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Rescuing Maximum Sustainable Yield

November 7, 2011

Editor’s Note: I am pleased to publish another excellent guest post by Sidney Holt that explores how we might best diverge from MSY to achieve rational and sustainable targets.  Importantly, his analysis leads us to consider how we should better regulate fishing inputs.  The mathematics may require a few readings, but you will find the examples are quite powerful. I also encourage you to read Sidney’s first post exposing MSY as The Worst Idea in Fisheries Management and his second post on how we might conduct An Overhaul for MSY to incorporate other standards, such as the concept of maximum economic sustainable yield (MESY).

By Dr. Sidney Holt

I promised Mark Gibson, the ‘master’ of this web-site, that I would offer some constructive suggestions about how to make fisheries management rules and procedures that conform with both the words and the intent of the UN Convention on the Law of the Sea (UNCLOS) This is my try at two things: suggest how far away from a hypothetical MSY target a satisfactory management aim might be, and suggest the reasons for, and implications of, trying to reach such an objective primarily by regulating fishing power and effort and the selectivity of fishing gears, practices and operations.

Wherever is MSY?

Many years ago, after completing our book on the theory of fishing, my colleague Ray Beverton and I prepared a set of tables of our simple population model which provides number for the sustainable yield per annual recruit from a single fish population. This was done to help scientists without access to calculation facilities; the tables were published by FAO of the UN in 1966 as FAO Fisheries Technical Paper 36  and later reproduced in part in John Gulland’s 1983 textbook on ‘Fish Stock Assessment’. The tables are little used now that everyone has access to a digital computer, but the advantage of such an exercise is that gives one a chance to see the wood for the trees. It is that sight on which I am now drawing. I shall not justify in detail all my conclusions and suggestions but that will, I intend, be provided in an article in a scientific journal.

First let us remember that for any given stock there are an infinite number of MSY-generating situations and which one we adopt depends on the pattern of exploitation, the selectivity of the fishery. Consider a generally unselective fishery. No commercial fishery exploits the eggs, larvae and baby fish as well as the mature adults. It’s convenient to assume, for this exposition, that exploitation by a gear such as a bottom trawl begins when the size of the fishes is at about 10% of the weight they are likely to attain if they live long enough. For orientation it is worth bearing in mind that most bony fishes become sexually mature when they are a bit less than one third of their theoretical final weight, and that this is also the size at the inflexion on the curve of weight against age; that is, it is at the point in life when the rate of growth is most rapid; e.g. in kgs/yr.

The biggest sustainable yield per recruit (which I’ll call potential MSY and represent as MSYp ) is obtained by catching all of each entire year class) only when that cohort has reached its maximum total weight, but that could only be achieved with a theoretically infinite fishing effort. So, these two situations – minimally selective fishing and extremely selective fishing – give us the full range of situations we need to look at in our tables. It will be convenient to talk about one or more intermediately selective operations, and I chose, to begin with, that pertaining when fish first become liable to capture, by specified gears and operational methods, when they reach 30% of their potential final size, if they live long enough – close to the growth-curve inflexion and attainment of sexual maturity. The MSYp and the age and weight at which it is reached depend only on a single constant parameter, a ratio of natural mortality rate and growth rate, which we call M/K

We express mortality rates – that due to natural causes of all kinds (M) and that due to fishing (F), as exponentials because they appear as the exponents in certain kinds of mathematical functions. The Reverent Thomas Malthus knew about these when he was writing, early in the 19th Century, about rates of increase of human populations, except that he expressed them as annual percentages and referred to the growth as geometric.  There is a simple relationship between the two. Survival rate is minus the natural logarithm (ln) – that is the logarithm (log) to base e rather than the usual base 10 (e is a magic number, 2.7813, which often appears in a branch of mathematics, differential and integral calculus, that plays a big part in modeling, differential being about rates of change, and integral about the sums of numerous events.).  As an example: a survival rate of, say, 0.7 ( 70%) – implying a mortality rate of 30% would be caused by an exponential rate (sometimes called an instantaneous rate) of  0.36.

One great thing about exponential rates, and a reason we use them, is that they are additive. That is, if the natural mortality rate in a fish population is M and the mortality due to fishing is F, then the total mortality is F+M, which is usually represented in the literature on this subject as Z. That cannot properly be done with percentage rates. Instantaneous rates are more familiar these days when we talk about the decay of radioactive substances, or how long a filament light-bulb is likely to last, which are exponential. But that are commonly expressed in terms of the half-life of the element or kind of object in question – the length of time before half of the atoms in the pile have transmuted or half the bulbs have failed. We can express mortality and survival rates the same way. For example: if, in a fish population, M or Z = 0.2 (that’s an annual mortality of 18%) then half the original number will survive for three and a half years; that is the half-life of the age-class or cohort.

Another exponential parameter we have to become familiar with is K. This is one of two parameters in an equation for body growth through time that generates a curve with an inflexion at 30% of the final size, Wmax . K determines the curvature of the S-shaped (sigmoid) growth curve. For example the growth rate at the inflexion is always K x 0.4444 x Wmax  . With this information we can easily define the equivalent of the idea of half-life, such as the age of the fish when it has grown to half its final size or, if you like, to maturity at 30% of that; the first of these is  t = 1.58/K and the second is t 1.11/K.  We could just as easily define part-lives, as insurers do when they estimate how many of their customers are likely to reach pensionable age. I use the term ‘likely’ here because the mortality and survival ratios are obviously closely linked to the concept of probability. We are not saying which animals will survive the half life of the population in question and which will not, but it does tll us about the probability that any one of them will die then or earlier. Before we continue we remind ourselves that, as Alan Longhurst showed in his fine recent book – The  Mismanagement of Marine Fisheries – most fishes continue to grow throughout their lives, which is why I refer to theoretically final size since that would only be reached if they lived for ever.

Now it turns out that in simple models of unexploited fish populations what determines their behaviours are not M and K separately, but their ratio,  M/K.  Similarly, the properties of exploited populations are determined (in addition to the role of M/K) not by F and M separately but by their ratio, F/M,  This relationship is sometimes expressed in a slightly different way; E = F/(F+M), E being referred to as the exploitation rate, and that is used in the tables already mentioned. I shall stay with F/M because F, and therefore F/M (but not E) is roughly proportional to the fishing effort exerted to generate it, provided the measure of effort is calibrated properly. When that is understood our consideration of MSY and associated numbers is simplified and more easily generalized. That’s why this little algebraic diversion was necessary. [Identities useful in consulting publications, including the reference tables, are F/M = E/(1-E) and  E = F/M/(F/M + 1) ]

So now let’s go back to MSYp , and for now we shall always be talking about the MSY per recruit, and expressing it as a fraction (percentage of the final individual size, W.  It, and the point on the individual growth curve where MSY is obtainable, wp , depends only on the value of M/K. If natural mortality is low compared with the growth rate the MSYp is relatively high, as is the wp .  If for example M/K = 0.5, the MSYè  per recruit would be 0.24 (24%) of W.  and obtainable when wp  is 0.64 (64% of W). If the ratio is bigger than one, say M/K = 1.5 – faster dying relative to the growth rate – then the MSYp would be much less – only 0.057 (6%) . and wp  would be smaller, at 0.287 (29% of W).

As I have said, the MSYp  could only be obtained by generating an infinite fishing mortality, and hence exerting an infinite fishing effort, at the selected size and age. But suppose we would be satisfied to catch a majority of the fish at the appropriate age but not all of them, That could be done with a finite effort.  In our case with M/K = 0.5 our tables tell us that the catch would be as much as 95.5% of the value of MSYp  if a fishing mortality rate were generated of four times the natural mortality rate. That’s pretty intensive fishing but it might be feasible, while trying to maximize the catch in this way would be crazy. This all comes about because the curves of sustainable yield against F/M are rather flat-topped. We shall see later how important that feature is when discussing in general whether aiming at MSY in any circumstances is rational. In the case of M/K = 1.5 generating a fishing mortality of four times the natural mortality would yield, sustainably, 97.2% of MSYp . If we would be content with ‘only’  95.5% of MSYp we could obtain it with less fishing effort, just enough to generate a value of F a bit more than three times the natural mortality rate, making a saving of 25% of the cost of taking the catch by deciding to forgo 1.6% of it. That’s better business!

The examples I have given are well within the parameter space we commonly find in fisheries research. In fact the value of M/K is relatively invariable, because natural mortality and growth rates often seem to be correlated, across species. I can quote as an example calculations Ray Beverton and I made for the plaice in the North Sea as our first such assessment, published in 1956. We had estimated M = 0.1 and K = 0.095 so M/K = 1.05. We found that the pre-WWII value of F/M was very high: 7.3.  At that time, with the cod-end mesh-size then in use and with the prevailing pattern of North Sea trawling the plaice first became liable to capture when they were between 3 and 4 years old, and had reched about 7% of their estimated final size of nearly 3kg. We also noted that the sustainable catch would be increased by nearly 50% if the fishing effort were to be reduced to 27% of the pre-war level (F/M down from 7.3 to 2.0).  We also calculated that, given the pre-war fishing intensity – resulting in extreme over-fishing – the sustainable catch would be doubled if mesh sizes could be increased and/or changes made in the geographical distribution of the fishing effort in such a way that plaice only became liable to capture when they were nearly ten years old. Beverton and I did similar sorts of calculations for North Sea haddock using data from the Scottish trawl fishery and advice from our Scottish colleagues;  M = 0.2, K = 0.2, so M/K = 1.0, F/M = 5.0,  F/M for maximum yield about 2.5, that is with half the effort; age at first liability to capture one year; final size 1.2 kg. (I should say that at the time Beverton and I were not aware that our results could be obtained simply by using ratios of the natural mortality and growth parameters; I later discovered that and published it in 1958. The algebra is included in the 1966 FAO booklet with the yield tables and in some more recent textbooks.)

Time for a tea-break, and then we’ll look at the rest of the tables and exemplary calculations.

So, simply as an exercise I’ll look at a situation in the same ball-park as the old plaice and haddock examples, these being very different sorts of fish but evidently – given the similar parameter-ratio values – not that different in terms of population dynamics. We’ll consider M/K = 1.0. and begin with a small size at first liability to capture of about 0.1 (10%) of the asymptotic weight. This provides a maximum sustainable yield per recruit at 8.5 of the asymptotic weight of individual fish, whatever that might be, a yield that is about still be 80% of MSYp , with F/M = 1.9. Not bad! But if fishing effort were reduced to just a bit more than half that, (F/M = 1.0), the yield would be 79% of the MSY for this selectivity. Very much better! By halving the effort we would forgo less than 3% of the ‘local’ MSY.

From now on I’ll refer to any MSY corresponding to a particular, specified size at first liability to capture other than that yielding MSYg as a local MSY and symbolize it as MSYl . Now, if selectivity were to be retained at the level necessary for MSYp but an effort was exerted simply to bring F/M to 1.9, as in the example above, the yield would be 85% of MSYp .That would be 8% more that obtained from the unselective fishery at its MSY level, and 9% more than would have been obtained by reducing F/M from 1.86 to 1.0. There is, in this case, obviously practical advantage in reducing the fishing effort far below what is needed for MSY and increasing the size and age at first liability to capture.

Are you still with me?  Now let us look at the intermediate selectivity example in which the fishery is entirely devoted to catching fish as they attain, or after they have reached sexual maturity and are reproducing, so conceiving a future recruit cohort.. The MSYL catch would be 99.8% of MSYp but it is 26% more than what would be gained from MSY applied unselectively; it would however require nearly five times as much effort (F/M = 9.0): probably not a good deal. This example shows, however, that while increasing selectivity can bring limited awards in size of sustainable catch, it is important not to overdo that and also to be prepared to pay more for it in fishing effort. Actually one could do better – even if one wanted to catch only adult fish, by sacrificing a little of the ‘local’ MSYL catch – say only 3% of it – by reducing the effort by nearly a half  (F/M from 1.86 to 1.00).

Other arbitrary benchmarks for looking at alternative strategies and consequences can obviously be chosen. Some of those that have been suggested by other scientists are defined and discussed in Emygdio Cadima’s ‘Fish Stock Assessment Manual’, published in 2003 as  FAO Fisheries Technical Paper 393.

We are used to considering ‘halves’ in many situations – half lives, glasses of water half-full and half empty and so on. One such could be selectivity such that the size at first liability to capture is 50% of the estimated final size. Another, perhaps more interesting, choice – because it involves the combined effect of natural mortality and body growth –  could be first liability to capture being at a size corresponding to the attainment of 50% of  the potential MSYp . Let’s look at the latter case first. For the M/K = 1.0 scenario it so happens that MSYp  per recruit is 0.1055 at 0.42 w. 50% of MSYp is coincidentally at 0.1w so we already know what the consequences will be. Now looking at the former 50% chosen selectivity, we find that MSYL for  w = 0.5 is 0.1032, that’s just a bit more than 2% less than MSYp . We would get the same value of local MSYL  with w = 0.35.  at F/M = 0.82.

As we used to say in London’s street markets where I grew up “Yer pays yer money an’ yer takes yer choice”. The results of which I have given examples for one vaiue of M/K will be quantitatively different but not qualitatively different for stocks with a different ratio of natural mortality to growth exponents.

The Yield-per-recruit tables can be used to provide comparative values for other metrics. One of the most useful is the average weight of fish in the catch. This will decline as exploitation begins and intensifies, not because of changes in growth rate as some have thought (If such changes occur they are most likely to be in the opposite direction.), nor mainly because some people think that fishermen deliberately go for the biggest fish (which they would like perhaps to do but usually in practice just cannot) but because the more intense the fishing the more – even unselective – fishing, the more the stock composition is influenced by recent recruitments. Again, the ‘half measures’ can be calculated – that is, at what selectivity or fishing intensity will the average size of fish in the catch be half of the size in the unexploited stock. And correspondingly for the average age of fish in the catch or population as a function of F/M and M/K.

Now I think we have to look at something else. We have been considering until now only catch-per-recruit. But adding fishing to the natural mortality, which reduces the biomass of each cohort and thus of the entire population, must reduce the total number of eggs laid, and the numbers of larvae. When that happens perhaps we have to expect that the number of recruits will eventually be reduced. In fact seeking to keep a fishery in the region of a local MSY – whatever selectivity is chosen – usually means that the F/M ratio will be lower than it is likely to be if fishing pressures are given full-rein. Many historical studies have failed to find the expected decline in recruitment as fishing intensifies, but recently, and for some types of fishes, intensification of fishing has increased (often resulting from a marketing and processing change, for example from fish for human consumption to fishmeal) and declines in recruit numbers have been observed and steeper ones feared. This has led some scientists to define a quantity they call ‘steepness’, which is a measure of how fast and far such a decline might happen; it has been quantified as the percentage that the recruitment  would decline if the biomass of the mature part of the stock were to be reduced to one fifth of its abundance in the pre-exploitation, un-fished  stock, on the assumption, that at least to a first approximation that biomass is roughly proportional to the numbers of eggs laid, then larvae surviving, followed by a corresponding – but not proportional – recruitment decline.

The equation most commonly used to express an overall relation between the spawning stock and the recruitment is one that Ray Beverton and I proposed in 1967. It is asymptotic, meaning that when a stock starts very large and is reduced recruitment will not change much, or noticeably (given that in practically all bony fishes the degree of variation in recruits from year to year is enormous). It is important however, to realize that the pre-exploited stock does not generally settle at an equilibrium producing near to the maximum numbers of recruits on average, but settles at something less than that. How much less is important, but quite difficult to measure. The Beverton-Holt stock-recruitment function predicts that when the stock is very greatly reduced, perhaps in severely over-fished situations, the recruitment begins to decline practically proportionately to the size of the parent stock; this is obviously a situation to be avoided at all costs. Furthermore, it is quite likely that at some low point the system will become unstable and the stock will move on its own accord to extinction even if a moratorium on exploiting it is declared. Some scientists have, throughout the history of fisheries science thought that this is unlikely to happen because fishing will become unprofitable before any danger point is reached and will cease or relax in the nick of time. That is however a dangerous hope because so many fisheries involve several species and operations aimed at the more abundant species or stocks will carry on and, incidentally continue to deplete those that were once preferred but are now not sufficiently abundant themselves to sustain an industry. The sorry case of the blue, fin and sei whales in the Antarctic is a classic example of such a situation.

Aiming at MSY should not in itself bring stocks to such low levels that recruitment is seriously affected and even the continued existence of the stock threatened. But we can say for sure that if there is any such effect the fishing effort required to obtain a real maximum sustainable yield – not merely an MSY per recruit, will be less than that required to take MSY if recruitment is not affected by a decrease in the size of the mature stock. The degree to which this shift occurs depends upon many circumstances, and calculations have to take account of the fact that fishing in any case shifts the age-composition of the population towards a higher proportion of immature fishes. But we can be practically certain of the direction of necessary adjustments – the fishing intensity must be less than that required for MSY catches, whatever degree of selectivity is chosen.

Another favoured stock-recruitment relationship was proposed by William Ricker in connection especially with his research on Pacific salmon. In Ricker’s model there can be a peak in recruitment at a finite spawning stock size and larger stocks have fewer recruits; his curve is not necessarily asymptotic. The consequences of exploiting such populations depend on whether the unexploited stock settles at a size greater of smaller than that for maximum recruitment. Nevertheless the ultimate result near the level for MSY per recruit is that the F/M for MSY with recruitment dependent on stock size is less than that for an invariant recruitment.

The assumption of recruitment dependent on spawning stock size introduces a form of density dependence that results in positive feedback in the system, and this is a source of possible instability; a chance reduction of the number of recruits below the norm for the given spawning stock size results in a smaller stock and hence a possibility for an even smaller recruitment. The feedback is stonger the steeper the S-R curve, which creates a clear danger from allowing fishing to reduce the stock too far.

A further consideration, if one is able to control the selectivity of the fishery is to accept that it will be in general beneficial to be less rather than more selective. That way the catch – or, rather, the yield per recruit – would normally be significantly less than it might be from a more selective operation but the costs will be very much less, and the rate of profit higher. As we shall discuss later there would possibly be other benefits from a lighter fishing-‘footprint’ on the stock.

The simple model for sustainable yield-per-recruit from which the tables I have used to select examples are derived can be combined with with the chosen stock-recruitment function to provide a more complex model of what Beverton and I called a self-regenerating system  A few years later John Shepherd derived a more flexible stock-recruitment function and also showed how the algebraic expression for a self-regenerating model incorporating it could be solved; without that rather tedious iterative calculations are needed.

Another problem we face in deciding what would be an optimal fishing intensity below any MSYL threshold, regardless of any changes in recruitment as a stock is reduced, is – recognizing the examples of how the cost of catching can be substantially reduced by forfeiting a little of the maximum sustainable catch – to determine just how far it could be reduced in certain circumstances in order to maximise the gross profit, that is the difference between the market value of the catch and the cost of catching it. There are of course many complications in that, two of the most important probably being the elasticity of supply and of demand – how much will the price change with changes in the quantity for sale – and the discount rate, which attributes lower market value to future catches and stocks than to current ones. Nevertheless, in looking at sustainable economic yields and MSEYs it will normally be the case that the curves of those against fishing effort will, like the physical yield-per-recruit curves, usually be rather flat-topped. This means that if a little total profit is forfeited then one could expect to be able to increase the rate of profit. In an important paper by John Gulland published in 1968, and a later one by Gulland and Luit Boerema in 1973 entitled ‘Scientific advice on catch levels’, a metric was offered that would place F/M a computable but nevertheless arbitrary amount below that for MSYL in general, which has since been used rather frequently in fisheries management. This idea, based on the notion of the marginal yield per recruit, was then elaborated by noting that an approximation to MSEY would be obtained when the value of F/M is set such that the marginal yield – expressed as monetary value –  is equal to the marginal cost of a unit of effort.

To illustrate this let us look at a curve of SY against F/M and assume that the value of the catch is proportional to its size and the cost of taking it is proportional to F/M. In reducing F/M below the level for local MSY we look at the slope of the curve. Assume the difference between value and cost at the local MSY is zero (no profit). Reduction of F/M will lead to a lost of value less than the reduction of cost of catching, producing a profit. However as effort is further reduce the profit will also be reduced, and it is straightforward to find the point of maximum profit.. Take an example: M/K = 1.0, w = 0.3. The local MSY per recruit is 0.103 of W, at F/M = 9.0   The ‘optimum, where profit is maximum is found at F/M = 1.86, and the SY is .0944 , showing a five-fold reduction in effort from that required to take MSY, for a sacrifice of only 8.5% of the catch. With information about rate of profit or loss at any value of F/M we can deduce the optimum effort.

There is yet another reason for choosing to aim at a management target that is more conservative that seeking MSYs and that is the asymmetrical consequences of estimation error and other uncertainties. Long ago an Australian engineer- computer expert turned biologist, William de la Mare, demonstrated, by simulations, how aiming at an MSY target, sought by setting TACs, must nearly always miss, on the dangerous side – that is towards unintended over-fishing and even stock depletion. He developed his method in the context of regulation of whaling but his approach is entirely applicable to fishing in general.

Now I come to the last of my reasons for caution with respect to how much catch we want and how much energy to expend to get it. There is much talk these days – and with good reason – about developing an ‘ecosystem approach’ to the management of fishing, as well as other human activities affecting life in the ocean. This is not the place to discuss the several ‘approaches’ to such an approach. But I think one thing is clear: that a basic management system for fishing that keeps the fishing intensity relatively low, and hence the fish stocks relatively abundant, will contribute to an ecosystem approach, even if the biomass removed from the marine system by substantial sustainable catches is large though not theoretically maximal. The relatively ‘light touch’ will also – especially if it is relatively unselective – not alter the ‘natural’ structure of the fish populations (by age, size, sex etc.) as much as would intense fishing, and especially highly selective intense fishing. There an be several possible exceptions to this rule but it is worth considering as the default.

So now for the last part of this long spiel: why is it far better to manage fisheries by regulating inputs (fishing power and effort) that outputs (catches) by setting TACs? First, what are the primary reactions of fishermen and fishing companies finding that their rates of catch are diminishing as ‘virgin’ stocks begin to be depleted?  For the fisherman, or the individual fishing unit, or company, it is to try to increase efficiency, usually by technical means, by improving gears, introducing new instruments such as echo-sounders to enhance search, and so on, and at the same time reduce the cost of exerting a unit of fishing effort. This is an illustration of what I long ago wrote about as Holt’s second Law of Fishing: The operators will always react to regulation in such a way as to negate the intended effects. (This is analogous to Isaac Newton’s law in mechanics – that to every action there is an equal and opposite reaction. The first law of fishing is due to Michael Graham, as expressed in his marvelous 1943 book ‘The Fish Gate’:

Fisheries that are unlimited become inefficient and unprofitable.

Then, setting a TAC appropriately requires estimating next year’s recruitment in advance, or making an assumption about it. Even if one were by chance to get that right any errors in the assessment are likely to generate unwanted positive feedbacks.

The greatest and most persistent trouble has come, however ,from very high TAC- caused discards of inadvertent but formally illegal catches after a TAC has been reached. Efforts have been made for many years to balance by setting minimum fish landing sizes, often linked to gear regulations such as for minimum mesh size. Since fishers can rarely be so precise in the selectivity of their operations as to avoid catching under-sized animals there is a wastage adding to fulfilled-TAC effect. This problem increases as fishing intensifies, the average size of fish in the population is reduced and the proportion of the stock that is under-sized increases These processes encourage falsifications of catch statistics and the measurement of the animals in the catch as both operators and law enforcers try to minimize negative consequences.

The other undesired contributor to discards is the unintended catching of unwanted species, including possibly endangered ones such as small cetaceans, sea-birds and turtles. Technical procedures can be sought to reduce those, but all such catches are – other things being equal – reduced roughly proportionately if the value of F/M is kept as low as possible.

Trying to regulate a fishery merely by setting catch limits is like controlling a land vehicle – car or locomotive – by using only its brakes. What really matters is control of the fuel flow, of the energy input. Brakes can have a secondary role – preventing disaster if an unexpected bend appears, or descending slope or obstruction ahead.  If brakes are used without appropriate adjustment of the fuel flow first the wheels will overheat and eventually the vehicle is likely to be destroyed! One of the most efficient machines ever designed, a modern yacht, has no brakes, only sophisticated controls, by main-sail alignment and rudder of the input of the energy of the wind.  Perhaps the better analogy to fisheries management is the control system of an aircraft – motor or, better, sailplane. Input in the landing routine is control of angle with the elevators, using adjustment to gravity to limit the approach speed. There are brakes – the airbrakes in the wings – but no pilot would dream of relying only or mainly on those to bring his craft to a safe standstill.

Possibly the worst fisheries disaster illustrating all these faults was the ‘management’ by the International Northwest Atlantic Fisheries Commission (ICNAF, precursor of NAFO) of the haddock fisheries on George’s Bank, fished by US and Canadian trawlers. The official purpose of ICNAF was

[T]he investigation, protection and conservation of the fisheries of the northwest Atlantic Ocean, in order to make possible the maintenance of a maximum sustained catch from those fisheries.

I was a member of the UK delegation when the convention was negotiated in Washington DC in 1949 and I was involved later, with Beverton, in efforts by the scientists to give useful advice regarding management of the haddock fishery. The time was the period during which the US Administration was seeking to use the MSY criterion as a tool to keep Japanese fishers out of the Northeast Pacific but before the steamroller really got going in the UN legal negotiations of 1955 and 1958. ICNAF had no brakes (TACs) nor power to regulate fishing effort (fuel flow) but only to specify higher octane fuel (increasing cod-end mesh size) Guess what that would do for a car journey! Furthermore, such improvement as was obtained by increasing meshes (entailing very complex and expensive enforcement): eventually an increase in catch rate as the stock moved towards a new steady-state. That simply attracted more boats into the fishery. The car analogy would be increasing the speed by using a higher octane fuel, encouraging an even heavier foot on the accelerator by enthusiastic drivers!

Regulation to control fishing effort by controlling the powers of fishing units, and the degree and places and times in which they may operate, calls for substantial work to calibrate different types units (taking due account of differences among the species targeted of course) and to monitor changes in their effective fishing effort. There are several known ways of doing that but those used have to include experimental comparative fishing, which can be costly. However enforcement of regulation is simplified: it would not be necessary to try to keep as close a watch on operations as is needed to monitor catches frequently. Put crudely, it is easy to cheat with catch statistics but not so easy to hide an extra fishing vessel or even surreptitiously to hide a clever way of increasing its efficiency. This is not to say that TACs in some form, and size limits and perhaps other regulation of output, should be excluded, but they should always be secondary to the primary control of fleet size, its operations and the gears used.

Returning for a moment to the yield equations, everything I have written so far, exploring the general dynamics of an exploited fish population, has dealt with theoretical steady-state situations. In reality, when considering management measures we are starting somewhere and hoping to navigate to a better place on a three dimensional diagram of sustainable yield, average size of fish in the catch and  rate of catch, against the variables F/M and w on what Beverton and I called a eumetric isopleth diagram. Whether or not our starting point is a steady-state situation we shall be out of that in transit to a better managed fishery. That calls for more complex calculations of transient- states but the principles remain the same. I have also, for my examples, assumed that the parameters M and K, and therefore the ratio M/K are constant. There are three types of inconstancy that have to be confronted in the real world. One, naturally, is random change to deal with which we have to use complicated stochastic models rather than relatively simple deterministic ones. That’s a whole different game. Then there is the possibility that either or both the ‘constants’ actually vary with the age and/or size of the fish, or as between the sexes. Dealing with that is, in computational terms, tedious but not in principle more difficult. Then there is the possibility that either or both are density-dependent, that is changing as the abundance of the population changes. The general consequences of such dependences can be explored and they have been, partially. In the self-regenerating model all density-dependence, which usually stabilizes the population through negative feed-back, has been subsumed in the stock-recruitment relationship. But all these dependencies present great difficulties when it comes to estimating them. However, looking at the region of local MSYs we find that the expected shifts in the location of MSY may not be great. They can, however, substantially alter the estimates of the absolute size of the MSYs, which is another good reason for not managing primarily by setting TACs. The likely density-dependences do not however generally change very much the ratios of catches that we have examined, such as the small losses of catch and big gains in saving fishing effort by moving somewhat down the F/M scale from the MSY region. The simple equations retain their usefulness.

One issue relating to parameter value variations is the possibility of possible large differences from place to place. Alex. McCall explored this in what is called his ‘basin theory’. The idea is that members of a species-population tend to aggregate in one or more hot spots with the most hospitable environment, where they will find the best food, fewer enemies and survive better generally, while around the periphery they survive in less ideal conditions. This reality can produce some complications, especially as we would expect the observable range of the population to contract as it is reduced by fishing.. That provides one of the reasons why fish density measures such as catch-per-unit-effort seem to decline more slowly than the population, though there are also other generators of that phenomenon. In general it is particularly important to try to observe and take into account density-dependent changes in geographical distribution. Changes in distribution resulting from change in the ocean climate are obviously of practical importance but do not necessarily greatly affect wise assessments made for management purposes unless of course such shifts force the fish to spend more time in less favorable locations, or to remain in a location that has become less favorable than before.

Lastly we cannot leave this without mention of migratory fish. Most fishes move about, and many move considerable distances. The truly migratory species, with distinct regular patterns of movement present other and diverse management problems but it is not, I think, possible to generalize about them so we’ll leave the matter right there.

Note: In 1983 David Cushing published a very useful compilation of ‘Key Papers on Fish Populations’ that contained many of the published studies that I have referred to in this posting, including a simplified version of my 1957 book written with Ray Beverton, but not the yield tables nor my preceding derivation of the simplified yield-per-recruit equation. Cushing’s paperback is, sadly, out of print but some secondhand copies of it are available, although at a price – over US $100. Around the same date Beverton wrote a couple of papers based on his experience about the advantages of managing fishing by regulating effort rather than catch.

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