Mathematical Model of Egg Production

1306

D. E. TURK

AND

BARNETT

Harris, P. C., and F. H. Wilcox, 1963b. Studies on egg cholesterol 3. Effect of dietary cholesterol. Poultry Sci. 42: 186-189. Miller, E. C., and C. A. Denton, 1962. Serum and egg yolk cholesterol of hens fed dried egg yolk. Poultry Sci. 41: 335-337. Oser, B. L., 1965. Hawk's Physiological Chemistry, 14th Ed., pgs. 1066-7. McGraw-Hill Book Co., Inc., New York, N.Y. Schiavo, A., 1963. Studies of serum and egg yolk cholesterol level of hens immunized against Newcastle disease. Poultry Sci. 42: 531-533. Steele, R. G. D., and J. H. Torrie, 1960. Principles and Procedures of Statistics. McGraw-Hill Book Co., Inc., New York, N.Y. Watt, B. K., and A. L. Merrill, 1963. Agriculture Handbook # 8 , Composition of Foods. Government Printing Office, Washington, D.C. Weiss, J. F., E. C. Nabor and R. C. Johnson, 1964. Effect of dietary fat and other factors on egg yolk cholesterol. 1. the "cholesterol" content of egg yolk as influenced by dietary unsaturated fat and the method of determination. Arch. Biochem. Biophys. 105: 521-26.

Mathematical Model of Egg Production J. S. GAVORA AND R. J. PARKER Department of Animal Science, University of Manitoba, Winnipeg, Manitoba, Canada AND I. M C M I L L A N

Institute of Animal Genetics, Edinburgh, Scotland (Received for publication January 29, 1971)

E

GG production in poultry is a complex quantitative trait showing considerable variation over time within the production period of a hen. Several methods of expressing egg production and its component characters (age a t first egg, broodiness, egg production during different periods of the total production period, etc.) which apparently contribute to the total variation in egg production have been investigated. I t has been well established t h a t heritability of egg production, as well as heritability of its component characters is low (King and Henderson, 1954; Jerome et al., 1956;

Morris, 1956; Saeki, 1957; Oliver et al., 1957; Hicks, 1958; B r a y et al., 1960; Carson et al., 1960; King, 1961; W h e a t and Lush, 1961; Van Vleck et al., 1964; Acharya et al., 1969). However, one of the major weaknesses of conventional analyses of egg production d a t a , as suggested b y Tonkinson et al. (1969), is " t h e failure to recognize the entire curve b y the analysis of egg production a t each period or by accumulated production." T h e objective of this research was to test the applicability of the egg production model (hereafter referred to simply as " t h e model"), developed by McMillan

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ferent dietary fats on cholesterol content and lipid composition of egg yolk and various body tissues. Poultry Sci. 44: 221-227. Collins, W. M., A. C. Kahn III, A. E. Terri, N. P. Zervas and R. F. Costantino, 1968. The effect of sex-linked barring and rate of feathering genes, and of stock, upon egg yolk cholesterol. Poultry Sci. 47: 1518-1526. Edwards, H. M., Jr., J. C. Driggers, R. Dean and J. L. Carmon, 1960. Studies on the cholesterol content of eggs from various breeds and/or strains of chickens. Poultry Sci. 39: 487-489. Friedman, G. J., 1968. Nutrition in relation to atherosclerosis, pg. 877-931 in Wohl, M. G., and R. S. Goodhart. Eds. Modern Nutrition in Health and Disease. Lea and Febiger, Philadelphia, Pa. Fisher, H., and G. A. Leveille, 1957. Observations on the cholesterol, Iinoleic and linolenic acid content of eggs as influenced by dietary fats. J. Nutr. 63: 119-129. Harris, P. C., and F. H. Wilcox, 1963a. Studies on egg yolk cholesterol. 2. Influence of season. Poultry Sci. 42 : 182-185.

B. D.

1307

MATHEMATICAL MODEL OF PRODUCTION

component of decrease

el al. (1970a, b) for egg production in Drosophila melanogasler, to egg production in the domestic fowl and in turkeys. The model was expressed by the above authors in the following form: N{t) = M{\ - e-S<(-«>>)e-

(1)

where N(t) = the number of eggs laid on day t M = the potential maximum daily egg production h — the initial day of egg laying £ = the rate of increase in egg laying a = the rate of decrease in egg laying. It implies that egg production is under the influence of two components. Initially the rate of production is increasing rapidly according to the component Mil - e-««-<°>).

MATERIA!, AND METHODS

This function describes the build-up of some factor (factors) which govern egg production. However, the actual build-up does not tend asymptotically to M and remain there but is dampened by some other factors which correspond to the

Egg production data and their adjustment. Information on the data used to test the model on egg production of chickens and turkeys is given in Table 1. In order to avoid the use of percentages

T A B L E 1.—Data used for testing the egg production

Species

Type

E g S T y p

M e a t T y p

Number Number of hens of per record records

model

Number Type of record

_„2„J_ Pe™^d

Characteristics of data

No.

C.D.A. Research Station, Brandon, M a n .

A random sample of d a t a from a selection experiment

1

1

150

12,000

3

Weekly, hen-day percent

59-61

Commercial flocks in Manitoba

Field records

2

20-258

4

Weekly, hen-day percent

34-48

University of Manitoba

D a t a from experiments in nutrition and microwave irradiation

3

75

16

Bi-weekly, hen-day percent

14

Harrison et al. (1969)

D a t a read graphs

published

4

20

24

Weekly, hen-day percent

28

University of Manitoba

D a t a from a nutrition experiment (thyroprotein)

5

240

2

Weekly, hen-day percent

34

University of Manitoba

D a t a from a nutrition experiment (fibre content in the diet)

6

2 0 - 35

12

Bi-weekly, hen-day percent

13

Leighton a n d Shoffner (1961)

D a t a read graphs

7

Weekly totals, 5 day trapnest

50

Source of data

from

e Turkeys

from

published

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This is the dominant component after egg production has reached its maximum value. The physiology of egg production in insects is similar, in general terms, to that of poultry. The shape of the egg production curve in chickens and turkeys, expressed on a weekly, bi-weekly or monthly basis, appears to agree closely with the pattern observed in egg production in Drosophila on a daily basis. Therefore, it was considered possible that the above model (1) may be applicable to egg production in these species. Three time scales (weekly, bi-weekly and monthly) were tested as to their suitability for this purpose.

1308

J. S. GAVORA, R. J. PARKER AND I. MCMILLAN

production was assigned to 1= 1 and a change was made in the age of female (females) at t=l. (2) All sets of data were examined as to whether, within the interval 1<£0 or N(tk-1) if N(tk)=0. Production data for periods t>tk or t>{tk— 1) were excluded. (4) All sets of data in which /OMAX> (/&—2) were excluded. Groups (categories) of records were formed to represent four categories of records: egg type chickens, individual hen records (Table 1, No. 1); egg type chickens, records on groups of hens (Table 1, Nos. 2, 3, 4); meat type chickens, records on groups of hens (table 1, Nos. 5 and 6); and groups of turkey hens (Table 1, No. 7). Estimates of parameters in the model. For estimation of parameters in the model the method of McMillan et al. (1970a, b) (slightly modified) was used. They have shown that for sufficiently large /, N(t)c^Me~at and therefore

Each set of data was examined to determine the period (OMAX in which a maximum number of eggs iV(foMAx) was laid. If within one set the same maximum was reached in more than one period InNit) = InM - at. (2) foMAX was assigned to the period closest to*=l. Thus estimates of a and M were obThe following restrictions and changes tained by log-linear regression (2) of were then applied to all sets of data in all number of eggs laid on time t in the intertime scales: val of production in which I>/OMAX: (1) If foMAX=l, all observed producLetting tions were shifted one period forward and /OMAX was changed to fcMAX=2. Zero F(t) = M(l - e-eci-fo)) = N(l)e°"

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and to be able to perform the calculations on the same basis as used by McMillan et al. (1970b), all original egg production data were transformed to number of eggs laid in the respective period (one week or two weeks). The individual hen production (Table 1, No. 1), recorded for 5 days a week, was recalculated to number of eggs laid in a 7 day week. The remaining data for groups of females (Table 1, Nos. 2 to 7) originally represented as egg production rates (percentages calculated on hen-day basis) were also transformed into number of eggs laid in 7 or 14 days. Weekly data (Table 1, Nos. 1, 2, 3, 5 and 7) were then summed into bi-weekly (two weeks) and monthly (four weeks) totals and similarly from bi-weekly data (Table 1, Nos. 4 and 7) monthly totals were calculated. In data sets (records) having an odd number of periods, the last observed production was excluded from the summation. By this procedure each set of data was expressed on either three or two different time scales and it was possible to compare the fitting of the model to weekly, bi-weekly and monthly records. Each of the three time scales consisted of a sequence of positive integers (1,2,3, . . .) and the initial observed egg production was assigned for practical purposes to time t=l while records were kept of the actual age of females at t=\.

1309

MATHEMATICAL MODEL OF PRODUCTION

and 'M -

F(ty

In

= - * ( * - to)

M

which can also be expressed as N(t)eal

~M M

= &- &

(3)

Me-at" T{t0, t£) =

«(1 + «7flt a/i a

\

g-aitL—to)

SSW=

£ ( F « - Y.)\

T h e variation (sum of squares) d u e to deviations from the model was then

SSE=

£ ( F t -

and the portion of total variation explained b y the model was expressed as SSM

-ii'L-to)

\

E s t i m a t e of " t o t a l potential egg production" for interval Me~at° (/„, oo) : ? ( / „ , oo) =

Yt)\

— SSw — SSE-

Total variation was similarly partitioned in each of the four categories of records on each of the three time scales by comparing Yn with Yu, i= 1, 2, . . . a, where a is t h e number of records in t h e group. T h e sum of squares within sets

a ( l + a/£) E s t i m a t e of time of maximum production: ("MAX = (o + ( l / 0 f a [ ( £ + « ) / o ]

ssWT =

H£4(.Yil-Yi.y. i—l t=tQ

was again divided into the " e r r o r " sum of squares

Estimate of the maximum production:

SSET= t t ^ « - Yty iV(/MAx) =

ea(°(£ + a ) a + « /{)

and the p a r t of variation explained b y the model

Comparison of the model with observed production. T h e closeness of fit of t h e egg SSMT = SSWT — SSETproduction curves, calculated on t h e basis of &, | , iQ and M, to the observed egg SSM or SSMT were expressed as percent production within each set of d a t a was of SSw or SSWT respectively.

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estimates of t0 and £ were obtained b y regression analysis of (3) within t h e interval lt0:

expressed b y partitioning the total variation in egg production a t all periods t within the interval t0
1310

J. S. GAVORA, R. J. PARKER AND I. MCMILLAN

Additional comparisons were also made between the total observed egg production over the interval (Ti, t{) and T(t0, ti), as well _as between observed and estimated average production. For testing the statistical significance of these differences as well as of some other comparisons, appropriate modifications of ttest were employed.

The portion of the total variation explained by the model (SSMT as percent of SSWT), distribution of sets according to percentages of the "error" variation and number of sets rejected due to restriction No. 4 are presented in Table 2. Of the three time scales tested data expressed on the monthly scale (number of eggs laid over a period of four weeks) showed the closest fit to the egg production curves based on the model in all categories of data used in this study. In data recorded for groups of hens the differences between the time scales, in the portion of total variation explained by the model, were

Table 3 shows means and standard deviations of the estimated four basic parameters of the model (|, &, M and l0) as well as those of the three additional characteristics estimated from the model (titAX,N (/MAX) and f (ta, » ) ) . Egg production in turkeys when compared to

TABLE 2.—Percent of total variation in egg production explained by the model and distribution of records according to percent variation due to deviations from the model. Comparison of time scales

Group of records

Time scale

Percent Number of records of total variation explained Rejected by the Total due to remodel strictions

Distribution of records according to variation due to deviations from the model (as percent of total variation) 0-30

31-100 Over 100

Number of records

6

20 57 75

125 87 56

4 6 13

6

7 19 15

— 4 2

— — —

26 26 26

—

23 19 21

2 5 4

1 2 1

12 12

— —

10 11

2 1

Egg type chickens, individual hens

Weekly Bi-weekly Monthly

48.0 60.6 64.5

150 150 150

Egg type chickens, groups of hens

Weekly Bi-weekly Monthly

89.6 86.2 91.9

7 23 23

Weekly Bi-weekly Monthly

77.8 73.4 90.7

ii-weekly lonthly

82.4 95.8

Meat type chickens, groups of hens Turkeys, groups of hens

1

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RESULTS

small and generally the model explained approximately three quarters or more (73.4 to 95.8 percent) of the total variation in egg production. However, fit of the model to individual hen data was markedly improved by using the biweekly or monthly time scale as compared to the fit using the weekly data. Nevertheless, even the best results obtained for individual hens on monthly scale (64.5 percent variation explained by the model) are less favorable than the poorest fit achieved on the weekly scale for data from groups of hens. The improvement in fit of the model to individual hen data expressed on monthly scale is indicated also by the distribution of sets according to the "error" variation as percent of total variation in Table 2.

1311

MATHEMATICAL MODEL OF PRODUCTION

TABLE 3.- -Means and standard deviations of estimated parameters of the model and of some parameters estimated from the model on the monthly time scale Potential

Group of records

No. of records

increase

Onset of Time of Maximum Total egg pro- max. pro- production potential duction duction (No. of production decrease $ % * & (months) (months) eggs) (No. of eggs)

1.7780* 1.5941

0.0393* 0.0581

29.64* 38.00

Standard deviation

1.2122

0.0873

Mean

2.9011

0.0340

Standard deviation

1.3771

Mean

2.2016

Standard deviation

1.0950

Mean

2.9914

Standard deviation

0.9512

Statistic

M Egg type chickens, individual hens

144

M e a t type chickens, groups of hens

26

Turkeys, groups of hens

12

^MAS

N(tMAX) 25.27* 25.30

T(lo, « )

5.5952* 4.7423

7.7511* 8.4217

699.54* 1,721.47

49.82

2.1576

2.1478

3.17

5.700.55

26.41

5.3040

7.0866

23.70

778.14

0.0174

1.10

0.1391

0.7307

1.35

252.47

0.0762

25.39

6.0038

7.8193

20.07

364.75

0.0402

3.97

0.3768

0.4955

1.44

143.74

0.2159

23.30

7.6514

8.6318

14.20

91.79

0.0830

5.45

0.0976

0.2931

2.03

35.68

* Estimates from the average production of the whole group (150 hens).

egg production in chickens in general showed a slightly greater rate of increase, markedly greater rate of decrease, lower potential maximum monthly production, lower peaking in production and substantially lower "total potential egg production." These differences together with the older age at sexual maturity and correspondingly delayed time of the peak production in turkeys, appear to be characteristic of the two species. In groups of meat type hens used in this study the rate of increase of egg production was slower and the rate of decrease of egg production was higher than in groups of egg type hens. This, together with higher potential maximum and greater estimated maximum monthly production seems to account for the difference in estimated "total potential production" which was in favor of the groups of egg type hens. Also, the mean estimated ages of sexual maturity and the mean estimated ages of maximum production for groups of meat type hens were greater than those estimated for groups of egg type hens. For egg production data from individ-

ual egg type hens two kinds of information are presented in Table 3: estimates based on average production of the whole group of 150 hens as well as means and standard deviations of estimates based on individual records of each of the 144 hens remaining after rejection of 6 sets due to restriction No. 4. The former are close to the means of estimates from 17 group records of egg type hens with the exception of the rate of increase in egg production. However, all means of estimates from individual hen records except the rate of increase in egg production differ significantly (P<0.05) from the means of parameters estimated from data from the 17 groups of egg type hens. Variation of estimated parameters of the model (especially M) and of egg production (especially T(t0,)) as expressed by their standard deviations in Table 3 was generally higher than that of any of the remaining categories of group data except | for groups of egg type hens. Comparison of means of observed and estimated total and average egg production expressed on the monthly scale in all

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Egg type chickens, groups of hens

17

Mean

1312

J.

S. GAVOEA, R.

J.

PARKER AND I.

MCMILLAN

TABLE 4.—Comparisons of observed and estimated total and average egg production. Estimates on the monthly time scale Average egg production

Total egg production No. of sets

Group of sets

Observed

Estimated

Mean

S.E.

Mean

S.E.

Difference

Observed

Estimated

Mean

S.E.

Mean

S.E.

Difference

144

239.33

3.04

233.97

4.07

5.36

20.35

0.21

20.95

0.25

0.60

Egg type chickens, groups of hens

17

176.86

13.60

165.17

13.85

10.69

20.40

0.39

21.05

0.43

0.55

Meat type chickens, groups of hens

26

118.43

1.73

109.79

8.64

16.72"

16.72

0.34

16.89

0.30

0.17

Turkeys, groups of hens

12

53.91

1.90

51.18

1.59

1.73

8.99

0.32

10.11

0.30

1.12*

•Significant (P<0.05). ** Highly significant (P<0.01).

categories of data is shown in Table 4. Significant difference between observed and estimated total egg production was found in the 26 sets of data on groups of meat type hens. Also the mean estimated average monthly production for turkey hens was significantly higher than the mean of their observed average monthly productions. In the remaining comparisons the observed total and average production did not differ significantly from their estimates obtained by the described technique. Examples of fitting the model to monthly egg production data are presented in Figure 1. In examples A, B, D, E and F, in Fig. 1 the model explains more than 90 percent of the total variation in egg production. Figure 1, C shows an example of an egg production record of one hen in which the model failed to explain a substantial part of the variation in egg production. DISCUSSION

Of the four component parameters of egg production estimated by the model the rate of increase (£) and especially the rate of decrease (a) of egg production seem to be the most valuable ones in application of the model to egg production in the fowl and in turkeys. They might

contribute new aspects to selection for egg production and possibly to evaluation of egg production records in general. The practical significance of the estimated time of the onset of egg production (ta) is questionable because, in the process of its estimation, it is at least partly influenced by or confused with egg production itself. Therefore, the conventional methods of expressing the age of sexual maturity directly as the observed age at first egg or the average age of groups of hens reaching 50% production appear to be more suitable for measurement of this trait. The model may be useful also in predicting egg production of flocks based on part-time production records and hence in timing replacement stock requirements in commercial operations. The "potential total egg production", r(/o,°°), estimated on the basis of the model seems to express the differences between species and types within species quite well and it may prove to be another criterion for the evaluation of genotypes as suggested also by McMillan et al. (1970b). This parameter represents, as was suggested by McMillan et al. (1970b), the number of egg cells present in the ovaries at toy without accounting for the losses of egg cells in the process of their

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Egg type chickens, individual hens

1313

MATHEMATICAL MODEL OF PRODUCTION

28

B

/*-"-£ ^^V,,,,^^ ° 0 O*--^^^

1

24

0

20 16 12 8 4 2

4

6

8

10 12

~l 0 2

8

10 12

0

11 10 12

I I I I I I 11

4

6

8

in

o U U.

O

(/)

cr u CD

Ql

0

2 4

I

I

2

I

6

8

I

I

4

10 12 14

I

6

MONTHS FIG. 1. Examples of fitting the model to egg production data. The open circles indicate observed production. A.—An egg-type hen, 5.25 months old at month 1; 95.3 percent of the total variation is explained by the model. B.—An egg-type hen, 5.25 months old at month 1; 98.7 percent of variation is explained by the model. C.—An egg-type hen, 5.25 months old at month 1; the model failed to explain a substantial part of the variation in egg production ("error" variation 164.2 percent of the total variation). D.—A group of 12,000 egg-type hens, 5.75 months old at month 1; 96.5 percent of the total variation is explained by the model. E.—A group of 240 meat-type hens, 5 months old at month 1; 92.7 percent of variation explained. F—A group of 30 turkey hens, 7.71 months old at month 1; 98 percent of variation explained.

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0

1314

J. S. GAVORA, R. J. PARKER AND I. MCMILLAN

suggested* that the production curve of an individual hen does not normally have the increasing slope and is rather similar to that shown on Figure IB. The increasing slope present in group records would then be only a result of variation in the age of sexual maturity of individual hens forming the group. Application of the model to egg production in groups of chicken and turkey hens according to the results of this study seems to be practicable and could be of interest in many areas of research and of the poultry industry. The use of the model for individual hen records requires, however, further and more extensive research. SUMMARY

A mathematical model of egg production, developed originally for Drosophila melanogaster, was applied to chicken and turkey egg production data. The model was tested on 150 individual egg-type hen records and on records of groups of egg-type hens (23 groups), meat-type hens (26 groups) and turkey hens (12 groups). The results indicate that egg production of groups of hens, regardless of time scale used (weekly, bi-weekly and monthly), was fitted closely by the model which explained 73.4 to 94.8 percent of the variation in egg production within a record. In individual hen data the model explained 40, 60.6 and 64.5 percent of variation on weekly, bi-weekly and monthly time scales respectively. Application of the model to egg production in groups of chicken or turkey hens according to the results of this study seems to be practicable. Its use for indi* Dr. R. S. Gowe, Research Branch, Canada Department of Agriculture, personal communication.

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development and between ovulation and oviposition. "Total potential egg production" estimated in this study (Table 3) for egg type hens seems to agree with the data on the number of visible oocytes published by Pearl and Shoppe (1921), who counted an average of 2484 oocytes in White Leghorns of various ages as well as with that of Hafez and Kamar (1955), who observed 1111 oocytes at the age of sexual maturity. The 99% confidence interval of T(t0,») for individual hen data in this study was calculated as 496-2,947 eggs. Restrictions imposed on the data, as described earlier, operated mainly on the sets of records of egg production of individual hens. However, a few of the monthly records of groups of hens were also rejected (Table 2) due to restriction No. 4 as the number of months, in which production was recorded decreased and hMAX approached tL. Examination of individual hen records as well as the model curves superimposed on them indicated that among these records essentially two types of curves could be distinguished depending on the rate of increase £: a steeply increasing type (£> 1) and a slowly increasing type (£<1). Distribution of the two types of curves in records in which the model explained more than 90 percent of variation (group A) and in records in which the model explained less than 10 percent of variation (group B) indicates that the steeply increasing type was better fitted by the model. Twenty-three sets of data of the total of 32 in group A belonged to the steep (more desirable) type, while 13 sets out of the total of 16 in group B were characterized by £ < 1 . In this connection the fitting of the model to a set of data can perhaps also be used for classification of egg production patterns. I t was also

MATHEMATICAL MODEL OF PRODUCTION

vidual hen records requires further and more extensive research. ACKNOWLEDGMENT

The authors are grateful to Dr. J. H. Strain of the CD.A. Research Station, Brandon, Manitoba and to members of the Department of Animal Science, University of Manitoba, Winnipeg for data used in this study.

King, S. C , and C. R. Henderson, 1954. Heritability studies of egg production in the domestic fowl. Poultry Sci. 33: 155-169. Leighton, A. T. Jr., and R. N. Shoffner, 1961. Effects of light regime and age on reproduction of turkeys. 2. Restricted vs. unrestricted light. Poultry Sci. 40:871-884. McMillan, I., M. Fitz-Earle and D. S. Robson, 1970a. Quantitative genetics of fertility I. Lifetime egg production of Drosophila melanogasler—• theoretical. Genetics, 65: 349-353. McMillan, I., M. Fitz-Earle, L. Butler and D. S. Robson, 1970b. Quantitative genetics of fertility II. Lifetime egg production of Drosophila mdanogaster—experimental. Genetics, 65: 355— 369. Morris, J. A., 1956. Genetic parameters associated with characters affecting egg production in the domestic fowl. II. Heritability of egg production for two part-annual periods of measurement and the genetic correlation between them. Australian J. Agric. Res. 7: 630-639. Oliver, M. M., B. B. Bohren and V. L. Anderson, 1957. Heritability and selection efficiency of several measures of egg production. Poultry Sci. 36: 395-402. Pearl, R., and W. F. Schoppe, 1921. The number of oocytes in the birds ovary. J. Exptl. Zool. 34:101— 124. Saeki, Y., 1957. Inheritance of broodiness in Japanese Nagoya fowl with special reference to sex linkage and notice in breeding practice. Poultry Sci. 36: 378-383. Tonkinson, L. V., M. L. Havens and D. I. Gard, 1969. Evaluation of egg production curves by principal component analysis. Poultry Sci. 48: 1882. VanVleck, L. D., and D. P. Doohttle, 1964. Genetic parameters of monthly egg production in the Cornell controls. Poultry Sci. 43: 560-567. Wheat, J. D., and J. L. Lush, 1961. Accuracy of partial trapnest records. 2. Rates of lay for specific periods of the year and heritability of yearly production. Poultry Sci. 40: 402-406.

NEWS AND NOTES (Continued from page 1278) plan to complete all requirements for the Ph.D. America and the Caribbean are offered to qualified degree except the dissertation prior to January 1, agricultural scientists who wish to work as regular 1973. staff members of local public agencies, research institutes, experiment stations, or private organizaProfessional Internships. Internships in Latin (Continued on page 1330)

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REFERENCES Acharya, R. M., J. S. Dhillon and M. S. Tiwana, 1969. Age at first egg and egg production—their inheritance and expected response to different methods of selection. British Poultry Sci. 10:175— 181. Bray, D. F., S. C. King and V. L Anderson, 1960. Sexual maturity and the measurement of egg production. Poultry Sci. 39: 590-601. Carson, J. R., B. F. Bacon, G. Beal and F. A. Ryan, 1960. Breed differences in the relationship between broodiness and egg production in the chicken. Poultry Sci. 39: 538-539. Hafez, E. S. E., and G. A. R. Kamar, 1955. Developmental changes in the reproductive organs of the domestic fowl. Poultry Sci. 34: 1002-1010. Harrison, P., J. McGinnis, G. Schumaier and J. Lauber, 1969. Sexual maturity and subsequent reproductive performance of white leghorn chickens subjected to different parts of light spectrum. Poultry Sci. 48: 878-883. Hicks, A. F., Jr., 1958. Heritability and correlation analyses of egg weight and egg number in chickens. Poultry Sci. 58: 967-975. Jerome, F. N., C. R. Henderson and S. C. King, 1956. Heritabilities, gene interactions, and correlations associated with certain traits in the domestic fowl. Poultry Sci. 35: 995-1113. King, S. C , 1961. Inheritance of economic traits in the Regional Cornell Random Bred population. Poultry Sci. 40: 975-986.

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