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Volume 77, 1948-49
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Some Aspects of The Production and Cropping of Fresh Waters

In fresh waters, as in any other environment, the production of living matter is basically limited by the supply of inorganic nutrients. These, or particular ones among them, control the development of green plants and determine the amount produced when conditions are otherwise suitable. The quantity of green plants determines the production of the animals which feed upon them. The production of the animal types which form higher links in the food-chain is in turn controlled by the quantity of the plant-eating animals. In most fresh waters fish form the last stage in the food-chain, and it is with, factors affecting the production of these that it is proposed to deal in this paper. It follows from the above that in general the quantity of fish flesh produced in a given time is fundamentally limited by the amount of inorganic nutrients available within the environment during the time, and is further controlled by any factors which limit the production of lower links in the food-chain. These limitations may be of considerable magnitude at all stages in the food-chain, but in the present paper discussion will be limited to the quantitative relationship between the climax of the chain—the fish—and the organisms upon which it feeds. It should, however, be pointed out that for a given body of fresh water the possible limit of production is not completely determined by the quantity of inorganic nutrients washing into it; organic material may also enter in forms which may be utilised by some of the animals of the food-chain, and thus increase the potential production of all subsequent stages. As examples of this may be cited the feeding of various types of insect larvae upon vegetable debris washing into streams, and the feeding of fish upon terrestrial insects which fall on to the water. Although quantitative data appear to be lacking regarding the importance of this effect, it seems that in some cases a significant addition may be made to the total production in this way.

In a simplified form the most typical food-chain found in fresh waters containing an exploited fish stock is:

Inorganic nutrients→Algae→Invertebrate bottom fauna→Fish→Man

It is the purpose of this paper to consider in some detail the quantitative effects which occur in the last two of these stages.

Before considering these relationships in detail, it is necessary to define precisely what is meant by the annual production of any form of living matter. Annual production may be defined as the actual amount of new living matter of the kind under consideration which has been produced during the year, either by the growth of old individuals, or by the production and subsequent growth of new individuals, whether these individuals have survived to the end of the year or not It is equal to the algebraic sum of the amount dying or otherwise leaving the area during the year and the increase in the standing stock. It is therefore apparent that the annual production bears no fixed relation either to the standing stock at a particular time, or to any increase in the stock during the year. It also follows that where the stock is the same at the end as at the beginning of the year—the average case in a stable population—the annual production equals the amount dying or otherwise leaving during the year.

If the annual production of an invertebrate population is a given amount, then in the ideal case the annual production of a fish population living on it would be an equal amount. For a number of reasons this ideal case is not approached in reality. While the factors to be considered are well established, either on theoretical grounds or on qualitative studies, in few cases is it possible to estimate their quantitative effect on the annual production of fish with any accuracy.

These factors arise from two main causes: the failure of the fish to consume the entire production of the invertebrates, and the incomplete conversion into additional fish material of that which is eaten. In the simple case of stable stocks, that portion of the annual production of invertebrates which is not eaten by the fish dies in other ways. Either it dies while immature, through disease or mishap or as the victim of some other predator, or else it survives to maturity and completes its life-cycle. Completion of the life-cycle does not necessarily mean, however, that the individuals concerned do not contribute to

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the production of the next stage in the chain, since fish may feed freely on the bodies of insects of aquatic origin which have returned to the water after breeding.

The food material available to the invertebrate bottom fauna is utilised in the production of a great number of different types, and these vary greatly in the extent to which they are consumed by fish. This probably arises chiefly from differences in the habits or structures of the animals, which cause them to be available to varying extents to the fish as food. As a result the proportion of the original vegetable food material which is ultimately converted into fish will vary according to the type of invertebrate through which it passes. Analysis of these relations is complicated by the fact that the relative extent of consumption of different invertebrates varies not only from one species of fish to another, but also for fish of the same species according to their size and age. Actually, for related fish of similar habits, e.g., the Salmonidae, the differences between size groups of fish are much greater than those between species (Allen, 1941). The differences in availability, and hence in extent consumed, may be very great, the fraction consumed being up to a hundred or more times as much in some cases as in others. As a consequence the proportion of the total fauna which is consumed by fish will probably be less for a fauna of normal composition than for one composed only of types of high availability, since it is unlikely that the susceptibility of an invertebrate to other causes of mortality will be proportionate to its availability to a particular species and size-range of fish.

Thus, only a proportion of the invertebrate fauna produced will be ingested by the fish. The only data apparently available regarding this is that of Borutzky (1939), who showed that in Lake Beloie it is about 24% for the total fauna, and ranges between 0% and 47% for the various components. The total annual invertebrate production of the bottom fauna of this lake is apparently about 40 Ib. per acre. Of the invertebrates consumed by fish, part will consist of material such as large chitinous structures which cannot be digested by the fish. These factors will inevitably reduce proportionately the amount of fish flesh which could be derived from a given production of bottom fauna.

Again, of the food actually consumed by the fish only a certain proportion is available for growth; the first charge on food consumed is for maintenance, and it is only the surplus which is converted into additional fish flesh. The maintenance level varies considerably with temperature, and with the size of the fish, in addition to any variations which may occur between species. The data of Pentelow (1939) and Brown (1940) suggest that the normal maintenance requirements for brown trout may be about 5% to 10% of body weight per week. It is only food in excess of this amount which is available for growth, and the above workers have shown that the efficiency of conversion of this excess is very variable and may range between 7% and 75% according to the conditions and the amount of food available to the fish. The work of the above authors and of Su°be (1935) and Tunison et al. (1939) suggests that the weight of flesh produced in trout supplied with abundant food is normally about 10% to 25% of the total food intake.

It is apparent, however, that the efficiency of conversion under natural conditions must vary between very wide limits, since it depends primarily on the excess of the food intake over maintenance requirements. Apart from the physical and other environmental factors, such as temperature, which control feeding activity, this must be greatly affected by the amount of food available to the fish; that is, by the relation between the standing stock of fish and the annual production of the invertebrate fauna.

As a result of factors such as those discussed above, the annual production of a fish population feeding upon an invertebrate fauna with a given productivity is held at a certain level. If this fish population is cropped by man, either in a controlled manner in farming operations or by relatively uncontrolled commercial fishing or angling, a steady state can be reached, even in theory, only if the crop does not exceed the production. In this sense an estimate of the annual production provides an estimate of the maximum crop obtainable.

Such a condition can, however, only be achieved if all the individuals of the population are ultimately removed as part of the crop; in other words, if no deaths take place through natural causes or mishaps, but all are due to cropping. Such a condition will not be achieved in practice, even under farming conditions, since some unwanted mortality will always occur. Schaperclaus (1933) quotes mortality rates during the growing season of 5% to 20% for various

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species, while Hobbs (1948) shows that in hatcheries the average mortality for brown trout is about 80% during the first year.

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The accurate estimation of the total production of a population during any period involves estimates of the average size and numbers surviving at a number of dates. From these data growth and survival curves can be drawn and the production calculated. Where data are only available as to the number and size at the beginning and end of the period, production can only be estimated if an assumption is made as to the nature of the growth and survival curves. That most generally made at present is that these curves are logarithmic in nature. This involves the supposition, which appears generally reasonable, that under a given set of conditions the rate at which an individual grows, or at which members of a population die, is proportional to the size of the indivdual, and of the population respectively. The use of curves of this type also conveys certain advantages in ease of mathematical handling. Making these assumptions we can write: Wt = W0 ekt and Nt = N0 e−m t where Wt is the weight of an individual after time t, and W0 is its initial weight, k may be called the instantaneous growth-rate. Similarly Nt is the size after time t of a population consisting originally of N0 individuals, and m may be called the instantaneous mortality-rate. It follows that the production during the period from t = 0 to t = T is given by ∫0TN0e-mt.W0ektk.dt=KN0W0/k—meT(k-m)—1} This expression may be used to calculate the approximate relation between the total annual production and the crop in such cases as those considered above, where the crop is the stock at the end of the period. The latter can be expressed as:

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N0 W0 eT(k-m)

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Therefore: Production/Crop=k/k − m 1—eT(m−k)} This result may be applied to a typical farmed brown-trout population during the first year, taking the above estimate of 80% for total mortality and assuming average weights at the beginning and end of the year of 0.1 g. and 80 g. The corresponding values of k and m are 6.683 and 1.610 respectively if T = 1 for one year, and hence we get Production/Crop = 6.683/6.683 − 1.610 1 − e1 610–6 683} = 1.309 Thus, in this hypothetical but apparently normal case, approximately 22% of the total production is wasted due to undesired mortality. This figure is based on the assumption that the instantaneous rates remain constant throughout the year; actually, it appears that the instantaneous growth-rate usually decreases markedly during the first year, but since there is evidence to suggest that the instantaneous mortality-rate behaves similarly, the above result has significance, since the formula quoted will remain approximately correct as long as k and m vary simultaneously in a similar manner.

In farmed stocks of the type so far considered the crop is formed by the stock at a certain time and may be a very considerable part of the total production. In wild populations which are cropped by angling or commercial fishing the position is very different. Cropping generally commences at a definite point in the life-cycle of the species, this point being determined by such factors as size limits, type of fishing gear, and migrations of the fish. The crop therefore can only be derived from that portion of the total production during the lifecycle which is formed by the standing stock at the cropping point plus the production produced by growth during the cropping period. The standing stock at the cropping point is, as pointed out above, only a part of the total production to this point. Since in general wild populations are exposed to much greater hazards from predators and unfavourable conditions, the natural mortality rate will be relatively high and consequently the standing stock at the cropping point will form a smaller proportion of the total production to this point than is the case with a farmed population. Thus, the crop cannot equal the total production during the life-cycle, and will form a proportion of the part available for cropping dependent upon the relative rates of natural and cropping mortality.

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In the present paper it is not proposed to consider depleted populations, but to discuss the position in exploited stocks in which exploitation is at such a level that the population remains in a healthy state. Under these conditions sufficient fish must survive and reproduce to maintain the population numerically. In some cases the point at which cropping commences may be so late in the lifecycle that sufficient spawning occurs before it is reached, and it is then possible for all fish to be removed as the cropping point is reached without the population being endangered. This condition is, however, probably not common in practice and therefore in general a sufficient proportion of fish must under stable conditions escape cropping long enough to enable the population to be maintained. The low rate of cropping mortality necessary to allow this will cause the ratio of cropping to natural mortality to be correspondingly low, and so will tend to reduce the proportion of the total available production which is taken as the crop. The above ratio will be further reduced by the fact that the increased survival to spawning may result in an increase of average natural mortality due to post-spawning mortality, or to increased mortality due to senescence.

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Information regarding the relative magnitude of natural- and cropping-mortality rates in normal populations is available from the work of Ricker 1945a), who has shown for several wild populations of blue-gill sunfish that even after the legal size limit is passed and the fish are exposed to angling the annual mortality from this cause is significantly less than that due to natural causes. The angling mortality is 16% to 36% per annum, while the natural mortality is 47% to 56% per annum. Where sufficiently precise data are available to enable the actual production to be calculated, this may be compared with the crop during any period of the life-cycle. The formula developed above has been applied to the data of Ricker (1945b) for another blue-gill sunfish population, and the production during each quarter-year after the commencement of cropping has been calculated. The total production from two and a half years onwards is found to be 345 arbitrary units of weight, while Ricker shows the crop to be 241 in the same units. Thus the crop forms only 70% of the production during a limited part of the life-cycle, and hence forms a much lower percentage of the total production. Since the standing level of the same stock at the commencement of cropping is shown by Ricker to be 211, production to this point must be considerably more than this, and the total production during the life-cycle must be in excess of 345 + 211. Therefore the crop must form less than241/345 + 211 × 100} or 43% of the total production.

A study of the production of the trout population of a small New Zealand stream (Allen, 1945) showed that here the crop formed about 5% of the total production. Since it was found that the greater part of the total production was accounted for by natural mortality prior to the commencement of cropping, the result appears to be of the same order as that derived from Ricker's data. In this trout population cropping began at about one and a half years.

Since the crop forms such a small proportion of the total production in wild populations, it is apparent that it does not provide an accurate measure of the total production. This is accentuated by the fact that the proportion which the crop forms of the total production will vary greatly with intensity of fishing, abundance of predators, relation of legal limit to maximum natural size, and many other factors. The magnitude of the crop has been determined by many workers for various types of fisheries, and has been found to range from very low values up to about 50 lb. per acre for Salmonidae, with a typical figure for productive water of about 35 lb. per acre. For other types of fish, crops have been recorded up to about 200 lb. per acre and occasionally to higher values. In view of the data previously considered, it is likely that the total production will range up to at least ten times the above figures. In the New Zealand trout population previously mentioned the total annual production was found to be about 650 lb. per acre.

The above figures refer to cases where a more or less steady fishery exists. Very much higher values may be obtained when an intensive fishery is suddenly set up on previously unexploited water. For example, the trapping of eels in Southland in 1946–47 gave yields which in several cases exceeded 1,000 lb. per acre, but it is apparent that here the accumulated stock of a relatively long lived species was being exploited.

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Thus we have seen that the crop obtained from a fish population feeding on an invertebrate population of given productivity is determined by the following factors:


Factors limiting the total production of the fish population.


Any factors which keep the production below the limit set by the food supply: e.g., unfavourable physical or chemical conditions, or excessive predation or cropping.


The amount of the invertebrate production which is available to the fish as food; this depends largely on the composition of the fauna.


The efficiency of conversion of the food eaten into additional fish flesh. This may depend on the level of the stock to a considerable extent.


Factors determining the proportion of the total production which is removed as crop.


The intensity and type of fishery. The latter includes the methods employed and the regulations (e.g., size limits) under which they are operated.


The incidence of natural mortality during the period prior to the commencement of cropping. So far as is known at present, the principal causes which generally operate here are disease, mishap and predation.


The incidence of natural mortality during the cropping period. The above-mentioned factors also operate here, although predation and mishap may become less serious as the size of the fish increases. On the other hand, death from old age and post-spawning mortality only become significant among older fish, and these may be the typical causes of mortality during the cropping period.

The various methods which are employed by conservation authorities with the object of increasing the yield of fisheries may be directed towards almost any of the factors listed above.

Methods intended to increase production: The fertilization of waters has as its object the increase of the quantity of inorganic nutrients and so increasing successively the production of each link in the food-chain until the fish are reached.

The stocking with young fish of waters deficient in suitable spawning conditions enables the productivity to be fully utilised where this would otherwise be prevented by a physical deficiency in the environment.

The destruction of predators may either enable the productivity to be fully utilised, or, more usually, make a greater proportion of the total fish production available for cropping.

The introduction of additional species of food animals of high availability may increase the average availability of the fauna, and so make a greater proportion of the invertebrate production available for conversion into fish. The introduction of small forage fish may make a greater proportion of the invertebrate production available to the larger individuals of the climax fish, since the small animals of the invertebrate fauna may have a low availability to these, but be highly available to the forage fish, which are in turn highly available to the large climax fish. The advantage gained in this way seems in some cases to outweigh the loss in efficiency of conversion which will arise from the insertion of another intermediate link in the productivity chain.

While the thinning out which is sometimes practised in waters containing an abundance of small, slow-growing fish has generally the main object of increasing the individual size, it may also have the effect of increasing the total production, by reducing the total stock and so giving increased efficiency of conversion.

The above practices all tend to increase the total production and so will give increased crop if the crop is proportional to the total production, as is probably usually the case for a fixed set of conditions. Direct additions of significant weights of fish will be equivalent to increasing the production in other ways. Stocking of this type, though rare in New Zealand, is a not infrequent practice in heavily fished waters elsewhere.

Methods intended to increase the proportion cropped: Conservational methods which have as their object the increase of the proportion of the total production which may be removed as crop are less frequent, although, as mentioned earlier,

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the removal of predators may have this effect. The proportion cropped depends upon the balance between the rate of cropping and the rate of natural mortality. Natural mortality is due to a variety of factors, operating at different rates at different stages in the life-cycle, and the only one of these which may in most cases be reduced on a practical scale is predation. Thus, the proportion is generally more easily affected by alteration in cropping procedure. Provided that the total production remains constant, an increase in the rate of cropping will increase the crop by increasing the proportion of the total production which it forms. In some circumstances, however, an increased rate of cropping will actually reduce the crop by lowering the level of the stock, and hence of the total production. Thus, exploited populations must range between two extreme types of conditions, and the optimum rate of cropping mortality must depend upon the position occupied within this range. One extreme is represented by the type of population which has been considered at length in this paper; here the total production is constant, and any reduction in either the number or average size of the components of the stock is compensated for by an increased rate of growth. In populations of this type the crop will continue to increase with the cropping mortality rate until the total mortality rises to such a level that the stock is reduced to a point where it ceases to be of this type and a decrease in production sets in. For this type of population the optimum cropping rate is therefore the maximum which can occur without decrease of production. The fact that comparison of wild populations has shown, for many species of fish, that there is frequently a type of inverse correlation between rate of growth and density of stock suggests that many wild populations belong to this type, since the food supply appears to be limiting growth by determining the maximum production obtainable.

At the other extreme are populations in which the rate of growth is constant and independent of the density of the stock. In these growth is limited by some factor other than food-supply, and hence production is limited only by this factor and those which determine the numerical density of the population. Naturally occurring stocks of this type will therefore generally be much more sparse than those of the type previously discussed. Ricker (1945b) has considered the influence of size limits and rate of cropping upon the crop obtainable from populations of this type, and has shown that the optimum combinations can be calculated for any given conditions of growth rate and natural mortality. In addition to their application to stocks of the type now under consideration, Ricker's methods may be applied to any type of population, provided that the variations in conditions do not alter the standing level of the stock, since in this case the growth rate at any stage in the life-cycle will be unchanged.

In view of the very different factors which determine the conditions for maximum crop in the two extreme types of population, it is apparent that the optimum cropping conditions can only be determined for a given population if the type to which the population belongs is known, and that it is therefore essential that investigations should be directed towards determining the relation between actual total production and the maximum which the food supply could support. Any determination of optimum cropping conditions based on production considerations must, however, be checked to ensure that an adequate survival for spawning will occur.


Allen, K. R., 1941. Comparison of Bottom Faunas as Sources of Available Fish Food. Trans. Amer. Fish. Soc., vol. 71.

—— 1945. The Trout Population of the Horokiwi River, an Investigation of the Fundamentals of Propagation, Growth and Survival. Ann. Rep. Marine Dept. of N.Z.

Borutzkey, E. V., 1939. Dynamics of the Total Benthic Biomass of the Profundal of Lake Beloie. Proc. Kössino Limnological Station, vol. 22.

Brown, Margaret E., 1946. The Growth of Brown Trout (Salmo trutta Linn.), pts. 1 to 3. J. Exp. Biol., vol. 22, nos. 3 and 4.

Hobbs, Derisley F., 1948. The Development and Management of Trout Fisheries in New Zealand. Fish. Bull., no. 9, Marine Dept. of N.Z.

Pentelow, F. T. K., 1939. The Relation between the Growth and Food Consumption in the Brown Trout (Salmo trutta). J. Exp. Biol., vol. 16, no. 4.

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Ricker, W. E., 1945a. Natural Mortality among Indiana Blue-gill Sunfish. Ecology, vol. 26, no. 2.

—— 1945b. A Method of Estimating Minimum Size Limits for Obtaining Maximum Yield. Copeia, 1945, no. 2.

Schäperclaus, W., 1933. Lehrbuch der Teichwirtschaft, 289 pp. Berlin.

Surber, E., W., 1935. Trout Feeding Experiments with Natural Food (Gammarus fasciatus). Trans. Amer. Fish. Soc., vol. 65.

Tunison, A. V., et al., 1939. The Nutrition of Trout. Cortland Hatchery Report, no. 8.