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Economic weights for sow productivity traits in nucleus pig populations
Livestock Science 99 (2006) 69 – 77 www.elsevier.com/locate/livsci
Economic weights for sow productivity traits in nucleus pig populations V.M. Quinton a,*, J.W. Wilton a, J.A. Robinson a, P.K. Mathur b a
Centre for Genetic Improvement of Livestock, University of Guelph, Ontario, Canada b Canadian Centre for Swine Improvement, Ottawa, Ontario, Canada
Received 19 November 2003; received in revised form 1 June 2005; accepted 9 June 2005
Abstract Economic values or weights measure the net economic gain per unit genetic increase of a given trait. These were derived for sow productivity traits for use as weighting factors in a dam line selection index used by purebred or nucleus dam line breeders. The profit function approach was used in order to provide flexibility to alternative production systems, market requirements or population trait levels. The approach accounted for constraints on perinatal survival rate imposed by larger birth litter sizes. The effect of accounting for these constraints was to reduce the economic value of birth litter size as the population average increased; without this, the economic weight for litter size was constant. Weights for the other traits were not affected. Economic weights were calculated for both the 100 kg finished pig and the 25 kg feeder pig market, and for a range of average birth litter sizes, with constant values for all other traits, using average market conditions, prices and costs in Canada as an example. The relative importance of litter size for the finished pig market decreased from 64% of the total breeding value when average litter size was 8 pigs to 29% when average litter size was 20 pigs, whereas that of perinatal survival increased from 17% to 42%, and that of survival to weaning increased from 7% to 18%. The relative importance of litter size for the feeder pig market also decreased from 45% to 15% as average litter size increased from 8 to 20 pigs, whereas that of piglet weaning weight increased from 22% to 41%, that of perinatal survival increased from 12% to 22% and that of survival to weaning increased from 5% to 9%. The relative importance of age at puberty and weaning to conception interval were both less than 8% of the total in both markets at all litter sizes. These results show that economic weights for litter size designed for populations with relatively small litter sizes should be reduced when the average litter size becomes large and more emphasis should be placed on other traits, particularly perinatal survival. D 2005 Elsevier B.V. All rights reserved. Keywords: Sow productivity; Economic weight; Profit function; Selection index; Pig breeding
1. Introduction * Corresponding author. E-mail address: [email protected] (V.M. Quinton). 0301-6226/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.livsci.2005.06.002
Pigs are selected for breeding based on the estimated economic worth of their offspring, usually
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calculated as a function of the predicted breeding values of economically relevant traits and economic weighting factors. Wilton et al. (2002) distinguished between selection indices appropriate for breeders at the nucleus level, which are linear (Goddard, 1993), and those used at the commercial level, which may be non-linear, in order to account for factors such as heterosis and non-linear price grids. Smith et al. (1983) and Wolfova et al. (2001) found that economic weights also depended on the type of crossbreeding system, the breeding role of the stock, the management system, and the criteria of economic efficiency used in the production system. National or regional selection indices for purebred breeding stock are based on the average market requirements and a typical production system. Many purebred breeders, however, supply commercial buyers who are producing pigs for defined markets. In some cases, breeding herds are closed for periods of time, and within-herd trait averages may differ substantially from national or regional ones. Recommendations based on national or regional averages are useful as a starting point in identifying which traits should be considered for recording, evaluation and/or a selection index. However, whenever possible, economic weights appropriate to the particular production system and market supplied should be used instead. Economic returns can be predicted by a system of equations, known as a bio-economic simulation model, which is a function of phenotypic traits and management variables contributing to revenue and/or costs, as was described for pork production in Tess et al. (1983). The economic weight of a heritable trait is calculated from the change in predicted profit, based on a single unit change in that trait, holding all other traits constant. The bio-economic model can be written in a single equation, known as a profit function, in some cases. In this case, the economic weights can be calculated directly from the partial derivatives evaluated at the relevant population mean (Moav and Hill, 1966). Relationships among traits with economic impact may be more complex than can be described by genetic and/or environmental correlations. Smith et al. (1983) noted that a change in a single trait might cause changes in the expression of other traits without changing their breeding values. McMillan and Quinton (2002) and De Greef et al. (2001) suggested the
phenotype might be subject to a genotype by environment interaction, in which the phenotypic expression of one trait depends on that of another, i.e. the dinternal environmentT of the animal. Bourdon (1998) suggested that complex interactions among traits are difficult to describe by means of a linear, or even nonlinear, profit function. Proportionately fewer pigs survive from large litters, probably due to limited nutrient supply, space, etc., for the piglets and the resulting increase in the proportion of small pigs, and other factors, rather than low genetic levels of the sow’s mothering ability and her piglets’ vitality. Lecour (2000) found the number of piglets born alive decreased at an increasing rate as the total litter size at birth increased. This type of effect cannot be described in terms of genetic or environmental correlations between the traits. In this case, profit cannot be expressed equivalently in terms of genotypic rather than phenotypic values. The objective of this paper was to develop a flexible method of calculating economic weights for sow productivity traits which would account for the effect of the phenotype of litter size in pigs on the expression of perinatal survival due to crowding and other factors by including trait dependency in the profit function approach.
2. Materials and methods 2.1. Derivation of the profit function. This study focused on the contribution of sow productivity traits to total revenue, so predictions of total revenue were based on litter traits alone. Income was estimated from litter size, survival, and market price minus costs associated with rearing progeny from weaning to market. Production costs for the litter depend on fixed breeding costs and costs over the number of days required to house and feed the gilt or sow in order to produce the litter. Net profit was expressed by the single equation T = Revenue Cost, where T ¼lswc T is the net profit derived from the sale of market pigs contributed by one sow from a single commercial litter. The revenue per litter, l s w is based on
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the surviving litter size, where l is the total litter size at birth, including stillborn, but excluding mummified piglets, s is the proportion of the litter surviving to weaning, and w is the net revenue from the sale of a market pig, after accounting for costs from weaning to market. The cost of producing an average commercial litter is represented by c. T is expressed here on the basis of a single litter, but the relative economic weights are equivalent to profit expressed, for example, per kilogram of product, under certain assumptions (Goddard, 1998). Survival was considered over two distinct time periods, s = ps sw, where ps = ps(l) represents the perinatal survival rate, from shortly before birth to the end of the neo-natal period, and was assumed to depend on constraints imposed by the total litter size at birth, l. Survival from the end of the neo-natal period to weaning, sw, was considered here to be determined by the maternal ability of the sow to raise a litter until weaning, rather than the viability of the piglets. As with all sow productivity traits, survival rates are a combination of direct and maternal effects. These were not separated here, and all sow productivity traits were assumed to be those of the sow. There is currently no published research on modelling the relationship between birth litter size and perinatal survival rate at constant genetic levels. In this paper, empirical estimates of the effect were obtained from a quadratic model fit to litter survival rate within sire and dam of sow in Canadian Yorkshire and Landrace pigs. Revenue and costs from weaning to market, w, depend on the target market. w ¼ market weight price per kg days to market cost per day where days represents the number of days required for the pig to reach market weight (based on growth rate) and the cost per day represents the daily cost of feed and maintenance. In this study, survival after weaning was considered to depend only on management practices, and is considered in the calculation of the costs from weaning to market. Either market weight or days to market could be considered constant since the resulting economic weights are equivalent, assuming optimised management (Wilton and Goddard, 1996).
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Two versions of the profit function were considered. The first was based on the 100 kg finished pig market. For this market, both weight and days, and therefore w, were considered constant in this study, representing revenue minus rearing costs of the average commercial pig from weaning to sale. The second version of the profit function was based on the feeder pig market. Weaned pigs can be sold in this market at any time until they reach approximately 25 kg, but assuming an integrated market system, prices minus rearing costs are equivalent throughout the period. Post-weaning growth of the litter was considered as a sow productivity trait for this market, since there is evidence of a positive association between both litter and average piglet weight at weaning and early post weaning growth (Roehe, 1999). Therefore, w was considered as variable, and for practical purposes, days to final market was considered constant and sale weight variable in this formulation, since prices are recorded for fixed weights. The sale weight of an individual pig sold at the age when the average pig weight corresponds to recorded prices was predicted from its weaning weight as follows, PP mw ¼ m þ rg ðww ww Þ
where m is the average weight of a pig at market, ww is the average weight of a piglet at weaning, adjusted P to 21 days, and ww is the population average piglet weight at weaning. For the example given below, average pig weight was 25 kg at 50 days, and the regression of weight at 50 days on weaning weight, r g, was estimated for the Canadian market to be 1.3 by Kennedy (1994). The cost of production of the average litter a sow produces over her lifetime is given by c ¼ c1 þ
1 ðt 1Þ cg þ fg ap z1 þ t t
ðcs þ fs iwcÞ z2 where c 1 is the cost of breeding plus the cost of sow feed and services during lactation, c g and c s are feed and service costs during gestation for a gilt and sow, respectively, f g and f s represent daily feed and service costs until breeding for a gilt and from weaning to rebreeding for a sow respectively, ap is the age at first conception (puberty), and iwc is the interval from weaning to conception. z 1 and z 2 are weighting factors
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according to the sizes of the first and subsequent litters relative to the average, and t is the total number of litters produced by a commercial sow in her lifetime. The weighting factors are based on t, and the size of the first litter is 92% of that of later litters. The net profit per litter sold is 1 T ¼ l psðl Þ sw w c1 þ cg þ fg ap t ð t 1Þ ðcs þ fs iwcÞ z2 z1 þ t Partial derivatives of this profit function, taken with respect to each trait, are given below. The economic weight for each trait was then calculated from the partial derivative with respect to that trait, evaluated at the appropriate commercial population mean. For the example, all means were based on Yorkshire field data, in which the first oestrus date and conception dates were not recorded. The dates of the last service before farrowing were used instead. Perinatal survival rate was calculated from the total number born, including stillborns but not mummified pigs, and the number of piglets alive 24 h after birth. Survival to weaning was calculated from the number alive after the last transfer event, and the number alive at weaning. General costs and revenues were obtained from Bancroft (2001), except that feed and service costs relating to the sow were obtained from NSIF (2001), and converted to Canadian currency.
perinatal survival rate was estimated from an analysis of data recorded in Yorkshire and Landrace herds registered on the Ontario Swine Improvement sow productivity program. The model accounted for the sire and dam of the sow, the effect of contemporary groups as defined by province, herd and season of farrowing, parity of the sow, type of litter (pure or crossbred) and the linear and quadratic effect of total litter size at birth. @T @psðl Þ j ¼ psðl Þ sw w þ l sw w j @l @l ¯ P ¼ sw w sv þ a þ 2bl þ 3cl¯2 The economic weight requires the appropriate population mean piglet viability unconstrained by litter size at birth, s v, which is not observed. In theory, the appropriate value would be that of survival at the smallest litter size observed. However, the observed survival rate was actually lower for small litters in the Ontario data. This may be due to unrelated health problems in sows producing these litters. Therefore, the estimate of mean piglet viability unconstrained by litter size at birth was taken from the predicted maximum value of survival over all litter sizes. Survival to weaning, sw: @T ¯ P ¼ l ps w ¼ l ps w @sw Age at first conception (puberty), ap:
2.2. Partial derivatives Perinatal survival, ps: @T ¯ P ¼ l sw w ¼ l sw w @ps Litter size at birth, l: The effect of constraints imposed by litter size at birth on perinatal survival for a particular litter was approximated by a quadratic equation in litter size psðl Þ ¼ sv þ a þ bl þ cl 2 where s v represents the expected phenotypic value of viability when survival is not constrained by litter size, and a, b and c are parameters of a quadratic equation in litter size. The relationship between total litter size at birth and the phenotypic expression of
@T 1 ¼ f g z1 @ap t Weaning to conception interval, iwc: @T ð t 1Þ f s z2 ¼ @iwc t Average piglet weight at weaning (feeder pig market), w: @T ¼ p l ps sw rg @w P P ¼ p l¯ ps sw rg where p is the market price per kg of a feeder pig, and r g is the regression of market weight on weaning weight.
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3. Results 3.1. Calculation of net profit and economic values As an example, the net profit from an average litter was calculated using average Canadian trait means, prices and cost estimates. For this population, the ratio of first to later parity litter size is 0.92, and a commercial sow produces t = 4 litters during her lifetime, so the litter size of second and subsequent parity litters, z, as a proportion of average litter size, l, is given by solving 1 ð0:92 zÞ þ t 1 z ¼ l t t z ¼ l=0:98
Table 2 Economic weights, as calculated from partial derivatives of the net profit function, for finished pig (100 kg) and feeder pig (25 kg) markets Market
Trait
Finished pig Litter size ($/pig) Per. surv. ($/%) Surv. wn. ($/%) Age pub. ($/day) Int. wn. con. ($/day) Feeder pig Litter size ($/pig) Per. surv. ($/%) Surv. wn. ($/%) Age pub. ($/day) Int. wn. con. ($/day) Pig wn. wt. ($/kg)
8 pigs 12 pigs 16 pigs 20 pigs 30.7 2.7 2.6 0.23 0.71 16.2 1.4 1.4 0.23 0.71 22.6
27.6 4.0 3.9 0.23 0.71 14.5 2.1 2.1 0.23 0.71 33.8
22.0 5.3 5.2 0.23 0.71 11.6 2.8 2.8 0.23 0.71 45.1
13.9 6.7 6.6 0.23 0.71 7.3 3.5 3.4 0.23 0.71 56.4
Per. surv.: adjusted % perinatal survival; Surv. wn.: % survival to weaning; Age pub.: age at puberty (days); Int. wn. con.: interval from weaning to conception (days); Pig wn. wt.: piglet weight at weaning (kg).
Then net profit is 0:98 T ¼ l psðl Þ sw w 103:4 þ 4 :92 3 0:98 ð102:365 þ 0:9 apÞ þ 4 ð107:752 þ 0:94 iwcÞ which, under the assumption of zero profit, is assumed to be equal to normal returns or expenses for that population. The economic weight for litter size requires the average population survival rate to weaning, revenue minus costs from weaning to market, unconstrained perinatal survival rate, P sv, and the linear and quadratic coefficients of the function ps(l) = s v + a + bl + cl 2. The linear and quadratic coefficients were estimated from the litters of purebred sows in herds registered on the sow productivity program offered by Ontario Swine Improvement (Table 1). Both linear and quadratic effects were statistically significant ( P b 0.0001) for the Yorkshire and Landrace breeds, and survival rates
Table 1 Estimates of linear and quadratic regression coefficients for perinatal survival rate on litter size at birth
Linear Quadratic
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Yorkshire
Landrace
0.01243 0.00080
0.00929 0.00071
decreased at an increasing rate as birth litter size increased for litters with 7 or more piglets. Survival rates were smaller for litters with fewer than seven piglets born, possibly due to unrelated health problems of the sow. Therefore the unconstrained survival rate was defined as that occurring at the litter size with predicted maximum survival rate, which occurs for the Yorkshire population at litter size L ¼ b=ð2 cÞ ffi 7:5 and a is the adjustment to litter size at the maximum a ¼ 0:0124 L 0:0008 L2 ¼ 0:048 The average population perinatal survival rate, adjusted to the predicted unconstrained survival rate occurring at 7.5 piglets, was calculated from the mean of adj s1 ¼ s1 a bl cl 2 For each litter, adjusted perinatal survival rate was predicted from the deviation of the observed from the expected survival rate based on the litter size, for litters with more than seven piglets, and directly from the observed rate otherwise. Economic values, based on the trait means and costs and revenues appropriate for an average Yorkshire breeding herd in Canada, are shown in Table 2
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for commercial mean litter sizes of 8, 12, 16 and 20 piglets in both markets. Mean unconstrained perinatal mortality rate, mortality to weaning, age at puberty and weaning to conception interval were assumed constant as litter size increased. The absolute economic values for age at puberty and weaning to conception interval were not affected by the population averages of the other traits since the profit function was linear in these traits, and were therefore the same in both markets. Economic values for litter size decreased, and those for the survival traits and piglet weight at weaning increased as average population litter size increased. The economic values for litter size and the survival traits were smaller in the feeder pig than in the finished pig market, but were proportionately the same. If the interaction between perinatal survival rate and litter size was ignored, the economic value of an extra pig born per litter would be 30.57 per pig in the finished pig market, and 16.07 in the feeder pig market for all values of the population mean litter size. Economic weights for the other traits would not be affected, providing all other population parameters remained constant. 3.2. Standardised economic values Breeders registered on the Ontario Swine Improvement Sow Productivity program record all the traits described above. Selection indices are calculated from genetic evaluations which are based on genetic and environmental (co)variances, and these were estimated from data from the example population using a REML procedure. The distributions of the survival traits and weaning to conception interval were skewed, and therefore the estimates, and corresponding evaluations, are expressed on a transformed scale, as follows: Adjusted perinatal survival (s v), % Survival to weaning (sw), % Interval weaning to conception (iwc), days
Ln (100 s v + 1) (log mortality) Ln (100 sw + 1) (log mortality) Ln (iwc) / 0.1823–3.8275, iwc z 6 (Ten Napel et al., 1995)
where s v was calculated from the recorded value for perinatal survival, using the equation given previous-
ly. The economic values derived above apply to a single unit change of each trait on the untransformed scale. The economic weights of a single unit change on a transformed scale, which are required to construct a selection index, were calculated by dividing the economic weight by the rate of change of the transformed value on the original value, evaluated at the population mean. For the example,
Rate of change, Divisor dt(x) / dx Adjusted perinatal 1 / (100 x + 1) 0.1059 survival, % Survival to weaning, 1 / (100 x + 1) 0.1297 % Interval weaning to 1 / (0.1823x) 0.3047 conception, days
All economic values are defined at given commercial population current means, as appropriate for nonlinear profit functions. The heritability for each trait, and genetic correlation and genetic standard deviation estimates on the transformed scale are given in Table 3, for the example from the Ontario Yorkshire breed. The unfavourable genetic correlation between adjusted perinatal survival and litter size was much smaller than previous estimates have found between unadjusted perinatal survival and litter size, although heritability estimates were similar. As a result, breeders might expect greater response in the index as a result of selection. The standardised economic values for each trait, expressed in $ per genetic standard deviation unit on the transformed scale, are given in Table 4 for commercial mean litter sizes of 8, 12, 16 and 20 piglets for each market. These values measure the importance of each trait in the total breeding value. The relative importance of each trait can be assessed from its standardised economic value expressed as a proportion of the sum (sign removed) of all the standardised economic values (Wolfova et al., 2001). When the population average was 8 pigs born per litter, the standardised economic weight of litter size was $30.3, which is 64% of the total, $47.2, in the finished pig market, and $15.9, as compared with a total of $35.2 in the
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Table 3 Genetic standard deviations, heritabilities (diagonal) and genetic correlations among sow productivity traits for Ontario Yorkshire pigs
Genetic std. dev. Age pub. Litter size Per. mort. Mort. wean. Wean.–con. Wean. wt.
Age at puberty
Litter size
Perinatal mortality
Mortality to weaning
Interval weaning–conception
Piglet weaning weight
13.02 0.097
0.99 0.297 0.102
0.32 0.050 0.181 0.059
0.16 0.187 0.263 0.447 0.018
1.13 0.315 0.075 0.040 0.206 0.049
0.35 0.052 0.199 0.079 0.368 0.130 0.107
Litter size: total number of pigs born; Perinatal mortality: 100 adjusted %perinatal survival; log scale; Mortality to weaning: 100 %survival to weaning; log scale; Age at puberty: days; Interval weaning–conception: days; transformed scale, Ten Napel et al. (1995); Piglet weaning weight: (kg).
feeder pig market. Therefore, litter size dominated the index in both markets for populations of Yorkshire pigs with an average of 8 pigs born per litter, having a relative importance of 64% in the finished pig, and 45% in the feeder pig market. For populations with an average of 12 or more pigs born per litter, the relative importance of average piglet weight at weaning was 29% or greater in the feeder pig market, and for populations with an average of 16 pigs born, the relative importance of perinatal survival was 32% or more in the finished pig, and 19% or more in the feeder pig market, whereas that of litter size was 43% or less and 25% or less in the finished and feeder pig markets, respectively.
Table 4 Standardised economic values, expressed in $ per genetic standard deviation Market
Trait
Finished pig market Litter size Per. surv. Surv. wn. Age pub. Int. wn. con. Feeder pig market Litter size Per. surv. Surv. wn. Age pub. Int. wn. con. Pig wn. wt.
8 pigs 12 pigs 16 pigs 20 pigs 30.3 8.1 3.3 2.9 2.6 15.9 4.3 1.7 2.9 2.6 7.8
27.3 12.1 5.0 2.9 2.6 14.3 6.4 2.6 2.9 2.6 11.8
21.7 16.2 6.6 2.9 2.6 11.4 8.5 3.5 2.9 2.6 15.7
13.7 20.2 8.3 2.9 2.6 7.2 10.6 4.4 2.9 2.6 19.6
Litter size: total number of pigs born; Per. surv.: adjusted %perinatal survival; log scale; Surv. wn.: %survival to weaning; log scale; Age. pub.: age at puberty (days); Int. wn. con.: interval weaning to conception (days); transformed scale, Ten Napel et al. (1995); Pig wn. wt.: pig weight at weaning (kg).
4. Discussion The profit functions given in this paper are simple, and do not attempt to model all of the complexities of swine production. Although such difficulties could be addressed, to a greater extent, with a more complex bio-economic simulation model, the advantage of using the profit function approach is the relative ease with which economic weights can be recalculated for different market objectives, production systems and sub-population, or herd averages. This type of flexibility may be important in a dynamic market, not only for individual breeders, but also from a regional perspective. In addition, the variation in trait profiles across sub-populations will be less likely to be reduced over time, which could help maintain the genetic diversity of the population. Previous estimates of economic values for sow productivity traits, discussed by Rydhmer (2000), are shown expressed as a percentage of live litter size in Table 5. These weights base selection on the composite trait, live litter size at birth, rather than on both total birth litter size and perinatal survival rate. This approach does not result in the optimum weighting of selection emphasis on component traits, (Bennett and Leymaster, 1989; Johnson et al., 1984), although, as noted by Bennett and Leymaster (1989), the optimum weights depend on the assumed model as well as the population averages of the component traits. Current estimates of economic weights for a commercial litter size of 12 pigs are also shown in Table 5, expressed as a percentage of total litter size. These estimates are quite similar to the ones given by others, at least for the finished pig market. However, the current estimated
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Table 5 Relative economic values for sow productivity traits per unit of trait, expressed as a percent of the economic value for litter size, including current estimates Kennedy (1994) NSIF (2001) De Vries (1989) Anderson and Palmo (1998) Current estimatesa Litter size (live pigs born) 100% Litter size (total pigs born) Litter birth wt. (kg) Perinatal survival (%) Survival to weaning (%) Pig weaning weight (kg) Litter weaning weight (kg) 6.8 Litter size at weaning (pigs) Piglet growth rate (g/day) Age at puberty (days) Age at 1st farrowing (days) 1.94 Interval weaning to conception (days) Oestrus return (%) Farrowing interval (days) 5.54 a b c
100%
100%
100% 100%
7.26 12.36
13.26
1.31 1.01
1.66
14.5 14.2 233.
8.14 44.44 .81b; 1.5c 2.6b; 4.8c
3.6 5.21
Current estimates of economic weights are given for a commercial litter size of 12 pigs. Value for finished pig market. Value for feeder pig market.
weight for piglet weaning weight in the feeder pig market was over twice those implied by weights for litter weaning weight given by others. The feeder pig market was not considered directly in the other studies, and it is difficult to compare the results. In addition, market prices for feeder pigs in Canada have been unstable recently, and the price used in the example is quite possibly inflated. Note that the economic weight for piglet weaning weight was a multiple of feeder pig price per kg. The weights given in Table 2 were based on the Canadian production system and market averages, and would be appropriate for dam line selection in an average herd in Canada. Breeders with herd averages differing substantially from national ones may prefer to recalculate the economic weights based on commercial stock bred from their own herd, particularly if the herd is closed. Those supplying stock for specific crossbred production systems should also use trait averages from commercial stock bred from their herd. Smith et al. (1983) suggest that in a 2-breed system, piglets from purebred sows with limited milk supply mated to boars with high growth potential show decreased survival rates and reduced growth, when compared to offspring from crossbred sows in a 3-breed system. Breeders supplying commercial buyers with specific management practices should also use specific cost and revenue estimates rather
than national averages. For example, an increasing number of producers use early weaning management systems, and sell their pigs to growers at much younger ages, rather than 25 kg. Breeders on the national swine improvement program in Canada would normally base selection within dam lines on a dam line index which combines the sow productivity index with a sire line index, rather than on sow productivity traits alone. Since most Canadian market pigs are crosses between a terminal sire line boar and a female from a either a dam line or F1 cross between two dam lines, the Canadian Centre for Swine Improvement publishes a dam line index calculated as a weighted sum of a sow productivity and a sire line index, with the sow productivity index receiving twice the weight of the sire line index. This form of the dam line index assumes the economic values for traits of the finished market pig, such as growth rate, feed conversion and carcass traits, are independent of those for sow productivity traits. This is a reasonable approximation for many independent breeders but may not be appropriate for a fully integrated system. It is evident from the results that population average litter size has considerable impact on the optimal weighting used for traits used in selection indices for dam lines of pigs. Many breeding programs have been very successful in increasing litter size, with the result
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that the economic weights previously used for selection may now be suboptimal. Breeders such as these should consider reducing the emphasis placed on litter size in their selection criteria, and increasing that placed on perinatal survival, and, depending on their target market, piglet weight at weaning. Breeders with herds producing litters with fewer than 10 pigs should continue to place most emphasis on litter size. Flexibility is therefore required in deciding appropriate selection goals.
References Anderson, S., Palmo, H., 1998. Landsudvalget for svin. Danske slagterier, Copenhagen, Denmark. Bancroft, J., 2001. Swine Enterprise Budgets—January 2001. Ontario Ministry of Agriculture and Food, Ontario, Canada. Bennett, G.L., Leymaster, K.A., 1989. Genetic implications of a simulation model of litter size in swine based on ovulation rate. Potential embryonic viability and uterine capacity: II. Simulated selection. J. Anim. Sci. 68 (4), 980 – 986. Bourdon, R.M., 1998. Shortcomings of current genetic evaluation systems. J. Anim. Sci. 76, 2308 – 2323. De Greef, K.H., Janss, L.L.G., Vereijken, A.L.J., Pit, R., Gerritsen, C.L.M., 2001. Disease-induced variability of genetic correlations: ascites in broilers as a case study. J. Anim. Sci. 79, 1723 – 1733. De Vries, A.G., 1989. A model to estimate economic values of traits in pig breeding. Livest. Prod. Sci. 21, 49 – 66. Goddard, M.E., 1993. Selection indices for non-linear profit functions. Theor. Appl. Genet. 64, 339 – 344. Goddard, M.E., 1998. Consensus and debate in the definition of breeding objectives. J. Dairy Sci. 81 (Suppl. 2), 6 – 18. Johnson, R.K., Zimmerman, D.R., Kittock, R.J., 1984. Selection for components of reproduction in swine. Livest. Prod. Sci. 11, 541 – 558. Kennedy, B.W., 1994. Report to Agriculture Canada on Services and Development Contract for Ontario Livestock Improvement Programs. Phase 1-Swine.
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Lecour, C., 2000. How to improve prolificacy and hyperprolificacy in French data. NSIF conference proceedings. http:// www.nsif.com. McMillan, I., Quinton, V.M., 2002. Selection strategies for limiting the increase in ascites while increasing growth in broilers. Poultry Sci. 81, 737 – 744. Moav, R., Hill, W.G., 1966. Specialised sire and dam lines: IV. Selection within lines. Anim. Prod. 8, 390 – 395. NSIF, 2001. National Swine Improvement Federation: Guidelines for Uniform Swine Improvement Programs: Appendix E: Selection Indexes. Roehe, R., 1999. Genetic determination of individual birth weight and its association with sow productivity traits using Bayesian analysis. J. Anim. Sci. 77, 330 – 343. Rydhmer, L., 2000. Genetics of sow reproduction, including puberty, oestrus, pregnancy, farrowing and lactation. Livest. Prod. Sci. 66, 1 – 12. Smith, C., Dickerson, G.E., Tess, M.W., Bennett, G.L., 1983. Expected relative responses to selection for alternative measures of life cycle economic efficiency of pork production. J. Anim. Breed. Genet. 56, 1306 – 1314. Ten Napel, J., De Vries, A.G., Buiting, G.A.J., Luiting, P., Merkes, J.W.M., Brascamp, E.W., 1995. Genetics of the interval from weaning to oestrus in first-litter sows: distribution of data, direct response of selection, and heritability. J. Anim. Sci. 73, 2193 – 2203. Tess, M.W., Bennett, G.L., Dickerson, G.E., 1983. Simulation of genetic changes on life cycle efficiency of pork production: 1. A bioeconomic model. J. Anim. Sci. 56, 336 – 353. Wilton, J.W., Goddard, M.E., 1996. Selection for carcass and feedlot traits considering alternative slaughter endpoints and optimised management. J. Anim. Sci. 74, 37 – 45. Wilton, J.W., Devitt, C.J.B., Miller, S.P., 2002. Sensitivity of rankings of beef sires for non-linear multiple trait breeding objectives. 7th World Congress on Genetics Applied to livestock production, Aug. 19–23, Montpelier, France. Wolfova, M., Nitter, G., Wolf, J., Fiedler, J., 2001. Impact of crossing system on relative economic weights of traits in purebred pig production. J. Anim. Breed. Genet. 118, 389 – 402.
Economic weights for sow productivity traits in nucleus pig populations V.M. Quinton a,*, J.W. Wilton a, J.A. Robinson a, P.K. Mathur b a
Centre for Genetic Improvement of Livestock, University of Guelph, Ontario, Canada b Canadian Centre for Swine Improvement, Ottawa, Ontario, Canada
Received 19 November 2003; received in revised form 1 June 2005; accepted 9 June 2005
Abstract Economic values or weights measure the net economic gain per unit genetic increase of a given trait. These were derived for sow productivity traits for use as weighting factors in a dam line selection index used by purebred or nucleus dam line breeders. The profit function approach was used in order to provide flexibility to alternative production systems, market requirements or population trait levels. The approach accounted for constraints on perinatal survival rate imposed by larger birth litter sizes. The effect of accounting for these constraints was to reduce the economic value of birth litter size as the population average increased; without this, the economic weight for litter size was constant. Weights for the other traits were not affected. Economic weights were calculated for both the 100 kg finished pig and the 25 kg feeder pig market, and for a range of average birth litter sizes, with constant values for all other traits, using average market conditions, prices and costs in Canada as an example. The relative importance of litter size for the finished pig market decreased from 64% of the total breeding value when average litter size was 8 pigs to 29% when average litter size was 20 pigs, whereas that of perinatal survival increased from 17% to 42%, and that of survival to weaning increased from 7% to 18%. The relative importance of litter size for the feeder pig market also decreased from 45% to 15% as average litter size increased from 8 to 20 pigs, whereas that of piglet weaning weight increased from 22% to 41%, that of perinatal survival increased from 12% to 22% and that of survival to weaning increased from 5% to 9%. The relative importance of age at puberty and weaning to conception interval were both less than 8% of the total in both markets at all litter sizes. These results show that economic weights for litter size designed for populations with relatively small litter sizes should be reduced when the average litter size becomes large and more emphasis should be placed on other traits, particularly perinatal survival. D 2005 Elsevier B.V. All rights reserved. Keywords: Sow productivity; Economic weight; Profit function; Selection index; Pig breeding
1. Introduction * Corresponding author. E-mail address: [email protected] (V.M. Quinton). 0301-6226/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.livsci.2005.06.002
Pigs are selected for breeding based on the estimated economic worth of their offspring, usually
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calculated as a function of the predicted breeding values of economically relevant traits and economic weighting factors. Wilton et al. (2002) distinguished between selection indices appropriate for breeders at the nucleus level, which are linear (Goddard, 1993), and those used at the commercial level, which may be non-linear, in order to account for factors such as heterosis and non-linear price grids. Smith et al. (1983) and Wolfova et al. (2001) found that economic weights also depended on the type of crossbreeding system, the breeding role of the stock, the management system, and the criteria of economic efficiency used in the production system. National or regional selection indices for purebred breeding stock are based on the average market requirements and a typical production system. Many purebred breeders, however, supply commercial buyers who are producing pigs for defined markets. In some cases, breeding herds are closed for periods of time, and within-herd trait averages may differ substantially from national or regional ones. Recommendations based on national or regional averages are useful as a starting point in identifying which traits should be considered for recording, evaluation and/or a selection index. However, whenever possible, economic weights appropriate to the particular production system and market supplied should be used instead. Economic returns can be predicted by a system of equations, known as a bio-economic simulation model, which is a function of phenotypic traits and management variables contributing to revenue and/or costs, as was described for pork production in Tess et al. (1983). The economic weight of a heritable trait is calculated from the change in predicted profit, based on a single unit change in that trait, holding all other traits constant. The bio-economic model can be written in a single equation, known as a profit function, in some cases. In this case, the economic weights can be calculated directly from the partial derivatives evaluated at the relevant population mean (Moav and Hill, 1966). Relationships among traits with economic impact may be more complex than can be described by genetic and/or environmental correlations. Smith et al. (1983) noted that a change in a single trait might cause changes in the expression of other traits without changing their breeding values. McMillan and Quinton (2002) and De Greef et al. (2001) suggested the
phenotype might be subject to a genotype by environment interaction, in which the phenotypic expression of one trait depends on that of another, i.e. the dinternal environmentT of the animal. Bourdon (1998) suggested that complex interactions among traits are difficult to describe by means of a linear, or even nonlinear, profit function. Proportionately fewer pigs survive from large litters, probably due to limited nutrient supply, space, etc., for the piglets and the resulting increase in the proportion of small pigs, and other factors, rather than low genetic levels of the sow’s mothering ability and her piglets’ vitality. Lecour (2000) found the number of piglets born alive decreased at an increasing rate as the total litter size at birth increased. This type of effect cannot be described in terms of genetic or environmental correlations between the traits. In this case, profit cannot be expressed equivalently in terms of genotypic rather than phenotypic values. The objective of this paper was to develop a flexible method of calculating economic weights for sow productivity traits which would account for the effect of the phenotype of litter size in pigs on the expression of perinatal survival due to crowding and other factors by including trait dependency in the profit function approach.
2. Materials and methods 2.1. Derivation of the profit function. This study focused on the contribution of sow productivity traits to total revenue, so predictions of total revenue were based on litter traits alone. Income was estimated from litter size, survival, and market price minus costs associated with rearing progeny from weaning to market. Production costs for the litter depend on fixed breeding costs and costs over the number of days required to house and feed the gilt or sow in order to produce the litter. Net profit was expressed by the single equation T = Revenue Cost, where T ¼lswc T is the net profit derived from the sale of market pigs contributed by one sow from a single commercial litter. The revenue per litter, l s w is based on
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the surviving litter size, where l is the total litter size at birth, including stillborn, but excluding mummified piglets, s is the proportion of the litter surviving to weaning, and w is the net revenue from the sale of a market pig, after accounting for costs from weaning to market. The cost of producing an average commercial litter is represented by c. T is expressed here on the basis of a single litter, but the relative economic weights are equivalent to profit expressed, for example, per kilogram of product, under certain assumptions (Goddard, 1998). Survival was considered over two distinct time periods, s = ps sw, where ps = ps(l) represents the perinatal survival rate, from shortly before birth to the end of the neo-natal period, and was assumed to depend on constraints imposed by the total litter size at birth, l. Survival from the end of the neo-natal period to weaning, sw, was considered here to be determined by the maternal ability of the sow to raise a litter until weaning, rather than the viability of the piglets. As with all sow productivity traits, survival rates are a combination of direct and maternal effects. These were not separated here, and all sow productivity traits were assumed to be those of the sow. There is currently no published research on modelling the relationship between birth litter size and perinatal survival rate at constant genetic levels. In this paper, empirical estimates of the effect were obtained from a quadratic model fit to litter survival rate within sire and dam of sow in Canadian Yorkshire and Landrace pigs. Revenue and costs from weaning to market, w, depend on the target market. w ¼ market weight price per kg days to market cost per day where days represents the number of days required for the pig to reach market weight (based on growth rate) and the cost per day represents the daily cost of feed and maintenance. In this study, survival after weaning was considered to depend only on management practices, and is considered in the calculation of the costs from weaning to market. Either market weight or days to market could be considered constant since the resulting economic weights are equivalent, assuming optimised management (Wilton and Goddard, 1996).
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Two versions of the profit function were considered. The first was based on the 100 kg finished pig market. For this market, both weight and days, and therefore w, were considered constant in this study, representing revenue minus rearing costs of the average commercial pig from weaning to sale. The second version of the profit function was based on the feeder pig market. Weaned pigs can be sold in this market at any time until they reach approximately 25 kg, but assuming an integrated market system, prices minus rearing costs are equivalent throughout the period. Post-weaning growth of the litter was considered as a sow productivity trait for this market, since there is evidence of a positive association between both litter and average piglet weight at weaning and early post weaning growth (Roehe, 1999). Therefore, w was considered as variable, and for practical purposes, days to final market was considered constant and sale weight variable in this formulation, since prices are recorded for fixed weights. The sale weight of an individual pig sold at the age when the average pig weight corresponds to recorded prices was predicted from its weaning weight as follows, PP mw ¼ m þ rg ðww ww Þ
where m is the average weight of a pig at market, ww is the average weight of a piglet at weaning, adjusted P to 21 days, and ww is the population average piglet weight at weaning. For the example given below, average pig weight was 25 kg at 50 days, and the regression of weight at 50 days on weaning weight, r g, was estimated for the Canadian market to be 1.3 by Kennedy (1994). The cost of production of the average litter a sow produces over her lifetime is given by c ¼ c1 þ
1 ðt 1Þ cg þ fg ap z1 þ t t
ðcs þ fs iwcÞ z2 where c 1 is the cost of breeding plus the cost of sow feed and services during lactation, c g and c s are feed and service costs during gestation for a gilt and sow, respectively, f g and f s represent daily feed and service costs until breeding for a gilt and from weaning to rebreeding for a sow respectively, ap is the age at first conception (puberty), and iwc is the interval from weaning to conception. z 1 and z 2 are weighting factors
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according to the sizes of the first and subsequent litters relative to the average, and t is the total number of litters produced by a commercial sow in her lifetime. The weighting factors are based on t, and the size of the first litter is 92% of that of later litters. The net profit per litter sold is 1 T ¼ l psðl Þ sw w c1 þ cg þ fg ap t ð t 1Þ ðcs þ fs iwcÞ z2 z1 þ t Partial derivatives of this profit function, taken with respect to each trait, are given below. The economic weight for each trait was then calculated from the partial derivative with respect to that trait, evaluated at the appropriate commercial population mean. For the example, all means were based on Yorkshire field data, in which the first oestrus date and conception dates were not recorded. The dates of the last service before farrowing were used instead. Perinatal survival rate was calculated from the total number born, including stillborns but not mummified pigs, and the number of piglets alive 24 h after birth. Survival to weaning was calculated from the number alive after the last transfer event, and the number alive at weaning. General costs and revenues were obtained from Bancroft (2001), except that feed and service costs relating to the sow were obtained from NSIF (2001), and converted to Canadian currency.
perinatal survival rate was estimated from an analysis of data recorded in Yorkshire and Landrace herds registered on the Ontario Swine Improvement sow productivity program. The model accounted for the sire and dam of the sow, the effect of contemporary groups as defined by province, herd and season of farrowing, parity of the sow, type of litter (pure or crossbred) and the linear and quadratic effect of total litter size at birth. @T @psðl Þ j ¼ psðl Þ sw w þ l sw w j @l @l ¯ P ¼ sw w sv þ a þ 2bl þ 3cl¯2 The economic weight requires the appropriate population mean piglet viability unconstrained by litter size at birth, s v, which is not observed. In theory, the appropriate value would be that of survival at the smallest litter size observed. However, the observed survival rate was actually lower for small litters in the Ontario data. This may be due to unrelated health problems in sows producing these litters. Therefore, the estimate of mean piglet viability unconstrained by litter size at birth was taken from the predicted maximum value of survival over all litter sizes. Survival to weaning, sw: @T ¯ P ¼ l ps w ¼ l ps w @sw Age at first conception (puberty), ap:
2.2. Partial derivatives Perinatal survival, ps: @T ¯ P ¼ l sw w ¼ l sw w @ps Litter size at birth, l: The effect of constraints imposed by litter size at birth on perinatal survival for a particular litter was approximated by a quadratic equation in litter size psðl Þ ¼ sv þ a þ bl þ cl 2 where s v represents the expected phenotypic value of viability when survival is not constrained by litter size, and a, b and c are parameters of a quadratic equation in litter size. The relationship between total litter size at birth and the phenotypic expression of
@T 1 ¼ f g z1 @ap t Weaning to conception interval, iwc: @T ð t 1Þ f s z2 ¼ @iwc t Average piglet weight at weaning (feeder pig market), w: @T ¼ p l ps sw rg @w P P ¼ p l¯ ps sw rg where p is the market price per kg of a feeder pig, and r g is the regression of market weight on weaning weight.
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3. Results 3.1. Calculation of net profit and economic values As an example, the net profit from an average litter was calculated using average Canadian trait means, prices and cost estimates. For this population, the ratio of first to later parity litter size is 0.92, and a commercial sow produces t = 4 litters during her lifetime, so the litter size of second and subsequent parity litters, z, as a proportion of average litter size, l, is given by solving 1 ð0:92 zÞ þ t 1 z ¼ l t t z ¼ l=0:98
Table 2 Economic weights, as calculated from partial derivatives of the net profit function, for finished pig (100 kg) and feeder pig (25 kg) markets Market
Trait
Finished pig Litter size ($/pig) Per. surv. ($/%) Surv. wn. ($/%) Age pub. ($/day) Int. wn. con. ($/day) Feeder pig Litter size ($/pig) Per. surv. ($/%) Surv. wn. ($/%) Age pub. ($/day) Int. wn. con. ($/day) Pig wn. wt. ($/kg)
8 pigs 12 pigs 16 pigs 20 pigs 30.7 2.7 2.6 0.23 0.71 16.2 1.4 1.4 0.23 0.71 22.6
27.6 4.0 3.9 0.23 0.71 14.5 2.1 2.1 0.23 0.71 33.8
22.0 5.3 5.2 0.23 0.71 11.6 2.8 2.8 0.23 0.71 45.1
13.9 6.7 6.6 0.23 0.71 7.3 3.5 3.4 0.23 0.71 56.4
Per. surv.: adjusted % perinatal survival; Surv. wn.: % survival to weaning; Age pub.: age at puberty (days); Int. wn. con.: interval from weaning to conception (days); Pig wn. wt.: piglet weight at weaning (kg).
Then net profit is 0:98 T ¼ l psðl Þ sw w 103:4 þ 4 :92 3 0:98 ð102:365 þ 0:9 apÞ þ 4 ð107:752 þ 0:94 iwcÞ which, under the assumption of zero profit, is assumed to be equal to normal returns or expenses for that population. The economic weight for litter size requires the average population survival rate to weaning, revenue minus costs from weaning to market, unconstrained perinatal survival rate, P sv, and the linear and quadratic coefficients of the function ps(l) = s v + a + bl + cl 2. The linear and quadratic coefficients were estimated from the litters of purebred sows in herds registered on the sow productivity program offered by Ontario Swine Improvement (Table 1). Both linear and quadratic effects were statistically significant ( P b 0.0001) for the Yorkshire and Landrace breeds, and survival rates
Table 1 Estimates of linear and quadratic regression coefficients for perinatal survival rate on litter size at birth
Linear Quadratic
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Yorkshire
Landrace
0.01243 0.00080
0.00929 0.00071
decreased at an increasing rate as birth litter size increased for litters with 7 or more piglets. Survival rates were smaller for litters with fewer than seven piglets born, possibly due to unrelated health problems of the sow. Therefore the unconstrained survival rate was defined as that occurring at the litter size with predicted maximum survival rate, which occurs for the Yorkshire population at litter size L ¼ b=ð2 cÞ ffi 7:5 and a is the adjustment to litter size at the maximum a ¼ 0:0124 L 0:0008 L2 ¼ 0:048 The average population perinatal survival rate, adjusted to the predicted unconstrained survival rate occurring at 7.5 piglets, was calculated from the mean of adj s1 ¼ s1 a bl cl 2 For each litter, adjusted perinatal survival rate was predicted from the deviation of the observed from the expected survival rate based on the litter size, for litters with more than seven piglets, and directly from the observed rate otherwise. Economic values, based on the trait means and costs and revenues appropriate for an average Yorkshire breeding herd in Canada, are shown in Table 2
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for commercial mean litter sizes of 8, 12, 16 and 20 piglets in both markets. Mean unconstrained perinatal mortality rate, mortality to weaning, age at puberty and weaning to conception interval were assumed constant as litter size increased. The absolute economic values for age at puberty and weaning to conception interval were not affected by the population averages of the other traits since the profit function was linear in these traits, and were therefore the same in both markets. Economic values for litter size decreased, and those for the survival traits and piglet weight at weaning increased as average population litter size increased. The economic values for litter size and the survival traits were smaller in the feeder pig than in the finished pig market, but were proportionately the same. If the interaction between perinatal survival rate and litter size was ignored, the economic value of an extra pig born per litter would be 30.57 per pig in the finished pig market, and 16.07 in the feeder pig market for all values of the population mean litter size. Economic weights for the other traits would not be affected, providing all other population parameters remained constant. 3.2. Standardised economic values Breeders registered on the Ontario Swine Improvement Sow Productivity program record all the traits described above. Selection indices are calculated from genetic evaluations which are based on genetic and environmental (co)variances, and these were estimated from data from the example population using a REML procedure. The distributions of the survival traits and weaning to conception interval were skewed, and therefore the estimates, and corresponding evaluations, are expressed on a transformed scale, as follows: Adjusted perinatal survival (s v), % Survival to weaning (sw), % Interval weaning to conception (iwc), days
Ln (100 s v + 1) (log mortality) Ln (100 sw + 1) (log mortality) Ln (iwc) / 0.1823–3.8275, iwc z 6 (Ten Napel et al., 1995)
where s v was calculated from the recorded value for perinatal survival, using the equation given previous-
ly. The economic values derived above apply to a single unit change of each trait on the untransformed scale. The economic weights of a single unit change on a transformed scale, which are required to construct a selection index, were calculated by dividing the economic weight by the rate of change of the transformed value on the original value, evaluated at the population mean. For the example,
Rate of change, Divisor dt(x) / dx Adjusted perinatal 1 / (100 x + 1) 0.1059 survival, % Survival to weaning, 1 / (100 x + 1) 0.1297 % Interval weaning to 1 / (0.1823x) 0.3047 conception, days
All economic values are defined at given commercial population current means, as appropriate for nonlinear profit functions. The heritability for each trait, and genetic correlation and genetic standard deviation estimates on the transformed scale are given in Table 3, for the example from the Ontario Yorkshire breed. The unfavourable genetic correlation between adjusted perinatal survival and litter size was much smaller than previous estimates have found between unadjusted perinatal survival and litter size, although heritability estimates were similar. As a result, breeders might expect greater response in the index as a result of selection. The standardised economic values for each trait, expressed in $ per genetic standard deviation unit on the transformed scale, are given in Table 4 for commercial mean litter sizes of 8, 12, 16 and 20 piglets for each market. These values measure the importance of each trait in the total breeding value. The relative importance of each trait can be assessed from its standardised economic value expressed as a proportion of the sum (sign removed) of all the standardised economic values (Wolfova et al., 2001). When the population average was 8 pigs born per litter, the standardised economic weight of litter size was $30.3, which is 64% of the total, $47.2, in the finished pig market, and $15.9, as compared with a total of $35.2 in the
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Table 3 Genetic standard deviations, heritabilities (diagonal) and genetic correlations among sow productivity traits for Ontario Yorkshire pigs
Genetic std. dev. Age pub. Litter size Per. mort. Mort. wean. Wean.–con. Wean. wt.
Age at puberty
Litter size
Perinatal mortality
Mortality to weaning
Interval weaning–conception
Piglet weaning weight
13.02 0.097
0.99 0.297 0.102
0.32 0.050 0.181 0.059
0.16 0.187 0.263 0.447 0.018
1.13 0.315 0.075 0.040 0.206 0.049
0.35 0.052 0.199 0.079 0.368 0.130 0.107
Litter size: total number of pigs born; Perinatal mortality: 100 adjusted %perinatal survival; log scale; Mortality to weaning: 100 %survival to weaning; log scale; Age at puberty: days; Interval weaning–conception: days; transformed scale, Ten Napel et al. (1995); Piglet weaning weight: (kg).
feeder pig market. Therefore, litter size dominated the index in both markets for populations of Yorkshire pigs with an average of 8 pigs born per litter, having a relative importance of 64% in the finished pig, and 45% in the feeder pig market. For populations with an average of 12 or more pigs born per litter, the relative importance of average piglet weight at weaning was 29% or greater in the feeder pig market, and for populations with an average of 16 pigs born, the relative importance of perinatal survival was 32% or more in the finished pig, and 19% or more in the feeder pig market, whereas that of litter size was 43% or less and 25% or less in the finished and feeder pig markets, respectively.
Table 4 Standardised economic values, expressed in $ per genetic standard deviation Market
Trait
Finished pig market Litter size Per. surv. Surv. wn. Age pub. Int. wn. con. Feeder pig market Litter size Per. surv. Surv. wn. Age pub. Int. wn. con. Pig wn. wt.
8 pigs 12 pigs 16 pigs 20 pigs 30.3 8.1 3.3 2.9 2.6 15.9 4.3 1.7 2.9 2.6 7.8
27.3 12.1 5.0 2.9 2.6 14.3 6.4 2.6 2.9 2.6 11.8
21.7 16.2 6.6 2.9 2.6 11.4 8.5 3.5 2.9 2.6 15.7
13.7 20.2 8.3 2.9 2.6 7.2 10.6 4.4 2.9 2.6 19.6
Litter size: total number of pigs born; Per. surv.: adjusted %perinatal survival; log scale; Surv. wn.: %survival to weaning; log scale; Age. pub.: age at puberty (days); Int. wn. con.: interval weaning to conception (days); transformed scale, Ten Napel et al. (1995); Pig wn. wt.: pig weight at weaning (kg).
4. Discussion The profit functions given in this paper are simple, and do not attempt to model all of the complexities of swine production. Although such difficulties could be addressed, to a greater extent, with a more complex bio-economic simulation model, the advantage of using the profit function approach is the relative ease with which economic weights can be recalculated for different market objectives, production systems and sub-population, or herd averages. This type of flexibility may be important in a dynamic market, not only for individual breeders, but also from a regional perspective. In addition, the variation in trait profiles across sub-populations will be less likely to be reduced over time, which could help maintain the genetic diversity of the population. Previous estimates of economic values for sow productivity traits, discussed by Rydhmer (2000), are shown expressed as a percentage of live litter size in Table 5. These weights base selection on the composite trait, live litter size at birth, rather than on both total birth litter size and perinatal survival rate. This approach does not result in the optimum weighting of selection emphasis on component traits, (Bennett and Leymaster, 1989; Johnson et al., 1984), although, as noted by Bennett and Leymaster (1989), the optimum weights depend on the assumed model as well as the population averages of the component traits. Current estimates of economic weights for a commercial litter size of 12 pigs are also shown in Table 5, expressed as a percentage of total litter size. These estimates are quite similar to the ones given by others, at least for the finished pig market. However, the current estimated
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Table 5 Relative economic values for sow productivity traits per unit of trait, expressed as a percent of the economic value for litter size, including current estimates Kennedy (1994) NSIF (2001) De Vries (1989) Anderson and Palmo (1998) Current estimatesa Litter size (live pigs born) 100% Litter size (total pigs born) Litter birth wt. (kg) Perinatal survival (%) Survival to weaning (%) Pig weaning weight (kg) Litter weaning weight (kg) 6.8 Litter size at weaning (pigs) Piglet growth rate (g/day) Age at puberty (days) Age at 1st farrowing (days) 1.94 Interval weaning to conception (days) Oestrus return (%) Farrowing interval (days) 5.54 a b c
100%
100%
100% 100%
7.26 12.36
13.26
1.31 1.01
1.66
14.5 14.2 233.
8.14 44.44 .81b; 1.5c 2.6b; 4.8c
3.6 5.21
Current estimates of economic weights are given for a commercial litter size of 12 pigs. Value for finished pig market. Value for feeder pig market.
weight for piglet weaning weight in the feeder pig market was over twice those implied by weights for litter weaning weight given by others. The feeder pig market was not considered directly in the other studies, and it is difficult to compare the results. In addition, market prices for feeder pigs in Canada have been unstable recently, and the price used in the example is quite possibly inflated. Note that the economic weight for piglet weaning weight was a multiple of feeder pig price per kg. The weights given in Table 2 were based on the Canadian production system and market averages, and would be appropriate for dam line selection in an average herd in Canada. Breeders with herd averages differing substantially from national ones may prefer to recalculate the economic weights based on commercial stock bred from their own herd, particularly if the herd is closed. Those supplying stock for specific crossbred production systems should also use trait averages from commercial stock bred from their herd. Smith et al. (1983) suggest that in a 2-breed system, piglets from purebred sows with limited milk supply mated to boars with high growth potential show decreased survival rates and reduced growth, when compared to offspring from crossbred sows in a 3-breed system. Breeders supplying commercial buyers with specific management practices should also use specific cost and revenue estimates rather
than national averages. For example, an increasing number of producers use early weaning management systems, and sell their pigs to growers at much younger ages, rather than 25 kg. Breeders on the national swine improvement program in Canada would normally base selection within dam lines on a dam line index which combines the sow productivity index with a sire line index, rather than on sow productivity traits alone. Since most Canadian market pigs are crosses between a terminal sire line boar and a female from a either a dam line or F1 cross between two dam lines, the Canadian Centre for Swine Improvement publishes a dam line index calculated as a weighted sum of a sow productivity and a sire line index, with the sow productivity index receiving twice the weight of the sire line index. This form of the dam line index assumes the economic values for traits of the finished market pig, such as growth rate, feed conversion and carcass traits, are independent of those for sow productivity traits. This is a reasonable approximation for many independent breeders but may not be appropriate for a fully integrated system. It is evident from the results that population average litter size has considerable impact on the optimal weighting used for traits used in selection indices for dam lines of pigs. Many breeding programs have been very successful in increasing litter size, with the result
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that the economic weights previously used for selection may now be suboptimal. Breeders such as these should consider reducing the emphasis placed on litter size in their selection criteria, and increasing that placed on perinatal survival, and, depending on their target market, piglet weight at weaning. Breeders with herds producing litters with fewer than 10 pigs should continue to place most emphasis on litter size. Flexibility is therefore required in deciding appropriate selection goals.
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