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W.G. Wohlfarth
Fish Culture Research Station
Dor, Israel


R. Moav
Hebrew University
Jerusalem, Israel

1 The Hebrew University of Jerusalem and the Fish Growers Association of Israel supported this research from its initiation. The Bureau of Commercial Fisheries, (Department of the Interior, U.S.A. Government) provided a generous grant from 1962 onwards. Other grants were received from the Ford Foundation and the Rothschild Foundation.


Research into the genetics of carp in Israel was initiated in 1958. Most of the work was carried out at the Fish Culture Research Station at Dor, and at a group of fish farms which later constituted the Carp Breeders Union (CBU).

Since little information was available on the basic genetic parameters of fish, considerable effort was devoted to basic research in the genetic make-up of traits of economic importance and to the development of experimental procedures for quantitative genetic research in fish. In addition, we searched for efficient methods of producing genetically superior breeding stocks, and served as consultants to the CBU.

All our work was carried out on carp. Therefore, any extension of our conclusions to other fish species, particularly those distinctly different from carp, should be made with reservation.


Evaluation of genetic parameters must be related to a specific population. Hence, a clear definition of a population under study is a prerequisite of any genetic investigation. In our case, the term “population” may mean either: a) The whole carp species. b) The Israeli carp population. c) A specifically constructed population of known origin and structure.

Consideration of the whole carp species as a single unit with definable genetic parameters is a fruitless approach. Even the consideration of the carp population of a single country or a single region as a base population for estimating genetic parameters is somewhat inadequate. The relatively small size of breeding populations in many countries, their unknown mating structure and history, probably do not allow generalization of broader interest. Thus, a base-population for genetic investigation should probably be restricted to a closed population of known genetic structure and ancestry.

Our previous work referred to the whole Israeli carp population. In the present study, we decided to construct genetically marked gene pools for future selection and inbreeding - crossbreeding experiments.

2.1 Fish marking

A necessary prerequisite for genetic experimentation on a large scale is an adequate method of marking fish for individual or group observations. For this purpose, we developed an electric branding instrument that can be attached to a car battery (Moav et al., 1960a, b). This instrument is used annually with excellent results for branding many thousands of fingerlings.

2.2 Genetic markers

Adequate genetic markers may be helpful in studying the genetics of quantitative traits and for marking parental lines of breeding stocks. We collected three known recessive mutants controlling body pigmentation: blue, grey and gold, (Moav and Wohlfarth, 1968). Through crosses between them we produced the double and triple recessives (the triple recessive is white). Each mutant, when in homozygous condition, appeared to have deleterious effects on growth rate and viability, but no deleterious effects were detected in heterozygous conditions.

A factor to be taken into consideration when planning a breeding programme for fish, is the practical impossibility of preventing illegal immigration of fish between adjacent ponds. Fry may immigrate through drainage ditches, or may be unintentionally transferred by birds from one pond to another. Technical mistakes, particularly the incorrect reading of brands, may also cause the introduction of fish into the wrong ponds.

Even if such inaccuracies are infrequent, they may cause considerable damage. Frequently, an illegal immigrant is larger than the majority of the fish in the pond it has infiltrated, and therefore it has a good chance of being selected for breeding. Due to the high fertility of fish, the potential damage of a single wrong parent may be extreme.

So far, the only practical solution to the problem of illegal immigration that we have found has been the use of genetically marked parental lines.


3.1 The problem

Commercial conditions are defined as fattening ponds (post-nursing) of stagnant (not flowing) water. In the present discussion, the object of our genetic improvement is limited to a single property, namely, yield under existing commercial conditions. This property may be defined as: growth rate (measured as average gained weight in grams per day per fish) under given commercial conditions.

The safest way to evaluate the genetic worth of different genetic stocks is to test them under commercial conditions. This requires growing each tested group separately in several ponds. In this method of testing, the pond effect cannot be separated from the between-groups or genetic effect. Variance between ponds is large relative to the expected variance between tested groups. To overcome this difficulty a prohibitively large number of replicated ponds is required for testing of each group.

A solution to the confounding of the pond effect with the between-groups effect, is to evaluate the stocks under test conditions, as different from the commercial conditions, but providing a practical experimental design. This raises another problem, namely, relative growth rate under test conditions is not, strictly speaking, the trait that we wish to improve. In other words, the genetic correlation between the two traits may be less than unity.

3.2 Test conditions

In our genetic investigation of growth rate of carp, we used the following test conditions:

  1. Communal ponds: defined here as ponds stocked with two or more groups of fish of the same species. In a communal pond tested groups of fish compete directly for the same resources.

  2. Ponds divided by nets: Each separate part of a divided pond was stocked with a different group of fish. Under these conditions the tested groups of fish share the same body of water but do not compete directly with each other. (Wohlfarth and Moav, 1966).

  3. Cages: Tested groups of fish are stocked in different cages and all the cages are placed in a single pond. This procedure is similar to that adopted in ponds divided by nets because tested groups of fish share the same body of water but do not compete directly with each other.


A fattening pond filled with fresh water and stocked with fish of 30–50 g mean weight will be considered.

The rate of growth of fish in a closed container is determined by two opposing factors:

  1. The absolute average weight of the fish: Ordinarily, the larger the fish, the higher is its potential growth rate. Growth potential may be defined as the expected growth rate of fish of a given weight in an unchanging environment.

  2. Environmental deterioration: The presence of fish in a stagnant pond causes deterioration of water as an environmental medium for fish growth. The major reasons for the deterioration are accumulation of growth inhibiting factors excreted by the fish and reduction in the amount of oxygen available.

Both growth potential and environment deterioration are functions of fish weight, but they operate in opposite directions. When the two are balanced, actual growth rate remains constant.

Variation in actual growth rate may be due to either heritable or non-heritable differences in growth potential, or to resistance to environmental deterioration. The latter may be subdivided into:

  1. Resistance to low oxygen levels,

  2. Resistance to inhibiting factors excreted by the fish,

  3. Lower levels of excretion and therefore slower deterioration of the environment,

  4. Higher behavioural tolerance to crowding.

Under varying test conditions, the relative contribution of the different factors determining relative growth rate may be altered. When tests are conducted in flowing water, for instance, an adequate supply of oxygen is provided and the excreta removed, (Sengbush, 1967). Under such test conditions only variation in potential growth rate and possibly resistance to crowding determine actual growth rate. If resistance to environmental deterioration is partially independent of potential growth rate, then tests in running water are disadvantageous to the stocks possessing higher resistance.

When two or more genetic stocks are tested in separate parts of a net-divided pond, the environmental deterioration of the pond is a function of the weight of all tested groups, while growth potential affects each tested stock separately. Under these circumstances differences in growth rate between tested stocks should tend to be larger than in separate ponds.

Testing in separate cages all located within a single pond is equivalent, as far as interfish interactions are concerned, to testing in the different parts of the same net-divided ponds.

When testing is performed in communal ponds, that is, when all the tested stocks are put into the same pond, then differences in relative growth rate between the stocks are expected to be even higher than in divided ponds. Major reasons for the expected increased variation between tested stocks in communal ponds are the following:

  1. The rate of deterioration of the pond's environment is a function of the average weight gains of all tested stocks. This favours stocks with high potential and is disadvantageous to stocks with low potential.

  2. In a communal pond larger and smaller fish have to compete directly with each other. This factor gives a futher advantage to stocks with a high potential.

Fig. 1 is a schematic presentation of weight gains of two stocks, one with a higher genetic potential (A), the second with a lower genetic potential (B) when the two are grown in: a) separate ponds, b) divided ponds (or cages) and c) communal ponds.

Fig. 1 is based on the assumption that competition in communal ponds is completely determined by relative growth potential, i.e., that the correlation between growth rate in separate and in communal ponds is unity. This assumption is not necessarily correct. We may imagine a situation where a genotype with a high growth potential in separate ponds. will show relatively poor growth in communal ponds due to lack of aggressiveness (points A and B of Fig. 1).

Summing up the above discussion, we find that when testing and evaluating genetic stocks under test conditions, the parameter determining the usefulness of the test is the genetic correlation coefficient between growth rate under test conditions and growth rate under commercial conditions.


5.1 Realized heritability

Genetic progress due to mass (individual) selection ∆ G is a function of three parameters:

  1. Selection intensity (i), measured in standard deviations

  2. Phenotypic standard deviation (σ p)

  3. Heritability (h2)


∆ G = i h2σ p

Growth rate has a relatively large phenotypic variance (in fattening ponds p is approximately 20 percent of the mean), and the high fertility of fish enables a high value of selection intensity (i). Thus, the most important parameter determining expected gain is heritability (h2) of growth rate. Estimates of h2 may be obtained either from analysis of the variation between family means (such as full-sibs, half-sibs, etc.) or from selection experiments.

Estimation of heritability from variation between family means is frequently in the upper direction, tending to yield misleadingly high expectations of genetic progress. The major reasons for over estimation are:

  1. The compounding of common environment with between-family-means genetic variation.

  2. The presence of non-additive genetic variance.

  3. The asymetry of both genetic and phenotypic distribution of body weight, (Nakamura and Kasahara, 1955).

Primarily due to the above reasons, estimates of heritability obtained from selection experiments are more reliable than those obtained from variation between family means.

Fig. 1

Fig. 1 - Schematic presentation of weight gains of two stocks, one with a higher growth potential (A), and the second with a lower growth potential (B), when the two are grown under three different conditions: 1) separate ponds, 2) divided ponds and 3) communal ponds

This is particularly true for traits with low h2 and large non-additive genetic variation. Heritability computed from selection experiments:

Selection Differential (∆ P = i σ p) Realized

5.2 Control of selection experiments

The method of repeat-mating probably provides the best control for selection experiments in fish. In this method, parents of the fish population in which selection has been carried out, are respawn at the same time and under the same environmental conditions as the selected individuals (Fig. 2).

Fig. 2

Fig. 2 - Results of some selection and inbreeding experiments in carp (values in the table are averages of gained weights, per fish in grams, corrected for initial weights)

For the selection experiment to provide maximum information concerning the genetic make-up of a population under study, two further controls should be made. These are: the progeny of randomly selected individuals and progeny of individuals selected in the downward direction.

When selection is performed with only one group of fish, inbreeding will increase and inbreeding depression may counterbalance the gain due to selection. To avoid this (at least partially), two or more groups of fish should be selected. In each generation, individuals of different groups should be mated, as illustrated in Fig. 2. Replications are also necessary to reduce the relatively large effect of sampling errors.

5.3 Correlations between relative body weight at different ages and densities

These correlations help determine at what stage selection for body weight is most effective. Growth of fish in ponds is density dependent. The smaller the mean weight of the population under selection, the larger the number of fish that a given pond can maintain and the higher the possible selection intensity. Table I shows that as population size decreases from 40,000 to 200,000, selection differential (mean of selected individuals minus mean of the total population) decreases from 3.6 to 1.8 (assuming normal distribution). The column headed selection differential shows that when the genetic correlation between selection weight and market weight (600 g) is unity and when the heritability of the two stages is equal, selection among 40,000 fingerlings of l g average weight is twice as effective as selection among 200 individuals of market weight.

The column headed by ra min shows the values of genetic correlations between selected weight and market weight (600 g), resulting in the same genetic progress as that obtainable when selection is performed on fish of market weight. Equal heritabilities were assumed for all stages.

When the correlations are positive, even of a small magnitude, the most efficient method of selection is probably a sequential one, that is, starting with small fish and doing the final culling at the market weight.

Analysis of the variation between progenies grown in replicated separate cages may be used in order to estimate the genetic covariance between gained weight at different stages.

Table I

The relationship between average fish weight, their density per dunam, selection intensity and genetic correlations that result in an equal response to selection at all stages

(At all stages heritabilities were assumed to be equal and only 20 individuals were selected)

Mean weight in gramsFish number in 0.4 acre pondSelection differentialra min
    140,0003.6  .49
  10  8,0003.2  .54
  50  2,0002.7  .57
100  1,0002.5  .67
200     6002.2  .81
600     2001.81.00

If y1 and y2 designate gained-weight per basket in periods 1 and 2 respectively, and analysis of variance is done for each period, then the expected mean squares are:

E (MSb) = K σ2 gi + σ2w                  E (MSw) = σ2w

when K is the number of baskets per progeny, i = 1, 2, designates the period of growth, σ2gi is the genetic variance and σ2w is the between-baskets-within-progeny variance.

The estimate of genetic regression of growth rate in period two on growth rate in period one would be:

and the genetic correlation between the two:

Two somewhat unrealistic assumptions were made in the above estimates: the absence of common environment, and that all the covariance between the two period is hereditary. If these assumptions are not made, the values of genetic regression and correlation are inflated. Progeny testing in communal ponds, with individuals marked can also provide estimates of the phenotypic and genotypic correlations.

5.4 Table qualities of fish

Fat content and intramuscular bones are major criteria of the table qualities of fish. Information gained from other livestock, particularly pigs, strongly suggests that fat content should have a high heritability and therefore should respond favourably to selection. The number of intramuscular bones has been shown, in one test involving 704 carp, to vary from 70 to 135 bones per fish, (Sengbusch and Meske, 1967). It is reasonable to expect that the latter trait has a reasonably high heritability and may therefore respond to selection.

Rapid methods for measuring both fat content (Ankorion et al., 1967) and number of intramuscular bones on live fish have been developed. (Sengbusch, 1967).

5.5 Genotype environment interactions

Our interest in genotype environment interactions has three aspects:

  1. Special interactions: These are defined as interactions between genotypes and average environmental conditions of different fish growing areas. The magnitude and distribution of these interactions determines the range for which genetic improvement gained in one location may be commercially used in other areas.

  2. Cyclical interactions: Interactions between genotypes and environmental conditions, varying from season to season and from year to year in the same area, reduce the overall efficiency of selection. The higher the interaction the smaller the rate of gain for average performance over a longer period.

  3. Genotype age interactions: These reduce the rate of selection gains in areas where fish have to be reared for two or three years before reaching market size.

5.6 Non-additive genetic variation

Improvement in performance of traits of low additive genetic variance (as appears to be the case with growth rate in the carp) must depend on non-additive genetic variation. When the dominance variance component is relatively high, mating between close relatives brings about inbreeding depression, while crossbreeding usually results in heterosis.

Results of inbreeding-crossbreeding experiments and asymetrical response to selection may be used for estimating the relative importance of the non-additive variance and in determining the total genetic and phenotypic variance of a trait.

A more sophisticated method of obtaining the same objective is diallel mating of individual males to individual females. This consists of a comparison of progenies of simultaneous, but separate matings, of each of several females with each of several males. The separate progenies can be obtained only be artificial fertilization.

5.7 Regression of gained weight on body weight

When different stocks of fish are tested for genetic differences of their growth rates, the regression of gained weight on initial weight should be considered and corrected. Environmental factors may affect the magnitude of this regression, so that a correction term appropriate to one set of conditions is not necessarily applicable to another.

When the variation in initial weights is due purely to environmental causes, the regression coefficient of gained weight on initial weight, may be estimated by the multiple nursing technique. The basic features of this method are as follows: two or more random samples from a fingerling storage pond containing individuals of a single spawn are introduced at varying densities into separate nursing ponds. Since growth rate is strongly density dependent, the fingerlings in the less densely stocked ponds grow faster than their counterparts in more densely stocked ponds. When the average weights of fingerlings in nursery ponds reach desired values, they may be brand-marked and stocked in test ponds. Figure 3 shows graphically the basic features of the technique and the expected growth curves of two multiple-nursed groups subsequently grown in: (i) separate ponds, (ii) divided ponds, and (iii) communal ponds.

The total regression of gained weight on initial weight within a single spawn can be estimated by either one of two methods:

  1. A random sample of nursed fingerlings may be taken from a single spawn, Each fish in the sample may be weighed and marked prior to its introduction into the fattening pond. At the termination of the experiment the fish are again weighed individually and the regression and correlation between the individual's initial weight and gained weight may be computed.

  2. A similar measure of the regression of gained weight on initial weight within a single spawn may be obtained when, instead of marking and weighing each individual, a random sample of fish from a single spawn is graded into several classes according to weight. Each class is marked differently, and all classes are restocked into a single fattening pond.

A single group of fish may first be multiple-nursed to several weight classes and each class further divided into two or more weight classes. Simultaneous use of the two techniques enables separation of the total regression into environment and genetic-plus-development components (Fig. 4). Crossing of the growth curves of the small-above-the-mean and the large-below-the-mean groups is due to the fact that the first group is genetically and developmentally superior to the second.

Fig. 3

Fig. 3 - Schematic presentation of the multiple-nursing technique used for formation of environmentally induced variation of initial weights within a single spawn


6.1 Regression of gained weight on initial weight

6.1.1 Random samples of a single spawn nursed to different initial weights

In 1962 and 1963, several genetic groups were multiple-nursed to two different initial weights. The groups were differentially marked and stocked together in several communal fattening ponds as a part of a progeny testing programme. Initial weight differences (d) and final weight differences (D) were calculated for each tested group.

In estimating the linear regression of D on d, the customary maximum likelihood method cannot be used because the independent variable d has a relatively large error variance which cannot be separated from the real differences. Thus, the regression line was determined from two points; the origin (0,0) and the intersection of the two means (d,D). Combined results of the two years show that D=4.2 d. That is, under the specific conditions of the present tests, one gram difference in initial weight of environmental origin results in 4.2 g difference in gained weight. Deviations around the regression line are rather large. This is primarily due to sampling errors plus probable deviation from liniarity of the true regression line.

6.1.2 Grading plus multiple-nursing

Two groups of fish, to be designated BG and CB, were tested in a series of ponds during the summer of 1964. This experiment was terminated on 24 September 1964, and the fish were used for a further experiment aimed at measuring the environment and genetic-plus-development regression coefficients of growth rate on initial weight. All earlier experiments on this subject had been conducted during the summer with fish of initial weight between 20–60 g and final weight between 300–800 g. In the present experiment, which took place during the fall season, initial weight was between 450–650 g, and final weight between 600–1,100 g.

Fish from several ponds were graded into above-the-mean and below-the-mean weight classes as illustrated in Fig. 4. The two classes were differentially marked and restocked in a single pond. This procedure was repeated in four ponds of BG and four ponds plus two half ponds (divided by nets) of CB (Table 2). The average difference in initial weights between the two weight classes was 93 g per fish, and the average difference in gained weights was 45 g per fish. Since the experiment lasted for 43 days (from 27 September to 9 November), growth rate of the larger fish exceeded that of the smaller fish by approximately 1 g per day per fish.

In order to investigate the regression of gained weight on initial weight when the differences in initial weight are of a purely environmental origin, the following procedure was adopted. At the termination of the summer experiment, CB was distributed in 14 different ponds (or half ponds), and BG in 9 half-ponds. Variations between the means of the ponds within each group were due to differences in pond fertility and were therefore of purely environmental origin. Fish of the same group, but from two ponds with different mean weights, were differentially marked and restocked in a single pond for the fall experiment. This procedure created environmental differences in initial weights of genetically identical fish. Stocking a single progeny in several ponds for the summer experiment served as a multiple nursing for the fall experiment. Using the above procedure, 11 ponds and half-ponds were stocked with CB and seven half-ponds with the BG (Table 3).

The mean difference in initial weights between the two samples within a pond over all the 18 ponds and half-ponds was 95 g, which is almost identical to that of the experiment presented in Table 3. However, the difference in growth rate presents an entirely different and somewhat unexpected picture. The mean gained weight of the samples with smaller initial weights was 8.4 g higher (although not significantly so) than that of samples with the higher initial weights.

Table II

Difference in growth rate between smaller fish (below the mean) and larger fish (above the mean) of a single spawn (Fall 1964)

  Initial weights in gGained weights in g
PondLarger fishSmaller fishDifferenceLarger fishSmaller fishDifference
A 2594523  7132128041
A 5641571  7035731443
A10b624546  7844440143
B 262451111335730057
B 3581537  4438435133
A 661850411431626155
A 961051010026922445
B 1637540  9735434311
B 462649413231522491
 621528  9335430945

Table III

The difference in growth rate between smaller fish (nursed in a less fertile pond) and larger fish (nursed in more fertile pond) when stocked together in a single pond Fall 1964

GroupPondInitial Weights in gGained Weights in g
Larger FishSmaller FishDiff.Larger FishSmaller FishDiff.
 A3653629  2433131219
 A4664623  41376388-12
CrossbreedsA11b680650  3042639828
 A12a612579  33397400-3
 A13b678619  5940535550
 A14a599599  40388429-41
 A15b619598  21371413-42
 A16a644588  56376400-24
 A17b636611  25386491-105
Means 667572  95285293-8

Fig. 4

Fig. 4 - Schematic presentation of the simultaneous use of the multiple-nursing technique and grading of a single spawn into two weight classes

The conclusion to be drawn from these results is that within the weight range of 500 g to 1,100 g in the fall season (the effect of the two factors cannot be separated) larger fish do not grow faster than smaller fish when the weight difference is due to environmental effects. When, however, the difference is due to genetic plus developmental effects, larger fish grow faster than smaller ones.

These results agree with earlier data in that they show that a large proportion of the variation in growth rate within a single spawn is due to genetic plus developmental factors, rather than temporary environmental effects. Separation of the additive genetic from the non-additive genetic and the developmental effects requires more complicated designs including analysis of between family variation.

6.1.3 The regression of individually marked fish

Each individual within a random sample of carp was differentially marked and the whole sample stocked within a single pond. The correlation and regression of individual gained weights on initial weights were calculated. The results of one experiment are presented in Fig. 5. Further experiments showed similar results, as did experiments with black and brown trout (Haskell et al., 1960).

In this experiment three major factors contributed to the regression: differences in initial weight, genotypic differences for growth capacity, and non-hereditary developmental differences that permanently affect growth capacity. The second and third factors interact positively and are positively correlated with the first.

6.1.4 Division of single progeny into several weight fractions

We divided a random sample of fish from a single spawn into five classes according to weight. Each class was differently marked and its average initial weight was determined (Table IV). All five classes were introduced into a 400 m2 nursing pond. Forty-two days later the pond was emptied and the fish were sorted, counted, weighed and transferred into a 2.5 dunam fattening pond. On termination of the experiment, the fattening pond was emptied and the fish were again, sorted, counted and weighed. Several observations were made:

  1. A very high correlation between gained and initial weight,

  2. In the fattening pond the regression is lower than in the nursing pond, despite the longer duration and the larger weight gains,

  3. The larger the final weight, and the lower the initial weight, the higher the regression of gained weight on initial weight.

In general, the results agree with our previous experiments, and fit our expectations.

6.1.5 Comparison of growth rates

For a comparison of growth rate of the fastest and the slowest growing individuals of a single spawn, after their initial weights were equalized, the largest (fast growing) and smallest (slow growing) fractions (each fraction including 15–20 percent of the whole population) were selected from a fingerling storage pond of a single progeny. The two groups were brought to similar weights by multiple nursing; then marked and stocked in communal and separate fattening ponds.

Fig. 5

Fig. 5 - Regression of gained weight on initial weight of individually marked fish of a single spawn

Table IV

Relative growth of five fractions of a single spawn in a nursing and a fattening pond

Initial WeightGained Weight  
Nursing PondFattening PondNursingFatteningTOTAL–6.118.8-6.11 
17.455.438.1230.4268.5Means (weighed)
      2.00     1.52      6.68Regression coef.
        0.995       0.930        0.981Correlation coef.

The experiment was repeated each year for two years. Although the large environmentally caused variation between ponds markedly reduced the sensitivity of the comparison of separate ponds, the results are rather clear (Table V and Fig. 6). In spite of the similar initial weights, the former jumpers (fast growing) grew faster in both communal and separate ponds. The growth difference in the communal ponds was approximately twice that of the separate ponds. The larger divergence between the former jumpers and the former laggards (slow growing) in the communal ponds is evidence of inter-fish competition.

6.2 Individual selection and growth rate

We carried out several one-step selection experiments which were aimed at finding the response to mass selection. Five typical results are presented in Fig. 2. Rows 1 and 2 show the gained weights of progeny of individuals selected for large weight (up), and individuals at the mean of the population (random). In both cases the progeny of the unselected parents had a faster growth rate (not significantly so) than the progeny of the up. An equivalent comparison carried out on progeny of crossbred fish is presented in row 5. When up males of one group were mated with up females of a second group, the mean gained weight of their progeny was 624 g/per fish. The unselected control in this case is the mean of the two repeated F1 progenies (578+672)/2=625. Again the upwards selected group showed no response. Downward selection, on the other hand, showed a noticeable response. The average difference between the up progeny and the down progeny as shown in the four comparisons in Fig. 2, was 33 g.

The difference between the means of the selected up parents and down parents was between 200 and 300 g. Thus, the regression of offspring on parents, or the realized heritability, based on the difference between the up and the down was 0.10 to 0.15. If, however, we divide the selection differential into two parts, down to random and random to up, we find a realized heritability of about 0.3 for downward selection, and heritability of zero for upward selection.

This asymmetry of response is characteristic of plateaued selected populations, i.e., population that, as a result of long continued selection, either natural or artificial, have exhausted their additive genetic variability, and no longer respond to selection. Such populations have been found to have a zero heritability in the up direction, but positive heritabilities in the down direction. In these cases considerable amounts of non-additive genetic variation have frequently been shown to remain in the population.

6.3 Individual selection and relative body weight

In the summer of 1964 a large group of fish were taken from a fattening pond. The fish were the offsprings of a single mass-spawning of known parents. Three samples were selected from this population:

  1. A random sample,

  2. Fish with the lowest height/length ratio (down selection)

  3. Fish with the highest height/length ratio (up selection)

Frequency distributions of the three selected groups are shown in Fig. 6.

In the spring of 1965, each one of the three selected groups were mass-spawned. Their progenies were nursed in separate ponds and were tested in three communal fattening ponds.

In the fall of 1965 the ponds were emptied and the fish were weighed and measured. The distribution of relative heights in the three ponds is demonstrated in Fig. 6b. The results of this experiment may be summarized as follows:

  1. The parental population on which selection was performed was skewed to the right. Thus a selection of equal intensity (9 percent), gave a selection differential of 0.049 in the up direction and only 0.030 in the down direction. The response to selection was also asymetrical being 0.023 in the up selection as against 0.010 in the down selection.

  2. The asymetrical response to selection provided three different estimates for the realized heritability of relative body height. They are:

    1. From the up selection: 0.023/0.049= 0.47

    2. From the down selection: 0.010/0.030= 0.33

    3. Combined: 0.033/0.079= 0.42

    The marked difference between the response to selection of relative height and the response to selection for relative body weight should be noted. In our selection experiments for body weight, the response to down selection was mild and there was no apparent response to the up selection. This is in strong contrast to the high response in both directions to selection for relative body height. In addition, the direction of the asymetry was reversed.

  3. The higher height/length ratio of the progeny of the up selection was due to both an increase in absolute height and a decrease in absolute length.

  4. An interesting result is the significant and consistent lower growth rate of the up selection progeny. Should this be verified by future experiments, it will have an important practical consequence, since in several carp-growing areas, breeders believe that selecting for increased relative body height increases the growth rate of the fish. It is probable that this selection procedure results in yield reduction. (Stegman, 1958).

Table V

Relative growth rate in communal ponds and yield in separate ponds of fastest (jumpers) and slowest (laggards) fractions selected from a single progeny and nursed to identical weights1

Method of stockingCommunal ponds
(g per fish)
Separate ponds
(g per fish)
Group of fish1961196219611962
Fast growers491483450483
Slow growers411422419451
Difference2  80 ± 14  41 ± 11  31 ± 23  32 ± 25
Number of ponds   5    4    5 × 2  10 × 2

1 Area of ponds - 400 m2; rate of stocking - 80 fish per pond

2± Standard error. (note the larger SE in separate ponds)

Fig. 6

Fig. 6 - Frequency distributions of the ratio (body height/body length) in selected parents and three replicated samples of their offsprings

6.4 Progeny tests and family selection

When low heritability is due to large environmental variation, the classical animal breeding solution is to make use of family-selection or progeny testing. That is, estimating the genetic worth of an individual from the means of several related individuals. If well designed, such selection schemes may greatly reduce environmental sources of variation and enable families, individuals, or parental pairs, with superior genetic merit to be selected. Seven years ago a progeny testing scheme was started. Most of the progeny tests are conducted in the settlements that now constitute the Carp Breeders Union. The method of testing was as follows: All progenies tested in one year were spawned within a single week, each in a separate pond, and nursed to an average weight of about 25 to 30 g. At this point, (5 to 6 weeks after spawning) random samples of each group were brand-marked, and in a single day all groups were stocked in several commercial fattening ponds at densities of 200 to 250 fish/ha.

The fattening ponds, each of which constituted a replication of the same progeny test, were located in different settlements. To illustrate, Table 6 shows the results of the tests conducted in 1964. Sixteen progenies were tested in five replications. The first six were the offspring of a single pair of parents and are therefore full-sib groups. Progenies 7 to 11 and 14 were each the offspring of mass-matings between a single female on the one side and several brothers, unrelated to this female on the other. The remaining four progenies were the offsprings of mass-matings between several sisters, on the one side, and several brothers, of an unrelated family on the other.

All the above progenies may be treated as the equivalents of full-sib families. With one possible exception (progeny 6) there was no immediate or known family relationship between the male and the female parents of the same spawn. In progeny 6, there is a fairly high probability that a first-degree relationship existed between the male and female parents, hence the poor performance of this group can be attributed to inbreeding depression.

In the last three spawns, one parent consisted of several individuals belonging to an inbred group imported from Holland. The remaining 13 progenies may be treated, with some reservation, as a random sample of full-sib groups of the Israeli carp population. An analysis of variance (TableVI) shows that the difference between the progeny means is highly significant, and the estimate of the between-progeny means variance is 2 077 g2. Similar tests were conducted in previous years and have been analyzed in the same fashion. By pooling the information accumulated over several years, the total variance between means of full-sib families was estimated to be roughly 1 500 g2.

Table VI

Progeny tests of carp conducted by the Israeli carp breeders union in 1964


b) Analysis of variance table of the first 13 progenies of the above table (See text for details).

Source of variationDegree of freedomMean square
Between progeny12  11510
Between ponds  4166999
Interaction44    1125

The variance between full-sib groups includes one-half of the additive variance, plus one-fourth of the dominance variance, plus a smaller fraction of the sum of the interactions variance plus the common environment variance component. Assuming that the last component is small, the total genetic variance of the population was estimated to be in the range of 2 000 to 4 000 g2. It should be noted that this figure relates only to gained weights under the following conditions: growing season - summer and autumn; growing period - from 30 g to about 600 g; density of stocking - 2 000–2 500 fish per ha; and fish in their first year of life.

Analysis of the progeny-tests results also provides estimates of the following variance components: progeny x pond interactions, progeny x year interaction, common environment effects, and the error variances. All were found to be in the range of 200 to 600 g2, and were thus small relative to the estimated total genetic variance. When progeny tests are replicated in as few as four ponds, about 70 percent of the differences between progeny means can probably be attributed to genetic variation. Hence, ranking progenies according to their performance in the progeny tests is highly correlated with their genotypic values, and progeny tests provide an effective tool for identifying genetically superior parents or progenies.

6.5 Inbreeding and heterosis

As mentioned earlier, the asymmetry of the response to up and down selection is reminiscent of the situation in plateaued populations, where additive genetic variation is small or non-existent, but non-additive genetic variation is found and is expressed as severe inbreeding depression and heterosis.

In order to investigate the degree of inbreeding depression, the experiments illustrated in the first and the third rows of Fig. 2 were carried out. Two unrelated parents (P1 and P2) were mated, and a group of their offspring were selected. In the following year, the mating of the original parents P1 and P2 was repeated (column 2 under the title F1 - repeat), and served as a control, while the group of selected offspring which were full-sibs, were mass-mated to produce the F2 generation. In almost every case, when the F1 -repeat was compared with the inbred F2, a sharp inbreeding depression was found. Our experimental results led to the conclusion that a single cycle of full-sib mating results in a 10 to 20 percent depression of growth rate. Other typical effects of inbreeding depression were also found, i.e., reduced viability and a considerable increase in the proportion of individuals with visible abnormalities.

Heterosis was also found as expected. Four examples are illustrated in Table VII. Only the first row is, strictly speaking, a comparison between an F2 (only one generation of inbreeding) and the four-way cross of four unrelated parents (F12 × F1'). Hol-A of rows 2 and 3, was an inbred group imported from Holland. The groups Gold, and Blue, were two inbred groups marked with recessive colour mutants. In each case, the crossbreds showed a faster growth rate than their parents.

A comparison of the crossbred (F1 × F1') with the mean of the two inbreds (F2 + F2')/2, shows the degree of heterosis, or reciprocally, the degree of inbreeding depression.

A high proportion of the breeding stocks of carp throughout the world suffer from a high degree of inbreeding. If generalizations can be made from the experience with the Israeli carp population it would seem that the single, and simple, step of using unrelated mates for the production of commercial fry should improve growth rate and yields in many carp growing areas. The use of crossbred fish should also improve viability, and increase uniformity.

Table VII

Heterosis in carp-values are corrected average weight gains per fish in grammes

YearTested GroupsF2F1×F1'F2'
1963Hol. AS4995785390.90
1963Hol. ADor4997076000.78

6.6 Correlations between relative gained weight in communal ponds and in separate ponds

Testing in communal ponds enables measurement of relative growth rate under intergroup competition. However, the trait to be improved is yield in mono-group ponds, where inter-group competition does not exist. The correlation between the two traits has been studied during the last seven years in a set of nine separate experiments. In each experiment the fish of two or three groups were grown simultaneously in several separate or divided ponds and were also mixed in several communal ponds. These experiments showed a high correlation between relative growth rate in communal and separate ponds. Divided ponds were treated as separate ponds. The assumption was made that the interactions between groups of fish located in different parts of the divided pond were small compared to the interactions between the same groups of fish when they were stocked together in the same communal pond.

The estimated regression coefficient obtained, of growth rate in separate (or divided) ponds on growth rate in communal ponds, had a value of 0.63. This meant that a little over a half of the between-group variation observed in communal ponds was expected to be found when the tested groups are grown in separate ponds. It was smaller than one, presumably because of competition interaction between the tested groups in communal ponds.

The relatively small variation found around the regression line indicated that genetic agressiveness independent of growth rate is of small importance in determining the ranking of the tested groups in communal ponds. These results also indicate that selection for improved growth rate in separate ponds may be conducted in communal ponds.


The following points summarize the major results relating to the genetic architecture of growth rate and yield capacity of the carp. The conclusions drawn from these results are, strictly speaking, valid only for the specific conditions under which our experiments were conducted, so that generalization should be made with some reservation.

  1. It appears that individual selection for faster growth rate does not yield a detectable response. This indicates that the realized heritability of growth rate, above the population mean, is zero or very close to zero. On the other hand, selection for slower growth rate appears to yield a response expected when heritability is 0.20–0.30. Thus we clearly have an asymmetrical response to selection.

  2. Relatively large differences in growth rate are found between means of full-sib families.

  3. Even a single generation of brother-sister mating usually results in a strong inbreeding depression of growth rate and viability.

  4. Inter-family crossbreds usually show a high degree of heterosis.

An interpretation of the above results in terms of components of variation of growth rate shows that the additive genetic variance component is very small, while the non-additive genetic variance is relatively large. The evidence for the last conclusion is ample. The asymmetrical response to selection, variation between full-sib families and the presence of inbreeding depression and heterosis.

In most animal species growth rate has a relatively high heritability (0.3–0.5). This is in contrast to what we have found in the carp. In carp, the composition of the variance components of growth rate are typical of those of a population that has reached a selection plateau. We may therefore speculate that in carp and probably some other fish species, growth rate is strongly correlated with reproductive fitness. This assumption can be rationalized as follows: body weight in fish is strongly correlated with egg number in females and with sperm number in males. Both egg and sperm quantities are major components of reproductive fitness in fish. Egg size which is also correlated with body weight appears to be another major component of fingerling viability during the critical period following hatching. A genotype for faster growth rate during the first few weeks of the fish's life is also likely to contribute to its ability to escape mortality during its early life.

Growth rate in carp may thus be the most important component of reproductive fitness. This puts growth rate in the same category as typical reproductive characters, such as egg number in poultry, litter size in pigs, etc., and these as a rule, have low heritability.


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