Calculating economic weights for sheep sire breeds used in different breeding systems 1

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1 Published December 4, 2014 Calculating economic weights for sheep sire breeds used in different breeding systems 1 M. Wolfová, 2 J. Wolf, and M. Milerski Institute of Animal Science, PO Box 1, CZ Prague Uhříněves, Czech Republic ABSTRACT: The objective of this paper was to adapt gene-flow methodology for the calculation of economic weights (EW) for direct and maternal traits and trait components in sheep and to apply this methodology to the Suffolk breed in the Czech Republic. Computer programs were developed in which annuallambing sheep production systems with purebreeding or partial terminal crossing were simulated. Using these programs, the EW for 12 production and functional traits were estimated for i) Suffolk sires whose sons were used both in purebreeding and in terminal crossing with the 4 dual-purpose breeds, Romanov, Sumavska, Romney, and Merinolandschaf; and ii) Suffolk sires used only for terminal crossing. For case (i), the EW were at first calculated separately for the purebreeding system and for the crossing systems with the 4 dualpurpose breeds in dam position. Compound EW for the general breeding goal for Suffolk were then estimated as weighted averages from the EW in the 5 subsystems. Standardized EW were calculated by multiplying the marginal EW with the genetic SD of the trait, and relative EW were defined as absolute values of the standardized EW expressed as percentage of the sum of the absolute values of the standardized EW over all traits. The 5 most important trait components for Suffolk sires whose sons were used both in purebreeding and in terminal crossing were (relative EW given in parentheses): the direct components of survival rate until weaning (21.0%), daily BW gain until weaning (14.1%), survival rate at birth (14.0%), the maternal component of survival rate until weaning (10.7%), and litter size at lambing (7.6%). There were only small differences between the relative EW calculated for the whole system with pure- and crossbreeding and the relative EW for the purebred system within the Suffolk breed. Therefore, selection of Suffolk rams using a selection index based on the compound EW is expected to be of high efficiency in all of the simulated breeding systems. Only direct traits were relevant for Suffolk sires used only for terminal crossing; the most important (range of relative EW calculated for the 4 crossing systems given in parentheses) were survival rate until weaning (35.2 to 36.5%), daily BW gain until weaning (24.2 to 26.3%), and survival rate at birth (23.7 to 24.8%). Key words: breeding system, direct and maternal trait, economic weight, gene flow, sheep 2011 American Society of Animal Science. All rights reserved. J. Anim. Sci : doi: /jas INTRODUCTION Crossbreeding has an important role in animal production and improves economic efficiency in comparison with purebreeding mainly because of complementarity and heterosis (Afolayan et al., 2009). In the Czech Republic, meat sheep breeds, which constitute 36% of 1 Thanks are due to R. Prošková (Prague Uhříněves, Czech Republic) for excellent technical assistance, to W. D. Hohenboken (Philomath, Oregon) for editing the English of the paper and for valuable comments, and to the Sheep and Goat Breeders Association of the Czech Republic for making the data available. The research was supported by the project MZE of the Ministry for Agriculture of the Czech Republic. 2 Corresponding author: wolfova.marie@vuzv.cz Received June 10, Accepted January 26, the sheep population, are often involved in terminal crossing with dual-purpose breeds to improve growth and meat quality of slaughter lambs. But meat breeds (especially Suffolk) are also kept in commercial flocks as purebred populations. Therefore, for Suffolks or any meat breed under consideration, the economic weights for traits expressed in purebred and crossbred progeny should be combined in a general breeding goal in which transmission of genes from that breed into all involved breeds and populations are taken into account. Furthermore, the delay between the time a selected breeding animal is used for mating and the time an evaluated direct or maternal trait or trait component is expressed in their purebred and crossbred progeny should be considered (Amer et al., 2001). On the other hand, farmers buying rams for terminal crossing are interested only in traits expressed in crossbred slaughter animals. These farmers would pre- 1698

2 fer customized subindices based on economic weights specific to their particular maternal breed in the crossbreeding system. Amer (1999) and Berry et al. (2006) presented equations based on gene-flow methodology (Hill, 1974; Elsen and Mocquot, 1974) for the calculation of the number of discounted gene expressions for several groups of traits and for different animal categories (sires or dams involved in purebreeding or in different types of crossing). Amer (1999) and Berry et al. (2006) obtained weighting coefficients for special indices and subindices to select breeding animals by multiplying economic values of traits expressed in certain animal groups (e.g., slaughter lambs or calves, hoggets or heifers, breeding and culled females) with the numbers of discounted expressions. Wolfová et al. (2005) applied an algorithm for the calculation of coefficients for weighting traits in breeding objectives for beef sires used in various breeding and production systems. The method was based on a matrix which specified the passage of genes between different sex and age groups of animals as introduced by Hill (1974) and applied in a general formula presented by Nitter et al. (1994) primarily for the evaluation of breeding programs. The algorithm can be applied in any breeding system after constructing the appropriate gene transmission matrix for all animal groups involved in the system. The first objective of this study was to adapt the methodology of Wolfová et al. (2005) to sheep breeding. The second objective was to calculate, using the methodology, economic weights for the aggregate genotype of the Czech Suffolk breed, which is used both in purebreeding and in crossbreeding production systems. MATERIALS AND METHODS Animal Care and Use Committee approval was not obtained for this study because the data were obtained from an existing database (database of the Sheep and Goat Breeders Association of the Czech Republic). Definition of Trait Groups For technical reasons it is useful to differentiate 2 groups of traits as done by Nitter et al. (1994) and Wolfová and Nitter (2004). The first group of traits, which will be called direct traits, occur only once in the life of an animal. The following traits were considered to belong to this group: growth rate and survival rate of lambs after weaning, conception rate of female lambs, and carcass traits. The second group of traits, called maternal traits in the following text, can be expressed several times during the lifetime of a ewe, usually in conjunction with an annual reproductive cycle. This group includes conception rate of ewes, litter size traits, milk yield, fat and protein yield or content, somatic cell count, mature BW, wool production, and productive lifetime of ewes. Although mature BW and productive lifetime are Economic weights for sheep sire breeds nonrepeated traits from the biological point of view, they were considered here as repeated traits for the following reasons. In the model used for the calculations, costs and revenues are calculated separately for each reproductive cycle. Therefore, the costs for maintenance occur several times for most of the ewes. The calculation of the economic weight for productive lifetime is based on the survival rates for individual reproductive cycles, so this trait is also based on repeated costs and revenues. Several traits have both a direct and a maternal component. Birth weight, for example, is influenced both by genetic and permanent environmental characteristics of the ewe (maternal component) and by genetic factors of the fetus (direct component). Growth rate until weaning and survival rates at birth and until weaning also belong to the group of traits with both direct and maternal components. Basic Principles of Gene Flow 1699 The differentiation between direct and maternal traits is important for developing gene flow algorithms. Sires used for terminal crossing transmit only direct traits, whereas sires producing female replacements transmit both direct and maternal traits and trait components to the next generations. The number of gene expressions for the 2 groups of traits transmitted by selected parents during certain time periods depends therefore on the breeding system. To take into account the time delay until genetic superiority of the selected parents for a trait is expressed in certain progeny groups in subsequent generations, the gene expressions in all groups and generations have to be discounted to a fixed time (usually to the time the animals were selected as parents of the next generation). The economic value of the expression of a trait or trait component can be calculated on the basis of the flow of genes of a determined age class of sires (or dams) through a population, which in turn can be used to define the times at which genes are expressed, and by knowing the financial impact of that expression and the number of animals involved (Hill, 1974). For this purpose, at any given time t, animals in a population (in the whole breeding system) are divided into several different sex and age classes. A gene flow diagram can then be constructed to follow the movement of genes through the population over time. In our study, time t is given in reproductive cycles (i.e., years as 1 lambing per year is assumed). A vector m k is defined, the elements of which represent the proportion of genes from the selected sex and age class of parents in each sex and age class of progeny. The dimension of the vector is the total number of sex and age classes in the whole breeding system (n). Assume that selection is practiced among animals of sex and age class k. Then, at time t = 0 all elements of m k with the exception of the kth element will be 0 and the kth element of m k will be 1. Let us write m k [t] for m k at time t

3 1700 Wolfová et al. and P for the transmission matrix, which is of dimension n n, and the elements p ij, which are the probabilities that genes from sex and age class j are transmitted to sex and age class i during 1 time unit. Knowing m k [0] (i.e., vector m k at time 0), m k [t] is calculated as (Hill, 1974): [t] k [t 1] 2 k [t 2] t k [0] k m = Pm = P m =... = P m. [1] Matrix P has a block structure: P P... P P P P P =... P P P b b b1 b2 bb where b is the number of blocks per row (column), the total number of blocks being b 2. The blocks are formed by the transmission probabilities between sex and age classes within the same pathway of genes (sires to breed sires, sires to breed dams, dams to breed sires, dams to breed dams, sires to breed slaughter animals, and dams to breed slaughter animals). In crossbreeding systems, these blocks are formed for each breed and certain additional blocks are necessary for combinations of breeds (e.g., sires of breed A to breed crossbred slaughter animals A B). The number of blocks may also be increased by including additional production levels (breeding herds, multiplier herds, commercial herds). Two examples for the structure of matrix P that were used in the calculations of the present study are shown in the Appendix., Calculation of Economic Weights Assume that selection is carried out in sex and age [ 0 class k. For t = 0, the kth element of m ] k is 1 and all remaining elements are 0. For any time t > 0, vector [] t m k is calculated according to Eq. [1]. Then the economic weight (ew rjk ) for trait r within the jth group of traits (j = 1: direct traits or trait components; j = 2: maternal traits or trait components) and for selection group (sex and age class) k is calculated as ew rjk T t = t h ev m [] ( 1 + u), j rj k t = 1 where T is the investment period in time units (in years in our investigation) during which the gene expressions are summarized, u is the discount rate per time unit, h j is a vector that describes the realization of trait group j ( h j is its transpose), ev rj is the vector of marginal economic values for all breeds and breed combinations involved in the considered breeding system for component j (direct or maternal) of trait r, and the symbol indicates the elementwise product. The sum [2] T t m k t = 1 [] ( 1 + u) t represents the vector of the cumulative number of discounted gene expressions from sex and age class k in all sex and age classes of the breeding system after time T. Although the concrete forms of h j and ev rj depend on the breeding system, some general rules apply to the structure of these vectors. For j = 1 (direct traits or trait components), only the elements referring to slaughter animals may be different from 0 in both vectors. For j = 2 (maternal traits or trait components), only the elements referring to sex and age classes of dams may differ from zero. The concrete forms of h j and ev rj for the systems analyzed in this study are given in the Appendix. All marginal economic values of traits, no matter whether manifested on lambs or ewes and whether expressed in purebred or crossbred progeny, must be given per ewe of the appropriate breed. The economic weights calculated from Eq. [2] are per ewe of the corresponding breeding system. The algorithm of Wolfová et al. (2009) with a slight modification was used for calculating marginal economic values. The modification referred to discounting revenues and costs. In Wolfová et al. (2009) costs and revenues were discounted to the birth date for all animal categories. In the present investigation, costs and revenues for all progeny groups were discounted to their birth date as before, whereas discounting for all ewe groups was to the date of lambing. This was appropriate because the time lag between subsequent reproductive cycles (aging of ewes) had already been taken into account in the transmission matrix P. For a better comparison of the economic importance of different traits, standardized and relative economic weights for traits were calculated. The standardized economic weight of trait r (ews rjk ) was calculated as the product of the economic weight and the genetic SD of the trait, where the indices in ews rjk have the same meaning as in Eq. [2]. The relative economic weight of trait r (ewr rjk ) was calculated as proposed by VanRaden (2002): ewr rjk 100% ews = ews rj, The indices in ewr rjk again have the same meaning as in Eq. [2], and ews rjk is the absolute value of ews rjk. Modeled Breeding System with the Czech Suffolk Breed Methods described above were applied to the calculation of economic weights for Suffolk rams in a breeding system with both pure- and crossbreeding as it is practiced in the Czech Republic. Suffolk is the most common meat sheep breed in the Czech Republic, rams of which rjk rjk. [3]

4 Economic weights for sheep sire breeds Table 1. Structure of the population involved in terminal crossing with Suffolk rams 1701 Subsystem Percentage of ewes crossed with Suffolk rams 1 Percentage of Suffolk ewes producing rams for mating 2 Relative population size, 3 % Percentage of ewes in subsystem 4 Crossing systems with Merinolandschaf Romney Sumavska sheep Romanov sheep Purebred system with Suffolk The fraction of replacement females mated with Suffolk rams was assumed to be 20% in all breeds. 2 Rams for mating with ewes of the breed in dam position given in the first column of the table. 3 Percentage of ewes of the breed given in the first column of the table in the whole breeding system (purebreeding and crossbreeding together). 4 These numbers were calculated for maternal breeds as relative population size of Suffolk (35) percentage of Suffolk ewes producing rams for mating in the given maternal breed + relative population size of maternal breed. For the Suffolk breed the value is are used in purebred commercial flocks as well as for terminal crossing mainly with the dual-purpose breeds Romanov, Sumavska, Romney, and Merinolandschaf. While producing Suffolk-sired lambs to meet market requirements for fast-growing, heavily muscled lambs, crossing takes advantage of the reproductive efficiency of the Romanov sheep and of moderate maintenance costs for the remaining 3 breeds used in dam position. Five breeds are involved in the described crossing system (relative population size in percentage of ewes given in parentheses; SCHOK, 2009): Suffolk (35%), Romney (22%), Sumavska (22%), Merinolandschaf (14%), and Romanov (7%). Further details on the structure of the sheep population involved in the crossing system are given in Table 1. The greatest percentage of ewes crossed with Suffolk rams (60%) occurred in the Romanov breed because of its high fertility. An equal percentage of ewe lambs (20%) of all dam breeds was assumed to be crossed with Suffolk rams (not shown in Table 1). Suffolk, Romanov, Romney, and Merinolandschaf are kept in similar, mostly submountain and foothill conditions in extensive and semi-extensive production systems, whereas Sumavska is kept in mountain conditions in an extensive production system. This autochthonous breed is included into the national conservation program for farm animal genetic resources. The basic features of production systems are similar for all breeds. Ewes lamb once a year in late winter or in spring. They are kept outdoors the entire year (Romney) or from spring to autumn (remaining 4 breeds). Lambs are weaned on average at 130 d of age; surplus purebred and all crossbred lambs are slaughtered immediately after weaning and evaluated on the basis of slaughter weight and carcass quality. Replacement female lambs are first bred at 7 to 8 mo of age if they have attained 75% (Sumavka, a late maturing breed) or 67% of ewe mature BW (remaining 4 breeds). The breeding season lasts 50 d on average and is the same for ewe lambs and older ewes. Only natural mating is used. Ewe lambs that do not conceive are mated, at most, in the 2 subsequent breeding seasons. Older ewes failing to lamb also are given at most 2 additional breeding opportunities. The ewe-to-ram ratio is 20:1 for young rams (age about 7 to 8 mo) and 40:1 for older rams. The dates of the main events in the flocks of all breeds are summarized in Table 2. Selected performance variables of ewes, rams, and progeny are shown in Tables 3 and 4 for all breeds. Average values presented in Tables 1 to 4 were calculated from individual records for the years 2005 to 2009, which were made available from the central database of the Sheep and Goat Breeders Association of the Czech Republic. Breed standards were inserted for traits were no individual data were available (mature BW, fleece weight). The structure of the ewe flock of each breed was derived as the stationary state of a Markov chain (for details, see Wolfová et al., 2009). The structure of purebred and crossbred progeny born per reproductive cycle at the stationary state of the ewe flock was determined mainly by the replacement management and marketing strategy for surplus progeny. Nutritional requirements of the flocks were provided mainly from pasture in summer and from hay in winter. Table 2. Dates of the main events in the flocks of involved breeds 1 during each year Event in the flock ML RY SA RV SF Start of the pasture period Apr. 24 Apr. 24 May 7 Apr. 24 Apr. 24 End of the pasture period Nov. 7 Nov. 7 Oct. 31 Nov. 7 Nov. 7 Average lambing date Feb. 22 Apr. 16 Feb 13 Mar. 11 Mar. 30 Average weaning date Jul. 2 Aug. 24 Jun. 23 Jul. 19 Aug. 7 Start of the breeding period Sep. 15 Nov. 7 Sep. 5 Oct. 7 Oct. 15 End of the breeding period Nov. 5 Dec. 27 Oct. 25 Dec. 26 Dec. 3 1 ML = Merinolandschaf; RY = Romney; SA = Sumavska; RV = Romanov sheep; SF = Suffolk.

5 1702 Wolfová et al. Table 3. Average values for selected performance characteristics for ewes and rams of involved breeds 1 Variable ML RY SA RV SF Replacement rate, % Lifetime, 2 yr Lifetime, No. of reproductive cycles Conception rate, % Litter size at lambing per ewe lambing Percentage of lambs stillborn or died within 24 h of age, % Singles Twins Triplets Quadruplets 12.7 Number of weaned lambs per ewe lambing Singles Twins Triplets Quadruplets Total (litter size at weaning) Age of ewes at the first lambing, mo Mature BW of ewes, kg Mature BW of rams, kg Fleece production of ewes, kg/yr Fleece production of rams, kg/yr ML = Merinolandschaf; RY = Romney; SA = Sumavska; RV = Romanov sheep; SF = Suffolk. 2 Lifetime of ewes in years takes into account that not all ewes survive to the end of their last reproductive cycle. 3 Total number of lambs born. Supplemental feeding with mashed oats was used for females in advanced pregnancy, for flushing of female replacement stock and ewes (from 14 d before until 14 d after the start of the breeding period), and for rams from 21 d before the start of breeding through the end of the mating season. For Romanov sheep, oats were provided to lactating ewes and to lambs until weaning because of the greater litter size of this breed. All animals were assumed to be fed to meet their nutrient requirements for maintenance, growth, lactation, gestation, and BW change during flushing and pregnancy. All equations used for the calculation of energy and protein requirements for all categories of animals are given in the manual of the program EWSH2 (Wolf et al., 2010). Feed cost also included provision of minerals and water. Nutrition values of all feeding components are given by Wolfová et al. (2009), the prices for feed and water are presented in Table 5. Zero value for roughage price was applied, as the subsidies decoupled from production (payment of 112 per ha of agricultural land per year and support for less favorable areas of about 120 per ha per year), fully covered the cost for producing roughage, pasture grass, and hay. Benefits from sheep Table 4. Average values of progeny growth characteristics for involved breeds 1 Variable ML RY SA RV SF Daily BW gain of purebred female lambs until weaning, g/d Singles Twins Triplets Quadruplets 179 BW of female lambs at weaning, kg Purebred lambs Crossbred lambs Daily BW gain of purebred male lambs until weaning, g/d Singles Twins Triplets Quadruplets 199 BW of male lambs at weaning, kg Purebred lambs Crossbred lambs ML = Merinolandschaf; RY = Romney; SA = Sumavska; RV = Romanov sheep; SF = Suffolk.

6 Economic weights for sheep sire breeds Table 5. Economic variables (equal for all breeds) used for calculating costs and revenues 1703 Variable, unit Value Price for roughage, /kg 0 Price for mashed oats, /kg 4.00 Price for minerals, /kg 8.00 Price for water, /100 L 0.08 Cost for drugs against endo- and ecto-parasites, Euro cents per kg of BW and per drenching 0.72 Cost for veterinary service and drugs, excluding parasite treatment Rams, per animal and per year 3.00 Lambs until weaning, /animal 0.20 Breeding lambs, per animal and per yr 0.80 Cost for shearing adult animals, per animal and per shearing 1.60 Cost for shearing young animals, per animal and per shearing 1.20 Cost for removing and rendering dead animals, /kg 0.30 Fixed costs per ewe including lambs until weaning, /yr Fixed costs per ram, /yr Cost for labor, /man-hour 6.00 Price for culled adult sheep, /kg of BW 0.80 Fleece price, /kg 0.40 Annual discount rate, % 3.00 Governmental subsidy, per ewe and per yr This value was 20% less for Romney because this breed is kept outdoors the entire year. grazing for supported landscape management and costs of grazing and roughage production are assumed to be equal. Nonfeed costs included veterinary care, labor and fixed costs, costs for shearing, tanning skin, purchasing rams for crossing, and removing and rendering dead animals. Revenues came from weaned slaughter lambs, culled ewes, rams and lambs for replacement, wool, raw and tanned skin, and manure (only in winter when sheep were kept indoors). The main variables for calculating costs and revenues are shown in Tables 5 and 6. These variables roughly represent the economic situation in the Czech Republic in the years 2008 to The investment period for the calculation of the cumulative number of discounted gene expressions (T in Eq. [2]) was set to 20 yr. Four sets of economic weights (one for each crossing subsystem) were calculated for Suffolk rams of age class 1 (i.e., up to 1 yr of age) producing sons used both for purebreeding and for terminal crossbreeding with each of the 4 maternal breeds. A fifth set of economic weights was calculated for a purebred system of the Suffolk breed. The programs EWSH2 (Wolf et al., 2010) and GFSH (Wolf and Wolfová, 2011) of the program package ECOWEIGHT were used for the calculations. Program EWSH2 calculated marginal economic values and program GFSH estimated the economic weights according to Eq. [2]. The forms of transmission matrix P and of the vectors included in the calculations are given in the Appendix for the 4 systems with crossing and the purebred system for Suffolk. The ratios between the number of ewes of the Suffolk breed and the number of ewes in each considered dam breed differed between the subsystems (18:82 for Merinolandschaf and Romney, 16:84 for Sumavska, and 26:74 for the Romanov breed) because of different ratios of purebred vs. crossbred matings among dam breeds (see Table 1). Table 6. Economic and production variables differing among breeds 1 Variable, unit ML RY SA RV SF Purebred lambs Dressing percentage, 2 % Carcass price, 2 /kg Crossbred lambs, sire breed SF Dressing percentage, 2 % Carcass price, 2 /kg No. of shearings per ewe and per year Cost for veterinary service and drugs, excluding parasite treatment for ewes, per animal and per yr Number of man-hours for ewes, /yr Frequency of crossbred lambings, 3 % ML = Merinolandschaf; RY = Romney; SA = Sumavska; RV = Romanov sheep; SF = Suffolk. 2 Weighted average from male and female lambs. 3 Calculated from the percentage of crossbred matings with ewes and female lambs and from conception rates.

7 1704 Wolfová et al. Table 7. Economic weights of traits for Suffolk sires used for purebreeding 1 in each crossing subsystem (in per unit of trait and per ewe in each subsystem) Trait, unit Trait group 2 Economic weights in subsystem with 3 ML RY SA RV SF Birth weight, kg d m Daily BW gain until weaning, g/d d m Daily BW gain in rearing, g/d d Mature BW, kg m Dressing percentage, % d Fleece weight, kg m Conception rate of ewe lambs, % d Conception rate of ewes, % m Litter size at lambing 4 (0.01 lambs) m Survival rate of lambs until 24 h of age, % d m Survival rate of lambs until weaning, % d m Productive lifetime of ewes, yr m Male progeny of these sires were used for purebreeding as well as for terminal crossing. 2 d = direct trait or trait component; m = maternal trait or trait component. 3 ML = Merinolandschaf; RY = Romney; SA = Sumavska; RV = Romanov sheep; SF = Suffolk. 4 Total number of lambs born. The compound economic weights for each trait or trait component to be used in the general breeding goal for the Suffolk breed were calculated as the weighted average of the economic weights for the 5 subsystems (purebred system for Suffolk and 4 crossbred systems of Suffolk with the 4 dam breeds). The fractions of ewes in each subsystem (last column in Table 1) were used as weights. In addition, 4 sets of economic weights were calculated for Suffolk rams of age class 1 used only for crossing with each of the 4 dam breeds. These weights may be applied to the construction of customized selection indices for Suffolk sires used only for terminal crossing. The genetic SD needed for the calculations were provided, as far as available, by the Sheep and Goat Breeders Association of the Czech Republic (unpublished data). Unavailable values were estimated by multiplying the phenotypic SD of the appropriate trait with the median of the heritability estimates for that trait in the review paper of Safari and Fogarty (2003). RESULTS The economic weights of direct and maternal traits and trait components for Suffolk sires are given in Table 7 for all 5 subsystems. The progeny of the Suffolk sires were used both for purebreeding (in all 5 subsystems) and for terminal crossing (in the 4 subsystems with crossing). These economic weights cannot directly be compared between the individual systems because the systems vary in the percentage of crossbred matings. The absolute, standardized, and relative economic weights of traits or trait components for the general breeding goal for Suffolk sires used for purebreeding are presented in Table 8. The absolute economic weights were calculated as the weighted averages from the values in Table 7 as described in the Material and Methods section. These standardized and relative economic weights give the breeders a first approximation of the economic importance of a certain trait or trait component. From this point of view, the most important traits were the direct component for survival rate of lambs until weaning followed by the direct components for daily BW gain until weaning and survival rate of lambs at birth (until 24 h of age). These 3 traits comprised 49% of the sum of standardized economic weights over all traits and trait components. The maternal components of survival rate at birth and until weaning, ewe conception rate, litter size, and dressing percentage were further important traits, adding 7 to 11% each to the sum of all standardized weights. Fleece weight was the least important trait, contributing only 0.15% to the total relative importance. For comparison, the relative economic weights of traits for Suffolk sires used only in the purebred system are given in the last column of Table 8. These values of the relative economic weights were similar to those in the whole system. The same 3 trait components as in the whole system were most important and covered 44% of the sum of standardized economic weights of all traits. The relative importance of all direct traits and trait components was slightly less in the purebred system compared with the whole system (54.0 vs. 59.1%). Only direct traits and trait components are expressed in terminal crossing. The economic weights for Suffolk rams used only for terminal crossing are presented in Table 9. The relative weights of traits were similar among breeds (see Table 10). Survival rate of lambs until weaning had a relative economic importance of

8 Economic weights for sheep sire breeds Table 8. Compound economic weights (absolute, standardized, and relative) for the overall breeding goal of Suffolk sires used for purebreeding 1 in the whole breeding system and relative economic weights for Suffolk sires in the purebred system 2,3, Trait, unit Trait group h 2 σ g Whole system with pure and crossbreeding Purebred system AEW 5 SEW 6 REW 7 REW Birth weight, kg d m Daily BW gain until weaning, g/d d m Daily BW gain in rearing, g/d d Mature BW, kg m Dressing percentage, % d Fleece weight, kg m Conception rate of ewe lambs, % d Conception rate of ewes, % m Litter size at lambing (0.01 lambs) m Survival rate of lambs until 24 h of age, % d m Survival rate of lambs until weaning, % d m Productive lifetime of ewes, yr m Sum for direct traits Sum for maternal traits Total sum Male progeny of these sires were used for purebreeding as well as for terminal crossing. 2 d = direct trait or trait component, m = maternal trait or trait component. 3 h 2 = heritability. 4 σ g = genetic SD. 5 AEW = compound economic weights calculated as a weighted average from the economic weights given in Table 7, in per unit of trait and per ewe in the whole crossing system. 6 SEW = standardized economic weights (AEW genetic SD) in per genetic SD of the trait and per ewe in the whole crossing system. 7 REW = relative economic weights (in %) calculated according to Eq. [3]. 8 Sum of absolute values (without sign). approximately 35% followed by daily gain until weaning and survival rate of lambs at birth, with relative economic weights of about 25% each. DISCUSSION Trait Groups and Calculation of Economic Weights Our one-step approach to calculate cumulative number of discounted expressions (NDE) and economic weights for traits or trait components as presented here can be applied to any group of selected animals (sires, dams) mated to any breed (meat or dairy breed used in sire or dam position) in any integrated breeding system (purebreeding or crossbreeding). Describing the gene flow in the whole breeding system via a transmission matrix that includes all possible pathways for gene transfer among breeds and production levels (nucleus, commercial flocks), the economic weights of traits for any sex and age group of animals involved in the breeding system can be calculated using one general formula (Eq. [2]). Table 9. Economic weights (in per unit of the trait, per ewe of each dam breed and per year) of traits relevant for Suffolk sires used for terminal crossing in the 4 considered production subsystems Breed in dam position 1 Trait, unit ML RY SA RV Birth weight, kg Daily BW gain until weaning, g/d Dressing percentage, % Survival rate of lambs until 24 h of age, % Survival rate of lambs until weaning, % ML = Merinolandschaf, RY = Romney, SA = Sumavska, RV = Romanov sheep.

9 1706 Wolfová et al. Table 10. Relative economic weights (in %) of traits relevant for Suffolk sires used for terminal crossing in the 4 considered production subsystems Breed in dam position 1 Trait ML RY SA RV Birth weight Daily BW gain until weaning Dressing percentage Survival rate of lambs until 24 h of age Survival rate of lambs until weaning ML = Merinolandschaf; RY = Romney; SA = Sumavska; RV = Romanov sheep. The approach applied in our investigation reduces the relatively large number of equations constructed for the calculation of NDE by Amer (1999), Amer et al. (2001), or Berry et al. (2006), which, although applying similar principles, split the sheep or integrated cattle populations into many separate pathways. That was necessary because the aforementioned authors distinguished among 5 or 6 groups of traits for which the NDE were calculated, assuming that the marginal economic values of those traits were expressed per animal of 1 of the following 6 categories: progeny at birth, progeny at slaughter, yearlings, replacement females, culled breeding females, and breeding females surviving to the next reproductive cycle. Differently from Amer (1999), Amer et al. (2001), and Berry et al. (2006), marginal economic values of all traits expressed in all animal categories in the present study were given per ewe in the population under consideration and per year. The numbers of animals expressing a certain trait and the time lag (starting from birth of progeny or from parturition in ewes) until the trait influenced revenues and costs were already taken into account when calculating marginal economic values (see Wolfová et al., 2009). As a consequence, the NDE of a trait for the whole investment period was split into a first part taking into account first generation descendents and a second part considering maturation of female replacement as well as the time lag among subsequent generations. Using this procedure, only 2 groups of traits must be differentiated, direct traits expressed in lambs once during their life and maternal traits expressed repeatedly by ewes in each reproductive cycle. Furthermore, differential impacts of changing the level of the same trait on different breeds or production levels were taken into account. Nevertheless, the resulting economic weights calculated either according to the approach of the aforementioned authors or according to our methodology should be the same when expressing economic weights on the same basis. Similar approaches for the calculation of NDE as in our study were used by Nitter et al. (1994) when evaluating breeding schemes, by Jiang et al. (1999) for broiler breeding programs, and by Wolfová et al. (2005) for the definition of the breeding objectives for beef cattle in different production systems. In many breeding programs of different livestock species, breeding values are estimated both for the additive genetic effect (direct effect) and the maternal effect of several traits. Therefore, when constructing selection indices, economic weights are needed for both the direct and the maternal components of such traits. The procedure presented in our investigation makes it possible to calculate these economic weights. However, care must be taken on what traits are deemed to be maternal. In mixed linear models used for genetic evaluation, the direct genetic effect is defined as additive genetic effect of the genes of the animal under consideration (i.e., as the effect of the genes transmitted from its sire and its dam). Often 2 distinct maternal effects are defined: the additive genetic ability of the dam to provide a suitable environment for expression of the trait of interest, which is called a maternal genetic effect, and the permanent maternal environmental effect of the dam, which may also contain nonadditive genetic effects of the dam (Mrode, 2005). Therefore, maternal traits may have a different meaning in the working definition for the present investigation and in the theory of mixed models. This must be taken into account when constructing selection indices. For example, milk production traits were considered to be maternal traits when calculating the economic weights, whereas they are usually treated as direct traits when estimating breeding values. On the other hand, the direct and maternal components of lamb growth rates are identical with direct and maternal effects on growth estimated in genetic evaluation. Economic Weights of Traits for Suffolk Sires in Different Breeding Systems The crossbreeding system practiced in the Czech Republic for sheep and presented in our example is somewhat atypical. Though Suffolk sires are used for terminal crossing with dual-purpose and prolific sheep breeds, there are also many purebred commercial Suffolk flocks because this breed is the most widespread in the Czech Republic. Therefore, crossbred slaughter progeny account for less than one-half of the total progeny of Suffolk rams with the consequence that the majority of Suffolk gene expressions occur in purebred

10 Economic weights for sheep sire breeds 1707 animals. This explains the small differences in the relative importance of direct and maternal traits or trait components between the purebred system and the crossbred systems. However, in a classical crossbreeding system where the ewes of the sire breed constitute only a minor part of all ewes in the system, direct traits and trait components will become much more important than the maternal traits in the breeding objective for the sire breed (Přibyl et al., 1999). To demonstrate this, a trial calculation was carried out (results not shown here) where all variables except the relative breed size were the same as given in the Materials and Methods section. In that crossbreeding system in which only 1.5% of ewes were Suffolk, 92% of the sum of the relative economic weights for Suffolk sires was for direct traits and 8% for maternal. The relative economic weights for Suffolk rams used for terminal crossing with different maternal breeds did not differ markedly despite the differences between those maternal breeds in productive and reproductive traits. The compound economic weights that can be used for the construction of a whole-breed selection index are affected rather by the ratio of the purebred Suffolk population to the individual maternal breeds than by the performance of maternal breeds. The comparison of the values of the economic weights calculated in the present investigation with values from the literature is very difficult because of differences in the definition of traits, models, production systems, breeds, and economic and marketing conditions. Nevertheless, similar results are found in the literature at least in certain respects. Among growth traits, daily BW gain until weaning (or weaning weight) generally had the greatest economic importance independent of the breed and the intensity of the production system (Kosgey et al., 2003; Conington et al., 2004), whereas the economic weight for mature weight was mostly negative under nonlimiting feed resources (Conington et al., 2004; Morais and Madalena, 2006). The negative economic weight of mature weight in our calculation was caused not only by the increased feed requirement for growth and maintenance for heavier adult ewes and rams but also by increased costs for prolonged rearing of replacements as the fraction of replacements mated at an early age (7 to 8 mo) decreased with increased mature weight (see description of mating management in the Materials and Methods section). On the other hand, keeping the mature weight constant and increasing daily BW gain in rearing of breeding animals increased the proportion of replacements mated at an early age and caused decreased rearing costs resulting in a positive economic weight of daily BW gain in rearing. In our investigation, the economic weight of birth weight was small, but positive. The positive effect of increased birth weight (holding daily BW gain and survival rate of lambs constant) on profit reflected the positive difference between the greater lamb market value (heavier lambs) and greater feed requirement for lamb maintenance. A possibly negative effect of greater birth weight on lambing difficulty could not be included because information about lambing performance was not available. Effects of birth weight on lamb survival were not considered because lamb survival was explicitly in the model as a further trait. Haghdoost et al. (2008) estimated a negative economic value for birth weight that was caused by including only changes in feed costs while keeping weaning weight constant. Within the functional traits, litter size was estimated to be of increased economic importance, but its economic value was variable among populations and production systems and was dependent on the level of the trait (Amer et al., 1999; Conington et al., 2004). In agreement with our results, Fuerst-Waltl and Baumung (2009) found that survival rate of lambs was more important than litter size. The greater relative importance of survival rates in our study could be caused by the inclusion of the costs for removing and rendering dead animals which are relatively high in the Czech Republic ( 0.30/kg). However, it should be noted that the lamb survival rates are already fairly high in the Czech sheep populations, so that there is some potential for shortterm improvement, but less potential for long-term genetic improvement, which would result in changes of economic weights over time. Other than Australia, New Zealand, and the United States (Borg et al., 2007), wool traits are of low importance in European countries (Conington et al., 2006; Krupová et al., 2009), which was also confirmed in our investigation. Therefore, these traits are often ignored in breeding goals. Productive lifetime of ewes was rarely evaluated in the literature, and the economic weight of this trait varies from a negative value estimated in dairy sheep by Fuerst-Waltl and Baumung (2009) to the greatest value within the set of evaluated traits (Conington et al., 2006). We estimated an intermediate value (3% of the total economic importance). Although the developed software (Wolf et al., 2010; Wolf and Wolfová, 2011) allowed for the calculation of economic weights for carcass quality traits, they could not be included in the analyses because there was not sufficient information on the distribution of carcass fleshiness and fat covering scores for the breeds and crosses under consideration. However, it was possible to consider price differences between purebred and crossbred animals. In the recent Czech sheep breeding program, the EBV for growth rate of lambs until 100 d of age (for the direct and maternal components), for litter size at birth, and in some breeds, for ultrasonic measures of fleshiness and fat covering are available. Performance data on all traits evaluated in our study except for mature BW are available in the central database of the Sheep and Goat Breeders Association so that the

11 1708 Wolfová et al. calculation of EBV may be realized in the near future. Then a selection index (total merit index) can be constructed using the estimated economic weights. If breeders decide not to explicitly include some economically important traits (e.g., lamb survival rate, growth rate in rearing, mature BW) the economic weights for the selected traits have to be reevaluated (e.g., as shown by Dempfle and Ponzoni, 1986) to take into account correlated changes in the excluded traits. Conclusions The method presented and illustrated in this study for the calculation of economic weights for direct and maternal traits is of general importance and may be applied to a great variety of breeding programs in sheep. The computer programs used for the calculations, including their source codes and detailed manuals, are freely available on ecoweight&site=genetikaslechteni_en. In the present situation in the Czech Republic, the relative economic importance of traits in breeding objectives for the Suffolk breed did not differ substantially between purebreeding and crossbreeding systems. Therefore, selection of Suffolk rams with a selection index based on the compound economic weights is expected to be of high efficiency in all breeding systems. LITERATURE CITED Afolayan, R. A., N. M. Fogarty, J. E. Morgan, G. M. Gaunt, L. J. Cummins, A. R. Gilmour, and S. Nielsen Genetic analysis of milk production and composition in crossbred ewes from different maternal genotypes. Anim. Prod. Sci. 49: Amer, P. R Economic accounting of numbers of expressions and delays in sheep genetic improvement. N. Z. J. Agric. Res. 42: Amer, P. R., J. C. McEwan, K. G. Dodds, and G. H. Davis Economic values for ewe prolificacy and lamb survival in New Zealand sheep. Livest. Prod. Sci. 58: Amer, P. R., G. Simm, M. G. Keane, M. G. Diskin, and B. W. 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