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Genetic Improvement as Related to Size of Breeding Operations1
Genetic Improvement as Related to Size of Breeding Operations1 A . W . NORDSKOG AND A . J . W Y A T T
Iowa Stale College, Ames (Received for publication April 17, 1952)
Adding more pens to a breeding enterprise can possibly affect breeding improvement four ways. First, more sires can be usgd., and hence a greater number of progeny tested sire and sire progeny groups will be available for selection. Second, J^er^jvill^^e^more^ Jidl^jb__g>roup;s frorn^ w^kh^Jajralv^elections can_bejnadg,. Third
> AJE^t?LJiliiafc£LjOofeLJndi-
vTduals will be available for mass selections. Fourth, unless flockjjze is increased correspondingly, the increaj5«i_nurrd2eXjof 1 Journal paper No. J-208S of the Iowa Agricultural Experiment Station, Ames, Iowa. Project No. 1039.
pens will resultjn decreased selection intensity ana in decreased accuracy of progeny tests and family information. These decrease breeding improvement. Breeders with some knowledge of population genetics are familiar with the principle that the. anjojrnt of_ irnjjna^gjngnj re : suiting from a generatioa^L^d££tiaa-.is H u Al-l2-lb£Jiej&ftb^^ by_ the selection differential (/). When the population consists of a single trait normally distributed and truncation selection is practiced, I is equal to z/b where z is the ordinate of the normal curve at the point of truncation above which the fraction b is retained for breeding. Strictly speaking, the above formula for expected improvement holds true only for an infinite population or, more practically speaking, when N is very large. In such a case values of z/b may be computed from tables of a normal curve or they may be found directly in tables of selection differentials such as given by Lush (1948) and Lerner (1950). When N is small the ordinary tabled values of z/b over-estimate I. Unbiased estimates of I may be had from Table XX of Fisher and Yates (1948). This table lists the mean deviations of ranked individuals for values of N from 2 to 50 as sampled from a normal population. For example, for N = 5 the table lists two values; namely, 1.16 and .50. This means that if a sample of 5 were drawn at random from a normal population, on the average the best of the five would be 1.16
1062
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
A N IMPORTANT question frequently •*• *• asked by commercial poultry breeders is: How many breeding pens do I need to do a good job of breeding? The answer to this question would seem all the more pertinent at this time since Lerner and Dempster (1951) showed that nothing is gained, in fact something is lost, from a multiple shift scheme of sire testing, as compared to testing more thoroughly a single group of males. Thus, breeders with only a few breeding pens cannot expect to compensate for this apparent deficiency by using more males on those pens they do have available. On the other hand, the belief is apparently common among larger breeders that they are able to exert an enormous selection pressure because they have a large scale breeding operation with many breeding pens. Actually, the same percentage replacements are needed in a large flock as in a small one.
SIZE OF OPERATIONS AND GENETIC IMPROVEMENT
TABLE 1.—Selection differentials obtained from a sampling experiment Selection differentials for b — . 2
W0
Number selected so t h a t b = .2
5 10 20 30 40 50
1 2 4 6 8 10
1.16 1.27 1.33 1.35 1.36 1.37
1,044 1,061 1,070 1,073 1,075 1,076
20%
1.40
1,081
Sample size
Very Large
Expected, Body weight a t 8 weeks in (grams) standard deviations Expected (») Observed (60) (30) (15) (10) (8) (6)
1057 ± 1 2 1058 ± 9 1074± 9 1066 ± 9 1068 ± 8 1051 ± 8
(1) 1072
(») =number of samples.
assuming a selection intensity of 20 percent. The table also includes the results of
an actual sampling experiment involving eight-week weights of a population of 4,688 New Hampshire cockerels. The mean and standard deviation of this distribution are 870 grams and 150 grams, respectively. From this distribution samples of 5, 10, 20, 30, 40, and 50 were drawn at random. Average body weights of the best 20 percent of each sample are given as the observed values in the table. Although the agreement with expected is not good, sampling errors could explain all of the discrepancies with the possible exception of the 1,051 + 8 for 6 samples of size 50. In this case the deviation from the expected value (1,076-1,051) exceeds twice the standard error. However, a slight skewness of the distribution is evidenced since the real mean of the 20 percent truncated distribution differs from its expected value by 9 grams. This is equivalent to about one standard error of the sampled values. The important point illustrated by this sampling experiment is that sample size N is not a very potent force in increasing the selection differential. "N".may be assumed to be number of birds, number of families, or number of pens (or sires). When N is equal to 50 practically all of the advantage due to the largeness of N is realized. The selection differential expected from selecting the best 10 out of 50 is 1.37 standard deviations. This is only .03 standard deviations less than expected when saving the best 20 percent for N infinitely large. Even when N is as low as 20 about 95 percent of the maximum selection differential is obtained. Thus, the benefits a breeder might obtain from employing a large number of breeding pens rapidly diminish as N reaches 20 or 30. Because the number of individual birds and number of families is ordinarily quite large, even when the number of breeding pens are as few as 10, the effect of producing more birds and
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
standard deviations above the sample mean. The next best would be .50 standard deviations above the mean, the third would be zero, the fourth would be .50 standard deviations below the mean and the fifth would be 1.16 standard deviations below the mean. It is important to emphasize that these rankings are expected values. The figures given in Table XX of Fisher and Yates may now be applied to the problem at hand. If we have five progeny tested sires drawn from a population of sire genotypes which we assume are normally distributed, on the average the best sire will be 1.16 standard deviations above the mean. The value of 1.16 therefore represents a selection differential for a selection intensity of 20 percent. That is, the best one out of 5 is saved. The selection differential for the best 2 out of 10 sires, still leaving the selection intensity at 20 percent, would average 1.27 standard deviations above the mean On the other hand z/b is 1.40 standard deviations for a selection intensity of 20 percent. This represents the maximum value that the selection differential approaches as N becomes infinitely large. Table 1 shows the rate at which this maximum is approached for selected values of N ranging from 5 to 50 and
1063
1064
A. W. NORDSKOG AND A. J. WYATT
more families (with constant selection intensity) could have only a negligible effect on genetic improvement. Thus, practically all of the benefit from adding
(z/b) for samples of infinite size. It is at once apparent that the sample size is a weak force as compared with the selection intensity. For example, the points of
Z.40
Nt>°
2 20
N-SO
2.00
I60
§ \
120
I
loo
i!( .60 40 20
SELECTION INTENSITY
(6)
FIG. 1. Influence of Selection Intensity and Sample Size on the Selection Differential.
more pens would be due to the increase in the selection differential among the sires heading up the breeding pens and possibly some due to selection of sire progeny groups. Figure 1 shows the relative importance of selection intensity (b) and size of the sample (N) as factors determining the selection differential. The heavy line in the graph represents the maximum values
intersection obtained when a straight edge is placed horizontally across the curves represents different situations giving equal selection differentials (or equal genetic gain). Thus, the selection differential obtained from the best 30 percent of N = 50 is about equalled by selecting the best 20 percent of N = 5. At this level a change of ten percent in selection intensity is about equivalent to increasing
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
N-ZO 180
SIZE OF OPERATIONS AND GENETIC IMPROVEMENT
Nby45. Figure 2 presents a generalized picture showing the influence of sample size and selection intensity on the ratio of selection differentials: IN Ix
The interpretation of this ratio is most easily explained by an example. If 20 per-
SUCCTION
INTENSITY
(i!
FIG. 2. Influence of Selection Intensity and Sample Size on Ratio of Selection Differentials.
cent of the best individuals are saved (b—'.2) only about 83 percent of the maximum selection differential is possible when samples of size 5 are drawn, i.e., the best one out of 5 is saved. When the best 10 individuals of samples of size 50 are drawn, about 98 percent of the maximum selection differential is obtained. For values of N less than infinity each of the curves are symmetrical and reach a maximum when the selection intensity is at §. This apparently results from the
limited range inherent in a truncated finite sample. For example, when N is equal to 10, the mean of the best 5 usually will approach more closely the mean of the best half of a very large population than the most extreme individual in a sample of ten will approach the mean of the best ten percent of the population. In other words, there tends to be less bias in the mean of the best half of a small sample as compared with the mean of any truncated portion less than half. If more than half of the sample is saved the bias would result from the truncated portion of the sample culled. Thus, this bias would be of the same order whether, say, the best 10 percent are saved or the poorest 10 percent are culled. This fact is responsible for the curves being symmetrical. The foregoing analysis shows that size of operations (number of breeding pens) is at best no more than a second order force so far as it affects possible genetic improvement. There appears to be considerable fallacy in the common opinion that small flocks are handicapped seriously because of size alone. Also it may be pointed out that if the number of breeding pens are increased without a corresponding, increase in additional facilities for brooding and rearing nothing more in effect would be gained than would be from a double shift to males. Indeed, just as with the double shift system, some reduction in possible genetic improvement could occur because of lessened accuracy and intensity of selection. Of course a sufficiently large number of breeding pens (or males) would need to be used in order to avoid the deleterious effects of inbreeding. Perhaps 8 to 10 pedigree breeding pens or possibly fewer if a multiple shift of males is employed would adequately take care of the inbreeding problem.
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
selection differential of a finite sample, N selection differential of an infinite population
1065
1066
NUNC DIMITTIS
SUMMARY
Size of breeding operations in terms of
number of breeding pens has only a slight influence on possible genetic gains from selection unless the number is very small. The advantages obtained from using many pens rapidly diminishes after the number reaches 20 or 30. When as many as 50 breeding pens are used practically all (about 98 percent) of the advantage due to the "large operation" factor is realized. Compared with selection intensity as a factor influencing selection pressure, size of operation is only a secondary force. REFERENCES Fisher, R. A., and F. Yates, 1948. Statistical tables for biological, agricultural and medical research. 3rd ed. Oliver and Boyd Ltd., Edinburgh. Lerner, I. M., 1950. Population genetics and animal improvement. Cambridge University Press, New York. Lerner, I. M., and E. R. Dempster, 1951. The theory of multiple shifts. Poultry Sci. 30: 717-722. Lush, J. L., 1945. Animal breeding plans. 3rd ed. The Collegiate Press, Ames.
Nunc Dimittis ALLEN GRIFFITH PHILIPS, affec•**• tionately and better known as "Chick," died at his summer home at Eagle River, Wisconsin, on September 17th. He had been in poor health during recent months. He is survived by his wife, Grace; two sons, Paul of Fort Wayne and Everett of Los Angeles; and two daughters, Helen Thiele and Marion Philips, Kenilworth. The home address is 625 Briar St., Kenilworth, Illinois. The funeral was held on September 22nd. Typical of "Chick" and his philosophy was the request that flowers be not sent but that those who wished to contribute might do so on behalf of the
National Foundation for Infantile Paralysis, Inc.,—one of his favorite charities.* "Chick" Philips was born in Westchester, Pennsylvania on January 5, 1886. In his early youth his parents moved to Kansas, where he completed secondary school education and graduated from Kansas State College with a B.S. degree in agriculture in 1907. He took further training the following year at Cornell University and in 1908 returned to Kansas State College where he served as Assistant for two years. In 1910 he was appointed Instructor at Purdue University, becom* This fund which was forwarded as the Philips' Polio Fund to the Fort Wayne Chapter amounted to $3000.
(Continued on page 1069)
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
Breeders should be more concerned about the actual intensity of selection practiced as well as about the accuracy of records on which selections are based. Greater intensity of selection is possible by improving the general laying condition of the breeding flock, improving hatchability, and by lowering chick mortality during the brooding and range periods. In addition, more rapid improvement is possible by increasing the accuracy of records on which selections are based, by better control of environmental factors including feeding and the seasonal influence of hatch, and by considering the optimum age composition (generation interval) of the breeding flock. These are some of the things that all breeders can do, regardless of size of operations, that will promote greater genetic improvement.
Iowa Stale College, Ames (Received for publication April 17, 1952)
Adding more pens to a breeding enterprise can possibly affect breeding improvement four ways. First, more sires can be usgd., and hence a greater number of progeny tested sire and sire progeny groups will be available for selection. Second, J^er^jvill^^e^more^ Jidl^jb__g>roup;s frorn^ w^kh^Jajralv^elections can_bejnadg,. Third
> AJE^t?LJiliiafc£LjOofeLJndi-
vTduals will be available for mass selections. Fourth, unless flockjjze is increased correspondingly, the increaj5«i_nurrd2eXjof 1 Journal paper No. J-208S of the Iowa Agricultural Experiment Station, Ames, Iowa. Project No. 1039.
pens will resultjn decreased selection intensity ana in decreased accuracy of progeny tests and family information. These decrease breeding improvement. Breeders with some knowledge of population genetics are familiar with the principle that the. anjojrnt of_ irnjjna^gjngnj re : suiting from a generatioa^L^d££tiaa-.is H u Al-l2-lb£Jiej&ftb^^ by_ the selection differential (/). When the population consists of a single trait normally distributed and truncation selection is practiced, I is equal to z/b where z is the ordinate of the normal curve at the point of truncation above which the fraction b is retained for breeding. Strictly speaking, the above formula for expected improvement holds true only for an infinite population or, more practically speaking, when N is very large. In such a case values of z/b may be computed from tables of a normal curve or they may be found directly in tables of selection differentials such as given by Lush (1948) and Lerner (1950). When N is small the ordinary tabled values of z/b over-estimate I. Unbiased estimates of I may be had from Table XX of Fisher and Yates (1948). This table lists the mean deviations of ranked individuals for values of N from 2 to 50 as sampled from a normal population. For example, for N = 5 the table lists two values; namely, 1.16 and .50. This means that if a sample of 5 were drawn at random from a normal population, on the average the best of the five would be 1.16
1062
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
A N IMPORTANT question frequently •*• *• asked by commercial poultry breeders is: How many breeding pens do I need to do a good job of breeding? The answer to this question would seem all the more pertinent at this time since Lerner and Dempster (1951) showed that nothing is gained, in fact something is lost, from a multiple shift scheme of sire testing, as compared to testing more thoroughly a single group of males. Thus, breeders with only a few breeding pens cannot expect to compensate for this apparent deficiency by using more males on those pens they do have available. On the other hand, the belief is apparently common among larger breeders that they are able to exert an enormous selection pressure because they have a large scale breeding operation with many breeding pens. Actually, the same percentage replacements are needed in a large flock as in a small one.
SIZE OF OPERATIONS AND GENETIC IMPROVEMENT
TABLE 1.—Selection differentials obtained from a sampling experiment Selection differentials for b — . 2
W0
Number selected so t h a t b = .2
5 10 20 30 40 50
1 2 4 6 8 10
1.16 1.27 1.33 1.35 1.36 1.37
1,044 1,061 1,070 1,073 1,075 1,076
20%
1.40
1,081
Sample size
Very Large
Expected, Body weight a t 8 weeks in (grams) standard deviations Expected (») Observed (60) (30) (15) (10) (8) (6)
1057 ± 1 2 1058 ± 9 1074± 9 1066 ± 9 1068 ± 8 1051 ± 8
(1) 1072
(») =number of samples.
assuming a selection intensity of 20 percent. The table also includes the results of
an actual sampling experiment involving eight-week weights of a population of 4,688 New Hampshire cockerels. The mean and standard deviation of this distribution are 870 grams and 150 grams, respectively. From this distribution samples of 5, 10, 20, 30, 40, and 50 were drawn at random. Average body weights of the best 20 percent of each sample are given as the observed values in the table. Although the agreement with expected is not good, sampling errors could explain all of the discrepancies with the possible exception of the 1,051 + 8 for 6 samples of size 50. In this case the deviation from the expected value (1,076-1,051) exceeds twice the standard error. However, a slight skewness of the distribution is evidenced since the real mean of the 20 percent truncated distribution differs from its expected value by 9 grams. This is equivalent to about one standard error of the sampled values. The important point illustrated by this sampling experiment is that sample size N is not a very potent force in increasing the selection differential. "N".may be assumed to be number of birds, number of families, or number of pens (or sires). When N is equal to 50 practically all of the advantage due to the largeness of N is realized. The selection differential expected from selecting the best 10 out of 50 is 1.37 standard deviations. This is only .03 standard deviations less than expected when saving the best 20 percent for N infinitely large. Even when N is as low as 20 about 95 percent of the maximum selection differential is obtained. Thus, the benefits a breeder might obtain from employing a large number of breeding pens rapidly diminish as N reaches 20 or 30. Because the number of individual birds and number of families is ordinarily quite large, even when the number of breeding pens are as few as 10, the effect of producing more birds and
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
standard deviations above the sample mean. The next best would be .50 standard deviations above the mean, the third would be zero, the fourth would be .50 standard deviations below the mean and the fifth would be 1.16 standard deviations below the mean. It is important to emphasize that these rankings are expected values. The figures given in Table XX of Fisher and Yates may now be applied to the problem at hand. If we have five progeny tested sires drawn from a population of sire genotypes which we assume are normally distributed, on the average the best sire will be 1.16 standard deviations above the mean. The value of 1.16 therefore represents a selection differential for a selection intensity of 20 percent. That is, the best one out of 5 is saved. The selection differential for the best 2 out of 10 sires, still leaving the selection intensity at 20 percent, would average 1.27 standard deviations above the mean On the other hand z/b is 1.40 standard deviations for a selection intensity of 20 percent. This represents the maximum value that the selection differential approaches as N becomes infinitely large. Table 1 shows the rate at which this maximum is approached for selected values of N ranging from 5 to 50 and
1063
1064
A. W. NORDSKOG AND A. J. WYATT
more families (with constant selection intensity) could have only a negligible effect on genetic improvement. Thus, practically all of the benefit from adding
(z/b) for samples of infinite size. It is at once apparent that the sample size is a weak force as compared with the selection intensity. For example, the points of
Z.40
Nt>°
2 20
N-SO
2.00
I60
§ \
120
I
loo
i!( .60 40 20
SELECTION INTENSITY
(6)
FIG. 1. Influence of Selection Intensity and Sample Size on the Selection Differential.
more pens would be due to the increase in the selection differential among the sires heading up the breeding pens and possibly some due to selection of sire progeny groups. Figure 1 shows the relative importance of selection intensity (b) and size of the sample (N) as factors determining the selection differential. The heavy line in the graph represents the maximum values
intersection obtained when a straight edge is placed horizontally across the curves represents different situations giving equal selection differentials (or equal genetic gain). Thus, the selection differential obtained from the best 30 percent of N = 50 is about equalled by selecting the best 20 percent of N = 5. At this level a change of ten percent in selection intensity is about equivalent to increasing
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
N-ZO 180
SIZE OF OPERATIONS AND GENETIC IMPROVEMENT
Nby45. Figure 2 presents a generalized picture showing the influence of sample size and selection intensity on the ratio of selection differentials: IN Ix
The interpretation of this ratio is most easily explained by an example. If 20 per-
SUCCTION
INTENSITY
(i!
FIG. 2. Influence of Selection Intensity and Sample Size on Ratio of Selection Differentials.
cent of the best individuals are saved (b—'.2) only about 83 percent of the maximum selection differential is possible when samples of size 5 are drawn, i.e., the best one out of 5 is saved. When the best 10 individuals of samples of size 50 are drawn, about 98 percent of the maximum selection differential is obtained. For values of N less than infinity each of the curves are symmetrical and reach a maximum when the selection intensity is at §. This apparently results from the
limited range inherent in a truncated finite sample. For example, when N is equal to 10, the mean of the best 5 usually will approach more closely the mean of the best half of a very large population than the most extreme individual in a sample of ten will approach the mean of the best ten percent of the population. In other words, there tends to be less bias in the mean of the best half of a small sample as compared with the mean of any truncated portion less than half. If more than half of the sample is saved the bias would result from the truncated portion of the sample culled. Thus, this bias would be of the same order whether, say, the best 10 percent are saved or the poorest 10 percent are culled. This fact is responsible for the curves being symmetrical. The foregoing analysis shows that size of operations (number of breeding pens) is at best no more than a second order force so far as it affects possible genetic improvement. There appears to be considerable fallacy in the common opinion that small flocks are handicapped seriously because of size alone. Also it may be pointed out that if the number of breeding pens are increased without a corresponding, increase in additional facilities for brooding and rearing nothing more in effect would be gained than would be from a double shift to males. Indeed, just as with the double shift system, some reduction in possible genetic improvement could occur because of lessened accuracy and intensity of selection. Of course a sufficiently large number of breeding pens (or males) would need to be used in order to avoid the deleterious effects of inbreeding. Perhaps 8 to 10 pedigree breeding pens or possibly fewer if a multiple shift of males is employed would adequately take care of the inbreeding problem.
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
selection differential of a finite sample, N selection differential of an infinite population
1065
1066
NUNC DIMITTIS
SUMMARY
Size of breeding operations in terms of
number of breeding pens has only a slight influence on possible genetic gains from selection unless the number is very small. The advantages obtained from using many pens rapidly diminishes after the number reaches 20 or 30. When as many as 50 breeding pens are used practically all (about 98 percent) of the advantage due to the "large operation" factor is realized. Compared with selection intensity as a factor influencing selection pressure, size of operation is only a secondary force. REFERENCES Fisher, R. A., and F. Yates, 1948. Statistical tables for biological, agricultural and medical research. 3rd ed. Oliver and Boyd Ltd., Edinburgh. Lerner, I. M., 1950. Population genetics and animal improvement. Cambridge University Press, New York. Lerner, I. M., and E. R. Dempster, 1951. The theory of multiple shifts. Poultry Sci. 30: 717-722. Lush, J. L., 1945. Animal breeding plans. 3rd ed. The Collegiate Press, Ames.
Nunc Dimittis ALLEN GRIFFITH PHILIPS, affec•**• tionately and better known as "Chick," died at his summer home at Eagle River, Wisconsin, on September 17th. He had been in poor health during recent months. He is survived by his wife, Grace; two sons, Paul of Fort Wayne and Everett of Los Angeles; and two daughters, Helen Thiele and Marion Philips, Kenilworth. The home address is 625 Briar St., Kenilworth, Illinois. The funeral was held on September 22nd. Typical of "Chick" and his philosophy was the request that flowers be not sent but that those who wished to contribute might do so on behalf of the
National Foundation for Infantile Paralysis, Inc.,—one of his favorite charities.* "Chick" Philips was born in Westchester, Pennsylvania on January 5, 1886. In his early youth his parents moved to Kansas, where he completed secondary school education and graduated from Kansas State College with a B.S. degree in agriculture in 1907. He took further training the following year at Cornell University and in 1908 returned to Kansas State College where he served as Assistant for two years. In 1910 he was appointed Instructor at Purdue University, becom* This fund which was forwarded as the Philips' Polio Fund to the Fort Wayne Chapter amounted to $3000.
(Continued on page 1069)
Downloaded from http://ps.oxfordjournals.org/ at Karolinska Institutet University Library on May 24, 2015
Breeders should be more concerned about the actual intensity of selection practiced as well as about the accuracy of records on which selections are based. Greater intensity of selection is possible by improving the general laying condition of the breeding flock, improving hatchability, and by lowering chick mortality during the brooding and range periods. In addition, more rapid improvement is possible by increasing the accuracy of records on which selections are based, by better control of environmental factors including feeding and the seasonal influence of hatch, and by considering the optimum age composition (generation interval) of the breeding flock. These are some of the things that all breeders can do, regardless of size of operations, that will promote greater genetic improvement.