A Profit Function for White Leghorn Layer Selection. By R.W. Fairfull, A.J. McAllister I, and R.S. Gowe 2

A Profit Function for White Leghorn Layer Selection By R.W. Fairfull, A.J. McAllister I, and R.S. Gowe 2 Animal Research Centre Agriculture Canada Ottawa, Ontario KIA 0C6 INTRODUCTION Selection index theory introduced the concept of weighting each trait in the index by its economic value (Smith, 1936; Hazel, 1943; Henderson, 1963). The estimation of relative economic weights continues to have many problems even though there has been much research on the general principles of indices and some for specific species. However, there is little published work on deriving economic weights for indices of egg type chickens. Possibly because of the complexities associated with the i0 or more traits of economic importance, the use of 3- and 4-way crosses, the importance of non-additive gene action for egg production, and major maternal and sex-linked effects. Relative economic weights and selection indices were created basically as a linear concept. Wilton et al. (1968) developed quadratic indices and economic objectives and, more recently, Akbar er al. (1986) published an economic model for broilers that included quadratic components. Harris (1970, 1972) suggested the substitution of breeding values into non-linear profit functions as selection criteria for layers. While it is not clear that quadratic models are adequate for all types of non-linearity, their properties are known. The properties of other economic models have not been clearly established. Economic evaluation'in layers has a serious problem that stems from the fact that the ideal bird or the more economical egg layer is quite unique in different parts of the world and it is costly to breed birds for each of these economic niches. Therefore, the profit function may vary in different markets IPresent address: Dept. of Animal Science, 404 W.P. Garrlgus Bldg., University of Kentucky, Lexington, Kentucky 40546-0215, U.S.A. 2Present address: Adjunct Professor, Centre for Genetic Improvement of Livestock, Dept. of Animal and Poultry Science, University of Guelph, Ontario, Canada NIG 2WI 36

around the world and over time. This is clearly illustrated with the different prices and grades in several major markets. Figure i shows egg prices in U.S. dollars for Canada, the U.K., and the U.S.A., all of which sell eggs by grades and these are mainly determined by weight ranges. Each country has a different number of steps and different price relationships among the grades. Also, over time prices change in all markets and from time to time FIGURE i. EGG PRICES IN U.S. DOLLARS 1.0, Canada 0.8.o...o o Do.o o o.,... USA Brown U...........- _..o...._ 0.6... VALUE ;... - USA White $ D. _ ' e 0.4., '--- 0 2 =.-. -_.. _,!, I ------J 50 60 70 EGG WEIGHT (g) the number of steps changes. The price is variably influenced by quality characteristics other than weight (grade). For example, in Canada, shipments 37

of eggs with sample Haugh unit scores lower than 65 are sent to breakers and, therefore, earn a uniform price regardless of weight. In Japan, eggs are sold by weight, but the price per unit weight is higher for a narrow mid-range of egg size. Intrinsic to the economic evaluation process is the problem that assessments are made in the present for a future that holds at least some surprises. Thus, economic objectives should be such that they will result in "progress" for most traits (except those where there is an intermediate optimum) even if this progress will not necessarily be optimal for all situations. There is a great deal of discussion in the literature about economic weights applied to selection programmes in enterprises that are mainly production units (i.e. milk or meat) and the breeding programme is only part of the overall business. This situation applies to many livestock enterprises where the sale of breeding stock is not the greatest source of return. In such cases, many factors come into play that are of little importance in the breeding programme of a major poultry breeder where the sale of breeding stock is the primary source of income and the sale of product is usually a by-product of that programme. The implications of this whole subject have been discussed by Smith et al. (1986). In addition, response from application of a selection index may be difficult to interpret since genetic and economic evaluation are combined. This is a practical consideration, in that, all "users" may not understand the implications of the index applied. It is difficult to understand how a selection program can be properly monitored in such cases and index errors may not be detected.quickly even by competent, experienced geneticists. Economic evaluation is not of secondary importance to genetic evaluation. If either are flawed, the other loses value. Gibson (1989) demonstrated that the method of derivation can have a large effect on relative economic weights, so that, methods and philosophy deserve serious consideration. The above represents some concerns in economic evaluation. It is important to keep them in mind; however, this paper will not address them all. It represents limited steps in a long difficult process. 38

Strictly economic issues are not the only concern in layer evaluation where selection can be based upon a part-record or a correlated character. These must be translated into the expected values of the target characters for global assessment of merit. Thus, there is a prediction component to assessment in layers. At the Animal Research Centre (ARC), we have initiated a comparison of selection methods one of which is the Multiple Trait Culling Levels (MTCL) scheme employed in Bob Gowe's long-term selection project (Falrfull and Gowe, 1990) and the other uses best linear unbiased prediction (BLUP) for genetic evaluation and a profit function for economic evaluation of the quantitative traits (McAllister et al., 1990). It is this latter method, especially the profit function, that forms the basis of the remainder of this discussion. METHODS Overall Evaluarion Breeding values (BV's) are estimated using multiple trait BLUP. The method used is recurslve prediction on a reduced, animal model (Hudson, 1984). The BV's of the seven traits for each selection candidate are substituted in the profit function. The inputs used are actually the BV (a deviation) plus the population mean, so that the results are in the range of actual performance as required for calculation of the profit function. The resulting value represents merit for the traits considered. The central issue of this approach is the idea that the profit function directly assesses relative economic merit. All selected traits are not considered in this manner. We believe that the genetic evaluation of several traits is difficult as adequate methods for assessment are not available. In this group are discontinuous traits, and all-or-none traits and traits that apparently have non-llnear inheritance such as, fertility and hatchability (Gowe and Fairfull, 1982; Gowe, 1983; Frankham, 1990). Table 1 lists the different traits under selection and the method employed to select the traits. Recently, theory has been published that leads to BLUP of all-or-none traits (Gianola and Foulley, 1983; Foulley et al., 1983), but the practical application will require extending the theory to an application level and testing which have not yet been accomplished. Also, for some all-or-none 39

traits, llke general mortality, intense selection is futile as mortality is specific in terms of disease organism and its virulence. If exposure levels or virulence of pathogens change, then previous selection gains may be of little worth in the new environment. For other traits such as fertility, which may have non-linear inheritance, current genetic theory is not adequate. For a discussion see Gowe (1983) and Frankham (1990). Table I. Traits and method of evaluation Selection Trait BLUP Hen-day rate of lay from first egg to 497 days (HDR) with Residual feed consumption (RFC) Profit Egg weight at 340 days (EWT) Function Egg specific gravity at 340 days (SGR) Age at first egg in days (AFE) Mature body weight (BWT) Haugh units at 340 days (HAU) Multivariate Fertility Culling Hatchability Levels Viability - Brooding Rearing Laying Blood spot incidence Egg shape Profi= Function The data used to calculate the functions relating selected traits to target traits were based on data from a long-term selection study (Fairfull and Gowe, 1990), and crosslng (Falrfull e_ al., 1983, 1986) and superimposed (Grunder e_ al., 1989) studies utilizing genotypes from the selection study. The function for Haugh units is not based on data except for the initial point at which penalization begins. This point was chosen, so that, Haugh units would be above 65 (the standard below which lots of eggs cannot be sold as shell eggs in Canada) at the end of lay. The standard of 65 Haugh units is not high even though Haugh units decline with increasing age of the hen. As long as the grading station will accept eggs from a flock, the penalty for producing eggs below the standard is 40

not severe in Canada especially as genotypes from most breeders should be above this standard for much of the first laying cycle. Consumer prejudice against eggs very low in Haugh units would seem to require selection against very low Haugh values_ however, the exact form is perplexing. The profit function shown below is restricted in that it is composed only from the quantitative characters considered (see Table i). There are a number of important assumptions implicit in the construction of this function. Two of the most important are: i) that the breeding program costs are a constant for a fixed set of traits, and 2) that a period of diminishing returns from selection gains has not been reached. Typical values of the functions of specific gravity, egg weight, Haugh units and body weight are shown in appendices. i. Gross profit - (Income Expenses) 2.0 Income - (egg income + spent pullet value) 2.1 Egg income - (expected breakage)(rate of lay)(length of laying period)(adjustment for albumen height) (income for expected grade-out) - (SBvSGR)({BvHDR)([DA ] [BvAFE]})(SBvHAU) (;IBvEWT), where BvSGR - breeding value of egg specific gravity, SBvSGR -- function relating egg specific gravity at 340 days to the expected proportion of intact eggs, - 4.931-0.02046(BvSGR ) 195.739(I/BvSGR), with the restrictions: if BvSGR < 70 (1.070) then (;BvSGR) - 0.702, and if BvSGR340 > 102 (1.102) then (_BvSGR340) - 0.926, BvHDR - breeding value of hen day rate of lay from first egg, DA - disposal age - 497 days of age (whole record length), BvAFE - breeding value of age at first egg in days, BvHAU - breeding value of Haugh units, _BvHAU - function of Haugh units at 340 days whereby under 75.51 Haugh units, the number of eggs is reduced, - 18.81791(BvHAU) 708.311-0.12481(BvHAU) 2, with the restrictions: if BvHAU < 72.57 then (SBvHAU) -- 0.0, and if _vhau > 75.51 then (;BvHAU) - 1.0, BvEWT - breeding value of egg weight, 41

JIsvEWT - function relating egg weight at 340 days to the revenue per egg generated by the expected full year grade distribution at that weight, - 0.113326 + 0.000118264(svEWT ) 2.85977(I/svEWT), with the restrictions: if svewt < 50.0 then (SIBvEWT) -- 0.0620, and if svewt340 > 69.0 then (]'lsvewt) - 0.0801. 2.2 Spent pullet value - (spent pullet weight)(price/unit weight) - (J,vBWT) (F/BWT), where svbwt - breeding value of mature body weight (365 d), ;svbwt - function relating mature body weight to final body weight, - 72. 809 + 0.578(svBWT) P/BWT - price per unit body weight. 3.1 Expenses - cost of feed consumed - (feed for maintenance + feed for egg mass + adult residual feed)(cost per unit of feed) - ({@F/gE}{Egg Number}{S_vEWT } + {[af/gbwt][svbwt] + [svrfc]}{phd}) (C/U) where af/ge - constant for feed per gram of egg lald, Egg Number - ({svhdr){[da] [svafe]}) S_vEWT - function relating egg weight at 340 days to the average egg weight expected over the full year, - 8.610573 + 0.8070588(svEWT), with the restrictions: if svewt < 50.0 then (;_vewt) - 48.96, @F/gBWT - constant for feed per gram of live body weight, svbwt - breeding value of mature (365 day) body weight, svrfc - breeding value of residual feed consumption, PHD - number of days in the laying year - ({DA} - {Housing age})/28, expressed as number of 28 day periods to correspond with ARC's Feed Consumption System), C/U - cost of feed per unit. 42

Comments At the Animal Research Centre, the third generation bred from parents selected using BLUP or MTCL are in the laying house. Table 2 shows means for the 1989 hatch (parents of the third generation). There are no significant interactions to complicate interpretation. There are statistically significant differences between the overall means of strains selected using BLUP or MTCL for age at first egg, hen day rate of lay, body weight, residual feed consumption and egg weight. However, for the most part, the differences are relatively minor although they reflect modest divergence in emphasis resulting from the two methods i.e. MTCL places slightly more emphasis on the rate of lay and BLUP places a little more emphasis on egg weight. Apparently, both methods are headed for a similar, satisfactory destination by slightly different routes. The separation of genetic and economic evaluation may offer no theoretical benefits, but there are practical advantages. Monitoring the selection programme is easier. Each generation, we print the BV's and phenotypic values and visually inspect the printout. This has allowed the identification and rectification of data errors and the establishment of editing procedures to reduce their incidence. Once sound editing procedures are in place, visual inspection is less important, but checking a few high ranking and low ranking individuals plus a few random ones is a sensible precaution. The results of both parts of the process appear to make sense and situations that were apparently illogical have, thus far, resulted from data error. The mathematical processes that make up the profit function can and should be improved. The function relating egg specific gravity to breakage indicence is based upon only one data set and that data set is not ideal. It is possible that the share of the egg weight curve across age of hen is changing with selection, so that, the equations involving egg weight may have to be recalibrated. Also, due to unaccounted for sources of variation, some functions may not predict absolute values adequately for some purposes; however, they should be adequate (more robust) for the prediction of rank. Finally, there is heterosis for several important characters in the profit function including age at first egg, rate of lay, egg weight and body weight. Probably, egg weight is the character where this is the greatest concern as egg weight is an intermediate optimum economically. For this trait, we fitted pure llne egg weight to egg grade distributions of strain crosses, but this may not be the best method to handle this 43

Table 2. Means for three strains I of the 2nd generation test populations (1989 hatch) that were selected using best linear unbiased prediction (BLUP) and the profit function compared with the means for the three strains I selected by multiple trait culling levels (MTCL). Trait BLUP MTCL Fertility, _ 89.7 88.1 Hatchability, _ 75.2 77.7 Brooding mortality, _ 2.6 2.6 Rearing mortality, _ 0.8 1.0 Laying mortality to 497 d 3.8 2.9 Age at first egg, d 144.7 147.2-* Hen housed egg prod'n to 497 d 286 292 ** Hen day rate AFE-497 d 81.9 83.7** Hen day rate AFE-357 d, _ 88.2 89.6** Mature body weight, g 1668 1742 ** Residual feed consumption, g 1087 1058 ** Egg weight at 340 d, g 62.1 60.2** Specific gravity at 340 d 85.6 84.8 Haugh units at 340 d 84.2 83.0 Blood spots at 340 d, % 3.2 2.3 Egg shape at 340 d 3.9 4.0 Egg weight at 450 d 65.4 63.8** Specific gravity at 450 d 82.4 81.5 Profit= 10.57 10.33 IOne strain from each of three genetic bases. 2Calculated using the overall means with constant value. The traits used are outlined in Table I. **P<0.01. 44

problem. In any case, each section of the function should be viewed critically and improved as better ideas or data are advanced. REFERENCES Akbar, M.K., D.L. Harris and C.R. Arboleda. 1986. Development of the relative economic weights for linear and quadratic bloeconomlc objectives in commercial broilers. Poultry Sci. 65:1834-1846. Falrfull, R.W., and R.S. Gowe. 1990. Chapter 29. Egg Production in Chickens. pp. 705-759. In: Poult. Breed. Genet. R.D. Crawford, Editor. Elsevier Science Publishers, Amsterdam. Fairfull, R.W., R.S. Gowe and A.J. Emsley. 1983. Diallel cross of six long-term selected Leghorn strains with emphasis on heterosis and reciprocal effects. Br. Poultry Sci. 24:133-158. Fairfull, R.W., R.S. Gowe and J. Nagai. 1986. Dominance and eplstasis in heterosis of White Leghorn strain crosses. Can. J. Animal Scl. 67:663-680. Frankham, R. 1990. Reproductive fitness and artificial selection. Proc. 4th World Cong. Genet. Appl. Livest. Prod. XIII:238-239. Foulley, J.L., D. Glanola and R. Thompson. 1983. Prediction of genetic merit from data on binary and quantitative varlates with an application to calving difficulty birth weight, and pelvic opening. Genet. Sel. Evol. 15:401-424. Glanola, D., J.L. Fo_lley. 1983. Sire evaluation for ordered categorical data with a threshold model. Genet. Sel. Evol. 15:201-223. Gibson, J.P. 1989. Selection on the major components of milk: Alternative methods of deriving economic weights. J. Dairy Sci. 72:3176-3189. Gowe, R.S. 1983. Lessons from selection studies in poultry for animal breeders. 32nd Ann. Nat. Breed. Roundt., pp. 23-51, St. Louis. Gowe, R.S., and R.W. Fairfull. 1982. Some lessons from selection studies in poultry. Proc. World Cong. Sheep Beef Cattle Breed. 1:261-281. 45

Grunder, A.A., R.M.G. Hamilton, R.W. Fairfull and B.K. Thompson. 1989. Genetic parameters of egg shell quality traits and percent intact eggs between ovlposltlon and grading. Poultry Sci. 68:46-54. Harris, D.L. 1970. Breeding for efficiency in livestock production: Defining the economic objectives. J. Anim. Scl. 30:860-865. Harris, D.L. 1972. Unpublished research. De Kalb AgResearch Inc., De Kalb, Ill. Hazel, L.N. 1943. The genetic basis for constructing selection indices. Genetics 28:476-490. Henderson, C.R. 1963. Selection index and expected genetic advance. pp. 141-163. In: Star. Genet. Plant Breed. W.D. Hanson and H.F. Robinson, Editors. Nat. Acad. Sci., Nat. Res. Council, Washington. Hudson, G.S.F. 1984. Extension of a reduced animal model to recurslve prediction of breeding values. J. Anim. Scl. 59:1164-1175. McAlllster, A.J., R.W. Falrfull and R.S. Gowe. 1990. A preliminary comparison of selection by Multiple Trait Culling Levels and Best Linear Unbiased Prediction. 4th World Cong. Genet. Appl. Livest. Prod. XVI:69-72. Smith, C., J.W. James and E.W. Brascamp. 1986. On the derivation of economic weights in livestock improvement. Anim. Prod. 43:545-551. Smith, H.F. 1936. A dlscriminant function for plant selection. Ann. Eugen. 7:240-250. Wilton, J.W., Evans, D.A., and Van Vleck, L.D. 1986. Selection indices for quadratic models of total merit. Biometrics 24:937-949. 46

APPENDICES Typical Values of Functions ;svsgr340-4.931-0.02046(svsgr ) 195.739(I/svSGR ) - expected proportion of intact eggs svscri 70 [svscr 0.702 74 0.772 78 0.826 82 0.866 86 0.895 90 0.915 94 0.925 98 0.929 102 0,925 170-1.070, 74-1.074, etc. SIsvEWT - 0.113326 + 0.000118264(svEWT ) - 2.85977(I/svEWT) - expected average return per egg in dollars svewt [lsvewt 50.0 $0.0620 54.0 $0.0668 58.0 $0.0709 62.0 $0.0745 64.0 $0.0762 68,0 $0,0793 SsvHAU - 18.81791(svHAU) 708.311-0.12481(svHAU) 2 svhau [BvHAU 75.50 1.000 75.40 0.995 75.00 0.976 74.60 0.917 74.20 0.819 73.80 0.680 73.40 0.502 73.00 0.284 72.60 0.026 72,57 0,004 47

SsvBWT - 72.809 + 0.578(svBWT ) - expected final body weight svbwt [BvBWT 210 194 200 188 190 183 180 177 170 171 160 165 150 160 S2svEWT - 8.610573 + 0.8070588(svEWT ) - expected average egg weight in the full year svewt [_vewt 50.0 48.96 54.0 52.19 58.0 55.42 62.0 58.65 64.0 60.26 68,0 63,49

Question: T. Wing Do your BLUP equations include heritabilities and genetic correlations? Response: R.W. Fairfull We use recursive prediction and an animal model for multiple trait BLUP. Multiple trait BLUP includes genetic variances and covariances similar to a classical selection index so that heritabilities and genetic correlations are considered. Question: J. Arthur Can and should the BLUP index be constructed to select for an intermediate optimum for egg weight? Response: R. W. Fairfull The profit function has an optimum for egg weight at about 69.1 g (a ridge on the response surface). This is probably too high on a practical basis. The profit function may not adequately account for the effects of very large egg size on breakage because of the egg size distribution of the flocks analyzed (few birds in the flock laid eggs in 69-72 g range at 340 days of age). However, the egg flats used for transportation of eggs in Canada are not roomy enough for very large eggs and so very large eggs will probably be exposed to more severe insults than smaller eggs,especially compression along both axes during packing and transport. Also, egg grading equipment is no longer set up to handle very large eggs although the size of the egg that can be handled without severe insult due to size varies with market. We will attempt to determine quantitatively the detrimental effects of very large egg size and consult with grading stations on the maximum size egg their equipment will now handle safely. At present, this function must be viewed as the theoretically optimum egg size given no upper limit on egg size as discussed above. In a practical programme, I would set a limit based on commercial acceptance which history has shown us can be different from the purely economic optimum. 49