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The Improvement of New Hampshire Fryers
The Improvement of New Hampshire Fryers I. MICHAEL LERNER, V. S. ASMUNDSON, AND DOROTHY M. CRUDEN
University of California, Berkeley and Davis (Received for publication April 28,1947)
T
It is generally conceded that the characteristics of birds desirable from the standpoint of meat production fall into five categories: 1) rate of growth, 2) conformation, 3) rate of feathering, 4) relative amount of meat, and 5) freedom from defects. These characteristics have been discussed by numerous workers (e.g. Asmundson and Lerner, 1942), and considerable information has been accumulated with reference to the hereditary basis of most of them (see Jull, 1940). Little effort, however, has been made to organize this information and combine it
so that the breeder in the field can apply it to his immediate breeding procedures to maximum advantage. Thus, it is not known exactly how much improvement the breeder can reasonably expect. How much emphasis should each character receive in making the selections? How can characters such as desirable market conformation be measured objectively? Poultry geneticists in providing answers to these and similar questions of the practical breeder can help considerably in placing his efforts on a sound genetic and economic basis. In the present study an attempt has been made to develop a selection index, or a numerical expression of "over-all" breeding value, by an analysis of four characters (body weight, shank length, keel length, and breast width) in New Hampshires at twelve weeks of age. Hazel and Lush (1942) have shown that selection on the basis of such an index is more efficient than selection for one character at a time or selection based on independent culling levels for each character. A completely satisfactory index cannot be formulated until more general agreement has been reached on a number of problems and these have been given particular attention in the present study. Material The foundation stock for the present experiment was obtained from a California breeder of New Hampshires, who for several years prior to the initiation of
515
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HE establishment of definite standards for measuring desirable traits of fryers, as well as reasonable assurance that predictable amounts of improvement can be made are needed before the adoption of an elaborate breeding program involving meat production may be regarded as a sound commercial venture. Recently a nation-wide attempt to stimulate interest in the improvement of poultry from the standpoint of meat quality has been initiated under the auspices of a commercial concern (the U. S. Egg and Poultry Magazine for 1946 may be consulted for a series of publicity releases on the "Chicken of Tomorrow" contest). The tacit assumption underlying such an effort is that breeders in the field can in a relatively short time produce by selection a bird markedly superior to the current product. The question, whether or not this assumption is fully justified requires examination.
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I. MICHAEL LERNER, V. S. ASMUNDSON AND DOROTHY M. CRUDEN
age three linear measurements were also made. The length of keel was measured by a rounded calipers from the tip to the posterior point of the sternum. The shank (tarso-metatarsus) was measured by means of the device described by Burmester and Lerner (1937). The width of breast was obtained by molding a piece of solder over the bird's breast about 1 cm. back of the anterior point of the keel and measuring the width at a given distance from the keel (1 cm. in the case of these birds, and 2 cm. in the case of their
this study had been practicing selection for the improvement of meat quality. From the standpoint of rapid growth, conformation, and early feathering, this stock compared very favorably with other New Hampshires in the state. In 1942 eggs were purchased from pedigree matings. The chicks hatched from them were raised on the University plant at Davis. At twelve weeks of age they were selected largely on the basis of individual rate of growth, and in the fall of the year were pen-mated. Their offspring, hatched in
Body weight Year of hatch 1943 ' 1944
Birds, no.
Sex
91 65 124 106
cf 9
Linear measurements at 12 wks
Hatch gms.
4 wks. gms.
8 wks. gms.
12 wks. gms.
Shank length cm.
Keel length cm.
Breast width cm.
39.1 38.6 41.5 42.6
321.5 296.8 282.9 276.0
942.1 808.0 927.2 813.9
1,653.4 1,346.2 1,656.9 1,359.8
11.3 10.0 11.3 10.1
9.9 9.3 9.8 9.2
3.5* 3.6* 2.3f 2.3f
* 2 cm. above keel. f 1 cm. above keel.
parents), as described by Asmundson (1944) for turkeys. The mean weights and measurements are presented in Table 1. The remarkable agreement between comparable statistics for the parental population and the offspring suggests not only limited interyear variation but also that randomness of selection and mating had been achieved by the means described. The data for the 1944-hatched chicks were then subjected to a statistical analysis. At first, the raw data themselves were analyzed separately for males and females, but it soon became apparent that the low number of birds in each mating would lead to results of questionable statistical validity. Accordingly, the data All of the chicks were weighed at hatch,i, were transformed into respective standard at 4, 8 and 12 weeks of age. At the latterr deviations for the two sexes (Table 2) and
December 1943, were weighed and measured at twelve weeks of age, and the males3 culled from a table of random numbers. In the late fall of 1944 the surviving females were placed in individually pedigreed matings with nine males selected att random among the male survivors. Thee distribution of females among the differ-, -. ent pens was also randomized by the usee of a table of random numbers with twoD restrictions: 1) no full sisters were placedi in the same pen, and 2) no pen containedi any full sisters to the male heading it. Ona December 21, 1944, a total of 244 chickss were hatched from these matings from 388 different dams. Mortality to 12 weeks ofif age reduced this number to 230 chicks onn which this report is based.
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TABLE 1.—Mean weights and measurements
T H E IMPROVEMENT OF N E W HAMPSHIRE FRYERS TABLE
2.—Standard deviations at 12 weeks {1944 flock)
Sex
Body weight gms.
Shank length cm.
Keel length cm.
Breast width cm.
Male Female
235.5 202.6
0.62 0.53
0.62 0.60
0.20 0.10
then combined. The analyses presented here are then based on the combined data for males and females. Live quality grade and rate of feathering.
517
At the time that the measurements were made, a grade A, B or C was assigned to each bird on the basis of its general ap- The degree of heritability. pearance, and a similar rating was made The statistical techniques for deterwith respect to feathering. It was found, mining heritability have been elucidated however, that all of the birds fell into the largely by Lush and his students on the top feathering grade. This particular basis of the theory originally developed by strain of New Hampshires apparently was Sewall Wright. The particular type of uniform for early feathering. Hence no . analysis applied here is based on the further analysis of this trait is possible methods presented by Whatley (1942) and it may be assumed that the selection and by Hazel, Baker and Reinmiller indexes to be presented apply to a situa- (1943) with a few modifications called for tion where no further improvement in by the nature of the data. rate of feathering is necessary. The statistical techniques at our disWith respect to quality, the grader posal enable us to estimate the proportion found several birds worthy of an A + of the observed variance which is due to grade, which was accordingly added to additive genetic differences between inthe classification scheme. Table 3 shows dividuals. Should non-additive interacthe average weights and measurements of tions such as epi,stasis or dominance be the birds assigned to the different grades. involved, the estimates of heritability It is apparent at first sight that the main might be slightly larger than the true, criterion of quality was body size. It may heritabilities. be suspected in general that where gradThe analysis of variance for each of the ing of live birds of a given age is at- four characters with respect to the parentempted, the body size overshadows the tage of the birds is presented in Table 4. TABLE 3.—Weights and measurements at 12 weeks in relation to market grade {1944 flock) Sex Market grade
Males
A+
A
Females B
C
A+
A
B
5 85 29 5 3 76 Birds, number 22 1,733 1,434 1,366 1,649 1,424 Body weight, gms. 1,886 1,216 11.9 10.8 10.6 11.5 10.6 10.3 Shank length, cm. 9.7 10.4 9.4 9.2 9.9 9.8 9.3 Keel length, cm; 8.8 2.30 2.21 2.16 2.31 2.40 2.30 Breast width, cm. 2.21
C 5 831 9.6 7.5 2.16
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other criteria of judgment for quality, particularly where superior strains of broilers or fryers are concerned. The main purpose of the grading was to find the proper contribution that each of the characters studied made to the aggregate value of a bird. Since the quality rating seems to have merely reflected differences in size, the grades contributed no additional information about the value of the birds. Moreover, although shank length is supposed to be negatively correlated with quality, the reverse condition prevailed here.
518
I. MICHAEL LERNER, V. S. ASMUNDSON AND DOROTHY M. CRUDEN TABLE 4.—Analyses of variance
Source of variation Total Between sires Between mates of a sire Between full sibs F* value for sires F* value for mates of a sire
Mean square
Degrees of freedom
Body weight
Shank length
Keel length
Breast width
229 8
0.977 4.256
1.255 5.989
1.121 4.909
2.038 4.414
E+G 0.25G
29 192
1.636 0.741 2.60
1.886 0.962 3.18
1.243 0.945 3.95
2.740 1.833 1.61
0.25G E+0.5G
2.21
1.96
1.32
1.49
Composition of mean square
Interpretation
r+ 23 % 8 D+ 23 %S r+ 2 3 %D T
'' The 5 % value of F for sires is 2.28; for mates of a sire, 1.52.
It may be noted that the F values for body weight and for shank length correspond to significant P levels for both sires and dams. Keel length has a significant P for sires but not for dams, while breast width approaches significance for dams but not for sires. Since separate estimates of the degree of heritability are possible on basis of the variance between
sires and of the variance between dams, a question of subjective judgment arises as to which one to use. Table 5 presents the estimates of the degree of heritability from sires, from dams, and on .the combined basis for each TABLE 5.—Estimates of
Basis of estimate
Body weight
Shank length
Keel length
Breast width
0.415
0.501
0.503
0.126
0.597
0.480
0.172
0.293
0.506
0.491
0.338
0.210
4S T+D+S 4D T+D+S 2(S+D) T+D+S
of the four traits. The agreement between the three estimates is very close for shank length, reasonably so for body weight, and not too close for the remaining measurements. The discrepancies, should they be significant, might be attributed in part to sex-linkage in cases where the estimates from the sires show an excess, and to maternal effects when the estimates from the dams are higher. However, in view of the relatively low number of degrees of freedom, probably the combined estimate can be accepted as the best for our purposes. Thus it may be concluded that in this group of birds the degree of heritabil-
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The total mean square contains both the genetic (G) and the environmental (E) variance. The latter, it must be understood, also includes most of the nonadditive deviations due to dominance and epistasis. The mean square between sires consists largely of one-quarter of the genetic variance, that between mates of each sire of another quarter, while the mean square for the families of full sisters contains the remainder of the genetic variance and all of the E term. The variance components in each can be isolated according to the scheme in the last column of the table, in which T is the component attributable to differences between full sibs, D to differences between dams mated to the same sire, and S to differences between sires. The reader is referred to the previously mentioned paper by Hazel, Baker and Reinmiller (1943) and to the references cited by them for a more complete discussion of the significance of these constants.
519
T H E IMPROVEMENT OF N E W HAMPSHIRE FRYERS TABLE 6.—Comparison of genetic correlation coefficients derived from sires and dams Characters correlated
From sire's contribution
From dam's contribution
From both parents
Body weight—Shank length Keel length Breast width
0.992 0.818 -0.134
0.773 0.883 0.228
0.868 0.791 0.099
Shank length—Keel length Breast width
0.788 0.186
0.632 0.113
0.710 0.139
Keel length —Breast width
-0.104
-0.070
-0.079
Correlations between characters. The correlation between the phenotypes of any two characters in a given bird is compounded of genetic and environmental correlations. Two characters of a bird may be correlated simply because they are subjected to identical environmental forces, though intrinsically they may be independent, or they may actually be related genetically. Since Hazel (1943) developed statistical techniques for separating environmental from genetic correlations, it is possible to compute the two separately. The methods of procedure have been described by Hazel and the estimates presented here are entirely based on them. As in the case of estimates
of h'eritability, estimates of the genetic correlations can be obtained from both sires and dams. The estimates of each of the six genetic correlations (Table 6) agree closely except for that between body weight and breast width. Here the estimate from sires is opposite in sign to that from dams, but both are fairly close to zero. The genetic correlations based on the average contribution of sires and dams are given in Table 7 along with the environmental and phenotypic correlations. The genetic correlation between body weight and shank length is higher than the environmental correlation. Thus changes in the genetic composition of a population for either of these characters will be accompanied by greater changes in the other than expected from the phenotypic correlation. The same is true for the shank length-keel length relationship, while the opposite is the case for the shank lengthbreast width correlation. In the other cases the two types of correlation are similar.
TABLE 7.—Correlation coefficients between the different characters based on average of sire and dam contributions Characters correlated
Genetic
Environmental
Phenotypic
Body weight—Shank length Keel length Breast width
0.868 0.791 0.099
0.571 0.830 0.157
0.658 0.802 0.132
Shank lengh—Keel length Breast width
0.710 0.139
0.406 0.519
0.522 0.376
-0.079
-0.068
-0.070
Keel length —Breast width
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ity of body weight and shank length is about 50 percent, in the vicinity of 30-35 percent for keel length and about 20 percent for breast width. Since sampling errors are likely to be large in samples as small as this, these estimates should be considered approximations rather than exact values.
520
I. MICHAEL LERNER, V. S. ASMUNDSON AND DOROTHY M. CRUDEN
Selection indexes. Hazel (1943) has formulated the principles governing the construction of selection indexes. In general, it is clear that the total genetic superiority of a bird is a function of the heritabilities of the characters selected for and of their economic importance. In addition, when several characters are involved, the genetic correlations between them need to be taken in account, since selection for one character will affect the other. Hence, the most efficient selection index is one in which each character is weighted so as to maximize the'rate of improvement of the aggregate value of the bird. The statistics needed for the construction of an index include the degree of heritability of each trait considered, the genetic correlations between the various traits, the phenotypic correlations between them, and the proper economic weight of each trait. All of these have already been given, except for the economic weights, which present somewhat of a stumbling block. For instance, the only
other indexes which have been constructed previously for poultry (egg production) by Panse (1946) are based on such manifestly arbitrary weights as to be of no practical value. The problem in the current case is even more difficult, because there is a wide discrepancy between what is considered desirable and what the poultry producer gets paid for. Thus, if we consider breast width, we find that packers and consumers are unanimous in agreeing that a broad breast is desirable on a market bird. Yet, the only price differential on the market is for overall grade which reflects only to a limited degree differences in width of breast. Two birds of identical body weight may fall into the same grade irrespective of their breast width. The effort that a breeder may make to increase breast width must be financed by himself and at the cost of improvement in other traits. Hence, the majority of breeders are unlikely to assign much weight to this and other similar characters. What weights then may be assigned to the four characters considered in the present study? Until definite information is available as to what the relative economic value of each one of them is, that is to say, how many grams of body weight are equivalent to each unit of breast width, shank and keel length in terms of actual dollars and cents, the only reasonable indexes that can be constructed are for each one of these characters separately. In the case of the present flock such indexes would mean that selection is to be practiced only for increased body weight, or only for reduced shank length, or only for increased keel length, and lastly, only for increased breast width. Since it has been demonstrated by Hazel and Lush (1942) that selection for total score is more efficient than selection for one character at a time, such indexes would fall
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The only negative correlations observed here are between keel length and breast width, suggesting that attempts to improve both simultaneously will (however, only to a small degree) exercise a pull in opposite directions. The more serious difficulty is with regard to the positive correlation between body weight and shank length, since it has been assumed that short shanks are desirable (see e.g. Jaap, 1941). Due to the positive correlation noted, selection for increased body weight and a reduced shank simultaneously will largely cancel each other out. This conclusion is supported by the previously reported unsuccessful attempt to establish differences in the relative growth pattern of the shank by selection (Lerner, 1943).
T H E IMPROVEMENT or N E W HAMPSHIRE FRYERS
The basic data for the construction of indexes, except for the economic value of each of the traits, are given in the tables previously presented. A brief description of the procedure will be given in case it is desired to construct indexes with other values than those given here. Table 8 explains the meaning of the symbols in the following formulas. Firstly, the values of correlation coefficients between each character and the aggregate genotype in terms of the economic weights and the standard deviation of the aggregate genotype (H) were computed from the formula (the example given is for body weight): Wh\
TWH
The resultant bx's are expressed in terms of respective standard deviations, and hence were then converted into actual units for the two sexes. The differences between the regression coefficients (in actual units) for males and females were not very great with the exception of those for breast width, because of the TABLE 8.—Explanation of symbols Symbol X B K S W bx
hi
H I r r° rt R12 Wx « • «
Explanation any phenotypic measurement width of breast in cm. length of keel in cm. length of shank in cm. body weight in kg. multiple regression coefficient heritability aggregate genotype value of bird according to an index correlation coefficient genotypic correlations between Xi and Xi phenotypic correlation between Xi and Xi multiple correlation coefficient economic weight standard deviation (square root of total mean square in Table 4)
difference in the standard deviations for the two sexes (Table 2). An intermediate value was selected for the sake of simplicity and all the coefficients were then divided by the one for body weight. The five indexes for the five types of weighting are presented in Table 9. The interpretation of index 1, for instance, is that if selection for body weight is desired the birds excelling in the value of their index 1 are to be saved for breeding. This value is obtained by adding the body weight ex-
wsWs+Vh2K
oBi\BWB).
OH OH
These coefficients were then used in solving four simultaneous equations for the regression coefficients of the following type (the example is again for body weight): bwow . _ bsos P 'ws OH ' WK OH
pressed in kilograms to 0.3 of the shank length in centimeters and subtracting 0.1 of the keel length and 0.4 of the breast width. In general, the use of these indexes should be considered as the most efficient OH
OH
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short of the ideal and would apply only to the case where all of the economic differentials were based on a single character. In addition to such indexes, a fifth one constructed on a completely arbitrary assumption of equal weighting of body weight (the most accurate basis of present payment for meat) and breast width (the factor apparently most stressed in the "Chicken-of -tomorrow" contest) was made. In the data at hand this means that a change of one-half pound of live body weight (cne standard deviation) will be rewarded equally with a change of 0.15 cm. of breast width one cm. above the keel (also approximately one standard deviation). This particular weighting may have no merit whatsoever, but can be used as an illustration of an index based on selection for more than one character.
521
522
I. MICHAEL LERNER, V. S. ASMUNDSON AND DOROTHY M. CRUDEN TABLE 9.—Selection indexes Economic weighting—Wx
Index No.
1 2 3 4 5
Body weight W 1 0 0 0 1
Shank length 5 0 -1 0 0 0
Keel length K
Breast width B
0 0 1 0 0
0 0 0 1 1
The efficiency of selection
indexes.
Off-hand the breeder may consider that if a single character is to be improved selection should be directed solely to that
W+0.35-0.LBT-0.4.B -TV+1.15+0.1Sir+1.25 -tf+4.35+4.8iT-5.5B
W-0.2S-0.2K+0.6B W+0.02S-OA5K+0.2B
deviation in the selection differential the amount of gain realized per generation will be equal to the product of heritability and the standard deviation (h2xax). However, the maximum possible gain when the genotypes of all birds are known, is not the selection differential itself but the selection differential times the square root of heritability. This is due to the fact that for each phenotypic standard deviation in the selection differential, the maximum gain obtainable is a genotypic standard deviation (
• • • +2WXlWW%l\/%tW*S't
character, and the best index would be the value of the character itself. Obviously, that is not nesessarily the case, since another character closely correlated with the desirable one may have much higher heritability. Hence selection may be more efficient when both the desired character and a correlated character are considered. Improvement in efficiency of selection for a single character will be obtained when other characters are also taken into account, provided the emphasis given each trait is properly calculated. It is possible to compute the increase in efficiency which is obtained by using an index over that obtained by direct selection for a character as shown in the first four columns of Table 10. Firstly, we may compute the efficiency of improvement on the basis of selection for a single character. For every standard
+
(see Hazel, 1943, whose notation is different from the one used here). In the simple case where all W's except one are given zero weight, this formula reduces itself to
Hence the percentage of possible improvement in the case under consideration is
'hi.
Thus only when hl=l, can the full selection differential (in phenotypic terms) be realized. The values of VAI are listed for the four characters against corresponding indexes in the second column of Table 10. The rate of improvement when the index is used is equal to the coefficient of multiple correlation between the ag-
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way of applying mass selection in this flock to the desired combination of traits. The latter in the case of the first four indexes is a single character, and in the case of the fifth the noted combination of body weight and breast width. Indexes for other combinations may be obtained by solving the equations given above.
Index in actual units W in kg., others in cm.
523
T H E IMPROVEMENT o r N E W H A M P S H I R E F R Y E R S TABLE 10.—Efficiency
of selection indexes*
Index number
\ X
m
Percent increase in efficiency
W
5
K
B
1 2 3 4
0.71 0.70 0.58 0.46
0.78 0.80 0.66 0.52
9.9 14.3 13.8 13.0
0.55 -0.55 0.32 0.03
0.48 -0.63 0.28 0.05
0.44 -0.45 0.40 -0.03
0.05 -0.09 -0.03 0.34
R
Rate of change in individual traits
* See text for explanation of column headings.
Ri
•V
T h u s when improvement body weight is sought for b y using index 1, shank weight will increase (at the rate of 0.48 for each a in t h e selection differential for this character, as will keel length (0.44 for each d) and breast width (very slightly, 0.05 p e r
bw
This value also indicates t h e fraction of the total improvement possible if the genotypes were precisely known which is gained b y using the index. T h e third column in Table 10 lists RTH values for t h e five indexes, while t h e fourth column represents the increase in efficiency when the index is used against t h e case when phenotypic selection for single characters is practiced. T h e increases obtained range from about 10 percent for body weight t o about 14 percent for shank length. T h u s , with respect to breast width, t h e use of the suggested index will increase the expected rate of improvement b y 13 percent over what it would be if breast width alone were used as a criterion of selection. Whether this increase is worthwhile will, of course, depend on how anxious t h e breeder is1 to obtain t h e gains sought.
v>on a). Reduction in shank length (index 2) will likewise lead t o reduction in t h e other characters. When selection is for increased keel length, breast width will, however, show a decrease with t h e reciprocal relation also holding true. I t m a y be worthwhile noting t h a t selection for breast width (index 4) will lead to least changes in t h e other characters, so t h a t it might be possible in this population t o improve t h e breast without much effect on body weight, shank length a n d keel length. However, it should be understood, t h a t since the selection differentials of t h e different characters will differ depending on t h e index used, a direct comparison of t h e figures in each column does not reflect t h e exact relative magnitude of the changes expected.
I n general, t h e point of greatest significance t o be drawn from Tables 9 a n d 10 is t h a t a proper economic weighting must be assigned to each character before most effective selection for an ideal type can be practiced. I t is possible t o improve a n y represent the p r o d u c t s of RIH
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gregate genotype (H) a n d t h e index value (7) for each animal. I t is obvious t h a t for the first four indexes, H is equal t o t h e respective genotypes for W, S, K, a n d B. The formula for this coefficient (derived from Hazel, 1943) is
524
I. M I C H A E L L E R N E R , V. S. ASMUNDSON AND D O R O T H Y M.
as increase in shank length under selection for other traits, or decrease in keel length under selection for wider breast) m a y occur. Until appropriate economic rewards are given t o the breeder undertaking a specific improvement project, not only does he lack an incentive, b u t he lacks assurance t h a t he is proceeding on an efficient basis. If he is to be paid for increased weight only, the index formulated along the lines of our index 1 is the only one he is justified in using.
CONCLUSIONS A randomly selected sample of the progeny of a New Hampshire breeding flock was studied with respect to body weight, shank length, keel length and breast width at 12 weeks of age. The heritability of these four characters was found to be approximately 50, 50, 30 and 20 percent respectively. T h e environmental and the genetic correlations between them were calculated and on the basis of these statistics several selection indexes constructed. The difficulty in the construction of such indexes lies in the impossibility of assigning proper economic weights to each of the traits studied. Until such weighting is agreed upon and producers are paid accordingly, the only indexes worthwhile are for selection for individual characters. The results expected from the use of such indexes were found to increase efficiency in rate of improvement by 10 to
14 percent. The rate of change in characters not selected for was also determined for each of the indexes. T h u s , it was found t h a t selection for breast width is possible with relatively slight effects on the other characters. An arbitrary index where an increase in half a pound of body weight was arbitrarily assigned an economic value equal to an increase of 0.15 cm. in breast width one centimeter above the keel was constructed as an example of the method. ACKNOWLEDGMENTS We are indebted for the grading of the birds to Mr. H . B. Mugglestone, foreman of the Berkeley poultry plant of the University of California, and to D r . L. N . Hazel, Iowa State College for a critical review of the manuscript. REFERENCES
Asmundson, V. S. 1944. Measuring strain differences in the conformation of turkeys. Poultry Sci. 23: 21-29. —and I. M. Lerner. 1942. Breeding chickens for meat production. Calif. Agr. Exp. Sta. Bull. 675. 45 pp. Burmester, B. R. and I. M. Lerner. 1937. A measuring device for shank length of living birds. Poultry Sci. 16: 211-212. Hazel, L. N. 1943. The genetic basis for constructing selection indexes. Genetics 28:476-490. , M. L. Baker, and C. F. Reinmiller. 1943. Genetic and environmental correlations between the growth rates of pigs at different ages. J. Animal Sci. 2:118-128. , and J. L. Lush. 1942. The efficiency of three methods of selection. J. Hered. 33: 393-399. Jaap, R. G. 1941. Body form in growing chickens. J. Agr. Res. 62:431-443. Jul], M. A. 1940. Poultry Breeding. 2nd ed. xiv+ 484 pp. Wiley, New York. Lerner, I. M. 1943. The failure of selection to modify shank-growth ratios of the domestic fowl. Genetics 28:80-81. Panse, V. G. 1946. An application of the discriminant function for selection in poultry. J. Genet. 47:242-248. Whatley, J. A. Jr. 1942. Influence of heredity and other factors on 180-day weight in Poland China swine. J. Agr. Res. 65: 249-264.
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T h e relationships presented are illustrative of the methods of constructing selection indexes. T h e y represent first approximations and m a y only hold for the flock under consideration. Experimental verification of the efficiency of selection indexes is needed and is being planned by us. Parallel tests elsewhere would be exceedingly desirable.
CRUDEN
University of California, Berkeley and Davis (Received for publication April 28,1947)
T
It is generally conceded that the characteristics of birds desirable from the standpoint of meat production fall into five categories: 1) rate of growth, 2) conformation, 3) rate of feathering, 4) relative amount of meat, and 5) freedom from defects. These characteristics have been discussed by numerous workers (e.g. Asmundson and Lerner, 1942), and considerable information has been accumulated with reference to the hereditary basis of most of them (see Jull, 1940). Little effort, however, has been made to organize this information and combine it
so that the breeder in the field can apply it to his immediate breeding procedures to maximum advantage. Thus, it is not known exactly how much improvement the breeder can reasonably expect. How much emphasis should each character receive in making the selections? How can characters such as desirable market conformation be measured objectively? Poultry geneticists in providing answers to these and similar questions of the practical breeder can help considerably in placing his efforts on a sound genetic and economic basis. In the present study an attempt has been made to develop a selection index, or a numerical expression of "over-all" breeding value, by an analysis of four characters (body weight, shank length, keel length, and breast width) in New Hampshires at twelve weeks of age. Hazel and Lush (1942) have shown that selection on the basis of such an index is more efficient than selection for one character at a time or selection based on independent culling levels for each character. A completely satisfactory index cannot be formulated until more general agreement has been reached on a number of problems and these have been given particular attention in the present study. Material The foundation stock for the present experiment was obtained from a California breeder of New Hampshires, who for several years prior to the initiation of
515
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HE establishment of definite standards for measuring desirable traits of fryers, as well as reasonable assurance that predictable amounts of improvement can be made are needed before the adoption of an elaborate breeding program involving meat production may be regarded as a sound commercial venture. Recently a nation-wide attempt to stimulate interest in the improvement of poultry from the standpoint of meat quality has been initiated under the auspices of a commercial concern (the U. S. Egg and Poultry Magazine for 1946 may be consulted for a series of publicity releases on the "Chicken of Tomorrow" contest). The tacit assumption underlying such an effort is that breeders in the field can in a relatively short time produce by selection a bird markedly superior to the current product. The question, whether or not this assumption is fully justified requires examination.
516
I. MICHAEL LERNER, V. S. ASMUNDSON AND DOROTHY M. CRUDEN
age three linear measurements were also made. The length of keel was measured by a rounded calipers from the tip to the posterior point of the sternum. The shank (tarso-metatarsus) was measured by means of the device described by Burmester and Lerner (1937). The width of breast was obtained by molding a piece of solder over the bird's breast about 1 cm. back of the anterior point of the keel and measuring the width at a given distance from the keel (1 cm. in the case of these birds, and 2 cm. in the case of their
this study had been practicing selection for the improvement of meat quality. From the standpoint of rapid growth, conformation, and early feathering, this stock compared very favorably with other New Hampshires in the state. In 1942 eggs were purchased from pedigree matings. The chicks hatched from them were raised on the University plant at Davis. At twelve weeks of age they were selected largely on the basis of individual rate of growth, and in the fall of the year were pen-mated. Their offspring, hatched in
Body weight Year of hatch 1943 ' 1944
Birds, no.
Sex
91 65 124 106
cf 9
Linear measurements at 12 wks
Hatch gms.
4 wks. gms.
8 wks. gms.
12 wks. gms.
Shank length cm.
Keel length cm.
Breast width cm.
39.1 38.6 41.5 42.6
321.5 296.8 282.9 276.0
942.1 808.0 927.2 813.9
1,653.4 1,346.2 1,656.9 1,359.8
11.3 10.0 11.3 10.1
9.9 9.3 9.8 9.2
3.5* 3.6* 2.3f 2.3f
* 2 cm. above keel. f 1 cm. above keel.
parents), as described by Asmundson (1944) for turkeys. The mean weights and measurements are presented in Table 1. The remarkable agreement between comparable statistics for the parental population and the offspring suggests not only limited interyear variation but also that randomness of selection and mating had been achieved by the means described. The data for the 1944-hatched chicks were then subjected to a statistical analysis. At first, the raw data themselves were analyzed separately for males and females, but it soon became apparent that the low number of birds in each mating would lead to results of questionable statistical validity. Accordingly, the data All of the chicks were weighed at hatch,i, were transformed into respective standard at 4, 8 and 12 weeks of age. At the latterr deviations for the two sexes (Table 2) and
December 1943, were weighed and measured at twelve weeks of age, and the males3 culled from a table of random numbers. In the late fall of 1944 the surviving females were placed in individually pedigreed matings with nine males selected att random among the male survivors. Thee distribution of females among the differ-, -. ent pens was also randomized by the usee of a table of random numbers with twoD restrictions: 1) no full sisters were placedi in the same pen, and 2) no pen containedi any full sisters to the male heading it. Ona December 21, 1944, a total of 244 chickss were hatched from these matings from 388 different dams. Mortality to 12 weeks ofif age reduced this number to 230 chicks onn which this report is based.
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TABLE 1.—Mean weights and measurements
T H E IMPROVEMENT OF N E W HAMPSHIRE FRYERS TABLE
2.—Standard deviations at 12 weeks {1944 flock)
Sex
Body weight gms.
Shank length cm.
Keel length cm.
Breast width cm.
Male Female
235.5 202.6
0.62 0.53
0.62 0.60
0.20 0.10
then combined. The analyses presented here are then based on the combined data for males and females. Live quality grade and rate of feathering.
517
At the time that the measurements were made, a grade A, B or C was assigned to each bird on the basis of its general ap- The degree of heritability. pearance, and a similar rating was made The statistical techniques for deterwith respect to feathering. It was found, mining heritability have been elucidated however, that all of the birds fell into the largely by Lush and his students on the top feathering grade. This particular basis of the theory originally developed by strain of New Hampshires apparently was Sewall Wright. The particular type of uniform for early feathering. Hence no . analysis applied here is based on the further analysis of this trait is possible methods presented by Whatley (1942) and it may be assumed that the selection and by Hazel, Baker and Reinmiller indexes to be presented apply to a situa- (1943) with a few modifications called for tion where no further improvement in by the nature of the data. rate of feathering is necessary. The statistical techniques at our disWith respect to quality, the grader posal enable us to estimate the proportion found several birds worthy of an A + of the observed variance which is due to grade, which was accordingly added to additive genetic differences between inthe classification scheme. Table 3 shows dividuals. Should non-additive interacthe average weights and measurements of tions such as epi,stasis or dominance be the birds assigned to the different grades. involved, the estimates of heritability It is apparent at first sight that the main might be slightly larger than the true, criterion of quality was body size. It may heritabilities. be suspected in general that where gradThe analysis of variance for each of the ing of live birds of a given age is at- four characters with respect to the parentempted, the body size overshadows the tage of the birds is presented in Table 4. TABLE 3.—Weights and measurements at 12 weeks in relation to market grade {1944 flock) Sex Market grade
Males
A+
A
Females B
C
A+
A
B
5 85 29 5 3 76 Birds, number 22 1,733 1,434 1,366 1,649 1,424 Body weight, gms. 1,886 1,216 11.9 10.8 10.6 11.5 10.6 10.3 Shank length, cm. 9.7 10.4 9.4 9.2 9.9 9.8 9.3 Keel length, cm; 8.8 2.30 2.21 2.16 2.31 2.40 2.30 Breast width, cm. 2.21
C 5 831 9.6 7.5 2.16
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other criteria of judgment for quality, particularly where superior strains of broilers or fryers are concerned. The main purpose of the grading was to find the proper contribution that each of the characters studied made to the aggregate value of a bird. Since the quality rating seems to have merely reflected differences in size, the grades contributed no additional information about the value of the birds. Moreover, although shank length is supposed to be negatively correlated with quality, the reverse condition prevailed here.
518
I. MICHAEL LERNER, V. S. ASMUNDSON AND DOROTHY M. CRUDEN TABLE 4.—Analyses of variance
Source of variation Total Between sires Between mates of a sire Between full sibs F* value for sires F* value for mates of a sire
Mean square
Degrees of freedom
Body weight
Shank length
Keel length
Breast width
229 8
0.977 4.256
1.255 5.989
1.121 4.909
2.038 4.414
E+G 0.25G
29 192
1.636 0.741 2.60
1.886 0.962 3.18
1.243 0.945 3.95
2.740 1.833 1.61
0.25G E+0.5G
2.21
1.96
1.32
1.49
Composition of mean square
Interpretation
r+ 23 % 8 D+ 23 %S r+ 2 3 %D T
'' The 5 % value of F for sires is 2.28; for mates of a sire, 1.52.
It may be noted that the F values for body weight and for shank length correspond to significant P levels for both sires and dams. Keel length has a significant P for sires but not for dams, while breast width approaches significance for dams but not for sires. Since separate estimates of the degree of heritability are possible on basis of the variance between
sires and of the variance between dams, a question of subjective judgment arises as to which one to use. Table 5 presents the estimates of the degree of heritability from sires, from dams, and on .the combined basis for each TABLE 5.—Estimates of
Basis of estimate
Body weight
Shank length
Keel length
Breast width
0.415
0.501
0.503
0.126
0.597
0.480
0.172
0.293
0.506
0.491
0.338
0.210
4S T+D+S 4D T+D+S 2(S+D) T+D+S
of the four traits. The agreement between the three estimates is very close for shank length, reasonably so for body weight, and not too close for the remaining measurements. The discrepancies, should they be significant, might be attributed in part to sex-linkage in cases where the estimates from the sires show an excess, and to maternal effects when the estimates from the dams are higher. However, in view of the relatively low number of degrees of freedom, probably the combined estimate can be accepted as the best for our purposes. Thus it may be concluded that in this group of birds the degree of heritabil-
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The total mean square contains both the genetic (G) and the environmental (E) variance. The latter, it must be understood, also includes most of the nonadditive deviations due to dominance and epistasis. The mean square between sires consists largely of one-quarter of the genetic variance, that between mates of each sire of another quarter, while the mean square for the families of full sisters contains the remainder of the genetic variance and all of the E term. The variance components in each can be isolated according to the scheme in the last column of the table, in which T is the component attributable to differences between full sibs, D to differences between dams mated to the same sire, and S to differences between sires. The reader is referred to the previously mentioned paper by Hazel, Baker and Reinmiller (1943) and to the references cited by them for a more complete discussion of the significance of these constants.
519
T H E IMPROVEMENT OF N E W HAMPSHIRE FRYERS TABLE 6.—Comparison of genetic correlation coefficients derived from sires and dams Characters correlated
From sire's contribution
From dam's contribution
From both parents
Body weight—Shank length Keel length Breast width
0.992 0.818 -0.134
0.773 0.883 0.228
0.868 0.791 0.099
Shank length—Keel length Breast width
0.788 0.186
0.632 0.113
0.710 0.139
Keel length —Breast width
-0.104
-0.070
-0.079
Correlations between characters. The correlation between the phenotypes of any two characters in a given bird is compounded of genetic and environmental correlations. Two characters of a bird may be correlated simply because they are subjected to identical environmental forces, though intrinsically they may be independent, or they may actually be related genetically. Since Hazel (1943) developed statistical techniques for separating environmental from genetic correlations, it is possible to compute the two separately. The methods of procedure have been described by Hazel and the estimates presented here are entirely based on them. As in the case of estimates
of h'eritability, estimates of the genetic correlations can be obtained from both sires and dams. The estimates of each of the six genetic correlations (Table 6) agree closely except for that between body weight and breast width. Here the estimate from sires is opposite in sign to that from dams, but both are fairly close to zero. The genetic correlations based on the average contribution of sires and dams are given in Table 7 along with the environmental and phenotypic correlations. The genetic correlation between body weight and shank length is higher than the environmental correlation. Thus changes in the genetic composition of a population for either of these characters will be accompanied by greater changes in the other than expected from the phenotypic correlation. The same is true for the shank length-keel length relationship, while the opposite is the case for the shank lengthbreast width correlation. In the other cases the two types of correlation are similar.
TABLE 7.—Correlation coefficients between the different characters based on average of sire and dam contributions Characters correlated
Genetic
Environmental
Phenotypic
Body weight—Shank length Keel length Breast width
0.868 0.791 0.099
0.571 0.830 0.157
0.658 0.802 0.132
Shank lengh—Keel length Breast width
0.710 0.139
0.406 0.519
0.522 0.376
-0.079
-0.068
-0.070
Keel length —Breast width
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ity of body weight and shank length is about 50 percent, in the vicinity of 30-35 percent for keel length and about 20 percent for breast width. Since sampling errors are likely to be large in samples as small as this, these estimates should be considered approximations rather than exact values.
520
I. MICHAEL LERNER, V. S. ASMUNDSON AND DOROTHY M. CRUDEN
Selection indexes. Hazel (1943) has formulated the principles governing the construction of selection indexes. In general, it is clear that the total genetic superiority of a bird is a function of the heritabilities of the characters selected for and of their economic importance. In addition, when several characters are involved, the genetic correlations between them need to be taken in account, since selection for one character will affect the other. Hence, the most efficient selection index is one in which each character is weighted so as to maximize the'rate of improvement of the aggregate value of the bird. The statistics needed for the construction of an index include the degree of heritability of each trait considered, the genetic correlations between the various traits, the phenotypic correlations between them, and the proper economic weight of each trait. All of these have already been given, except for the economic weights, which present somewhat of a stumbling block. For instance, the only
other indexes which have been constructed previously for poultry (egg production) by Panse (1946) are based on such manifestly arbitrary weights as to be of no practical value. The problem in the current case is even more difficult, because there is a wide discrepancy between what is considered desirable and what the poultry producer gets paid for. Thus, if we consider breast width, we find that packers and consumers are unanimous in agreeing that a broad breast is desirable on a market bird. Yet, the only price differential on the market is for overall grade which reflects only to a limited degree differences in width of breast. Two birds of identical body weight may fall into the same grade irrespective of their breast width. The effort that a breeder may make to increase breast width must be financed by himself and at the cost of improvement in other traits. Hence, the majority of breeders are unlikely to assign much weight to this and other similar characters. What weights then may be assigned to the four characters considered in the present study? Until definite information is available as to what the relative economic value of each one of them is, that is to say, how many grams of body weight are equivalent to each unit of breast width, shank and keel length in terms of actual dollars and cents, the only reasonable indexes that can be constructed are for each one of these characters separately. In the case of the present flock such indexes would mean that selection is to be practiced only for increased body weight, or only for reduced shank length, or only for increased keel length, and lastly, only for increased breast width. Since it has been demonstrated by Hazel and Lush (1942) that selection for total score is more efficient than selection for one character at a time, such indexes would fall
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The only negative correlations observed here are between keel length and breast width, suggesting that attempts to improve both simultaneously will (however, only to a small degree) exercise a pull in opposite directions. The more serious difficulty is with regard to the positive correlation between body weight and shank length, since it has been assumed that short shanks are desirable (see e.g. Jaap, 1941). Due to the positive correlation noted, selection for increased body weight and a reduced shank simultaneously will largely cancel each other out. This conclusion is supported by the previously reported unsuccessful attempt to establish differences in the relative growth pattern of the shank by selection (Lerner, 1943).
T H E IMPROVEMENT or N E W HAMPSHIRE FRYERS
The basic data for the construction of indexes, except for the economic value of each of the traits, are given in the tables previously presented. A brief description of the procedure will be given in case it is desired to construct indexes with other values than those given here. Table 8 explains the meaning of the symbols in the following formulas. Firstly, the values of correlation coefficients between each character and the aggregate genotype in terms of the economic weights and the standard deviation of the aggregate genotype (H) were computed from the formula (the example given is for body weight): Wh\
TWH
The resultant bx's are expressed in terms of respective standard deviations, and hence were then converted into actual units for the two sexes. The differences between the regression coefficients (in actual units) for males and females were not very great with the exception of those for breast width, because of the TABLE 8.—Explanation of symbols Symbol X B K S W bx
hi
H I r r° rt R12 Wx « • «
Explanation any phenotypic measurement width of breast in cm. length of keel in cm. length of shank in cm. body weight in kg. multiple regression coefficient heritability aggregate genotype value of bird according to an index correlation coefficient genotypic correlations between Xi and Xi phenotypic correlation between Xi and Xi multiple correlation coefficient economic weight standard deviation (square root of total mean square in Table 4)
difference in the standard deviations for the two sexes (Table 2). An intermediate value was selected for the sake of simplicity and all the coefficients were then divided by the one for body weight. The five indexes for the five types of weighting are presented in Table 9. The interpretation of index 1, for instance, is that if selection for body weight is desired the birds excelling in the value of their index 1 are to be saved for breeding. This value is obtained by adding the body weight ex-
oBi\BWB).
OH OH
These coefficients were then used in solving four simultaneous equations for the regression coefficients of the following type (the example is again for body weight): bwow . _ bsos P 'ws OH ' WK OH
pressed in kilograms to 0.3 of the shank length in centimeters and subtracting 0.1 of the keel length and 0.4 of the breast width. In general, the use of these indexes should be considered as the most efficient OH
OH
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short of the ideal and would apply only to the case where all of the economic differentials were based on a single character. In addition to such indexes, a fifth one constructed on a completely arbitrary assumption of equal weighting of body weight (the most accurate basis of present payment for meat) and breast width (the factor apparently most stressed in the "Chicken-of -tomorrow" contest) was made. In the data at hand this means that a change of one-half pound of live body weight (cne standard deviation) will be rewarded equally with a change of 0.15 cm. of breast width one cm. above the keel (also approximately one standard deviation). This particular weighting may have no merit whatsoever, but can be used as an illustration of an index based on selection for more than one character.
521
522
I. MICHAEL LERNER, V. S. ASMUNDSON AND DOROTHY M. CRUDEN TABLE 9.—Selection indexes Economic weighting—Wx
Index No.
1 2 3 4 5
Body weight W 1 0 0 0 1
Shank length 5 0 -1 0 0 0
Keel length K
Breast width B
0 0 1 0 0
0 0 0 1 1
The efficiency of selection
indexes.
Off-hand the breeder may consider that if a single character is to be improved selection should be directed solely to that
W+0.35-0.LBT-0.4.B -TV+1.15+0.1Sir+1.25 -tf+4.35+4.8iT-5.5B
W-0.2S-0.2K+0.6B W+0.02S-OA5K+0.2B
deviation in the selection differential the amount of gain realized per generation will be equal to the product of heritability and the standard deviation (h2xax). However, the maximum possible gain when the genotypes of all birds are known, is not the selection differential itself but the selection differential times the square root of heritability. This is due to the fact that for each phenotypic standard deviation in the selection differential, the maximum gain obtainable is a genotypic standard deviation (
• • • +2WXlWW%l\/%tW*S't
character, and the best index would be the value of the character itself. Obviously, that is not nesessarily the case, since another character closely correlated with the desirable one may have much higher heritability. Hence selection may be more efficient when both the desired character and a correlated character are considered. Improvement in efficiency of selection for a single character will be obtained when other characters are also taken into account, provided the emphasis given each trait is properly calculated. It is possible to compute the increase in efficiency which is obtained by using an index over that obtained by direct selection for a character as shown in the first four columns of Table 10. Firstly, we may compute the efficiency of improvement on the basis of selection for a single character. For every standard
+
(see Hazel, 1943, whose notation is different from the one used here). In the simple case where all W's except one are given zero weight, this formula reduces itself to
Hence the percentage of possible improvement in the case under consideration is
'hi.
Thus only when hl=l, can the full selection differential (in phenotypic terms) be realized. The values of VAI are listed for the four characters against corresponding indexes in the second column of Table 10. The rate of improvement when the index is used is equal to the coefficient of multiple correlation between the ag-
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way of applying mass selection in this flock to the desired combination of traits. The latter in the case of the first four indexes is a single character, and in the case of the fifth the noted combination of body weight and breast width. Indexes for other combinations may be obtained by solving the equations given above.
Index in actual units W in kg., others in cm.
523
T H E IMPROVEMENT o r N E W H A M P S H I R E F R Y E R S TABLE 10.—Efficiency
of selection indexes*
Index number
\ X
m
Percent increase in efficiency
W
5
K
B
1 2 3 4
0.71 0.70 0.58 0.46
0.78 0.80 0.66 0.52
9.9 14.3 13.8 13.0
0.55 -0.55 0.32 0.03
0.48 -0.63 0.28 0.05
0.44 -0.45 0.40 -0.03
0.05 -0.09 -0.03 0.34
R
Rate of change in individual traits
* See text for explanation of column headings.
Ri
•V
T h u s when improvement body weight is sought for b y using index 1, shank weight will increase (at the rate of 0.48 for each a in t h e selection differential for this character, as will keel length (0.44 for each d) and breast width (very slightly, 0.05 p e r
bw
This value also indicates t h e fraction of the total improvement possible if the genotypes were precisely known which is gained b y using the index. T h e third column in Table 10 lists RTH values for t h e five indexes, while t h e fourth column represents the increase in efficiency when the index is used against t h e case when phenotypic selection for single characters is practiced. T h e increases obtained range from about 10 percent for body weight t o about 14 percent for shank length. T h u s , with respect to breast width, t h e use of the suggested index will increase the expected rate of improvement b y 13 percent over what it would be if breast width alone were used as a criterion of selection. Whether this increase is worthwhile will, of course, depend on how anxious t h e breeder is1 to obtain t h e gains sought.
v>on a). Reduction in shank length (index 2) will likewise lead t o reduction in t h e other characters. When selection is for increased keel length, breast width will, however, show a decrease with t h e reciprocal relation also holding true. I t m a y be worthwhile noting t h a t selection for breast width (index 4) will lead to least changes in t h e other characters, so t h a t it might be possible in this population t o improve t h e breast without much effect on body weight, shank length a n d keel length. However, it should be understood, t h a t since the selection differentials of t h e different characters will differ depending on t h e index used, a direct comparison of t h e figures in each column does not reflect t h e exact relative magnitude of the changes expected.
I n general, t h e point of greatest significance t o be drawn from Tables 9 a n d 10 is t h a t a proper economic weighting must be assigned to each character before most effective selection for an ideal type can be practiced. I t is possible t o improve a n y represent the p r o d u c t s of RIH
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gregate genotype (H) a n d t h e index value (7) for each animal. I t is obvious t h a t for the first four indexes, H is equal t o t h e respective genotypes for W, S, K, a n d B. The formula for this coefficient (derived from Hazel, 1943) is
524
I. M I C H A E L L E R N E R , V. S. ASMUNDSON AND D O R O T H Y M.
as increase in shank length under selection for other traits, or decrease in keel length under selection for wider breast) m a y occur. Until appropriate economic rewards are given t o the breeder undertaking a specific improvement project, not only does he lack an incentive, b u t he lacks assurance t h a t he is proceeding on an efficient basis. If he is to be paid for increased weight only, the index formulated along the lines of our index 1 is the only one he is justified in using.
CONCLUSIONS A randomly selected sample of the progeny of a New Hampshire breeding flock was studied with respect to body weight, shank length, keel length and breast width at 12 weeks of age. The heritability of these four characters was found to be approximately 50, 50, 30 and 20 percent respectively. T h e environmental and the genetic correlations between them were calculated and on the basis of these statistics several selection indexes constructed. The difficulty in the construction of such indexes lies in the impossibility of assigning proper economic weights to each of the traits studied. Until such weighting is agreed upon and producers are paid accordingly, the only indexes worthwhile are for selection for individual characters. The results expected from the use of such indexes were found to increase efficiency in rate of improvement by 10 to
14 percent. The rate of change in characters not selected for was also determined for each of the indexes. T h u s , it was found t h a t selection for breast width is possible with relatively slight effects on the other characters. An arbitrary index where an increase in half a pound of body weight was arbitrarily assigned an economic value equal to an increase of 0.15 cm. in breast width one centimeter above the keel was constructed as an example of the method. ACKNOWLEDGMENTS We are indebted for the grading of the birds to Mr. H . B. Mugglestone, foreman of the Berkeley poultry plant of the University of California, and to D r . L. N . Hazel, Iowa State College for a critical review of the manuscript. REFERENCES
Asmundson, V. S. 1944. Measuring strain differences in the conformation of turkeys. Poultry Sci. 23: 21-29. —and I. M. Lerner. 1942. Breeding chickens for meat production. Calif. Agr. Exp. Sta. Bull. 675. 45 pp. Burmester, B. R. and I. M. Lerner. 1937. A measuring device for shank length of living birds. Poultry Sci. 16: 211-212. Hazel, L. N. 1943. The genetic basis for constructing selection indexes. Genetics 28:476-490. , M. L. Baker, and C. F. Reinmiller. 1943. Genetic and environmental correlations between the growth rates of pigs at different ages. J. Animal Sci. 2:118-128. , and J. L. Lush. 1942. The efficiency of three methods of selection. J. Hered. 33: 393-399. Jaap, R. G. 1941. Body form in growing chickens. J. Agr. Res. 62:431-443. Jul], M. A. 1940. Poultry Breeding. 2nd ed. xiv+ 484 pp. Wiley, New York. Lerner, I. M. 1943. The failure of selection to modify shank-growth ratios of the domestic fowl. Genetics 28:80-81. Panse, V. G. 1946. An application of the discriminant function for selection in poultry. J. Genet. 47:242-248. Whatley, J. A. Jr. 1942. Influence of heredity and other factors on 180-day weight in Poland China swine. J. Agr. Res. 65: 249-264.
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T h e relationships presented are illustrative of the methods of constructing selection indexes. T h e y represent first approximations and m a y only hold for the flock under consideration. Experimental verification of the efficiency of selection indexes is needed and is being planned by us. Parallel tests elsewhere would be exceedingly desirable.
CRUDEN