the unknown, we have calculated equations based upon the data of the International Egg Laying Contest at Storrs, Conn., during the six contest years, 1911-1917, inclusive. We have then used these equations to predict the annual production (and the production of groups of months) for the birds of the 1917-'18 contest, using as a basis of prediction the individual months of the laying year separately, pairs of successive months and groups of three months. Our conclusions concerning the value of the equations depend, therefore, not upon a priori considerations but upon the results of actual tests of accuracy of prediction for series which were unknown as far as the determination of the constants of the equations is concerned.

Consider first of all the results of the attempts to predict the annual egg production of 415 White Leghorn birds observed at Storrs from Nov. 1, 1917 to Oct. 31, 1918 from the records of a single month's production. The results of the three criteria of accuracy of prediction are summarized in table 1.

TABLE 1

ERRORS OF PREDICTION OF ANNUAL EGG PRODUCTION from the RECORDS
OF INDIVIDUAL MONTHS

Considering first of all the absolute values we note that the average errors with regard to sign are generally low. Thus the prediction from November and from January production gives on the average 3 eggs too many for the year. For December, February, March and August the prediction is in error by less than 2 eggs. The values predicted from April, May, June, July, September and October records are from 4 to 7 eggs in error.

The average deviations without regard to sign are of course much larger since they constitute a measure of the error of prediction of the records of individual birds. They range from 24.8 to 30.1 eggs. The significance of errors of this magnitude will be more clearly brought out later.

The square root of mean square deviation also shows considerable regu

larity from month to month. These measures are naturally considerably larger than the average deviation without regard to sign.

from 32.9 to 38.8 eggs.

They range

It is clear that the annual egg production of birds similar in origin to the series upon which the prediction equations were based and maintained under similar conditions may be predicted with a relatively high degree of accuracy providing their record for any month is definitely known.

The order of the errors will be more readily understood by expressing them in relation to the average production of the flock, as shown by the percentage deviations.

We note that in predicting from December, February and August records the average error with regard to sign is less than one per cent of the average annual yield of the flock. In predicting from November, January and March the error lies between one and two per cent. When April, May, June, July, September and October records are used as a basis of prediction the average errors of prediction are from 2.50 to 4.50 per cent of the average annual yield.

The average deviations without regard to sign are less than 20 per cent of the annual production. The values for the individual months range from 15.7 for September to 19.1 for January.

The square root of mean square deviation is less than 25 per cent of the average annual production. The individual values range from 20.9 for September to 24.6 for January.

These two latter tests may at first seem to indicate very unsatisfactory prediction. Such is not, however, the case. These give the average errors either above or below the true record made in the prediction of the results for an individual bird. The thing which is required in practise is generally the prediction for a group of birds of a particular grade of egg record for the month used as a base of prediction. In a flock of 415 birds this has been shown to be possibe with an error of less than 5 per cent of the annual production when prediction is made from the record of any month of the year; and with an error of less than 1 per cent when prediction is based upon the records of a number of the individual months.

Lack of space precludes a discussion of the results of the prediction of the annual record of the bird from the combined record of two consecutive months. We may, however, illustrate the accuracy of prediction from the combined record of two consecutive months by means of the figures in diagram 1 which shows the accuracy of prediction from November plus December and from April plus May in comparison with the results of prediction from November and April. In these the estimated production is shown by a straight line.

The actual production for the year for which prediction is made is shown by solid dots for each group of birds as classified by monthly or bimonthly

record. The shaded areas are determined as follows. The birds were first grouped into classes of five eggs range with respect to number of eggs laid during the period of time used as a basis of prediction. The birds of these classes of five eggs range were further subdivided into those in which actual egg production was greater than the predicted and those in which the actual number was less than the predicted number. The average

error of prediction was determined for each of these groups, and these averages represent the upper and lower limits of the shaded areas. The upper limit represents, therefore, the average deviation (for the period for which prediction is made) of all birds which make a higher record than that predicted for their class. The lower limit of the shaded area marks the average deviation for all birds which show an egg record lower than that predicted. These diagrams, which are quite typical of the whole series, certainly indicate excellent prediction.

The results for the combined records of three consecutive months are shown in table 2. These show that greater accuracy of prediction may be obtained when the records of three months are used as a basis of prediction. Such a result is to be expected on a priori grounds. A careful comparison of the constants in tables 1 and 2 will show, however, that the improvement resulting from the trebling of the number of months used as a basis of prediction is not great.

TABLE 2

ERRORS OF PREDICTION OF ANNUAL EGG PRODUCTION FROM THE RECORD
OF THREE CONSECUTIVE MONTHS

Prediction of the number of eggs which will be laid in the period subsequent to the month or group of months used as a basis of prediction may also be made. The errors for such a series of predictions, in which each individual month of the year (with the exception of the final month) has served as a basis for the prediction of the egg production of the remaining months of the year, are shown in table 3. The constants in this table show that when the period for which prediction is made is a long one a degree of accuracy fairly comparable with that for the whole year is attainable. The absolute values of the average deviation without regard to sign and of the square root of mean square deviation necessarily become smaller as the period for which prediction is made becomes shorter. The relative (percentage) error, however, increases. Thus the accuracy of prediction decreases rapidly as the period for which prediction is made becomes shorter.

TABLE 3

+ 0.24

+ 2.37

+ 0.09

Apr.-Oct. March

0.24

ERRORS OF PREDICTION OF THE RECORD OF A PERIOD OF MONTHS FROM THE RECORD OF INDIVIDUAL PRECEDING MONTHS

AVERAGE DEVIATION
AVERAGE DEVIATION
WITH REGARD TO SIGN WITHOUT REGARD TO SIGN

SQ. ROOT OF MEAN

SQ. DEVIATION Actual Percentage Actual Percentage Actual Percentage deviation deviation deviation deviation deviation deviation + 2.39 19.49 38.65 25.46 19.53 36.63 25.16 19.06 34.61 24.91 18.66 30.86 23.92 20.36 28.40 25.34

1.57

29.59

0.16

28.43

1.71

26.48

0.77

24.07

The results of this investigation, taken as a whole, show that in the case of a flock of White Leghorn fowl which is essentially identical in genetic composition and maintained under essentially uniform conditions from year to year it is quite possible to estimate annual egg production from the record of either a single month or of two or three consecutive months with a high degree of accuracy. The same is presumably true of other breeds as well. This point is now under investigation.

It is not possible to use the equations given in this paper for flocks differing greatly in genetic composition or in conditions of maintenance from that upon which these equations were based. The problem of the determination of corrective terms to be used when the equations are applied to flocks other than that upon which they are based is now under investigation.

A detailed account of these investigations is now in press in Genetics. 'Alder and Egbert, Bull. Utah Agr. Exp. Sta, No. 162, 1918.

Harris, Blakeslee and Warner, These PROCEEDINGS 3, 1917 (337-341); Harris, Blakeslee, Warner and Kirkpatrick, Genetics, 2, 1917 (36-77).

"Harris, Blakeslee and Kirkpatrick, These PROCEEDINGS 3, 1917 (565-569); Genetics, 3, 1918 (27-72).

'A range of five eggs was used in order to obtain a number of birds sufficiently large to reduce somewhat the irregularities due to the errors of random sampling. The errors of prediction were in each case determined for classes of unit range. Grouping is used for graphic representation merely. The average deviations represented by the limit of the shaded zone are to be thought of as measured from a line perpendicular to the ordinates and intersecting the prediction line on the mid-ordinate of the 5-egg class.