave an indication that recruitment to this stock might have declined in the period 1922­1937 when the spawning biomass was declining, after the partial recovery allowed by the drastic reduction of fishing effort in the region during the First World War. But these data were inadequate for determining the parameter values of a Beverton­Holt Stock­Recruitment function. Accordingly a series of five options were calculated in addition to the assumption that recruitment had not changed. These predicted recruitment towards the end of the 1930s decade to be in a range from 0.9 to 0.1 of the recruitment after the First World War. How much less that number was than the steady­state number in the original ‘virgin’ stock is not known, so that, at best, only an over­
estimate of steepness, h, can be calculated from these data.
The yield­per­recruit model gave, for the 70mm cod­end mesh being used at the time (implying wc = 0.2), an fmsy = 3.03. The average values pre­war were F = 1.0, M = 0.2 so f = 5.0. The values for fmsy with density dependence were, as expected, less than with constant recruitment (f about 2.0), but not very much less. The option with the most vigorous density­dependence had an fmsy at about 1.8. The msy predicted from the extreme option was, however, seven times that from constant recruitment. The less extreme options gave msys double or triple those with constant recruits.
55
APPENDIX 3
MSY and wMSY
Quinn and Deriso provide an expression for the time (age of fish) in a cohort – t* ­ when the cohort, declining in number exponentially at a rate M and in which the individuals are increasing in body size according to the L. Von Bertalanffy equation with parameters K and W, attains its maximal total weight:
ln[(3+m)/m]/K
Substituting and re­arranging gives us:
3 wMSY = (3/(3+m))
and
m
MSY = (m/(3+m)) x (3/(3+m))
3
Thus MSY is a simple function only of the fundamental life­history parameter m = M/K
A feature of these expressions is that they show that if m ≤ 1.50, and since fish will always be caught before they reach the maturity size ws = 0.3 ( 8/27 = 0.2963), any attempt to reach MSY would quickly exterminate the population since there would be no following cohorts.
The expression used for the index of biomass of the total unexploited population, derived from the simple sustainable yield­per­recruit model, is:
3
Btotal = ∑ U / (1+n/m)
n
where
n=0
Uo = +1 , U1 = ­3 , U2 = +3 , U3 = ­1
56
APPENDIX 4 THE STOCK­RECRUITMENT RELATIONSHIP
Annex 3 to this brief refers to relevant consequences of annual recruitment depending on the size or activity of the spawning parent stock. I suggest that the easiest way to think about this question at its root may be as follows.
Consider that the mature females in a parent stock (s) shed N viable eggs one spawning season. In the period until the age at which the survivors become the number of recruits R to the stock, this new cohort diminished in number by a pre­recruit mortality rate. The various exponential rates vary at each phase or moment during the pre­recruit period in a manner which is itself linearly density­dependent in relation to the number surviving at each time.
Beverton and Holt, 1957, showed that in this case the initial magnitude of the spawning is related to the number of recruits produced by the cohort by a simple equation involving the asymptotic number of recruits, R* that would theoretically be produced by an infinite number of eggs, and a scaling factor, b. It is convenient to write the ratio r/R* as r*, thus:
r* = 1/(s +1/b).
We know that r* tends to unity when s tends to infinity, and r* = 0 when s = 0.
Now suppose we have two sets of observations for two time­
periods, giving us one average r1 from average spawners s1 and another, r2 from spawners s2 . These can, but need not, be absolute numbers; more usually they would be indices of both quantities that are presumed to be directly proportional to the absolute numbers, most likely from catch per­unit­effort data. R* and b can easily be estimated from the two linear simultaneous equations. Two likely situations where this approach can be followed are:
1. An apparently stable situation where fishing has been continuously intense for several years, the stock possibly 57
having been over­fished for several years with near­zero gross profit – an example is the point of intersection of all the graphs in Appendix 3; and 2. Data are available pertaining to the original unexploited stock or, more likely, from the very early years of exploitation. In this case we can refer to the r/R estimate as Ru , that being the value at which the unexploited stock had settled in a steady­state. Ru alone sufficiently defines the stock­recruitment relationship for use in calculating the self­
regenerating model for that stock, from the yield­per­recruit model results.
Some researchers have defined ‘steepness’, h, as the relative amount by which recruitment would be reduced if the spawning stock in the unexploited population were to be reduced by fishing to 20% of the original effective size . This specified degree of reduction is an arbitrary choice but, however defined, steepness is a simple function only of R*.
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ANNEX FIGURE 1
This illustration is from Quinn and Deriso, 1999, p241, Figure 6.1a It is from data for an unfished population of Sablefish in the Gulf of Alaska. The graph labeled N shows the exponential decline in number of a cohort (M = 0.1) . Graph W shows the average weight of an individual fish as a function of its age, with fitted L. von Bertalanffy function (K = 0.15. Winf = 6.20kg). Graph B shows the product of graphs N and W, that is the cohort biomass as a function of age/time, with a maximum (MSY in our terms) at about eight and a half years.
So, m = M/K = 0.67. The formulae in Appendix 3 of this Brief give us wMSY = 0.55 (54.7%), MSY/R.Winf = 0.175.
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ANNEX: FIGURE 2
North Sea haddock, data from Marine Laboratory, Aberdeen, Scotland, courtesy Basil Parrish/Cyril Lucas.
The above graph is taken from Beverton and Holt, 1957, p325, with the original legend. It is typical of a Yield­per­Recruit curve with constant parameters and with fairly low selectivity as defined in this brief so it has a maximum with finite fishing mortality. In terms of definitions in this brief m = M/K = 1.0; fmsy = 2.50; pre­
war relative fishing rate, f, was 1.0/0.20 = 5.0; t ­lamda is not relevant in the present context, but tells us that ten cohorts contribute significantly to the recruited stock, and nine of them to the exploited phase.
60
wMSY = 0.42, MSY/R.W = 0.1055. wc = 0.04, thus fish were liable to capture long before maturity at ws = 0.3.
This graph, produced in 1948, shows that a reduction of the pre­
war fishing rate by one half would lead to a sustainable catch about 15% bigger, thus with a catch­rate 120% higher. The scale of the peak of the curve indicates that by ‘sacrificing’ only about 5% of the potential msy 95% of the theoretical msy would be secured by exerting only about 80% of the effort required to obtain msy.
The geometry of the figure also shows that a sustainable catch of the pre­war size could have been obtained with only about one quarter of the pre­war effort. Furthermore, if – as was likely ­ the pre­war situation produced just a bare profit or none, a very large maximum gross profit could have been obtained by exerting less than about one­fifth of the pre­war effort.
.
These estimates of the benefits of much less fishing effort in terms of yield per constant recruitment, are minimal because, as will be seen in Figure 3, there was evidence that recruitment was density­
dependent, and average annual recruitment would have been higher with a larger spawning stock being available as a consequence of the imposition of a much lower exploitation rate.
The adjacent Figure 17.25 in Beverton and Holt 1957 (not reproduced here) shows the benefits that would have been available in the pre­war situation by substantially increasing cod­
end mesh size so that age of first liability to capture would be increased by anything up to five years (from 1.8 years), keeping fishing effort unchanged, so that the catch rate would be increased proportionately. The amount of increase in sustainable catch would have been about the same as from reducing the fishing effort to msy level, but of course the gain in catch rate would be only one half of the catch­rate gain from reducing effort by 50%.
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ANNEX 3 EFFECTS OF DENSITY­DEPENDENT RECRUITMENT
This graph is reproduced from the front cover of the 2nd ­ 1993 ­edition of Beverton and Holt 1957, and continued on the 3rd edition; it is not in the book itself. It gives results for analyses of data for the haddock exploited in the North Sea bottom­trawl fishery. The x­axis is the fishing mortality rate; the y­axis is sustainable yield, sy. The figure was prepared by Beverton, I think in about 1990.
The thickly dashed curve is the same as that in Figure 2 of this brief. Above it are three higher curves (two with thin lines, the 62
third – upper – bolder) whose peaks are indicated by a near­
vertical, left­leaning dashed line. These are for three degrees of density­dependence of recruitment on spawning stock abundance as given by the B&H self­regenerating model, using the well­
known B&H stock­recruitment function, R = S/(S+1) (see text). The data series available at the time (1949) indicated density­
dependence but with a low degree of statistical significance; the three sample graphs are all compatible with the data. (The three curves ­ one bold, the others thin ­ whose peaks are joined by a right–leaning dashed line, are not relevant to this discussion. They are there essentially to illustrate the consequences of possible density­dependence of growth rate.)
The important points here are that:
1. if recruitment is density­dependent on spawning stock size, whether weakly or strongly, the value of fmsy is somewhat lower than for constant average recruitment;
2. weak or strong density­dependence of recruitment on spawning stock size has very big implications for predictions of msy but relatively little for fmsy. So, efforts to regulate towards msy by control of catches are likely – I think virtually certainly ­ to fail because of the inevitable great uncertainty in estimates of the strength of density­
dependence of recruitment on parent stock. Control of fishing effort is far more likely to be successful.
In the present context – discussion of f less that fmsy – this matter of recruitment dependence is less important than in broader consideration of rational fishing, because attention is directed mainly to the benefits of maintaining a relatively large stock – closer to the original unexploited size ­ in which recruitment density­dependence is likely to play a rather small part, at least as far as most of the bony fishes are concerned.
Finally, it is worth noting, from this example, how perilously close to collapse and extinction persistent overfishing can bring the stock and fishery. 63