THE RELATIVE IMFCRTANCE OP GENETIC AND ENVIRONMENTAL FACTORS 0M THE PUTTERFAT PRODUCTION OF HOLSTEIN-FRIESIAN CATTLE By Chen Kanp Che I A THESIS Submitted to the School of* Graduate Studies of Michigan State College of Agriculture and A m l i e d Science in martial fulfillment of the requirements for the degree of DOCTOR CF PHILOSOPHY Department of Animal Husbandry v 1951 An Abstract of tbs thesis THK RSLATZVE IMPORTANCE OF CSMBTIC AND SNTZBOMKKMTAL FACTORS ON THE BUTTKRFAT PRODUCTION OF ROL3TEDUFRISS1AV CATTLB Chan Gfcal An Abstract 3afesd.ttsd to ths Sohool of Oradsato dtadisa of M shl^an •tats College of AfriouXtort sad Applied Sslsass in partial faiflllosnt of the rsqulreasnts for ths dsgrss of DOCTOR OF PRILOSOPHT Dspartosnt of Arloal Hsshantiry 1951 CHKN KAMO CHAI THB BBLATZVB D V O K A N G K OF OBMETZO AMD MMTXBONNBMrAL FAOTGMS OM THK BDTTKBFAT PBQDOOTZCMI OF B0L3TKXM-FKIK3IAM OATTLB It Is | W M n 1 1 y rmmmmrtaod that belli taradllgr aaA onvirnsuMt m taporUal in U m Ilfo of an Individual and in tin u p t w i i — oluuniat«i4iti«i «f varl«n the individual, and that their relative importance n r i u a g m i deal. Inttarfat production of dairy aattlo la sonaldsrod as a oharaotorlatla that la laharltad on qaantltatlvo haala and la hliMjr effected by eovironsMnt. L m f i l f a t e n havo ototainod dlfforont valuas as sstinatoo of horitaM 11ty of this trait ranging frou .17 to •Ml. Lash oonoidorod tho intra slro oorrolation and regression of daughtor on dan nothod aa tho boot ootluoto of herltabillty of butterfat production and ho roportod valuoa between .17 sad .20 for dlfforont sots of data* Tkuroo Mlohlgan State Institution Hards, tho Tr&verse City hord, tho Ionia Hospital hard, and tho Ionia Reforest017 hood, were eotabson than twenty years ago. Tho butterfat production of tho oows in thlso holds has boon naasarod and roOOidod. This data ossnsd to be quit* worthy notorial for a study of tho offsets of various factors on buttorfst production, in another s— pie of individuals under differ­ ent environssnt than others* Therefore, this study was node which besides yielding a horltaM Itby ostlnato, separated various oonpononts of environsant as far as this data poiulttod* There wore 473 daughter-dsoi pairs for tho horltaM 1.1ty analysis, 2299 records for the hord comparison and repeatability analysis, 1017 records for nonth and year offset on butterfat production, and 1071 reeords for tho analysis of oalvlng interval effect on butterfat pro­ duction* OHSM KAMO CHAI H m p— lad M t l M l * of I w i U M l t y of Ilfotlao boiUaftt produotlon for tho throo hordo was .11 hr intra-slro w t r w i oa of danghtor on 4am nothod. O— prtid to t slnglo r*oord boos, it lo oqoal to o horltablllt? valuo for slnglo rooordo of .17• Tho hord dlfforonooo aooountod for about 26 poroont of tho total varlanoo and tho sow dlfforonooo (Intra-hord) aooountod for 34 poroont. Thooo m l a M M # of oouroo, insludo both onoos oanood tar onvtroonontal offooto. dlfforunsss and diffor— Tho portion of varlanoo aooountod for by dlfforonooo in rooordo of tho amao so* (lntra-hord) was shout 66 poroont. Tho ropoot.ability ootlnato was .34 on an JLntrm hord haoo. Toarly dlfforonooo aooountod for aboot 5 poroont of tho variation in buttorfat production. significant. Though aaall, thla valuo la otatlotloally ho yearly trond was foond. Month of salving aeooontod for aboot 2 poroont of tho total varlonoo. It waa a significant offoot. Thoro oao a rathor doflnlto pattorn for tho sffoot of dlfforont nonths of salving on buttorfat produotlon. Tho high poak was In Marshj this droppod gradually In tho suaaaor, lneroasod In doptonbor, and foil again aftor that until January. Tho rolatlonshlp of oalMLng lntorval and buttorfat produotlon was Don>llnodr. Tho offoot of salving lntorval on buttorfat produotlon aoonuntvd 15 poroont of thousriaass for tho sans location, and 3 poroont for tho noxt laotatlon. Both woro significant. 400 to 419 days ooonod to bo tho aoot favorabls lntorval ao far as a olnglo rooordo woro concerned. CHEN KANG CHAI Ftriwrtui of Total Observed Varlanoo Accounted for bj Varlooo ^oootlo and f t w i w i n l a l Factors Varlanoo aooountod for Poroantago 26 Hord dlfforonooo Qsnotlo dlfforonooo tootusan hordo hnrlrnnsoritil dlf foronooo betwo an herds 4 22 Dlfforonooo within hordo Cow dlfforonooo Booord dlfforonooo (within oow varlanoo) 74 25 49 100 66 tatovlrcaneatal offooto Tear of calving Month of calving Proceeding ealvlag lntorval Present calving lntorval Othoro 4 2 3 15 42 Genetic Addltlvoly gonotlo Doartnanoa and lntoraotlon 34 17 17 Tho portion of varlanoo aooountod for tagr dnarl nance and lntoraotlon in tho above tablo lnoludoo a — 11 portion duo to penaanent onvlrow anfit< peculiarities and also lntoraotlon between heredity and anvirecaaent. Therefore, tho portion aooountod for toy genetlo offoot actually should bo loss than 34 poroont and for tho environmental offoots should bo a llttlo soro than 66 poroont. 31noo tho rooordo uood for oaeh kind of analysis aro not exactly tho sane, and booauso an allowanoe amot bo node for oaspllog error, tho figures listed in tho above table oan only by considered as approximate Ackno wledgment The writer is indebted to Dr. Ponsld H. Nelson, Frofessor of Animal husbandry, for his assistance in conducting this study, his kindly guidance and criticism in tho preparation of this manuscript. Gratitude is also expressed to Dr. xiliiam D . -aten, Professor of Mathematics, for his in- valuatle help with she statistical analysis. Appreciation is especially expressed to Dr. larrison P. Kuna, Frofessor of Poology, for his continuous encouragement and timely advice. Table oT Contents Acknowledgment Pape Introduction ........................................... 1 Literature Review...................................... 2 Source of Data......................................... 15 CoT^arison of F e r d ..................................... Variance Due to Ferd Difference..................... R erea ta t i1 ity ........................................ 18 22 25 I rritability Analysis.................................. Discussion of rethoc................................. 26 27 r roceoure for Feritatility Analysis................ F'eri tatl li ty; Analysis forreformatory Fe r d ........ 1. Preliminary Analysis........................ 2. lntr-8 -sire Degression or Correlation of Fa u yb ter on Dam Vethod. .............. 3. Paternal Half-sib Correlation Method...... 35 35 35 Feritatility Analysis forTraverse City Ferd...... 1. Preliminary Analysis ....................... 2. Intra-sire Repression or Correlation of Daughter on Dam Method............... . 3. Paternal T'alf-sit Correlation v etPod...... -eritat ility Analysis for Ionia Ferd.............. 1. Preliminary Analysis........................ 2. Intra-sire Repression or- Correlation of Daughter on Dam T' /,etv'od................ 3. Paternal valf-sit Correlation 'Dthcd....... ■v^rare of the Pstimete of Feritatility of the Three Ferds.................................... Conversion of Repress ior. Coefficient of the Average cf I ecords into the Value of single I ecord............................................ 3& I4J4. 1|6 I46 L}.9 53 55 55 ^6 60 61 65 Fffec t of Yearly fnvironmental n! ar-'es on Put terf a t 1 reduction............................................ 66 ■ffec t of Month of CsIvinp on iut terfa t P roouction... 72 ■ffect of Calvin/' interval on Futterfat 76 1. 2. 1 x-oauction .. .Analysis of Variance............................ Repression of Futterfat Production on Calvinr Interval.............................. 77 63 Tape Calculation of linearrepression.............. 85 Test Linearity................................. 09 Calculation of Non-linear Repression............. 91 Discussion....... 97 Cun.msry and Conclusions............................. literature C i t e d ............................................. 110 m Illustrations figure 1. A Diagram Illustrating the Delations Between Two Mated individuals and Their Progeny figure 2. Intra-sire Degression of Butterfat Froauction of Daughter on Dam Fi cure 3. Average Yearly Butterfat Production b igure I4.. Distribution of Records In Same Calving Interval Figure P. Distribution of Records In Previous Calving Interval Fip-ure 6 . Semi-lotrarithm Plotting of Futterfat Production Against Same Calving Interval Fi cure 7. Semi-logarithm H o t t i n g of Butterfat Production Against Previous Calving Interval Figure P. Average Observed Futterfat Production Against Same Calving Interval and Their Linear and 'Ion-linear Regression Line 9» Average Observed Butterfat Production Arainst Irevious Calving Interval and Their Linear and Con-linear Regression Lines FI gure F i "ure 10. A Comparison of Month of Calving Affects on F u t t e r f a t : r e d u c t i o n or TTilk P r o d u c t i o n three D i f f e r e n t S t u d i e s for THE RELATIVE IMPORTANCE OF GENETIC AND ENVIRONMENTAL FACTORS ON THE FUTTERFAT PRODUCTION OF HOLSTEIN-FRIESIAN CATTLE By Chen Kang Chai Introduc tion Until recent years, little was known about the relative importance of heredity and environment in the development of an organism. There was considerable controversy as to whether heredity was more important than environment, or vice versa. With advancing knowledge in the field of genetics, it became more generally recognized that both heredity and environment are indispensable in the life of each individual, and that the relative Importance of each varied a great deal depending on both the organism and char­ acter in question. Heredity is fundamental and may be thought of as furnishing the foundation, with environment comoleting the structure. This is true even for a qualitative characteristic, since genes cannot express themselves unless they have the proner environment. A being cannot develop beyond the limits set by Its inheritance even In the optimum environ­ ment. A quantitative characteristic tends to be modified by environment more than a qualitative one. The greater the effects of environment on the expres­ sion of the genes the more difficult It is for livestock breeders to recognize the true quality of an animal. 2 Consequently, mistakes are often made by breeders in cull­ ing animals with better genes than some of those which are saved. For this reason a measure of the approximate degree of modification of a characteristic by environment would be of value to breeders in selecting their animals. Butterfat production is a quantitative character. The number of pairs of genes involved, and their behavior, as to the degree of dominance, etc. still has not been determined. However, it is an economically important and physiologically complex character, and is modified considerably by environ­ ment. The relative importance of heredity and environment is usually expressed as the portion of variance due to either one of them, and varies with different populations. The purpose of this study is to determine the portion of variance in butterfat production determined by genetic dif­ ferences and the portion by environment in three Michigan State Institution herds; the Traverse City herd, the Reformatory herd and the Ionia herd. These herds may be con­ sidered as sub-populations of the Holstein-Freisian breed. There are many environmental factors. They are generally divided into tangible and intangible factors. latter have no way of being controlled. The The tangible factors, such as light, temnerature, feeds, handling, etc. may be partially controlled by well designed experiments. In this data the only information available about environmental factors was for such things as calving interval, date of calving and year of calving. The approximate portion of variance resulting from each of these causes was determined. The optimum season of freshening and length of calving interval were found. In addition, the hereditability of butterfat production was calculated for each herd and for the three herds combined. The portion of variation due to herd differences and cow differences and the repeatability of a cow’s production from year to year were computed. Literature Review Most of the literature concerned with hereditability of milk yield, butterfat production, or test of dairy cattle before 19U1 has been tabulated by Lush (19UD» Hence, the table, with minor remarks, is reproduced here. In addition, some studies made since that time have been inserted in the same table. Table la - Summary of Evidence on Hereditability of Hilk Yield, Futterfat Production and Test Author Characteristic Difference between high and low groups Heredita­ Dams Daughters bility a Notes Gifford fat (lbs.) Gifford Copeland Edwards Rice fat (lbs.) fat (lbs.) milk (lbs.) milk (lbs.) Rice test (^) HBrain Truster" milk (lbs.) Lush (191+1) butterfat (lb s.) “ W 7 1 " Lush ( 1 9 W ) milk (lbs.) Lush (1914.2 ) fat (lbs.) 278.7 32.2 240.0 241*. 0 2856 £>1 .6 52 592 1813 8373 1.09 5023 2629 047 91*5 11*.1 1*32 .23 .51 43 .1*1 (.5?) (. 8 6 ) .36 .28 .33 .171* 21 Holstein-Freisian bulls** 18 Guernsey bullsc 2b Jersey bulls® 23 bullsfe lb bulls dairy breeds** lb bulls dairy breeds** 1 bull with 151 daughters 103 hulls 676 daugh ter-dam comparison 103 bulls 676 daugh ter-dam comparison 263 bulls, 2151* daughter-dam com­ parisons a. Twice the intra-sire regression of daughters on dams# b. A. R. records. Each bull had at least 21* daughter-dam comparisons. The mates of each bull were divided into high, medium, and low, thirds (approximately). Those given here are averages computed from Gifford’s Table 12, giving equal weight to each sire. (Continued) c. A. R. records. Each bull had at least 17 daughter-dam comparisons. Mates divided approximately in high, medium, and low thirds. The figures quoted are from the summary of Copeland's Table 3» d. R of M records. Each bull had at least 19 daughter-dam comparisons. Mates were divided approximately into high, medium, and low thirds. The figures quoted are from the summary of Copeland's Table 3» e. Data from Eritish milk recording societies in East Anglia and Lancastershire and from Agricultural College herds at Reading, St. Albans, and St. Paul. Mates are divided into high and low halves. The figures quoted are averaged from columns 4 and 5 of Edward's Table 3> giving each cow equal weight. As Edwards used average records where available (un to three lactations per cow), the hereditability figure shown here pertains to differences between average records rather than single records. If the intraherd repeatability of single records in Edwards' material was .lj, the hereditability of differences in single records would be somewhere between the 1 shown here and the which would be approached if every mate had three records. f. The data are official records from several dairy breeds. Each bull had at least 17 daughter-dam comparisons. For each bull the five "highest producing" mated and the five "lowest producing" mates were selected. Division seems to have been primarily on total fat production and was for milk and test only in so far as they were dependent (statistically) on total fat production. This makes the records for the dams' milk and test come much nearer to representing the dam's real ability than if division into high and low groups had been primarily on the milk records and the test records, respectively. The figures for hereditability, therefore, are much too high to be fairly comparable with the others, and come nearer to indicating the fraction of the differences in real ability (not records) which are due to additive hereditary differences between the cows. g. The data are from Iowa Dairy Ferd Improvement Associations prior to January 1, 1937* All records were age-corrected. Where the bull's mates had only one record, the data for her and her daughter were discarded. The mates of each bull were then divided into a high half and a low half, solely on the basis of the first record of each cow. If a bull has an even number of mates with two or more records each, all were used. If he had an odd number of such mates, the one whose first record was (Continued) vn median in size was discarded and her daughter was discarded with her. If a mate had more than one daughter she was used again as many times as she had daughters. h. The data are from Iowa Dairy Herd Improvement Association during the period January 1, 1936 to December 31» 1939. It included seven breeds. Only the 30£ days of lactation were studied. All records were corrected for age and were on the basis of twice a day milking. The intra-sire daughter-dam regressions varied some what from breed to breed, but their differences were not statistically significant. The result listed in Table la was pooling all the seven breeds together and was corrected to a single record. 7 Besides the different hereditability values given by different investigators in Table la, Gowen (193U) studied the Jersey Register of Merit data on milk yield and fat percentage. He assumed that there was no correlation be­ tween the environment of daughter and dam. ^e came to the conclusion that about 5 0 to 7 0 per cent of the variance in milk production and about 7 5 to 8 5 per cent of variance in fat oercentage came from differences in the genetic make­ up of the individual cows. Flum’s (1 9 3 5 ) analysis of the records of cows in Iowa Cow Testing Association led him to the figures shown in Table lb. Table lb - Relative Importance of Cause of Variation in Butterfat Production Causes of variation______________ Fercentage of total variance Breed 2 Herd feeding policy of herd other causes (genetic or environmental) 12 21 33 Cow (mostly genetic) Residual (year to year variations) feeding variations within the herd other year to year differences length of dry period season of calving other factors Total 26 6 1 1 3 28 39 100 Among all the heritability values above, probably the result worked out by Lush is more accurate than others, since he used a large number of sires; hence fewer numbers of daughter-dam pairs for each sire. Then there would be less environmental portion contributed to the daughter-dam correlation as the large number of daughter-dam pairs of a sire is more likely to separate to different herds. his sample size is quite large. Also The results computed by Gowen are higher than all the others. It is likely due to a large environmental contribution to the daughter-dam correlation. The only report about repeatability of milk and butter­ fat production is given by Lush (1914-1 ). In fact, the terminology is originated from the same investigator. He estimated repeatability for milk production .3 3 * and butter­ fat production .I4.3 from same set of data as he used for heritabillty estimates Lush (19i|-l) • Gowen (1935) reported a correlation of .I4.O between butterfat records of the same cow in a population of cows belonging to the same herd, or to a correlation of .60 between records of the same cow in a population of cows kept in many herds. The Influence of the m o n t h of calving on milk yield has been studied by numerous investigators. thoroughly reviewed by M orr o w et al. (1914-5). It has been !he high lights of all those investigations will be brought here mostly from his review for the time before 19l(-5. McCandlish (1920) and Moore (1921) both found fall freshening cows to excel in m ilk and butterfat production. 9 McDowell (1922) reported on a group or animals in cow test­ ing associations totaling IO 8 7 O cow years. Milk production decreased in the order of fall, winter, summer, and spring calving. In a study of II4.IO lactations from cows in the Knglish milk Recording Societies, Hammoittd and Sanders (1923) found the highest milk yield was secured on October freshenings, 6 0 7 7 lbs., with a low three-consecutive-month oeriod for ^ay, June, and July, all below 514-00 lbs. Turner (1923) reported on 3615 lactations of Guernseys, Holstein, and Jerseys, that had completed Advanced Register or Register of Merit records. There was a slight difference between breeds in their relation to month of freshening and milk yields. With the Guernseys the variation was not great, although May, June, July, and August freshening were the lowest in milk yield, with November being the highest, followed by January, February, and December. For the Holsteins, November was the high month, followed closely by January, March, and December. gave the lowest milk yields. considerable variation. April and July freshenings The 305 Jersey records showed January calvings resulted in a lactation yield of 9213 pounds of milk, with August showing 9126 pounds, and July 8 9 I4 .9 pounds. The two lowest months were September with 7 I4-I6 pounds, and June 75814- pounds. Sanders (1927) observed from his studies In England that the months of October, November, and December were most favorable for freshening, with June and July resulting in 10 the poorest yields. These figures were obtained after mak­ ing corrections for length of dry period and length of ser­ vice period. The shape of the lactation curve showed con­ siderable seasonal variation, a factor considered to be largely responsible for the differences in total yield. Cannon (1933) studied the records of 6800 cows in Dairy Herd Improvement Associations in Iowa. Highest milk yield was secured on animals calving in November--7798 pounds-with a uniform and regular decrease until June, when there was a yield of 6705 lbs. Plum (1935) also used data from Iowa herds In Cow Test­ ing Associations to study the causes of differences In but­ terfat production. He concluded that although cows calving during November to January produced 13*6 t>er cent more but­ terfat than cows calving in May to July# the actual In­ fluence of season of calving, as a factor, accounted for on­ ly 3 per cent of the total variation In butterfat production. Using the records of 319 Jerseys in the Florida Experiment Station herd, Arnold, and Becker (1938) found the seasonal Influence on milk yield to be non-significant, although winter and autumn freshenings gave somewhat larger yields than summer and spring. They suggest that the narrow range of seasonal variations In Florida temperature probably ac­ counted for the small differences observed. It Is logical to suppose that the effect of calving on milk yield is Influenced by the variations in feeding and 11 m a n a g e m e n t that a c c ompany the different seasons. point It Is int eresting to note that Wylie On this (1925), wo r king with 2900 records of Registe r of Mer it Jerseys where f e e d ­ ing levels were m a i n t a i n e d rather uniformly throughout the year, found m u c h less seasonal influence than other i n v esti­ gators. A l t h o u g h July freshenings resulted in the highest and Augrust in the lowest yields, with these two months e x ­ cepted, fall a nd winter calvings gave h i g h e r average lacta­ tion yields than spring and summer. The findings of Gooch (1935) on 679 lactations of 99 Jersey cows in a single herd varied considerably from the majority of data renorted. With a low for August freshen­ ings, production increased gradually up to April calvings, with a decline again to August. Early snring was apparently the most favorable season. Dickerson ( 19i+0) in studying the relative importance of various sources of environmental variation in production, found the data on 1 5 7 U lactations of Holsteins to show low­ est production for cows calving from April to September, and highest for cows calving from October to March. Morrow (19U5) studied 1+030 lactation records from D. F. I. A. herd record books of 33 New Hampshire dairy herds. The study included five breeds; Ayrshire, Holstein, Jersey and M i l k i n g Shorthorn. Guernsey, For each breed, with the exception of Jersey, mil k yields f o l l owing summer freshenings were enings. lower than those for fall and winte r f r esh­ Jerseys showed no significant relation between m o n t h of freshening a nd m ilk yield. 12 The lactation records of l5 *M 4-2 cows In Dairy Herd Improvement Association herds from 12 states were ana­ lyzed by Woodward (19U5)- He found the variation in total milk production between the groups calving in different months of the year is somewhat less than might be expected, ranging from 8 8 8 6 pounds for the cows calving in July to 9108 pounds for the cows calving in November. Prick (19U7) reported there were highly significant differences among cows freshening in different months. Four breeds (Guernsey, Holstein, Ayrshire, Jersey) with 22212 Connecticut cows were studied. He showed that cows freshening in February have the highest average and lowest was for cows freshening in July. In general, however, average milk yields consistently increased from the least favorable to the most favorable month, and consistently de­ creased from the most favorable to the least favorable month. Cows freshening in February produced 13-7 per cent more milk than those freshening in July. Under western Oregon conditions the butterfat records of 2690 first-calf heifers was studied by Olonfa (19U8). The season of the year in which a cow freshens had no appre­ ciable effect on her yearly butterfat production in that data. The calving interval equals the days of dry period plus the days of lactation. Hence, in general, the longer the dry period the longer will be the calving interval. course, there are some variations about the length of Of 13 lactation, and that may cause the calving interval to fluc­ tuate without relationship to the dry period. However, by using large samples, this error can be materially reduced. Therefore, literature dealing with either calving interval or dry period are reviewed here. Sanders (1927) claimed that cows should calve at inter­ vals of not less than a year, and not more than thirteen months. This optimum will probably be subject to a slight variation in particular cases. The work of Dickerson and Chapman (19^4-0), who compared production records of lacta­ tions following dry periods of different length with those of the first lactation, found that low producing cows showed a higher percentage increase through lengthening the dry period than did high producing cows. Dix, Arnold and Becker (1936) studied 291 lactations of Jersey cows in the Florida Agricultural Experiment Station herd. The yield following the dry period, 31-60 days, was used as 1 0 0 per cent, the percentage of base yield for the various classes were: initial lactation, 9 1 . 8 7 per cent; 3 0 days or less, 9 2 . 3 8 per cent; 6 1 - 9 0 days, 914-.68 per cent; 91 days or more, 88.77 per cent. Maximum daily yield was highest for the 31-60 day class. Klein and Woodward (19U3) have reported only on the production records of the same cow following dry period of different lengths. It was found that cows dry 1 - 2 months gave 9 - 2 per cent more milk Uj. than when dry 0 - 1 month; cows dry 2 - 3 months gave I4..3 per cent more milk than when dry 1 - 2 months; and that cows dry months gave l.lj. per cent more milk than when dry 2 - 3 months. Seath and Neasham (191+2) are of the opinion that an ideal renroduction record would be one in which 1 2 . 5 per cent of the cows were dry each month during the year. Trans­ lated into dry period this would mean i+7 days of rest on the basis of calving at yearly intervals. Johansson (191+0) has reported the optimum calving interval is ll| months for heifers and 1 3 months for subsequent lactations. Morrow (19U5)> by using 2631 lactations being available with the length of the preceding dry period known, found the highest oroduction was in the group of dry periods from 6 0 to 09 days. However, he concluded if a smoothed curve were prepared from the data, the high ooint would coincide with a oeriod approximately 65 days, with very little dif­ ference occurring between U5 and 85 days. On either side of these limits, oroduction values were considerably decreased. In regard to the year effect on production trend, Plum (1 9 3 5 ) has reported only 2 . 8 per cent of the total variance WS3 due to changes in yearly averages based on 5 8 6 0 records from 1922 to 1932. significant. However itwa* statistically Source of Data The data Tor this investigation were taken from three of the Michigan State Institution herds. Traverse City herd, Reformatory herd. They are the the Ionia Hospital herd, and the Ionia The former is located at Traverse City and the latter two are located at Ionia. The Traverse City herd is the oldest and largest herd of the three. It was established in 1 8 8 8 , and has 1214. cows and four bulls in service at the present time. cows and three herd sires. The Reformatory herd has 72 The Ionia Hospital herd is the smallest, having I4I4. cows and one bull in service now. The better sires were exchanged among the various Michigan State Institution herds to extend their use with a mini­ mum of inbreeding. Most of the records are D. F. I. A. records with a small percentage of K. I. R. records. The records used here are from 1927 for Traverse City herd, 1929 for Reformatory herd, and 1921; for Ionia Hospital herd up to 191|5» There were fewer records made during the earlier yea rs and also considerably more of them were incompletely recorded than in the later years. For this reason, only the records from 1 9 3 0 on were used for studying the effect of month of calving and year on butterfat production. However, f o r the h e r i t a b i l i t y , and repeatability estimates and the effect of calving interval, from the earlier dates were used. the records starting It would be better to use exactly the same set of data for the different analyses, 16 but this would considerably reduce the numbers available for each, either because requirements were different for each kind of study or because of some incompleteness in the records. In order to bring the samples for the different analyses as close as possible, the following procedure was used: 1. Select the sires with the most mates; 2. List all the cows having the same sire in one group and use all the available records for each cow; 3. Find the daughter or daughters of each cow and copy the number of the daughter and all her available records following her dam; I4.. All the available records were used for heritability estimates, herd comparisons, effects of calving Interval, month of calving and year of calving. Some more descriptions will be given at the beginning of each analysis. Records were corrected for length of lactation, times milked daily and age. 305 days, three-time milking and six to nine years of age were used as the basis for the conversion. The Holstein-Friesian Association conversion factors were used. Records shorter than 270 days were discarded and those from 2 7 0 to 3 0 5 days were treated as 305 day records. 17 Table 2a - Conversion Factors for Age and Times of Milking Age I4JC 2 2£ 3 3i 4, 4i 5 6-9 10 11 and over 2X _3X 1.00 .83 .79 .76 .73 -71 .9 6 .9 2 .88 .86 .8 I4. .82 .80 .82 .84 .6 9 .67 .66 .68 .6 9 1.25 1.20 1.15 1 .1 0 1 .0 7 1 .0 5 1 .0 2 1 .0 0 1 .0 3 1 .0 5 Table 2b - Conversion Factors for Length of Lactation Period Days 306 320 330 340 350 360 36$ - Factor 319 329 339 349 359 361+ .99 .97 .96 .95 .9 I4 .92 .90 For examrle, for a cow that had a record of $00 pounds of butterfat on 4 times a day milking, with a 320-day lactation at three years of age, the calculation would be as follows: £ 0 0 x .97 x 1.15 x . 8 3 m Lj.62.93 pounds If it is 3 times or 2 times milking, the factor 100 or 1,2$, respectively would be used instead of . 8 3 for the above equation. 18 Comparison of Herds A general survey of 1he three herds to determine their average production level, and the variability of their pro­ duction caused by herd differences, cow differences and individual record differences, served as a basic step for the further studies. This analysis is based on at least U.0% of the records of each herd. Therefore, these records are a very large sample of its own oarent population. Table 2c - Average Production of the Three Herds No. of cows Herds No. of records Ave. no. of records per cow Ave. butterfat produc tion lbs. Stan­ dard deviation lbs . Traverse City 1+77 1182 2.5 ¥+3 73 Reformatory 216 651 3.0 1+92 99 Ionia 108 1+66 1+.3 550 121+ Weighted A v e . 801 2299 2.9 1+78 Table 2c shows that the Ionia herd has the highest average; the Reformatory herd, second; and the Traverse City herd, the lowest. The standard deviations are proportional to average production in each herd. That is, the higher the production, the greater the variation of butterfat production. If we assume that the genes which are respon­ sible for butterfat production have only an additive ef­ fect, the above order of the observed standard deviations is an unexpected result. If the Individuals of a popula- 19 tion carry more or less than 50^ "good" genes, it is ex­ pected that that population will be less variable than a population of individuals with about genes. "good” or "bad" The more they tend toward the extreme, the less their variation should be. The proof for the above statement is, according to Castle (1921), that the variance of a population is equal p to 2q(l-q)<* , where q is the gene frequency of the "good*1 genes and c* is the value increased from "bad” gene to 11good" gene. Therefore, when the value of q = is the largest, and when q > o r < « 5 * the variance the variance is smaller; the more the decrease or Increase of q, the smaller the variance will be. Of course, there have been some assump­ tions for the behavior of the genes#. According to Table 3c, the Ionia herd had the highest butter fat production. more ” good" genes than The cows in that herd must have had cows in the other two herds. Simi­ larly, the Reformatory herd must have carried more ” good” genes than the Traverse City herd. The Traverse City herd must have had more than £0^ ”good” genes because its aver­ age production was higher than the breed average. From this It was expected that the variation in production in each herd would have been In the reverse order, that Is, the Traverse City herd, the largest; the Reformatory herd, second; and the Ionia herd, the smallest. These results Assumptions oT the behavior of the genes: 1. genes have equal effects; 2. no dominance; 3. genes combine additively; ij.. all genes combine freely. 20 indicate that the genes for butterfat production behave not only additively, but that they show some degree of dominance and interact in various ways with each other, and that environment also plays an important part. These fac­ tors confuse the additive gene effects and helped cause the large variation in the herds of high producing individuals. Tab±e 2d - Analysis of Variance of Each Herd Herds Sources of variance Traverse City Total Reformatory I onia Degree of* freedom Sum of squares Mean square s 1 ,1 6 1 6,263,5*4-7 5301t Between cows hlS 3,3*4-2,152 7021 Within cows 10$ 2,921,i|25 h 1*4*4- 'Total 6S0 6,221,529 9572 Between cows 2 IS 3,20U,830 1*4-906 Within cows hhS 3,016,699 6779 Total U6S 6,035,679 12980 Eetween cows 107 U, 0 *4.0 ,*4.05 37761 Within cows 358 1,995,27*4- 5573 F 1.69-a-H- 2.20** 6.7 8*::-*- 21 Table 2e - Portion of Variance Due to Cow Differences tTrecord Herd s Y CD Ko (7cow 2.U6 1160 .22 .28 .87 -1 Traverse City hikk 7021 Peforma tory 6779 11+906 G • 0 2709 Ionia 9973 37761 k -30 71 4 6 8 (1 ) K~0 — 1 n- 1 0c ow t frecord + (fcow (^record * K 0 (f’cow ( SK - SK 2 ) Sk j K is the number of records of each cow n is the number of c ows 5 is t he s ign f'^r siurvr.a ti 0 n It is obvious from Table 2d that the differences be­ tween cow's were highly significant. This was exrected. Table 2e rives the oorticns of variance due to cow differ­ ences in each herd. Since the results show that the Ionia herd had the highest cow variance, and the other two were cuite similar, the variance between records of the same cov; v/ill be in tie reverse order. Consequently, the greater variation of the Ionia herd than the l.eformatory herd and of the reformatory herd than the Traverse City herd shown in Table 2d was mainly cue to the difference between cows. 22 The differences of cow variances among the three herds make one wonder whether there was any genetic background involved. For this reason, a few cows were chosen at ran­ dom from, each herd and their pedigrees were checked. found that most of the cows in the It was Traverse City herd were related to bull L(12017> and bull I4.8 6 O 8 O, and also some slight inbreeding was found. Animals in the reformatory herd showed the same tendency, but to a lesser degree than the Traverse City herd. helationshir among animals in the ionia herd were very seldom found, although some of the bulls were related to the bull in the Traverse City herd. This may have been due to the comnaratively late establishment of this herd. Very oossibly, this different intensity of relationship of tie animals in each herd was the main cause for the different variation of animals among the three herds. Variance Due to ^ e r d Dlffeience The procedure used for this analysis in combining the three herds is that given by 1lum (1938). Because quite s. few analyses will follow the same procedure later, the detailed steps for the calculation will be omitted in the later ones. aregiven here. They 23 Table 2f - Analysis of Variance of Herd and Cow Differences Degree of freedom Sources Total Fetween herds Within herds Eetween cows Within cows Sum of squares Mean squares 2298 22,538,822 9808 2 14,018,037 2009018 2296 18,520,785 8066 800 10,587,387 1323U 11+96 7,933,398 5303 Total sum of squares = sum of squares of record of each herd - grand correction term = 114.7,01^0,282 4- 163,893,765 4- 237,982,767 - 1,100,065 — — = 22,538,822 Sum of squares for herds - sum of' the correction fern of each herd - grand c erection term = 1141,0014.,603 ♦ 157,672,236 + 231,719,190 - 1,100,065 229$ — z 1 4 0 1 8 ,0 3 7 Sum of squares within herds - total sum of squares - sum of squares for herds = 22,538,822 - 14,018,037 = 18,520,785 Sum of squares within cows within herds - sum of sum of squares of the within term of each of the three herds = 2,921,385 4. 3,016,699 + 1,995,2714 = 7,933,398 2k Sum of squares between cows within herd - sum herds within herds - sumof squares of squares within cows within « 1,852,078 - 7,933,398 * 10,587,387 According to formula (6), K 0 (for between herds) s 706.5 records a z 0 (within herd) + KQ Q (between herds) - 2,009,018 (T (between herds) s 2832 Fortion of variance due to herd difference ^(between herds)_________________ between herd) = (T*{ within herd) i 2832 . 263 1UE9E Fortion of variance due to within herd difference = 1003 - 26< 71+3 K c (cow difference intra-herd) = 2 . 8 7 ^ ( c o w difference intra-herd) s 2763 Fortion of variance due to cow difference intra-herd = 31+3 Fortion of variance due to record difference intra-herd *663 Portion of variance due to cow difference inter-herds - .7*4- x .314- • 253 Fortion of variance due to record difference inter-herds = .71+ x .66 = 1+93 According to the above analyses, record differences caused the main cart of the total variation, and it is mainly due to environmental effect. However, both the genetic com- cosition of the individuals and the environmental effect on them were important causes of herd differences and cow differences. 25 Plum (1935) has treated the portion of variance of herd differences as the correlation coefficient between the individuals within the herd, and he reported a value of «3U as compared with .26 from this data. He used 119 herds and the average number of records of each herd was about fifty records. Compared with the data used here, his herd size was much smaller and so the individual cows tended to be more correlated. Therefore, the value of the correlation coefficient between the individual cows within herds found here i 3 reasonable. Repeatability "Repeatability", speaking in general terms, is the con­ sistency of the cow’s life time production. Statistically, it means the correlation between the records a cow has made. A machine cannot have exactly the same amount of out-put year by year. So, a cow, with a much more complicated mechanism, can never be expected to have the same produc­ tion every year, since both external environment, such as management, and the internal functioning of every organ within the body are closely related to the milk production. Nevertheless, because of the inherent ability of a cow, the variation of a cow’s record has, in general, certain limits. Numerically, this is called the coefficient of repeatability This coefficient serves as a predicting factor for succeed­ ing records based on preceding records that have been made by that cow. 26 Table 2e shows 22^ of the total variance accounted for by cow differences in the Traverse City herd, 28^ in the Reformatory herd, and 5?7^ in the Ionia herd. They are still the results expected, as the Ionia herd is the smallest one and the records of many of the cows in the herd are close as Is seen by a rapid glance. This merely indicates that the Ionia herd has been under a quite constant management month to month and year to year. Most of the cows were kept in a healthy condition and disease and other kinds of temporary internal disturbances were probably controlled better than in the other two herds. Table 2f, by combining the three herds together, gives the average repeatability coefficient. It amounts to .25? for the Inter-herd base, and .3i| for the Intra-herd base. The latter one, .3U» is really the average of the coeffi­ cient of repeatability of the three herds. It will serve as a conversion factor later on. Ferltability Analysis Definition: "Heritability11 is the fraction of the ob­ served variance which is caused by differences In heredity. In other words, It is the extent to which observed differ­ ences between Individuals are caused by differences in the genetic make-up. Let Op = the part of variance due to differences In the genetic make-uo of different Individuals in the population. 27 s the part of variance due to differences in the environment under which different individuals developed. &~0 s the observed variance of the different indi­ viduals in the population. Then 0~H + ^ Therefore, = /«-*• (To 0 F r 2 cov.xy O ’’Selection of the dams will tend to lower the correla­ tion coefficient, but will not bias systematically the regression of offspring on dam, although the dependability (fiducial limits) of that regression will be decreased.” Frocedure for Heritability Analysis The first step for the analysis of heritability was the analyzing of each herd. After that was done, the three herds were combined and the weighted average was computed. For each herd, a preliminary analysis, an intra-sire regressionand correlation and a half-sib correlation analysis were carried out. The method of analysis closely followed the method outlined by Snedecor (19l|.6) or some other route statistical procedure. An interpretation will be given following the result of each analysis. 35 Perltablllty Analysis of Butterfat Production for the Ionia Reformatory Herd 1. Preliminary Analysis There viere 120 dam-daughter pairs under nine sires available for the heritability analysis in the Reformatory herd. The average production and the variance in produc­ tion of the dam and daughter groups are given in the following tables: Table 3a - Average Production of Dam and Daughter Groups Sire Number of damdaughter pairs Average butterfat-production of dams of daughters 1+80572 11 1+99 1+63 808309 8 516 51+7 6291+7$ 22 517 1+72 576509 8 1+79 1+71 575183 29 1+90 1+72 71+1+578 19 512 1+95 6 9 I+8 I4I+ 10 506 1+95 1+01108 8 1+60 531 51+5551 5 507 1+89 522685 2 1+65 528 120 500 1+87 Total 36 Standard deviation of the dams’ oroduction s 7U lbs. Standard deviation of the daughters’ production s 6U lbs Coefficient of variation of the dams' production - 15^ Coefficient of variation of daughters' production s 13^ According to the results of Table 3a, the average of the dam's oroduction was higher than the average of the daughter's production. This was logical because the dams were usually selected. however, the fact that the varia­ bility of the dams' rroducticn was higher than that of the daughters' oroduction was due to the tendency of the daughter's production toward the herd average as a result of their dam's being selected. Table 3b - Analysis of Variance of the Dams' Production Degree oT Sources_________________ freedom Total retween mate groups Within mate groups Sum of squares Mean squares 119 638051 5362 9 33160 368U 110 6GL,.89 5U99 F______ Non-signi ficant According to the results shown in Table 3b, there was no difference between the dams mated to different bulls. That means that the dams mated to different bulls were distributed at random, as far as butterfat production was c one erne a . Table 3c - Analysis of Variance of Daughters Between Different Sire grouos Sum of squares yean squares Source Degree of Freedom Total 119 521*727 1*558 9 68572 7619 110 1*56155 1*11+7 Between sires Within sires F Non-significant Table 3d - Analysis of Covariance and Test of Adjusted Means Between Daughter Groups Sum 'of squares ~ancTp roducts Error sT of estimate Degree of (l)Sum of Degree of* Mean Source_ _ _ _ _ _ _ _ Freedom______ Sx^_ _ _ _ Sxy_ _ _ _ _ _ S y ______ squares freedom_ square_ _ _ _ Total Between sires Within sires 119 9 110 638051 633160 601*891 12161*6 -5875 127721 521*727 68572 1*56155 For test of significance of adjusted means (1) Sy2 . (Sxv)2 Sx2 F = 8083 - 2.01*# W 7 5011*95 118 1*29167 109 72272 3937 8030 38 There was no statistically sijniilcant difference be­ tween daughters by different 3 Ires even at th e 5^ level, accordin'? to Table 3c. The analysis of variance of table 3c and 3d are a orelimi nary analysis of the daughters1 butterfat production. Table 3c cives the result before adjusting. In it ^ives the results in which the effects ofthe dams’ nrc- buction ’were tlanded. other words, It turns out non-sipnifleant, but the r value is close to the 3 * level of sipnificance. after the ‘ "ffect of tv e dams’ production is deducted by the covariance method, eh e F value shows si m i f icance at the 3^ level. That means the dams’ production ability did have some erfect on -he variation of trc caud'ters’ product ion, al thouyh there -as ' reon no si T.ificant ifforencc .etT.\'-en oh e different a am •rct>r'S as was s> own in far le 3l':• The i rv e m i e ta tion for this ■-•'ay be ( 1) due to the difference of tie intrinsic factor, e. tv e genetic make-jp, of the c&ns ceinp different amonr -he aiLTerent prawns; (2) due to the different penetic com­ position of the sires for milk or butterfat orocuction. We cannot expect all z^~ e sires to have the same transmitting ability for butterfat production unless they all come from ~ve sa^e highly inbred line. table 3d is reasons'ie and exreoted. 2. Consequently,the F value in intra-sire Correlation and ; e m e s s i o n of Daughter on .Jam "ethod The results of the calculations of intra-sire correla­ tion coefficlent and repression of dauyhter on dam are f ntered in 1 r-3© • 39 Table 3e - Observed Intra-sire Correlation and Repression Coefficients Number of d am-daughter pairs Sires [+80572 808309 6291+78 576509 675183 71:1]578 691+81+1+ 51+5551 1+01108 522685 Total Regression coefficient 11 8 22 8 29 17 10 5 8 2 .37 .17 -.57 .01 -.01 -.10 .37 8.9 2 .81+ 1.5U 120 .21 Correlation coefficient .21+ Table 3f - A Comparison of Daughters’ Average, Equal Farent and Regression Indexes Mean Deviation production from herd average of dam Sire 14.80572 6291+78 576509 675183 71+1+578 6 9 I+8 I4J+ 1+01108 51+5551 522685 808309 1+99 517 1+79 1+90 512 5C6 1+60 507 1+65 516 7 25 -13 - 2 20 - 6 -32 5 27 21+ Herd average s 1+92 Mean production of daughter 1+63 1+72 1+71 1+72 1+95 1+95 531 1+89 528 51+7 (10) (7.5) (9) (7-5) (1+.5) (1+-5) (2) (6) (3) (1) Equal parent index 1+27 1+27 1+63 1+51+ 1+7? 1+81+ 602 1+71 591 578 (9-5) (9.5) (7) (8) (5) (1+) (1) (6) (2) (3) Regress ion index 1+26 1+67 1+71+ 1+72 1+91 1+91+ 538 1+88 522 51+2 (10) (9) (7) (8) (5) (k ) (2) (6) (3) (1) b = .21 Regression index s herd average {P daughters' average / expected daughters' average Expected daughters' average s herd average - b (devia­ tion of dams' average from herd average) 4o Table 3g - Analysis of Error Variance Degree of Freedom Source Within sire unadjusted Sy2 Due to regression Error for adjusted production Sum of squares Mean squares 110 456155 4149 1 26968 26968 109 42918 3937 F 6 •85* The intra-sire correlation and regression of each sire group was carried out by straight forward correlation and regression methods using formulae (1) and (2). The intra- sire correlation and regression of the whole herd was calcu­ lated according to the covariance method. For the total regression and correlation, the covariance method is a de­ terminative method by which almost the total effect due to sires is left out. Therefore, we consider those coefficients as being due to the dam's effect on the daughter, and hence are called intra-sire correlations and regressions of daugh­ ter on dam. In order to get the heritability value, based on formula^ (1) and the explanation in the discussion of re­ gression, both the coefficients need to be multiolied by two. In regard to the regression value for each sire group shown In TabUe 3e, some values are quite high, such as for sire 545551* b = 8.9166, wftile some other values are low, such as, in the 576509 group, b = .0074- The latter one shows U1 almost no regression. tive values. Xn addition, there are also nega­ The cause of this heterogeneity among the regres sion values was (1) the effect of environment and (2) the small numbers included in each sire group. These values give us a clue to the imnortance of environmental effects, and the unreliability of small sample numbers for the butterfat production analysis. The effect of either one of them could bias the result an unbelievable amount. Table 3f gives a comparison of three kinds of sire in­ dexes. As we compare these computed values for regression index and equal parent index, the former gives lower values for bulls with high record daughters and higher values for bulls with low record daughters than the later one. As far as the rank is concerned, there are some minor changes among the three different indexs. well. In general, they agree fairly Nevertheless, on the genetic base, the latter two indexes seem more logical than the index based only on daughters' average. Since environmental effects contribute a large portion of the variation in production of either milk or butterfat, any sire index is an approximation. Graves and Fohrman (1936) take a very sane view of the problem and state, "Environment plays a prominent part in the making of production records, and the use of correction fac­ tors often makes the effect cf environment even more confusing....It is presumptuous to state a sire's ability in exact pounds of milk or fat when the estimate is based on a number of his daughters' records made under such varying conditions. k-2 If hairsplitting; exactitude is set up merely as a means for deciding competitions between bull own­ ers, then it is apt to prove detrimental to breed betterment because this competition offers a tempta­ tion to the overzealous.n Since a sample was theoretically taken from a random bred copulation, there should be no correlation or regres­ sion among the individuals themselves. That is, the expected value of correlation or regression should be equal to zero. In this data, an assumption was made that there was no correlation or regression between the dam and offspring, a test is given in order to determine whether this hypothesis Is correct. For testing the significance of the correlation coefficient with the 3i?e of sample like this, the formula, (r - o) r — , was applied. The result .2J132- 2.66 7^915 " is signifi- Jri cant for 1% level. Table 3g indicated that the variation in nrodaction due to regression Is highly significant. it also shows that on the average the higher the d a m ’s production, the higher* the daughter’s production. In other words, the daughters’ records tend to follow their dams' production. that, to This shows some extent, butterfat production is inherited. relationship between the r and b values and the The question of which should be used as the better measurement for heritability will be discussed later. The standard error of the correlation coefficient was calculated as follows: Sr = (1 - r2 )///n - 2 = [l-( .2i+31)2]//^L17 = . 0 8 7 U3 Since the heritability estimate is obtained by multiplying the correlation coefficient by two, the standard error of heritability is likewise obtained by multiplying the stan­ dard error of the correlation coefficient by two, which is, 2 x .08? = .17U» Thus the heritability of butterfat pro­ duction in the Reformatory herd by the intra-sire correla­ tion method is 0 .14.86 £ •1 7 ^i• The standard error of the regression coefficient was calculated as follows: sum of squares of standard error of estimate of error term 2 = I I --------- - Sum oT squares of x oT error term Sy2 iSxtL 2 Sx‘ — US61S5 = Sx2 ~' 2 I-12 ??2 1 ?. 6U691______ 119 - £ = .0061 6 O I 4 .8 9 I Sb - , .0061 = .0779 The heritability estimate is obtained by multinlying this regression coefficient by two which is equal to, 2 x . 2 1 1 J 4 .2 2 . Similarly, the standard error of heritability is calculated by multinlying the standard error of regression by two, which is equal to 2 x .0799 ■ .II4.6 . Thus the heritability of butterfat production of cows in the Reforma­ tory herd by che intra-sire regression method is .14.22 ♦ .II4 .6 The comparison of the variability of the correlation and regression coefficient may give some information about kb the reliability of those estimates. coefficient of variation is O' . m The formula for the In this case, the mean of the correlation coefficients is . 2 4 3 and the mean of repres­ sion coefficients is .211. Therefore, the coefficient of variation of the correlation coefficient is equal to • °?7 - .398* and of the repression coefficient is equal to .21)3 •0779 -.369. 72TT“ is very close. The variability between those two coefficients Therefore, as far as variability only is concerned either value may be used for the estimation of the heritability. 3. Paternal Half-sib Correlation Kethod The records used for this method of analysis were the same as for the daughter-dam correlation and regression methods. The distribution of daughters under each sire has already been listed in Table 3 b., Tade 3h - Senaration of Components of Variance of Eutterfat Production of the Daughters Source petween sires VI thin sires Degree of freedom Sum of squares ■Mean squares Components 9 68*572 7619 E + K0 A 110 4961 99 *aij7 B In the Table 3h, the variance was divided into varia­ tion between sires and between daughters by the same sire. The variance comoonent E represents variation between daughters by the same sire, while component A Is the addi­ tional variance which can be ascribed to differences be­ tween sires. each sire. K q is the average number of daughters under It Is calculated by the formula (6 ). For Table 3h K q = 11+.29 E = 1+11+7 B + 11+. 29 A = 7619 A = 21+8 The ratio A Is the average correlation between daughA + B ters by the same sire. The average correlation multiplied by four is the estimated heritability of butterfat oroduction by the half-sib method, and for this set of data Is equal to 1+A = 14.(21+8) = 992 = .23 uiitT-zne i r m A" + ^ The standard deviation of the half- 3 ib correlation Is B(B - K q A) _ (A + B)^y-£(K 0 -l)I£i 1+11+7 (1+11+7 - 11+ x 21+8) _ (1+11+7 + 2l+8)-y^(13)ll+ . 10) Table 3i - Summary of the Observed Values of the Estimation of Heritability Correlation K ethod___________________ coefficient Regression coefficient Heritability Intra-sire regression of daughter on dam .21 + . 0 7 8 .1+2 + .15>6 Intra-sire correlation of dam and daughter .21+ £ .O8 7 .1+9 + •171+ Paternal half-sib correlation 056 ± ,05k 23 + .217 46 Heritability Analysis for the 1 raverse City Herd: The calculations Tor the Traverse City herd, the largest of the three herds, were :he sane as for the Reformatory herd. 2 8 0 daughter-darn pairs by 1 5 sires were included. 1. Preliminary Analysis Table 4a - Average Production of Daughter-Dam Groups P ecris tration Number of Average Average numbers dam-daughter -production -production of sire________ pairs________ of dam____ of daughters_______ 6 5oP62 21 U3U 470 -83353 38 440 407 7 C C2? 8 35 426 435 7281c4 71 456 454 813CQL 10 434 19l| 70 .030l| 81309U 10 •Oil.6 7 769913 15 7^7611 9 .1710 822688 1| •k727 383211 7 •k3 07 6097 7U 8 .6122 I;8601+0 30 .6 3 I4-O 6 .0776 6667I 4I4 18 -.1209 680028 11 -.7376 280 .0862 612017 Total Correlation coefficient .0710 So Table 1+f - Test of Significance of Regression Coeffic ient Degree of freedom Sourc e Due to regression 1 Sum of squares Mean squares 5286 5286 Error for adjusted production 261+ 1014 +2 0 ^ 3955 Within sire of unadjusted production 265 101+91+90 3960 F 1.31+ The method of calculation for the coefficients listed in Tat le 1+e was the same as that for Table 3e of the Reformatory herd. The fluctuation of the regression coef­ ficients may be interpreted the same as for Table 3©• For testing the significance of the correlation coefficient, tory herd. the same formula was used as for the Reforma­ The result of this testing gave the value, 1.19, which is non-significant. According to the results of the analysis of the signi­ ficance of the regression and correlation coefficients, the value for either was not significantly different from zero. Since there were quite a few negative regression coefficients as Table l+e shows, this was to be expected. This means that in this set of data there was no way to predict the daughters' production from the dam's records. The reason for the low heritability may be (1) domin­ ance effects, (2 ) the environmental conditions were not 51 good enough and the animals with genes for high production could not show their true ability. The result is pprhapa the production records did not represent their true ability. have visited this herd. I This herd is a part of the Traverse City Mental Hospital, and some of the people work­ ing in the herd are just recovered or partially cured per­ sons. The management appears below the average of the other two herds studied. For this reason (2) is more likely to have existed or Played the main effect. There may have been some sampling error, but as the sampling size of this herd was the largest among the three, it should not have played any important role. For obtaining a dependable heritability estimate, these three samples from each herd are pooled later. The data from this herd is considered as part of the total sample. Therefore, both the regression and correlation coefficients calculated for this herd are taken at face value, even though they are non-significant. Furthermore, this regres­ sion coefficient is used to compute the regression indexes to compare them with the other sire indexes. 52 fable 1+g - A Comparison of Daughters* Average, Equal Parent and Regression Indexes (lbs. Butterfat) Mean Mean Devia tion production production from herd of of dam average daugh ter Sire Equal parent index Regression index 659863 1+31+ _Q 1+70 (1) 506 (1) 1+71 (1) ^53353 1*l+o -3 1+07 (13) 371+ (13) 1+07 (13) 700278 126 -17 1+35 (10) 1+10+ (6) 1+36 (10) 729191+ 1+56 13 1*51+ (5) 1+52 (5) 1+53 (5) 813091+ 1+31+ -9 399 (11+) 361+ (11+) 399 (li+) 769913 1+68 25 1*1+1 (8) 1*11+ (9) 1+39 (8) 787611 1+80 37 1+58 (1+) 1+36 (7) 1+55 (1+) 522658 1+20 -23 1+1*1+ (7) 1+66 (1+) 1+1+6 (7) 353211 1+68 25 1*39 (9) 1+10 (10) 1+37 (9) 609771* 1+22 -21 1+62 (2) 502 (2) 1+61+ (2) 1 8601+0 1+57 11+ 1*29 (11) 1+01 (11) 1+28 (11) 1+12017 1*75 31 1+50 1*25 (8) 11+8 (6) 56671+1+ 1+53 10 1+15 (12) 377 (12) 1+11+ ( 12) 65002 5 1*1+9 6 1+61 (3) 1+73 (3) 1+61 (3) b • (6) .086 Herd average = 1+1+3 lhs . It appears in fable 1+g that the regression indexes rank exactly the same as the daughters' averages, and the actual values are also very nearly the same. rhi., results from the low regression coefficient which causes the expected 53 daughter’s production to be very close to the herd average, e. g., regression index * W + D - e, where W is the herd average, D is the actual daughters’ average, and e is equal to w - bx. As b value is small and bx is very close to zero, e will aporoach W. The result is, W + D - e = W + D - W It is statistically true also that when t the mean is the predicted value. zD. value is zero, Since the equal parent Index is based on the assumption that the regression of daughter on dam is unity, the values based on it depart con­ siderably from the regression index in this case. The calculation of the standard error of the regression and correlation is exactly same as the calculation for the Reformatory herd. Sy 2 - (S x y ) 2 /3x 2 n - 2 b = 3b r = 10^9^90 - (61302)2/710972 277 *.0053 A 0053 = .073 3r = (l - r2 )//n - 2 = 1 - (.07096) 3. 280 = .0598 Faternal Half-sib Method Table Zjh - Separation of Components of Variance of the Butterfat Production of the Daughters Sourc e Between sires Within sires Degree oT freedom Stun of squares li| 116UhS 265 10I4-9U70 Mean Comsquares ponents 8318 B + K0 A 3960___B_______ 5k K q = (280)- 98U8 = 19 (SW T (1 3 UA ^ = U( U( 229) 229) y - M~-r 229 — 3*360 S .22 The standard deviation of the half-sib correlation Is, (Tr = B(B ♦ K 0A ) = 3960(3960 - 229 x 19) (A + P)2 y i(K0 - l)K0n (3960+229)2/ i ( 18)(19)(1U) .038 Table l|_i - Siurmnary of the values of Tstimation of Feritabili ty Correlation coefficient Method Intra-sire regression of daughter on dam Regression coefficient Heritability .066 £ .073 .17 £ .15 Intra-sire correlation of dam and daughter .071 +.060 .11* + .12 Faternal half-sib correlation .056 £.038 .22 ± .15 According to Table i+i, the heritability estimated by the correlation between half-sibs is higher than either the regression of daughter on dam or correlation between dam and daughter. This is logical since, as it was -pointed out be­ fore, the correlation between half-sibs usually Includes some environmental correlation, If any exists. Moreover, correlation due to interaction contributes more in the halfsib correlation than to the dam and daughter correlation. 55 Heritability Analysla for the Ionia Hospital He r d: There were 73 daughter-dam pairs by six sires in the Ionia herd for the heritability analysis. Their distribu­ tion and the averages of the butterfat production of the dams and daughters are listed in Table 5a. 1. Preliminary Analysis Table 5a - Distribution and Average Butterfat Produc­ tion of Dam and Daughter Groups Number of dam-daughter pairs Sire Average production of dam Average product ion of daughters 51907U k 576 14-96 671583 15 56Q 597 568009 11 517 561 5 0 Z4J4.02 16 573 570 5714.1914- 25 587 503 2 5314- 522 73 568 514-6 507031 Total Standard ueviation of dams' production = 6I4. lbs. Standard deviation of daughters' production = 8 3 lbs. Coefficient of variation of dams' production s 11% Coefficient of variation of daughters’ production = 15^ Table 5a shows that the averages of daughters' produc­ tion were more heterogeneous than the averages of the dams' production. The mean of all the dams' nroduction was higher 56 than the mean or the daughters' production, but their styidard deviations were in the reverse order. This is flso shown by the values of the coefficients of variation. The results of this table simply indicate that the dams were selected. Table 5b - Analysis of Variance of the D a m s ' Froduc tion Source Total Between mates Within mates Degree of freedom Sum of squares Mean squares 72 30116U 5 401U9 8030 67 261015 3898 F 2.06 (non-significanl Table 5c - Analysis of Variance of Daughters' Production Source Total Eetween sires Within sires Degree of freedom Sum of squares Mean squares F 3.61* 72 507539 5 107808 21563 67 399731 5966 The interpretation of Tables 5b and 5c are approxlmately the same as for the Traverse City herd. 57 Table 5d _ Analysis of Covariance and Test of Adjusted Means Between Daughter Groups Source De cree of freedom Total 72 Ee tween s ires W i thin s ires Sum of squares and products Errors of estimate Degree of Mean Sum of _Sy2 . .. sqs. freedom sqs Sx^ Sxy 301161+ 3711+5 507539 5 1+011+9 -251+67 106808 67 261015 62572 399731 502958 71 2U9731 66 3788 5 5061+5 For test of significance of adjusted means 253227 P = 506U5 = " 3 m 13. 38* The P value of Table 5d comes out highly significant. It means that these sires differed in the level of nroduction they transmitted to their daughters. Since the adjusted means are the average of the daughter groups by the dif­ ferent sires after adjustment for the dams' producing ability, the residual variation is accounted for as the effect due to the sire differences. It also indicated there was a certain amount of heterogeneity among the sires, and that the selection of sires should be carefully done in order to increase the nroduction level. 58 2. Intra-sire Daughter-Dam Correlation or Regression of Daughter on Dam Method Table 5>e - Intra-sire Regression and Correlation Coef f ic ientj> Number of dam-daughter nairs Sire Regression coeffic ient Correlation coeffic ient 515074 3 -.6532 - .9966 671563 14 .2945 .2 6 5 0 566009 10 .3183 .3651 501^10 2 15 .1462 .1575 574194 24 .3855 .6 3 6 6 507031 1 -.1793 -.9629 67 .2 3 9 7 .1937 Total The method of calculation for the coefficients listed in Table 5e was same as that for Table 3© of Reformatory herd . Table 5f - Test of Significance of Regression Coeff ic ient Degree of freedom Sum of s ouares Mean squares 1 15000 15000 Rrror for adjusted nroduction 66 249731 3784 Within sires of unadjusted production 67 399731 5966 Sourc e Due to regression P . 15000 = 3.96 5825 59 The F value of i'able 5f Is non-significant at the 5% level. An F value of 3.99 for 1 and 66 degrees of freedom is needed in order to be significant. However, it closely approaches the level of significance. For testing the significance of the correlation coeffi­ cient, the seme formula was used as for the Reformatory herd. The calculated value for this test is 1.61|, which is non­ significant . Table 5g - A Comparison of Daughters* Average, Equal Parent and Regression Indexes (Lbs. Eutterfat) Mean De v i ation p r o d u c t i o n Mea n of produc t ion from h erd average daughter of dam Sire Equal parent index Reg ression Index 51907*+ 576 26 1+96 (6) 1+16 (6) 1+90 (6) 671583 569 19 597 (1) 625 (1) 592 (1) 568009 517 -33 561 (3) 605 (2) 568 (2) 50hU02 573 23 570 (2) 567 (3) 557 (3) 57U19U 587 37 503 (5) 1+19 (5) 1+91+ (5) 507031 53U -16 522 (1+) 510 (i+) 526 (1+) b = .214Herd average r 5 5 0 lbs. Table 5f shows that the rank by the equal parent index and regression index were the same, but there was a shift between (3) and (2) In comparison with the daughters* average. As far as the calculated values were concerned 60 the regression index was closer to the daughter average than to the equal parent index. The reason for this was the low regression as has been pointed out in the interpretation of the heritability analysis of the Traverse City herd. The calculation of the standard error of regression and correlation was exactly the same as the calculation for the Reformatory herd. Sy2 - (Sxy) SB = 399731 - (62572)2/26l050 /S x 2 N -2 Sx^ Sb s / .02l " ' ' 021 7 0 ---- ---------- 261350 r .li|9 sr = (l-v2 ) / / ^ 2~ - l - ( .iQ77 )2 / y 7 2 - 2 = .115 3. Paternal Half-sib Method Table 5h - Senaration of Components of Variance of Eutterfat Production of the Daughters Source Degree of freedom Sum of squares Between sires Within sires A -B 67 k(lllU) r .63 5966 i I H I 4- Mean squares 107808 215616 399731 5966 Components E + K0A E 61 The standard deviation of the h a l f - s i b correlation is ______ B(B -fKfyA )______________ 5 9 6 6 ( 5 9 6 6 - l l i x l l H + ) ______________ „ (A ♦ B)2y i ( K Q - l)$n “ (1111+ ♦ 5 9 6 6 ) V i d 3 ) d U ) ( 6 ) " Table 5i - Summary of the Values of Estimation of Heritability Correlation M ethod___________________coefficient Intra-sire regression of daughter on dam Regression coefficient .21+ + .11+ Heritability .1+© + .29 Intra-sire correlation of dam and daughter .19 + .11 .39 + .23 Faternal half-sib correlation .63 £ .l+lj- .16 + .11 Average Estimate of H e r i tab ility of Butterfat Produc­ tion for the- Three H e r d s : Since the three herds are located in two different sec­ tions of Michigan, and since their managemen t and breeding systems cannot be the same, to generalize on this situation and to make the estimate of h e r i tabilit y applicable to more than a single herd, a summation of the estimates from each herd and an average of the estimated value of h e r i t abili ty is quite necessary. In addition, the size of the sample will be enlarged and the estimated value will be more r e ­ liable. The number of daughter-darn pairs sampled from each herd is fairly proportional to their herd size. Therefore, the pool of the three samples can be assumed as a stratified sample. 62 The method of calculating a weighted average is very useful method for pooling samoles together. worked out by Hazel and Terrill (191*5) • It has been Their averages were calculated by v.e ight Ing each of the individual estimates by the reciprocal of its squared standard error. They pointed out that this method is not without disadvantages, but it does, in general, give greater weight to those esti­ mates which are based on the greatest amount of data. The following are the formulae used and the fundamental set­ up for calculations. General formula for weighted average of the standard deviation is / / n £ ( irl 1 IT) si Weighted average of standard deviation for intra-sire regression of daughter on dam is 1-----------------1-- ?--- 1--- J--- 1-- = .0i±99 702T .0061 T0057 Weighted average of standard deviation for intra-sire correlation of dam and daughter is r " v tvii 5 0 )^ + 1 (.067) + 1 (.0 5 9 8 ) = .01*53 63 W e i g h t e d average of standar d d e v i a t i o n Tor paternal h a l f - s i b c o r r e l a t i o n is i Z “ .... + 1 4 ,/77 1 (.109 ) 2 J ( -03&3)2 - .0 3 0 1 - 1 (.051+2) 2 The general formula for the w e i g h t e d average of r e g r e s ­ sion and c o r r e l a t i o n Is 2 iH) i= l sf i= l °i i*l b i W e i g h t e d average of intra-sire r e g r e s s i o n of daughter on dam Is . 0 8 6 2 4- .2 1 1 1 + . 2 3 9 7 ( .0 7 2 8 ) 2 ( .0 7 8 ) 2 ( .Ilf5 7 ) 2 1 + 1 1 ♦ O0 6 I .0 2 1 '.3052 = .1551 Weighted average of intra-sire c o r r e l a t i o n of da m and daugh ter is .21431 ♦ .071 + ,.1937 ( .0598 ) 2 ( .115 ) 2 = .1367 ( .087 ) 2 1 3+ .1 3 a I ~+ (.0598 ) 2 ( . l l 572 ( .087)^ W e i g h t e d average of Faternal h a l f-sib c o r r e l a t i o n is .1573 + .0561+ .051+7 + (.0750 ) 2 (.051+2)2 ( .0 3 8 2 ) 2 1 4. 1 1 4 (.051+2)2 ( -0383)2 (.0750)2 - .0630 61+ Table 6a - A Summary of the Regressi*on and Correiation Coefficient of the Three Herds Herd Paternal half-sib correlation Traverse .05.5 + .038 .0 8 6 + .0 7 3 .071 + .060 Reformatory .056 + .051*. .211 + .078 .21+3 ± .087 Ionia .157 + .109 .214.0 + .1^5 .191+ ± .115 Average .063 + .030 .155 + .050 .137 ± .01+5 Intra-s ire regression of daughter on dam Intra-sIre correlation of dam and daughter Table 6b - A Summary of Estimation of Heritability Herd Paternal half-sib correla tion lntra-s ire regression of daughter on dam Intra-s ire correlation of dam and daughter Traverse .22 + .15 .17 + .15 .11+ + .12 Reformatory .2 3 + .22 .1+2 i .16 .1+9 + .17 Ionia .63 ± -30 .1+8 + .29 .39 ± .23 Average .25 ± .12 .3 1 i .1 0 .27 ± .09 By looking at Table 6a and 6b, we find tbat among the averages of the three herds, the intra-sire regression of daughter on dam had the highest value and the intermediate variability, and that the intra-sire daughter-darn correla­ tion had the intermediate value, and the lowest variability, while the half-sib method was lowest heritability with the highest variability. i'or this set of data, it is believed 64a 600 550 £500 .Daughters!- 500 600 Sam's production 700 eoo Pigure 2 - Intra-sIra Regression of Butterfat Production of Daughter on Saa The above graph is aade for the average of the ianghters based on the daughters' production lfc the three herds, and for the average of the daae based on the dams' production of the three herdr| the regression is based on the equation, T = k€9 - b (X - USO) 65 that the average of the intra-sire regression coefficients is the most reliable estimate of heritability. The reason for this will be given in the discussion. Conversion of Regress ion Coefficient of the Average of the Records o f a Cow i n t o t h e Value for Single Records: For the comparison of this heritability value, which was derived by using the life time average of butterfat nroduction, with others, it is desirable to express the re­ pression coefficient b of the total records of each cow in terms of what they would be if each cow had only one record. The calculation follows the formula which was (d v e n by Lush (19U2). b = b '^ 1 - (m-l)rad 4m Pm (l-rd d )^) m3 Where b equals the regression of daughter on dam when single lactation records of each are used, b' equals the regres­ sion when life time averages are used and m equals the average of the number of dam's records during life time, r^d is the repeatability value. (Tm number of records of b - .1551 ( 1 - is the variance each dam of the three herds (1) (3) (2) (3.96-Q.3U _ b .56 (1. - .3b )} 3.98 (3.98)3 = .0853 h 2= .0853 x 2 = .17 of the 66 (1) m n l *1 + n2x2 * ■■■■nkx k nl - n2 + _ ” k 502 + 9W+ + U37 120 + 2 ^° + 7 3 " 3 *98 x = the average number of records of each dam of a certain herd n = (2) the number of dam-daughter oairs of a certain herd p 2 . 2 A ,-- n lsl * n 2 s2 * --- nksk _ 0 = n x + n2 + ___ nk- k 2 s 930 .U * 1080.8 4- U30.7 =L.99 120 * 280 + 7 3 - 3 s the variance of the number of records of each dam for a certain herd (3) dd = .3 U » the repeatability The Ef f ec t of Yearly Environmental Changes on Eutterfat Froduc t ion The factors which account for this effect such as crons, economics, and climate, all have a direct or indirect ef­ fect on the butterfat production of dairy cattle. »Je were not interested in the factors, but rather in their results, and whether there was any significant difference between yearly averages, or whether any trends existed among the con­ secutive years, and what portion of the variation in the butterfat records was due to the differences between years. These were the main purposes of this analysis. The m e t h o d used for class number There were no herd, thus eleminating for analysis t ha t h e r d . records this study of v a r i a n c e from 193^4- to those three was given 1 93 6 years the by unequal Snedecor in the from sub­ ( 19i(.6) . Traverse the City analysis 67 The average yearly butterfat production figures for each of the three herds are given in Table 7 & • These figures in graphic form are shown in Figure 3. Tables 7b and 7c indicate that there was a highly signi­ ficant difference between different years for butterfat ’■'reduction either for a single herd or after combining the chree herds. However, there was no indication that the averages of the late years were higher than the averages of the earlier years. The nortion of the intra-herd variance which was accounted for by differences between years was close to five per cent. For the trend analysis, there were several methods available, but some of them required tedious calculations. [he method used here was a kind of test of randomness of sequences, the so called "runs11 simplified by Hoel (191+8). The average production for each year for each herd and the three herds together were assigned the letter a if they were less than the median and the letter b, if they were greater than the median. The four sets of averages gave rise to the following sets of arrangements. Table 7a - A List of lear Averages of Butterfat Production Year 1930 1931 10 32 1933 Wit 193? 1936 1937 1936 1939 1940 1941 1942 1943 1944 1945 1946 Av. Traverse City Number of Averages records 35 1*8 63 32 Reformatory Number of records Averages 12 10 27 27 36 29 31* 93 69 442.36 469.62 434-43 452.66 21* 1*71.50 5014.52 562.67 539.30 539.25 1*65.36 1*73.29 1*73.27 1*61.07 1*92.26 1*79.14 536.62 522.01* 1*92.76 507.59 4*9.09 508.58 7142 441-76 29 501.92 1*21.25 429.13 447.ee 445.ie W 82 83 420. ?6 431.69 439.01 81* 79 91 75 442.12 86 462.75 426.63 1*0 29 38 27 26 275 29 39 31* Ionia Total Number of Humber of records Averages records Averages 9 10 17 545.44 56 74 107 77 55 43 65 451.96 466.67 499.66 506.36 535.14 510.77 532.98 470.78 460.12 516.86 481.33 35 30 29 35 36 32 26 17 563-70 591.47 565.72 527 •37 573.63 598.45 553-58 536.37 580.51 592.80 600.21 573.91 516.22 544-47 543-35 578.35 157 153 110 477.29 471.79 494.42 467*30 464.41 21*.76 564.il 110.65 464-91 18 19 16 31 29 30 119 141 146 141 134 153 140 507.22 03 Year Figure 3 ~ Avrrafp Yearly Butterfat Production a 1 c A - Trr.vrrsf Jit,,v r.erc I'.pfornatcry herd Ion ia h»rd The f.:.r*e herd* 69 Table 7b - Analysis of Variance of Year Effect on Eutterfat Froduction of Each Herd Source of variance Herd Traverse Reformatory Degree of freedom Yean squares 11*71*6 Total Between years Within years 966 11 993 1*939092 191693 U7U3399 Total Between years Within years 1*92 3673279 Total Between years Within years Ionia Sum of squares 2 •9 6 *--::- 1*977 14.66 281*122 3262881* 1*20 3690632 16 E 25690 6859 3 •7l*r*"M' 2 .1 1 « 281*122 17798 16 1*01*____ 31*06510____ 814-32 Table 7c - Analysis of Variance of Year Effect on Putterf 8 t Froduction of Three Herds Degree of freedom Source Total Between herds Within herds Sum of squares Mean squares i860 16882308 6980 2 1*58331*5 2291672 1676 12298923 651*9 1*5 686210 19691* Within years 1033 111*12713 6226 Between 7/ears F 3.16-::-::- Portion of Intra-herd variance due to difference between years - 691*9 - 6226 = 1*.9< — -------------- Fortion of total variance due to difference between years - 8 9 8 0 - 6226 = 3 .7 ^ 8 9 H S ------ 70 Traverse City Herd, A v e r a g e s - 14-2 1 , 449, 445,421, 432, 439, 442, 463, 427, 4 4 2 , 469, 434, 453• M e d i a n - 440. sequence of letters R e f o r m a t o r y Herd, A v e r a g e s - 472, 505, 4 9 2 , 479, Median - aacbaaatbabbab. 563, 539, 539, 539, 522, 493, 465, 473, 5 0 8 , 509. 473, 461, - 493 Sequence Ionia Herd, Averages of letters 545, 564, *61, 593, - - abfcbtaaaaaafcbbbab. 591, 566, 527, 600, 574, 516, 574, 596, 544, 543, 554, 536, 576. Median - 566 Sequence Total of letters - aabbabbaabbbbaaab. 467, 500, 506, 535, 5ll» 533, 471, 460, 517, 4 6 1 , 50?, 477, 4 7 2 , 494, 467, 464- - 452, averages T'edian - 4 8 1 . Sequence of l e t t e r s e x p l a n a t i o n of - aabbcbbaabbbaabaa. symbols, n a - the number of a's nt> = the number of b !s r a - the number of r u n s of a •s rb - the number of r u n s of b ’s u - ra + rb For- T r a v e r s e — 7, City *-’erd: n b r 7, r a — 4, **b = 4 , 71 - 8.( 1) non-significant u For Reformatory Herd: na = 8, u = For nb = 9, 6. ra - 3, ^^non-significant Ionia Herd: 8* na = u - 8. For T o t a l nb ^ u 9» = ra = = ?• all Ioni a year r b = U, Averages: ra = U, n b - 9, within herd the close to concluded, then, that for ^ , one sees u values the p ( u #q£) a n d p(u. 9 ^), a l t h o u g h the was trend rb = 3, ^^ n o n - s i g n i f i c a n t By i n s p e c t i n g the T a b l e we re k> ^ non-significant na a 6, was rb = 3, either a the significant the value butterfat single herd or of u #gcj. production had the total of It no the three h e r d s . (1) i’he table for the test of runs is built un according to the formula: F (fa, fb) = K (n a - D 1 (nb-l) ! n a ; n b i_____________ (^a-l) '• ( i v r» ) ! ( *t>-D !(nb-rb) ! n! na, nb cr u .05 u .95 & 10 15 20 25 30 ko 50 60 70 80 90 100 6 11 15 19 2*4 33 U2 51 60 70 79 88 15 20 26 32 37 1*6 59 70 8i 91 102 113 72 I n the and foregoing smallest integers, a n d r £u*u.9£j 2. 0 .95* 5'b c r i t i c a l or l a r g e . values Only from 5 to Foel (19U6). T he herdsman would year yield and is advantage feeds. of that due The same effect was therefore u u #q £ a n d the above on the m o n t h for table, Butterfat of to h a v e h i s calving needs meantime, outh o w to d i f f e r e n c e set used for the used study production. r e p r e s e n t e d all another group records in F e b r u a r y , the of the month of r e c o r d s records of in of f o r the Thus, so on for the number the average (=nt>) to total Interest on this at w h a t to to subject time Is total of and Interested variation study one each of m o n t h group all of of y e a r of calved the lactation in J a n u a r y , cows the of c a l v ­ that h a d twelve calendar months. Table 8a shows c alendar month, and the take of m i l k also effect that h a d represented and small of f r e s h e n i n g . the cows the prices research man a oortion na in o r d e r and favorable the large calve u s e d as according on In d e c i d i n g cows be ^ ^ Produc tion Information to a h e r d s m a n largest is u n u s u a l l y extension workers. ing on b u t t er f a t calved may the that p £ u £ u # considerable I n the is in a subject of m a r k e t finding such of test in of of C a l v i n g is be h e l r f u l it values are testing whether listed influence butterfat These Tor the M o n t h fin d respectively, the v a l u e s 1 0 0 are Effec t of table, of c o w s that butterfat calved in e a c h p r o d uc ti on for 73 that m o n t h In t h i s show Tor Table, sh o w s butterfat the lowest the h i g h e s t lowest cows and freshening and nroduction. those the three herds. for the cows while the Ionia h e r d production of of Frick in J a n u a r y a n d h a d the lowest in M a r c h h a d the calving the the t h r e e h e r d s s h o w s and August by of production in August, results total Feformatory herd freshening obtained che and average in J u n e The results The for City herd butterfat in October. production and the T r a v e r s e the h i g h e s t in ’'arch, the each herd three herds that butterfat the h i g h e s t are similar to a l . , ( 19U7 ) a n d W o o d w a r d et. (19U5). As faias the a v e r a g e different months of c a l v i n g there were other in S e n t e m b e r . to case , is two peaks; the h i g h be smoothed, of shows soring;then it d r o o s earl y fall, when Tables traverse herds, significant the respectively. located the as a rise summer slowly that at is obvious in M a r c h , and and from the m o n t h effect the sum this the c u r v e until early natural on butterfat for of showed of c a l v i n g . the due again until 1'^ l e v e l and that January. Feformatory herd herd, As January and rises until in for the in J u l y w a s m a i n l y the for month Ionia it three herds s a m p l i n g error. Ionia h e r d The difference near show the F e f o r m a t o r y herd, I n the 8c one rise a gradual drops C i t y herd, significant is it 8b a n d p r o d u c t i o n was the of concerned, sudden considered It is the h i g h e s t The average might butterfatyield As the the three a non­ this h e r d environment should Table 6a - Average butterfat ironuction of C ows fresh ening in Different Months Month Traverse City No. of records Average Reformatory N o . of records Average Ionia No. of records Average Total No. of records Average Januarv 83 1*35 1+9 501* 32 620 161* 1*92 February 71 If 33 38 519 21* 597 133 1*87 March 51* 1*63 1*1 522 1*2 570 137 511* Anrll 77 m 36 5014 31 565 11*6 1*87 May 92 kbk 28 bQB 1*1 51*1* 161 1*79 June 82 1*31 28 1*79 20 576 130 1*61* July 96 1*30 55 505 1*5 561* 196 1*82 August 81 U2ii 39 1*79 39 525 159 1*62 September 65 1*56 1*7 1+82 1*9 570 161 1*98 October 100 1(1*9 1*3 509 28 519 173 1*87 November 72 1*53 1*2 501* 36 562 i5 o 1*91* December 91* 1*1*5 1+5 5 il 31* 571 173 1*87 80.58 1*1*2 35.08 561* 156.75 1*85 Average 1*1.16 502 75 Table 8 b - A n a l y s i s of Varia n c e of M o n t h D i f f e r e n c e S o u r c e of variance Herd D e g r e e of S u m of freedom squares 966 Total Between months Within month Traverse 3673279 11 1+82 9221*1 3881038 1*20 11 3690632 266199 31*21*1*33 1*09 - A n a l y s i s of V a r i a n c e of of n a c h M o n t h f o r the 801*8 8386 71*30 • 8c 1+93 8109 101*07 2 .06* H Table 988 F H Total Between months Within month io n i a Mean squares 1+938082 111*1*73 1*820879 11 Total Between months Within month Hefo r m a t o r y of B u t t e r f a t P r o d u c t i o n for Each Herd 31*300 2 .9 0 ** 8373 Futterfat Froduction Three F e r d s _____ S o u r c e ________________ f r e e d o m S u m cf i8 6 0 Total Between herds Within herds Between months Within month Iortion of squares Me a n squares F 16882306 2 1*88331*8 1678 1298923 1*72913 33 2291672 681*9 11*331 61*10 11826010 181*8 intra-herd variance due to m o n t h effect, 681*9 - 61+10 = 2.12^ — I o r t i o n of total varia n c e 8980 - KqTO to m o n t h effect, 6 b 1 0 = 1.88 -- 88 s i g n i f i c a n t l e v e l f o r the t h r e e h e r d s is t . o8( due ni the dii'ference of m o n t h average no ) = . 0 3 3 x 80.6 x 1 . 9 8 9 9 = 8 . 2 1 of 76 not be too was likely out the different. the whole result year, According nificance to there all m o n t h s of that both the June the of line with cows for cows Effect ing with calvin^ calvings the calving interval yield The s’ sorter caries of length mil] or the interval, has calf the tnree end Au ust herds. other Calvin two the The herds for the of three the production of c e r t a i n usual than s , Therefore, high the results only for This result among higher in J u l y . for management adverse conditions month. on Put terf at is the cow. been oeriod It known to The have of o*’ c a l v i n g , the the P r o d u c t ion oetween Is h i g h l y production Interval shorter true .for the cry p e r i o d . during was the production same the of significantly July average peak hi^h interval of the Deculiarity of sig­ any month. exceeding Interval the of the culvers the through­ for July that butterfat the t he in herds, M a r c h was tris c o m e n s at e d f o r of C a l v i n g The was needed for bc^n in three that June calving calving management averages average tne the have that the production from may the However, variation errors. only July the the cow3 The calving average Heior^atory practices and of doubt of smaller of d i f f e r e n c e from year. c^ws resulted there no August, herd higher herds is the a nd production level this constant sampling averages average Reformatory v. s i n or d i f f e 7 ent Therefore, is of m o r e the between for M a r c h was Therefore, the the lactation. perio d of time correlated cry an tv.o s u c e e d - period effect same ox* on the lec.tat'on. longer the cow The longer the the cow carries 77 the calf longer during lactation. of c a l v i n g calving un h e r interval system fetus the effect of w as broken I nto during following should calving the too ( wh i c h , so slat frequent the total simplify one on was for the longer and build growth of Therefore, effect and the on the butter- o t h e r was are and factor, to h o w too closely in s o m e After it cases, is h o w choose to a t t e m p t If to common on reduce her interval It induced to 191+6. hecorcs is on order of study to in questions. records un in to determined, a very is n o t ihe records Is it these analysis yield it ignore the the important interval for over of r e s t undermine A n a l y s i s of h f f e c t of C a l v i n g cn E u t s e r f a c ' r e d u c t i o n used cow knowledge periods The m a i n p u r p o s e to a n s w e r a production related), tv e optimum ask Is short of p r o d u c t i o n . we m a y frequently or b u t t e r f a t and the h e r d m a n a g e m e n t . is as 1. are l i a b l e a b u t t e r f a t -production the a maximum. calving, variation section With in a interval to re cover, and lactation, q u e s t i o n one m a y influential thi s at lower plane. second the of p r e g n a n c y . interval same results believed time lactation her milk in p ra c t i c e , the more often arises c o w ’s c o n s t i t u t i o n , a much is lactation. later part a l c n F -period ma;- be tha t next it usually lactation. question calve the two p a r t s ; of it a l s o the n e x t cow has the the fat p r o d u c t i o n T he the for and In ad dition, influences the the lactation, without all the the date of 76 freshening, carded. and fhe calving days excert February, l e n g +h of range was divided interval. age for each 9a each m o n t h which intervals d ay f able of fhe interval was was into from eleven are were counted 300 listed 519 counted days as as 28 days. days to 519 classes. distribution interval beyond of in the ube were 30.5 d e y s The days. n,ach c l a s s records dis­ and following ran^e in Ihis had a 20- the aver­ table: - D i s t r i b u t i o n of R e c o r d s a n d t h e A v e r a g e Eutterfat Production for Different Calving I n t e r v a l s of S a m e L a c t a t i o n Travers e N o . of Intervo1 records Av. P e f o r m a t ory No. of records Av . Ionia Total N o . of W o . of rec o r d s Av . r e c o r d s Av 3CC-31Q 16 112 7 U56 5 168 28 1+37 320-33° 68 121 12 192 16 519 96 6+1+7 32+0-359 96 122 17 l c5 31 529 II 4I+ 1+1+9 360-379 QU 118 96 1+69 90 ^52 200 2*65 0 - ^° ° 67 161 61 911 Ul 562 169 510 6 ■'6-61° 2j C 162 16 903 15 607 131 526 2*20-1+39 13 162 19 161 21 590 63 509 U + C -^ 9 9 22 166 16 5 72 16 573 56 531 20 131 10 530 12 551+ 1+2 1+90 2+6 0 - 1 + 9 9 17 IP l li 512 11 519 1+5 521 900-91° 22 1°1 31 526 2lg 592 77 537 ?ba y i f irf ^ — Distribution of Hscords in Suao 0*lTing Intorvtl ioa Re f ornc-tory n f lo 1 2 3 ^ ^ 6 7 8 9 10 11 1 2 3 4 7 < 6 8 9 10 11 Calving Irxt«rvRl * • C&lTinr 1 — * 2 _ ^ -— 4 --5 --- Interval (da/*) 100-319 320-339 ->U0-3 <9 -poo 1 6 0 -3 7 9 3 8 0 -3 9 9 The three herd* -L75 400—419 7 " - 420-439 8 -- i;A0-469 9 -- 460—479 10 — 480 - 4 9 9 11 — 600-519 -Jc0 I I -125 -100 TU 3 O r o CQ >4 r 50 25 o 25 00 3 U * 6 7 8 9 1 0 1 1 2 3 Calvin*: Interval 4 5 6 7 8 9 10 11 78b yipire 5 - Distribution of Keoords in Prrrioai Calving Interval 1^5 Reformatory Tr*.vrr«g _ ICO d o 75 O flnl Ir-.n n n ** 5 6 7 8 9 10 11 1 2 3 on 0 5 6 7 8 9 10 U Calving Interval • Calving Interval (days) 1 - - 300-319 2 - - 320-339 3 - - 3**0-359 4 --- 360-379 . * --- 380-399 6 -7 — 8— 9 -10 — 11 — UOO-^19 ^20-^39 4^*0—^<9 460-^79 U8O-A99 .rrp :irrd«i ■17'- ■1£0 .1 2 ' '00-519 lioo I *75 0 -**>0 O C J '0 ianiet 001 x n a 1 2 3 ^ 5 6 7 nnn IT 8 9 10 11 Calving Interval 7' ** * 6 7 e 9 10 11 00 79 Table 9b-»- Distribution of Records and tbe Average Putterfat Production for Different Calving Intervals of Next Lactation Traverse No. of Interva1 records Av. Reformatory No. of records Av . Ionia Total No. of N o . of records A v . records A v . 300-319 16 419 7 470 6 507 29 447 320-339 68 419 12 464 16 523 96 440 340-359 99 438 17 478 31 553 143 468 360-379 93 434 56 503 51 540 200 480 260-399 66 4 94 61 494 40 564 169 494 400-4.19 41 444 45 480 45 606 131 512 4 20-439 42 499 19 503 21 560 82 498 440-4 99 23 441 20 523 15 553 58 496 460-479 20 397 10 513 12 567 42 473 480-499 16 4 62 11 457 17 572 44 503 900-919 22 466 31 520 24 591 77 527 As far as the distribution of th e records was concerned, the highest frequency was in the interval of 360-379 days for both Tables 9 a and 9 b, exce rt for the Traverse City herd which had the highest frequency in ti e interval of 3 4 6 399 days. Adding the three herds resulted in the highest concentration of records falling in the interval of 3 6 0 - 3 7 9 days, which is about one full year. By looking at the average butterfat production of each interval, we find a general trend for the longer the interval t^e higher the pro­ duction, although there are some sudden drops in the eo ci:’ferer.t Intervals shew a consistent da;.- I n t e r v a l the total, tut throe herds 'Ives Tlrm a year tc increase the the in of e a c h h e r d . T.efcrms t ory edder.ee interval herd had about frc~ 300 tc herd have 3 CC d a y s , This ruction the may herd the total be one Traverse difference The Tailing herd of and the in the herd than City interval ano failing nulled This less rraverse records factor which City with reformatory their 300-319 in o r d e r . calves less. and °b Ionia in that d o w n the rrc- herd. c c - A n a l y s i s of V a r i a n c e of F f f e c t of ''alvinc I n t e r v a l on f u t t e r f s t T r o d u c t i o n of C a m e Lac ta t i on C e gree of freedom. Total w bum of s quare s 21 -2 ~ l 8 “ ean squares 6 28 810 uW 0075 10 ithin interva1 hefor— a t cry auc having the lQ h of S o u r c e of v a r i anc e .r a v e r s e each recor-ds while 15'" a n d interval. Table its the for to r r o e u c e 35'- of only of tend cows frcT Qa interval c t have some that Tables in p r o d u c t i o n 35*-3 5C da; Table rcth ic t a I 285186 21 6ij630’ 288 19 9382 287 2000^16 -Lw 2 02 078 20208 lb°7U38 6850 Te t w e e n interval 2 .Q ..i t h i n Interval Ior it ic t a 1 277 277 21-722^ 10 Q 7 6 L 7U Q 76T 7 1180771 liUll he t w e e n Interval >.i th I n interval 267 22 .08 81 Table 9d - Analysis of Variance of Effect of Calving Interval on Butterfat Production of the Following Lactation Source of variance F era Traverse T ef orma tory Ton 1a Degree of freedom Sum of squares Total Between Interval Within Interval 503 10 1|93 2388681 192491 2436390 Total between Interval Within Interval 288 10 278 2479784 33174 2426110 Total Between Interval Within Interval 277 10 267 2699844 189344 2B10H10 Mean squares F 13249 3.08*~* 4942 3317 .61 8727 18933 2.01* 9I|02 Table 9e - Analysis of Variance of •.fleet of Calving Interval on Butterfat Froduction for the Three Herds Lac ta t ion In the s a m e interval F o l l o w i n g the last interval Source of variance Degree of freedom 1070 Total 2 Eetween herds 1066 W ithin herds Eetween interval 30 'Within I n t e r v a l 1036 Total Between herds --ithin h e r d s E e tw ee n inter- va 1 Within interval 1070 Sum of square s 93147149 160317 9194232 1466740 76671492 2 1068 106842Q7 2913783 7768909 30 1038 7373910 3949^9 Mean squares 8971 46891 7 I4O6 7273 13167 7103 F 82 Calculations of o o r t i o n ing effect interval on of intra-herd the butterfat variance due production to of the calv­ three herds, ror lactation 0 4- following /rz Ko 0 (interval) the last interval, = 13166.6, where K Q = 31.93 according to f o r m u l a (6 ) = 7103.6 (interval) $ rcr = 18^.86 189.68 - 2.6 " ( i n t e r v a l )_____ (T 2 4. ^ ( i n t e r v a l ) _ lactation same v in 7 2 9 3 •66 the calving interval, 2 3 J4689I, (T 4- K c 0 ( i n t e r v a l ) K 0 3 31*92 where O'1- 7406 X 0"( i n t e r v a l ) = 12Q9.65 i O'( interval ) (T * 4> Cne effect was (T( i n t e r v a l ) rur'ose the of inr tables interval the three : -'-re f o r nr:.; f rc r cut t:e the tables calvin? statistically th r e e if cf 1299.65 8706.65 Qo interval are h i g h l y effect herds on and effect of the their herds cf The and to results next the effect find fat for in the both the o n the the calv- cf e a c h reformatory next lactation calculated be h i g h l y non-significance the production lactation results tc whether shown although interval bince the Q e was total, the -cf significant calving chow 1U.93 or. b u t t e r f a t same r.c r.-2i g.n if ic s n t . three and sirnifleant. above = of significant, the latter A 83 is che small creases, the The tables due sample F value was interval to f i n d The tion. on the tc d i s c o v e r indicate lactation what that calving five quires duction the record Table Qf el'fect fcr the cf P.e f o r m a t o r t ih.r c o m p a r i n g and lactation was former more in than breed the f o r e g o i n g and the the w h i c h was next the on production sam e lacta­ regula­ which re­ pro­ Fe£?istry ) . differences interval, tie left values is 10 m o n t h significant interval the in re­ latter for the calving The affected for was lactation important. of each these the association (Advanced of variance next support period in­ significant. it a f f e c t e d ^reduction tr e b u t t e r f a t ana ll|-.9 give sarrrle compare anoarently levels F value. more is this w i l l herd be to tv e c a l v i n g non-sirnii'icant calving of the effect which the to analysis calf-carryinc gives of tv e t o t a l registration re t w e e n a v e r a g e s the expected Polstein-1riesian a certain size -portion of interval times the the same the Incidentally, t i o n of As be of interval effect an a t t e m p t 2.6"''. may other narrose to c a l v i n g su l t s size. next out can of except lactation because serve any for as two of a the case different intervals. 2. repression Interval vince m o s t ciiferent of intervals of rutterfat tv e a v e r a g e s are Production of b u t t e r f a t significantly on C a l v i n g production different from one for [able 9f - Significant Level of Difference for the Averages of Froduction of Different Calving Intervals Fffect of calving interval on the same lactation Herd t .09 :* ~ ■* ■ ■ cf was to were of p r o d u c t i o n n o n - s i g n i f l e a n t , there reason herd. interval a regression coefficient interval was of in n r o d u c t i o n a c c o r d i n g of c a l v i n g intervals In l e n g t h riot shows interval some was p l o t t e d likelihood of 1 i near-i ty . fhe cient for formula :e formula herd is ( 1j ) on Fage 32. and independent the for each rc-'bined obtained used calculating the r r :r s s i o n route Pv u s i n g dependent the effect represented variable, equation regression according covariance co ffici- rt for- tv e herd difference variable, the wss the represented to method t ’-ree h e r d s eliminated. interval the coeffi­ X, in d a y s , butterfat •-a s the Y, rroduc- 66 ticn. To save tedious calculations, the average of each class for the calving interval was used for all the X values of that class. The calculation of regression coeffi­ cient, b, of butterfat production on same calving interval of Traverse Cit^ herd Is illustrated as follows, and omit­ ted for the other herds. fX *z = 1Q9690 X2 = 1937600 + 4- 9 7 2 2 2 0 0 0 « 77113700 36276922 9 0 0 = 7979966-6 (£X)2 = — n f Y + 7609200 9^9---- 103690100 f X Y rn 6 6 0099120 £ XZY m 07600060 n b = 66099120 77 1 13700 Table 9g - - 67600060 7979966.6 = .36 - C a l c u l a t i o n of t v e C o m b i n e d C o e f f i c i e n t f o r the T h r e e Regression Herds j e g r e e of S u m of. s q u a r e s -curce______________ f r e e d o m _______ x ___________ x y __________ y Total r-e t w e e n h e r d s sit-in herds 1070 2979699 166306 9316760 2 10^139 696661 2609970 1009073 6709179 1066 2670766- 87 Table 9*1 - Observed Regression Coefficient of Butterfat Production on Calving Interval Regression of buttarfat Regression of butterfat production on the same production on the pre­ calving Interval vious calving Interval b2 bl Herd Traverse .38 .16 Reformatory .3 6 •1U Ionia .29 •31 Total •33 .20 Table 9*1 indicates b^ Is larger than t>2 for each herd and t h e i r total, except In the Ionia herd where t>2 is little lar g e r than bp. the T r a v e r s e Reformatory The quantity bi has the largest value f o r Citp herd, and b2 has the lowest value In the herd* h.-rfer ^han b2 • For the total, bp *s about 1 . 7 6 These results times agree with the above analysis of variance. In these herds each additional day In length of calving interval resulted, on the average, in an increase of f-pnroximately one-third of a pci nl of outterfat for that lactation and one-fifth of a pound for the next lactation. Table 9 ^- Indicates all the regressions were highly significant except for the regression of the succeeding lactation of the Reformatory herd, which Is non-significant. The results also agree with the foregoing analysis. 06 Table 91 - Test of Significance of Regression of Futterfat Production on Calving Interval On same calving interval Degree of Sum of freedom s quare s Mean squares Herd Source Traverse Total Due to regression 001+ 2 b 02010 1 109060 109060 Res idual 603 22632 03 14+99 Total Due to re gres s ion 267 2099016 1 96706 96706 hesidual 266 2000606 6996 Total Due to 277 210721+0 1 67066 67086 276 2009609 7071 Total 1071 Due t o regre s s ion 1 93114 71+9 301062 301062 106Q 2009609 8086 Total Due to re gre s s ion 003 2006601 1 30292 30292 Fes idual 002 2 6 03 06Q 0007 Tota 1 268 2679761+ Heforma tory ionia regression Res idual Three herds Res idual On crevious c a 1 vine ir.terval Traverse Peforr.atory Due to re gre s s i on Ionia Ihree herds 1 101+36 101+36 r e s i dua1 207 2L6 i 366 i otal Due to regression 277 2699614+ 1 772b 3 7721+3 Res idual 276 2622601 9002 iGtal L ue t o re gre s s i on Res idual 1070 1 1069 F 1+2.13-*-* 11+. 11*-*- 6 . 9 3-** 1+1.97-*-* 6 . 91+-*-* 1.60 6*^66 8.1 3*-* 10661297 113623 1O07O67U 113623 9 688 11.1+9-*-* 69 Test of Linearity ^.uite a few investigators who studied the effect of the dry reriod or calving interval on milk or tutterfat -produc­ tion concluded that the calving interval had no further ef­ fect when it exceeded a year in length. Moreover, some statistical analysis showed a slight decrease in production if the calving interval was too long. cal ’"oint of view, From the physiologi­ there should net te too much effect from, exceedingly long calving intervals. For these reasons, the writer was quite doubtful whether the relationship betv;een the celvinc interval and tutterfat production was linear. test of linearity has been developed. cr. .he method illustrated by Lindquist (19^0). It is based Ihe results were sinnificsnt for tve effect of calving interval on butterfat "reduction both Lor the sate or the succeeding lactation x&'rle c-i - .est of Linearity of Regression cf Butterfat ireduction on Calving Interval of Same c ta t ion Degree oT Sum of freedom_____ squares -etween intervals 10 v ean s quare s 111 667U0 •ithin interval 7667U92 ue to linear repressicn - (Sxy)2 2.x2 7266 (1009073)2 267076U 90 Table 9j - Continued Degree of freedom Between intervals 10 Due to linear re pres s ion 1 Due to denarture from linearity 9 F = 123873 ' Sum of squares Mean squares II4I4-6 6 7 I1O 351882 111+858 3 1 7 .0 6 -* for 9 and 1 0 5 8 123873 degree of freedom ' Table 9k - Test of Linearity of Regression of Butterfat Production on Calving Interval of Frevious Lactation Degree of freedom Between intervals Within intervals Due to reuression z Sum of scuares 10 39^999 1058 7373510 Sum of s quare s 10 391+999 Due to Linear re m e s s ion 1 113623 Due to denarture from linearity 9 281376 F - 31261i _ 7103 (*xy)2 = ( 5 7 1 i4 0 i; ) 2 = 113623 * x2 2873551 Derree of freedom r-etween intervals M ean squares Mean squares 31261+ for 9 and 1058 degree of freedom M 91 Calculation of Non-1lnear Regression The results of testing of linearity in Tables 9j and Qk show that the regression of butterfat production on calvin« interval denarted significantly from linearity in both cases. Therefore, the a&ta were re-examined and different methods of clotting were tried. The clots made on semi- lom ^arer were closer to a parabola than either non-log­ arithm clotting or oouble logarithm clotting. is shown on Rig. 6 and Fig. 7» The clotting Eased on this clotting, a curvalinear equation was sec up as follows: 92 — v C x 4- d x 2 y ab Ui ,, log y = log a 4 (ex — dx2;iog b log y = log a + c log bx + d lo., bx2 log y * A 4 Bx 4- Cx2 y » 10A‘*"Bx’*‘Cx^ The normal equations are formed as follows, .»a + S i x 4- C £ x 2 = l o g y '.xA 4- Bix*^ 4 0 £;<3 * i x xog y 5 x ^ ^ 4- Bix-* 4 C S x ^ ■ 2x*-log y a s e d on t he n o r m a l e q u a t i o n s , b u t t e r f a t p r o d u c t i o n on t he same U) „ y t2' y the r e ^ r - 3 3 ion e q u a t i o n s f or calvir.g i n t e r v a l were , = iq2. .-'23154 .00121x 4 .^wdGO.^x^ ac t_q2 .61121 4 .eUG79w 4 .oU0GG23x'i The c a l c u l a t i o n s , are l i s t e d - (.111; (IV; oeiow: 1071a 4 9 O 2 0 B 4 1123610 G = 2 ^ . 2 2 7 l 8 94320A 4 H286A00B 4 1618272000C = 25 306.18 11286400A 4 lol8272000B 4 259o36lOGOOOC = j>Oo29235.75 simplify the abo.w; ecuntions as follows, A. 4 88.067226B 4 10533. 1386092 - *..o9.,o23 (1/ A 4 119.6861038 4 17157.2519030 = 2.706809 (2; 4 1/.3.382978B 4 21>003. 7893310 = *..713322 (ji; A .6, - .1; 31.6133320 4 tol9.0632990 = .Oiy/do (l> 93 (3) - (2) 23.696370B ♦ 5851.537423C = .007013 (5) simplify equations (4J and (5), B 4- 20V .3389420 = .00040 6 (.6, b + 246.938135C : .000296 (7) (7) - (6) 37.5991930 = -.000140 C = -.00000372 substitute C in (6>, b - .00077874 = .00C4 j 6 b — .0012147 substitute 0 in { 7 ) B - .OOOV1S61 = .000296 3 = .00012146 substitute 6 ar.i 0 in (lj , A f .1069752 - .0392021 = 2.693023 A — 2.62 325 .tltute b and 0 in (2J, A + .1453-27 - .063825 = 2.706809 A — 2.62525 Jubstitute B and C in (t) A + .1741667 - .0355927 = 2.71^322 A — 2.^2523 _ in2.62525 - .0012lx - .OOOOO^7x2 \ j The calculations are lisa^a below: 1071A f> 942oOB + 112772000 = 2377.22633 94260A + 11277200B + 16161360000 = 254156.41040 11277200A + 1616136000B + 2591950400000 = 30466.70400 Simplify the above eauations as follows, A 4- 8B.01120B -f 10529.59850G = 2.63649 (l; A * 119.63930B -4 17145. 51241C = 2.696^3 (2> A 4- 143• 31004B 4- 22983.988930 = 2.70160 (3) (2 ) - (1 ) 31.62810B 4- 6o15.91j91C = .00934 (4) 23.670743 + 583 '.^76520 = .005-7 (5> (3, - (2) Reduce equations (4J and (5;, B 4- 209.1783 50 = .000311 (6) + .,^6.653740 = .000223 (7J B (7; - (6) 37.275390 = -.000038 0 = -.000 023 -ubstitut-e 0 in (6 , 3 - .00048111 = .000.511 3 = .00079*" 11 -ubstitutee 0 in (7>, B - ,OoO,6730 = .000-.23 3 = .0007903 -ubs.i^ut-- 3 and 0 in (l;, A 4- . J69--2 A = 2. .4121 o i+30 - .0 2 2 1 3 0 7 6 5 5 = -.63649 ub3titute B and C in (2), A f .09451 "■■>470 - .0^94340785 = 2.69633 A = 2.o4i21 ubstitute B and o i.i {3 ), A 4 .1132149316 - .052331745 = -.7CxoO A = ’ 64121 y - i o 2 *6 2 1 2 1 * • ° 0 ° 7 9 x 4 .0000023x2 95a B-uttorffct production O o I— * 3 71,nr* 6 - Sn..i-1,3, rr‘ .-u . .F'-j'tinr of Butt^rfpt Pro^.o*.lor. A^nlntt Son* CU Butterfat production jr ^ 5 s o o Jlfure 7 . S leaves a value of .17- .17 from the repeatability This 17 ner cent, accord­ ing to Lush (19U1), i-s due to three -possible causes: (1) Fermanent differences between the dams caused by environmental peculiarities; (2) Dominance exists; (3) Genes have the effects of complementary, inhibitory or other enistatic interactions with other rrenes. 101 heritability The ly m o s t not resemblance useful include t i o n of interaction by errors by spring and dominance than this fo r former effects. other it however, two is a n d has less correlation daughter parents in m o s t as tend Lush regression pression or n o t is P o p u l a r l y will to herds, of set t.v is the has in the be h i g h e r an of data, the dams and be were not on d a m w a s bias for an unselected among in­ s e l e c t i o n of set considered the be o f t e n b e e n as systematically this re­ interchangeable question may well the is of h e r i ­ dam and been practiced Since it error, estimate would off­ interactions correlation coefficient o f f s p r i n g o n dam, estimating heritability. is m u l t i ­ a higher standard s e l e c t i o n has but w i l l offspring should for if the supposed. to l o w e r ( I 9 I4.O), of that half-sib or r e g r e s s i o n of as Por­ the h e r i t a b i l i t y between daughter although smaller than more on d a m m e t h o d s general the s a m p l i n g includes reliable selection usually raised wh ether for half-sib method estimating heritability cense Generally, the Gome inp maternal resemblance is it a o e s Paternal Therefore, because rrour. dams this a correlation correlation The of in the two. because includes the reason gression by and by the tability. offsnring present. but resemblance. computed on da m lower ror the of serious parent-offspring than that deviations instead are m o r e computed deviations is o f t e n u s e f u l , four and in e s t i m a t i n g h e r i t a b i l i t y dominance resemblance plied between parents of d a t a the best the aou>rdthe the re­ basis 102 The heritability value found in this study for single lactation records was .17. Incidentally, this value Is the same as the .17U recently confuted by Lush. This Is a little less than has teen found in rrevious studies which have more often riven values of around .20 to .30. Lush (1QT|2) retorted the 5^ fiducial limits for his value of .17b were .03 and .31. Therefore, it is very probable that most of the difference between the values reoorted in recent rutlications are the result of sampling variations. Lush (19^1) has pointed out that heritability estimates based on the intra-sire repression method, include only one-fourth of tve two eristatic gene interactions, oneeighth of the three gene Interactions, one-sixteenth of the four gene interactions, ad infinitum. Thus, the 17 ner cent of variance accounted for ty heritability includes not cr:h the trulv additive effects of genes, tut includes also about one-helf of the effects which depended on the inter­ actions of different numbers of sets of renes. That such interactions exist cannot be denied in these cata, since cue-half of the two gene interactions, three-fcurths of the three gene interactions, seven-eighths of the four gens interactions ad infinitum, are included with the dominance deviations and the permanent environmental effects, which all together constitute less than .3^4 - *17 s 17/ of the variance for* single records or .17/. 3U variance in permanent abilities. of the 103 The rate at which the average production of a herd can be increased ty culling lew rrcducing females and replacintr them with the better daughters can be estimated from the exrected regression of daughters toward the herd aver­ age. Ihe regression coefficient is about .085 in these data - a little higher in some of the other studies. snnuai turnover in dairy herds The is around 25 to 30 per cent ci the average number of cows in the herd during the year. Amonc the cows leaving the herd, at least one-third are due to old age, deaths, sterility, chronic disease, and sales which are not actually low rroducers. If one-eighth of the cows which have the lowest records will bediscarded, the heifer calves sired by bulls with the same level of trans- Titting ability would average, for Traverse more for reformatory herd, for Ionia herd, .2q ( 12q ) ( .17 ) - 5«0 rounds duction would of than heifers cows it tutterfat the h e i f e r average. differential. the .2l\ ( 7 3 )( •17 ) = 3-0 City herd, per is verj or he i f e r s * t-ccordin? to Lush hard year wh e n calves S e l e c t i o n of however, .21; (99 ) ( •17 ) * l+.C from the to r e a c h that the sire in c u l l i n g intop r o ­ preceding year can the the are l o w e s t they c o m e raise the selection c o w s and y o u n g ideal, and c u l l i n g in p r o d u c t i o n , or only p'ro- (l^ij 7 )> Butterfat increase = (selection differential)(standard deviation) (heritability) For one-eighth oortion culling, e. g. 87.5^ of animals saved, selection differential equals to .2l(.. lOij. d u c in g ability will a c c o m p l i s h it. average Because of this, the increase per year will be even lower than the above computed figures. Effect of M o nt h of C a l v i ng on Butterfat Pr od u ct io n The results of the effect of month of cal vi n g on butter fat p r o d u c t i o n In this study coincide roughly with most of the findings by other workers. Since there were g e o g r a p h ­ ical differences for different herds or subponulations, cannot expect all to have the same peculia r it y of the results effects. of this study was the high pr o d u c t i o n pe a k in March, However, that, we a besides there was another peak in September which ranked next to March and was significantlv hir h er than anv other m o n t h . the results of two recent Fig. A comparison was made with investigations, and is shown in 10. Since butterfat pro d uc ti o n is closely related to milk ’■■roduction, it would not be unreasonable to compare the m o nth of calving effects on the butterfat p r o d u c t i o n with its affect on milk yield, which was given by W oodward for 12 states and Frick for Connecticut. Figure 10 shows p r o d u c ti o n on rer cent basis for esch of the averages relatively small found by records for different months of calving. The influence of month of calving on milk yield Woodward may have been due to his combining of different states. If climatic differences should 105 cause the association of m o n t h of calving w ith m i l k yields to vary among the different states, a combination of records f ro m several 3tates w o u l d tend to minimize f l u c t u a ­ tion in yields. Although +~his study is fairl close to the results of tne Connecticut data except in July, and the results from C onnecticut data have snown that July is the least the small? favorable month. /jump in July !n the This both the Woodward stu dy gives more evidence that resent study must be due to Particular envir on m en ta l effects in the R e f o r ma t or y herd which apparently c '»mpensat«d for the usual adverse conditions for cows calving in that m^nth. If this set of data sample, then the next Is considered as a fairly rand o m thing is to seek the factors in closing this effect. Obviously, involved the climate which af­ fects t:.e animal directly and Indirectly through the crops are the most volved. there important, First, although o ther factors may be i n ­ for the indirect effect, it is known that is a d^-y s sson usually during July and August In Michigan, and the pastures during this time are less pros- perois than before and durlnr the later growing months. Cows freshening from the middle of May to the middle of June have their h igh producing stage exactly in the hot, lio3t farmers d e e r ases flow. know that to is season Some herds may have some k i n d during this period, but dry season* the cow's milk of temporary pasture generally it cannot be managed well enough to completely make up the gap. Second, it has Percentage of milk or butterfat production about their averages O Hj O 'O J\ M o O H o A ------------------------ ------ H c VfT t, v 106 been established cemoerature. tion, she High and hence fact that that the thyroid temoerature reduces thyroxin decreases the m e t a b o l i c the m i l k secretion has and ( 19U1} ) . Therefore, duction tional for the decrease che lack be during small of the of r & s t u r e balanced by the yet and milk thyroid .Tethtr secretion cycle the importance specially* " e signed bined For is about 11 d e g r e e s .hen one or of The of f r e e d o m , be that does not due to between not Play a role factors, the could p r o d u c t i o n has In the To d e t e r m i n e th e r e to t e s t w h e t h e r Is, the higher production months for was the must of e a c h be a should be com­ equals 29.09. significant. of of cows greater lower production months distribu­ three herd s month, the p a t t e r n number tie that it was h i g h l y follow the the f u n c ­ activity species. result not in Peineke interpretation thyroid light in e a c h m o n t h d i s t r i b u t i o n aces freshening The to is a r e l a t i o n s h i p these been made eq u a l . that the a few records all; func­ in b u t t e r f a t u r c - time m a y butterfat quite by lower production there the at gl a n d . of inspects level the experiment. t e s t has t i o n of f r e s h e n i n g to In a d d i t i o n , b e e n due winter although of thyroid rate. drop have the increase reproduction relative the caused teen dete rmi ned , the been reported this could during cv at lev/ t e r m e r a t u r e . light summer cron is r e l a t e d or t h y r o n r o t e i n a d m i n i s t r a t i o n stimulates Turner activity however, the production freshening and the the should be in the number less. 107 The reason for this unreasonable distribution of freshening in each month may be, (1) farmers1 ignorance of the effect and no control of the renroductIon, (2) an increase In price rer nound of butterfat can balance the decreased production due to freshening In the undesirable season. The distribution of records in each calvinp Interval shows the most records in the class from 3&0-379 days. Since che classification of records for each month is made by noolinp all the records of cows in the month they are freshening, records of the same cow may appear in a cer­ tain month more times than other months . r'or this reason tve month variation may Include a nortlon of the cow’s vari­ ation. In other wcrcs, this may cause a portion of varia­ tion due to month cf freshening. however, its contribution should not be very rreat; hence can be considered un­ important . Fffec t of Calvlnp Interval on Butterfat 1roduc tion What is the ontlmum calving interval? In other words, how long should the calving interval be in order to obtain the maximum life time production? Different authors disa­ gree. Some clai'p one year and others claim more than one year. Since different herds have different circumstances *-:nd different levels of management, a certain calving Inter­ val may be suitable for one herd, but too long or too short for another. 108 There has to d e t e r m i n e been optimum time production. more lactations may be er the cows higher single shorter the life may As neriod even cows shorter is not right 20 d a y s for calving of Prom days and a diminishing 860-U79 day days interval of decreases therefore, interval to take for slowly 380-399 for the dependinn rate, on tiis the the the next with da t a , days tyre and less than ti at of either to d e t e r m i n e it w a s found 10 p o u n d s the ex­ for is less than interval is year peak at a n d I4.8O-I4.99 length there lacta­ 10 p o u n d s the Then, set the every next reaches arbitrarily of m a n a g e m e n t . for the exactly that - lactation one the 3 8 0 3Q 0 d a y the increasing or a b o u t inter­ lactations lactation. although, calving Cn less finally same a i^erds . than to with intervals. Probably increase for da;;s was 380-379 up end be h i g h ­ have lu00-i(.19 d a y o n the interval very more interval and but longer life sinple may have longer be no w a y either, lactation Ul9 with the;; w i l l is cows with commercial there tio n . at for their intervals intervals. in n r o d u c t i o n w a s the s a ^ e cows be u s e d will have nroduction may these cows time interval Increase total can the m a x i m u m intervals calving the tor neriod, production may naner, calving increase time short however, though correct In t h i s longer a longer life with their than design which interval a certain but with find t h e i r treme cows records. live with calving lower other hand, vals satisfactory within records than no production of as interval, the still as the optimum good reason ontimum, 109 Since with a day) was lated gradual calving leveling has off , set of T a b l e interval 9L» been interval the occur larger to 1+00 d a y s Interval as the standard. a set of connated uo Using (1|00-J319 the correction factors and in the listed calcu­ for follow­ table: Table 10a - Conversion for same factors for F a c t o r s ^^ lac c a t i o n For Calving next interval lactation 1.11+ 320-339 1.13 1.10 31+0-389 1.10 360-379 1.08 H 380-309 1. 02 1.02 1+o -I+i q 1 .00 1.00 1-20-1+39 .9P .96 U 14-0 -L4 80 .07 .96 )i60-l.|79 .97 .97 1+60-1+99 .97 .97 800-829 .96 •96 predicted nredicted butterfat bu"terfat nroduction nroduction 0 fU O • o -0 1.21 • 300-319 H Interval (1 of tentatively values calving ing effects of 1+00-1+19 int. o f x d a y s int. 110 Comparing uhis table with the conversion factors Tor ape, times of milking and length of lactation neriod, as listed in Tables 2a and 2b, these factors appear of the same imnortance as the factors for age and times of milking, and more imnortance than the factors for length of lacta­ tion . Summary and Conclusion An analysis of variance of butterfat nroduction records based on records converted to a 305> day lactation, twice a day milking and mature equivalent basis, of tve Traverse fit?/, the Ionia Teformatory and the Ionia Fosnital herds of Michigan has been carried cut. Due to the snecial require­ ments for certain hinds cf analyses and the incompleteness of 3ome records, the same set of records could not be used for each analysis. There were 1+73 daughter-dam pairs for the heritability analysis, 2299 records for the herd com­ parison and reneatabilitj- analysis, l8l? records for month and year effect on Lutterfat nroduction, and 1071 records for the analysis of calving interval effect on butterfat nroduct i on. The nooled estimate of heritability of lifetime butter­ fat nroduction for the three herds was correlation method, .28 by half-sib .27 by intra-sire correlation of dam and daughter method, and . 3 1 by intra-sire regression of Ill daughter on dam method. I'he last one, All are based on life time averages. .3 1 * Is taken as the most accurate value. Comnuted to a single record base, the latter is equal to a heritability value for single records of •1 7 • The herd differences accounted for about 26 per cent of the total variance and cow differences (intra-herd) ac­ counted for 3 I4 ner cent. These variances, of course, include both genetic differences and differences caused by environ­ mental effects. The portion of variance accounted for by intra-herd record differences was about 66 per cent. repeatability estimate was The .3^4 on an intra-herd base. v early differences accounted for about 5 per cent of the variation in butterfat nroduction. value is statistically significant. Though small, this No yearly trend was f ound. T'onth of calving accounted for about 2 o<-.r cent of the total variance. It v/as a significant effect. There was a rather definite pattern for the effect of different months of calving on butterfat production. 7 arch; fhe high peak was in this dropped gradually in the summer, increased in September, and fell again after that until January. The relationship of calving interval and butterfat pro­ duction was non-linear. The effect of calving interval on butterfat production accounted for 1 ^ rer cent of the variance for the same lactation, and 3 per cent for the 112 next lactation. seemed to to both were significant. „be mos t favor-able 1(00 to l|la days Interval as far as a si nrle reo ord v;as concerrieG fable 11a - i crcenta^e of fetal Observed Variance A c c o u n t e d Tor Various Genetic and environmental factors Variance a c c o u n t e d for Fercentape Ferd differences 26 Genetic differences b e t w e e n herds Fnv i ronmen ta 1 differences between Differences 6 22 herds with in hards Cow differences F-ecord differences 76 2^ 69 (within cow variance) - - h n v i r o n m e n t s 1 effects Year of calvinr "onth of c.alvinr ’-reeedin~ calvinf 1 ritci-vsl -resent calvirp Interval ( thers 66 6 2 3 19 62 36 Genetic Dcditively "enetic Dominance and interactions 17 17 --------------------------------------------------------------------------------- 113 The r'ortion of variance accounted Tor by dominance and interactions in the foregoing table includes a small nortion due to permanent environmental neculiarities, and also interaction between heredity and environment. There­ fore, the nortion accounted for by genetic effect actually should be less than 3U eer cent and for the environmental effects should be a little more than 66 ner cent. Since the records used for each kind of analysis are not exactly the same, and because an allowance must be made for sam^linr error, the figures listed in Table 11a can onlv be considered as annroximate estimates. 11U Literature Cited A r n o l d , P. T . D i c k a n d Ce c k e r , h . P. 1939 The ’ ■ f f e e t of S e a s o n of t h e Y e a r a n d A d v a n c i n g l a c ­ t a t i o n ur>on "'ilk Y i e l d of J e r s e v n o w s . J. n a i r v Sci. IP: 6 2 1 - 6 2 P . 1939. n a n n o n , C. Y. 1°39 S e a s o n a l I f f e e t on Y i e l d of D a i r y Soc. A n i m . T r o d . : 6 6 - 7 0 . 1939. ^astle, -st • . 1Q 21 t i n r v>u m b e r of Seres. Cows. Sci. 91) : 9 3 - 9 6 , D i c k e r s o n , 0. m . 191+6 " S t i m a t e s of i r o d u c i n p +.b i l i t y in D a i r y Ap r . r e s e a r c h 61': 961-966. 19/rO. r'z*i o k , Li. , e t al. The H e i s t ion of ticn. J. D a i r y I r o c . Am. 223 • Cattle. J. 196.7 S e a s o n oi' r'restenim/ to T-^ilk Fr-oduco d . 30: 6 2 1 - 6 /4.6 . 196-7 • G-coch, !va j o r i e . 1935 A n A n a l y s i s of the rime i n d i v i d u a l i_ac tat ions. Chan.re in M i l k P r o d u c t i o n J.A y r . Sci. 29: 71-162. in 1Q 35* 0 o v;e n , J . . 1Q 3 9 The i n f l u e n c e of I n h e r i t a n c e a n a Pnv i r o n r r e n t on the TTilk P r o d u c t i o n a n a H u t t e r f a t P e r c e n t s pe of J e r s e y Cattle. J. Ac-r. Hes. L c<: 1433 - 9 6 9 . 1939. P a r m o n d , J. and o s n d e r s , u . S o m e Mac tors I T e c t inc 7/i-llQ. 1^23. 9. 1923 "'ilk Vie la. J. •r r . Sci. 7 oe1 , Iau 1 G . I n t r o d u c t i o n s to mra th ema 1 1 c a l S t a t i s t i c s . •John 11 ley ? cons, inc. 'Hew Y o r k . J ohensiion, Cause Dairy, 1st 13: Edition i., e t a 1 . 1 9 i|6 oi' V a r i a t i o n In TM l k a r-d -utf.erfat v iela of Cows. D a i r y Sc i . /its t r a c t P : 1/+3* 1966 • 1 e i rj, J. .. a no ,,og a w a r d , P. h • 191+3 I n f l u e n c e of L e n p t h of D a y + u l c u i u r o n tr.e ^ u a l i t j of T-‘ilk 1 r o u u c e d in S u h s e a u e n t lac ta t i o n . J. D a i r y Sci. 2 tl : 7 0 9 - 1 3 . l°l! 3 • [ Lnoouist, s. 196 0 S t a t i s t i c a l .analysis in Ivaucat i o n r e s e a r c h . 1st t i o n r ouri t o n *'ifflin C o m p a n y . Dos ton, I 9 /4 O. edi­ 1921. 115 Lush, J. L. I960 I n t r a - s i r e C o r r e l a t i o n s and R e g r e s s i o n s of O f f s p r i n g o n D a m as a M e t h o d of E s t i m a t i n g h e r i t a b i l i t y of Characteristics. P r o c . Am. S o c . A n i m . P r o d . : 2 9 3 3 0 0 . lQ^O ______________ 19U1 c 1 . 3 : 6 39 . 1966 • 116 Sanden, H. G. 1927 The length of t h e Sci. 17: 21-32. The V a r i a t i o n s Year, Service, tion. F a r t I, 1927 . Interval B e t w e e n Calvings. J. Agr. 1927. in ’"ilk Y i e l d s C a u s e d fcy S e a s o n o f t h e Age, and D a y I e r i o d and t h e i r e l i m i n a ­ Season. J. A g r . Sci. 17: 3 3 9 - 3 7 9 . S e a t h , D. M . a n d F e a s h a m , E. W. 198-2 F a c t o r s A f f e c t i n g I r-of its f r o m D a i r y . Sta. P u l . 338. 19U2 . Fer-ds. Sneoec.or, G. v . 19 90 S t a t i s t i c a l Me Ihod. i r e s s. Am.es, Iowa. IowaState i|th E d i t i o n The Id 90 . Turne r , G . w . 1923 S e a s o n V a r i a t i o n s in F i l k a n d D a i r y Sci. 6: 1 9 8 - 2 0 8 * 19 23* Woodward, f. .1. Fat iroduction. Agr. La. College Jr. 1G89 S o m e S t u d i e s of 209-218. 198.9. Lactation hecords. J. Dairy Sci. 28: '.■■/right, S e w a l l . 1921 S y s t e m of v a t i n g . 1. The r i o m e t r i c R e l a t i o n s E e t w e e n P a r e n t and O f f s o r i n g . C c n e t i c 6: 1 1 1 - 1 2 3 * 1921. W y l i e , C. P.. 1P2 9 The E f f e c t of S e a s o n o n t h e T^Ilk a n d F a t J e r s e y Cows. J. ~ a i r y Sci. 8: 1 2 7 - 1 3 1 * Production 1P29. of