J. Anim. Sci. 2003. 81:1150-1157
© 2003 American Society of Animal Science
Evaluation of strategies for selection for lean growth rate in pigs1
P. Chen*,
T. J. Baas*,2,
J. C. M. Dekkers*,
K. J. Koehler
and
J. W. Mabry*
* Departments of Animal Science and
and
Statistics, Iowa State University, Ames 50011
2 Correspondence:
109 Kildee Hall (phone: 515-294-6728; fax: 515-294-5698; E-mail:
tjbaas{at}iastate.edu).
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Abstract
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Lean growth rate (LGR) in pigs is a nonlinear biological function of growth rate and lean quantity. According to animal breeding theory, genetic progress for LGR is maximized with selection on a linear index of its component traits, but selection on direct EBV for LGR is also common. In this study, the performance of five criteria for selection on estimated LGR in pigs was evaluated through simulation over five generations: linear indexes of multiple-trait EBV of component traits with or without updating index weights in each generation; a nonlinear index of multiple-trait EBV of component traits; and direct selection on EBV for LGR from a single-trait model or a multiple-trait model that included LGR and component traits. The nonlinear index yielded the highest response in LGR in Generation 5, but the linear index with updating performed almost as well. Not updating weights for the linear index reduced response in LGR by 1.1% in Generation 5 (P < 0.05). Direct selection on single-trait EBV for LGR yielded the lowest responses in Generation 5. Direct selection on EBV for LGR from a multiple-trait animal model yielded a 3.1% greater response in LGR in Generation 5 than direct selection on EBV for LGR based on a single-trait animal model (P < 0.05), but yielded a 1.9% lower response than the nonlinear index. Although differences in response in LGR were limited, alternative selection criteria resulted in substantially different responses in component traits. Linear index selection for LGR placed more emphasis on lean quantity, whereas direct selection for LGR emphasized growth rate. Based on the relative changes in the responses in LGR, selection for estimated LGR based on a nonlinear index or a linear index with updating is recommended for use in the swine industry.
Key Words: Growth Rate • Lean • Pigs • Selection Index
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Introduction
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Lean growth rate (LGR) is an important trait for genetic improvement programs in pigs because consumer demands are for lean products, and lean tissue can be deposited more efficiently than fat tissue. Fowler et al. (1976) proposed that selection for lean tissue growth could be accomplished by using LGR as a biological index that combines lean percentage and growth rate into one single trait. Lean growth rate is defined as lean gain per day and is a nonlinear biological function of component traits; therefore, several alternative strategies exist for selection for LGR. Most selection experiments for LGR have been based on a classical linear selection index that combines ultrasonic measures of backfat thickness and ADG (McKay, 1990; 1992; Cameron, 1994; Cameron and Curran, 1994b).
Several studies have evaluated strategies for selection for profitability when biological traits contribute to profit in a nonlinear manner (Goddard, 1983; Dekkers et al., 1995; Meuwissen and Goddard, 1997). In theory, a linear index of biological traits is expected to give the greatest increase in profit if genetic parameters of the biological traits are additive (Goddard, 1983; Dekkers et al., 1995). Meuwissen and Goddard (1997), however, showed by simulation that direct selection on EBV for profit or selection on a nonlinear index of EBV for biological traits can result in similar responses to selection when compared to selection on a linear index of EBV for biological traits. Linear indexes have also been proposed for selection on ratio traits (Lin, 1980; Gunsett, 1984). Similar considerations apply to selection for LGR as a nonlinear function of carcass composition and ADG. Therefore, the objective of this study was to evaluate alternate strategies for selection on LGR, including linear indexes of component traits, a nonlinear index of component traits, and direct selection for LGR. Stochastic simulation was used to evaluate response in LGR over five generations.
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Materials and Methods
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Lean Growth Rate
In this study, the fat-free lean prediction equation for barrows developed by the National Pork Producers Council (NPPC, 2000) was used to model the relationship of kilograms of fat-free lean in the carcass with backfat (BF) and loin eye area (LEA), both measured by ultrasound, at a fixed BW of 113.5 kg:
 | [1] |
Phenotype for LGR was calculated by dividing by days from birth to 113.5 kg (DAYS), resulting in the following biological function for LGR:
 | [2] |
Figure 1
illustrates the nonlinear relationship between DAYS and LGR based on Eq. [2], when setting BF and LEA equal to population means of 16.94 mm and 44.06 cm2, respectively. Eq. [2] was used for both sexes.
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Figure 1. Nonlinear relationship between phenotypes for days to 113.5 kg and lean growth rate at base population means for backfat and loin eye area.
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Selection Criteria
Five criteria for selection for LGR were derived: 1) a linear index without updating index weights (ILIN); 2) a linear index with updating index weights (ILIN, UP); 3) a nonlinear index (INL); 4) direct selection for EBV for LGR based on a single-trait animal model (ILGR, ST); 5) direct selection for EBV for LGR based on a multiple-trait model (ILGR, MT). All criteria used EBV derived using BLUP based on an animal model.
Linear Index.
The most common approach to select for LGR is to include EBV for the component traits of LGR in a linear index as follows:
 |
where v is a vector of biological values for DAYS, BF, and LEA in relation to LGR and û is a vector of multiple-trait EBV for DAYS, BF, and LEA. The biological value of a trait is defined as the increase in LGR if the population mean for the trait is improved by one unit, similar to the concept of economic values in selection index theory (Hazel, 1943). Biological values were derived as first derivatives of the biological relationship of LGR with ADG, BF, and LEA, using either the relationship at the individual animal level or the relationship at the population level. In the individual animal approach, biological values were derived as first derivatives of the LGR prediction Eq. [2]. In the population average approach, the LGR Eq. [2] was converted to a population-level function that describes the relationship of the population average for LGR with the population average for ADG, BF, and LEA. Biological values were then derived as first derivatives of the population-level function. Derivation of the population-average function is given in the Appendix.
Biological values for the linear index were either updated ILIN,UP or not updated ILIN over generations. Without updating, biological values were derived as first derivatives evaluated at the population means in the base population. With updating, biological values were updated each generation t by evaluating first derivatives at the mean in Generation t.
Nonlinear Index.
Substituting multiple-trait EBV for component traits in Eq. [2], the following nonlinear index is obtained:
 | [3] |
where µi = the population mean of trait i in Generation 0, and ûi = the individual’s multi-trait EBV for trait i.
Direct Selection for Lean Growth Rate.
It is assumed that all three traits are recorded such that the LGR of every animal can be predicted using Eq. [2]. A simple strategy then is direct selection on EBV for LGR: ILGR, ST = ûLGR, where ûLGR is the single-trait EBV for LGR. In order to increase the accuracy of EBV for LGR, records for DAYS, BF, and LEA can be included in a multi-trait animal model for LGR and selection for LGR can be on the multi-trait EBV for LGR, ILGR, MT = ûLGR, MT.
Data Simulation
To evaluate genetic progress over five generations using the five alternate selection criteria, selection in a closed nucleus-breeding scheme over five generations was simulated and replicated 600 times for each selection criterion. In each generation, 500 males and 500 females were simulated, and 20 males and 100 females were selected. Population parameters are summarized in Table 1. Phenotypes for the component traits DAYS, BF, and LEA were simulated as: Yi = Gi + Si + Ei, where Yi is a vector of phenotypic records of the three component traits for animal i; Gi is a vector of genetic values for animal i, which is assumed to be distributed N(µ, 
g), where g is the genetic variance-covariance matrix among the three component traits; Si is the sex of animal i; and Ei is a vector of residuals for animal i, which is assumed to be distributed N(0, e), where e is the residual variance–covariance matrix among traits. Vectors Gi and Ei were assumed to be independent. Phenotypic and genetic parameters for DAYS, BF, and LEA were based on estimates for the overall U.S. pig population that were obtained by Chen et al. (2002) and are shown in Table 1. Phenotypes for LGR were calculated using Eq. [2].
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Table 1. Mean, phenotypic variance, lower and upper bounds, heritability (diagonal), genetic correlations (above diagonal), and phenotypic correlations (below diagonal) assumed for traits in the simulation and genetic evaluation
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Genetic Evaluation
Breeding values for evaluated traits were estimated under a single- or multiple-trait model, depending on the selection criterion, with fixed effects of sex and generation, a random animal effect, and with the true genetic parameters, as listed in Table 1
. Since it is not easy to derive genetic parameters for LGR because of the nonlinear relationships, true genetic values for LGR were obtained for 10,000 individuals by inserting simulated true breeding values for DAYS, BF, LEA, and their base population means into Eq. [2]. Then, heritability of LGR was derived as the ratio of the variance of LGR genetic values to the phenotypic variance of LGR, and genetic correlations were obtained as correlations of the simulated genetic values for LGR, with the true breeding values for DAYS, BF, and LEA.
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Results
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Simulated genetic parameters for LGR that were used in genetic evaluations based on LGR phenotypes are in Table 1. Simulated parameters were similar to those observed in the literature (Chen et al., 2002).
Figure 2 shows biological values for DAYS as a function of the population mean when derived based on the population-average biological function for LGR (see Appendix). Biological values for BF and LEA did not depend on population means for the traits because the relationships of BF and LEA with LGR are linear in Eq. [2]. Biological values for DAYS, BF, and LEA at the base population means (Table 1) were -1.49 g/d, -1.6 g/mm, and 2.2 g/cm2 based on the individual biological function, and -1.52 g/d, -1.6 g/mm, and 2.2 g/cm2 based on the average biological function. These two sets of biological values are nearly identical, which indicates that there is not a high degree of nonlinearity in LGR as a function of DAYS (Figure 2). Population-average biological values were used in the remainder.
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Figure 2. Biological values for days to 113.5 kg based on individual or population-average biological functions as a function of the population mean for days.
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Table 2 presents cumulative responses in LGR and component traits at each generation for the linear index without updating, along with standard errors of the means. Standard errors of cumulative responses in each trait were similar for the five selection strategies (results not shown).
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Table 2. Cumulative responses over five generations in lean growth rate (LGR) and its component traits for selection on the linear index without updating (means of 600 replicated simulations)
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Figure 3 shows cumulative responses from alternative selection criteria relative to responses to the linear index without updating. In general, differences in response between strategies were limited (less than 5%) but increased over generations. The linear index with updating and the nonlinear index yielded the highest LGR in each generation except in Generation 1. Responses to the nonlinear index and the linear index with updating were not significant (P > 0.05) (Figure 3). Direct selection for LGR from a multi-trait model yielded the highest LGR in Generation 1, but differences with other indexes were not significant (P > 0.05). Direct selection on LGR from a single-trait model resulted in the lowest response in every generation. The linear index without updating and direct selection for LGR from a multi-trait model yielded intermediate responses in LGR in Generations 2 to 5. The difference between these two indexes was not significant (P > 0.05). Linear index selection without updating resulted in 1.1% lower response in LGR in Generation 5 than selection on the linear index with updating (P < 0.05).
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Figure 3. Cumulative responses in lean growth rate for different selection strategies relative to the linear index without updating. Means of cumulative responses from 600 replicate simulations; ILGR, ST = direct selection for LGR based on a single-trait model; ILGR, MT = direct selection for LGR based on a multi-trait model; ILIN = linear index without updating; ILIN, UP = linear index with updating; INL = nonlinear index. b,c,dMeans with different letters in each generation differ, P < 0.05.
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Direct selection on EBV for LGR based on a single-trait model yielded 1.3, 1.1, 1.2, 2.0, and 3.1% lower responses in LGR in Generations 1 to 5 than selection on a multi-trait EBV for LGR (Figure 3). Base population parameters were used for genetic evaluation (Table 1). The BLUP animal model accounts for changes in genetic parameters resulting from the Bulmer effect, but not for changes in genetic parameters that result from nonlinear relationships between traits. Heritability of LGR and its genetic correlations with DAYS, BF, and LEA derived by simulation, but using means in Generation 5, were 0.33, -0.89, -0.29, and 0.31, which are quite different from corresponding genetic parameters using the base population means (Table 1).
Although the alternative selection strategies resulted in limited differences in LGR, responses in component traits were substantially different, as illustrated in Figures 4, 5, and 6. Direct selection for LGR resulted in large responses in DAYS (Figure 4), but this was at the cost of selection for BF and LEA (Figures 5 and 6). In general, the linear indexes put more emphasis on BF and LEA and less on DAYS (Figures 4, 5, 6). The nonlinear index resulted in intermediate responses in DAYS, BF, and LEA (Figures 4, 5, 6).
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Figure 4. Cumulative responses in days to 113.5 kg for different selection strategies relative to the linear index without updating. Means of cumulative responses from 600 replicate simulations; ILGR, ST = direct selection for LGR based on a single-trait model; ILGR, MT = direct selection for LGR based on a multi-trait model; ILIN = linear index without updating; ILIN, UP = linear index with updating; INL = nonlinear index. b,c,dMeans with different letters in each generation differ, P < 0.05.
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Figure 5. Cumulative responses in backfat thickness for different selection strategies relative to the linear index without updating. Means of cumulative responses from 600 replicate simulations; ILGR, ST = direct selection for LGR based on a single-trait model; ILGR, MT = direct selection for LGR based on a multi-trait model; ILIN = linear index without updating; ILIN, UP = linear index with updating; INL = nonlinear index. b,c,dMeans with different letters in each generation differ, P < 0.05.
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Figure 6. Cumulative responses in loin eye area for different selection strategies relative to the linear index without updating. Means of cumulative responses from 600 replicate simulations; ILGR, ST = direct selection for LGR based on a single-trait model; ILGR, MT = direct selection for LGR based on a multi-trait model; ILIN = linear index without updating; ILIN, UP = linear index with updating; INL = nonlinear index. b,c,d,eMeans with different letters in each generation differ, P < 0.05.
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Discussion
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In this article, selection for LGR over multiple generations was formulated as selection for a nonlinear biological function. The results for the linear index in this study agree with the findings of Meuwissen and Goddard (1997) for selection on nonlinear profit. They found that the selection response over generations achieved by the linear index with updating of index weights was greater than response by direct selection on single- or multi-trait EBV for profit. The efficiency of linear indexes over direct selection on single-trait EBV in this study is also consistent with the findings of Gunsett (1984), who found that a linear index of feed intake and ADG was superior to direct selection for feed conversion, as a ratio of these two traits, when component traits have different genetic parameters. In this study, the nonlinear index gave a greater response than selection on a linear index with updating, which agrees with the findings of Meuwissen and Goddard (1997), who found that a nonlinear index resulted in a slightly larger response in nonlinear profit than a linear index with updating.
A linear selection index of growth rate and lean percentage has been used to select for LGR in many experiments (Cameron, 1994; Cameron and Curran, 1994b). In most cases, the linear index for LGR was derived by approximating LGR by a linear function at the base population mean. Goddard (1983) demonstrated that a linear selection index is optimal for a nonlinear profit function when biological traits exhibit no nonadditive variance, provided that weights of the linear index are optimized. Pasternak and Weller (1993) developed an iterative algorithm to derive linear selection indexes that maximize average profit in the last generation of a planning horizon. Groen et al. (1994) used a general derivative-free search algorithm to derive linear selection indexes that maximize average profit in the last generation of a planning horizon. Dekkers et al. (1995) used optimal control theory to derive linear index weights that maximized a combination of short- and longer-term responses, with response in each generation weighted by a discount factor. Dekkers et al. (1995) showed that optimal linear indexes are derived from economic values that are obtained as first derivatives of the profit function at future rather than the current population mean.
In the present study, linear indexes were derived from biological values evaluated at the base population means or at means in the current generation for the linear index with updating. Following Dekkers et al. (1995), the optimal linear index has to be linearized at the mean of the population after five generations of selection if the objective is to maximize response over five generations. The difference between linearization at the current vs. future means is, however, not expected to be large for LGR because the degree of nonlinearity is not very strong.
An attractive alternative to linear index selection is to substitute the EBV of component traits into the nonlinear biological function. This strategy yielded the highest response in LGR and does not require updating index weights. The resulting selection criterion provides maximum likelihood estimates of genetic values for LGR, rather than of breeding values for LGR because LGR will have nonadditive genetic variation as a result of the nonlinearity of the biological function (Meuwissen and Goddard, 1997). Therefore, the nonlinear index might not be the optimal selection procedure if the aim is to improve the additive genetic value for LGR. Many researchers (Goddard, 1983; Groen et al., 1994; Weller, 1994) already have shown that, in theory, linear indexes are optimal. In our study, the response by the nonlinear index was, however, greater than responses by other indexes. The better performance by the nonlinear index may be due to the fact that the linear indexes maximize profit of an average individual, but not necessarily the average profit in the population.
Direct selection for phenotypes for LGR has been used in several selection experiments (Stern et al., 1993; Chen et al., 2001) because of its simplicity. In this study, direct selection for LGR based on single-trait EBV resulted in the lowest response in LGR. Direct selection on multi-trait EBV for LGR yielded higher responses in LGR than selection on single-trait EBV for LGR in each generation. This agrees with Meuwissen and Goddard (1997), who found that direct selection for single-trait EBV for profit was worse than direct selection for multi-trait profit, the linear indexes, and the nonlinear index.
All five selection strategies for LGR that were evaluated in this study resulted in increased ADG, decreased BF, and increased LEA. These results are consistent with the results of several selection experiments (Stern et al., 1993; Cameron and Curran, 1994a). Stern et al. (1993) reported increased lean percentage and growth rate using direct selection on phenotypes for LGR that were estimated from ultrasonic measurements of fat depth and loin muscle area, along with growth rate. Cameron and Curran (1994a) also reported decreased BF and increased ADG using a linear index of BF and ADG. McKay (1990) reported that the main effect of selection on a linear index of BF and ADG was a reduction in BF.
Although differences in response to LGR were limited between the five strategies, they did result in substantially different responses in component traits. Linear indexes for LGR yielded larger responses in leanness. In contrast, direct selection for LGR yielded larger responses in growth. The nonlinear index resulted in balanced responses in both leanness and growth rate. Gunsett (1984) found that responses in component traits when selecting on a ratio of traits are difficult to predict and are mediated by the complex relationships among heritabilities and phenotypic and genetic correlations of component traits, as well as selection intensity.
Most studies on selection for nonlinear profit functions used profit evaluated at trait means as the objective function. However, Elsen et al. (1986) argued that the objective should be to maximize average profit, which is not necessarily equal to maximizing profit evaluated at the mean of component traits in the case of a nonlinear function. Chen et al. (1998) derived economic values of meat quality traits based on individual and average profit functions and found there were only small differences in two sets of economic values because the degree of nonlinearity of the nonprofit function is not high. Here we quantified biological values of component traits at the population level, accounting for the distribution and inherent variability in traits within a population of pigs. Although differences between biological values derived from average vs. individual biological functions were small, differences between the two methods of deriving biological values will be greater if the individual biological function exhibits a greater degree of nonlinearity.
In this study, the equation to predict LGR from component traits, as derived by NPPC (NPPC, 2000), was used as the true functional relationship between traits. In addition, although the relationship was derived at the phenotypic level, it was assumed to apply also at the genetic level. Finally, relationships among component traits (DAYS, BF, and LEA) were assumed to be linear and the only degree of nonlinearity was between component traits and LGR. Violation of these assumptions may affect the comparison between selection strategies. Since all strategies depend on knowledge of the nonlinear relationship between LGR and component traits at one point or another, it is unclear which method will be more robust to uncertainty about the true relationships. More research on estimating and accommodating nonlinear relationships in genetic evaluation and selection procedures is therefore warranted.
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Implications
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Lean growth rate is an important biological criterion for selection. Results of this study indicate that alternative methods for selection for lean growth rate result in different responses in lean growth rate and, in particular, in its component traits. Selection on a linear index of component traits, with updating of index weights over generations, yielded the highest response in estimated lean growth rate. However, a nonlinear index of component trait estimated breeding values yielded almost the same response in estimated lean growth rate and did not require updating of index weights. These two indexes should be useful selection criteria in genetic evaluation programs in the industry. Direct selection on estimated breeding values for lean growth rate is not advocated.
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Appendix
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Equation [1] gives f(x) for lean growth rate (LGR) from birth to 113.5 kg:
 | [1] |
Where BF is backfat, LEA is loin eye area, and DAYS is days to 113.5 kg. The next step is to apply this individual biological function to the distribution of the trait that is represented in a population or herd of animals. This step is needed because the extra LGR that can be obtained by improving a trait differs across the range of trait values that are present among animals in a population due to the nonlinear relationship between LGR and its component traits. Therefore, an average biological function is defined as the relationship between the population average for the trait and the average LGR for animals in the population. Given the distribution of the trait in the population, g(x/µ), the average LGR of the population for a given population mean of the trait (µ), AP(µ), can be derived by integrating the individual biological function f(x) over the distribution of the trait in the population to obtain
 | [2] |
where U and L are the upper and lower bounds for the trait in the population, respectively, and where
 | [3] |
Here, distributions for each trait were assumed to be truncated normal distributions. According to the above definition, average LGR levels can be calculated based on Eq. [1] and [2] for a range of population means. Average LGR levels will depend on the population mean (µ), the standard deviation of component traits (
), the upper and lower bounds of the population range, and the individual biological function f(x).
According to the definition, the biological value of a trait is the marginal change in the LGR mean if the population mean of the trait is changed one unit by selection. Therefore, the biological value can be found as the first derivative of Equation [2] with regard to µ and evaluated at the given population mean. Because AP(µ) is nonlinear in µ, the biological value is a function of µ as well:
| [4] |
The parameters of the distribution were based on the results of the national genetic evaluation program (Chen et al., 2002), as shown in Table 1. Based on Eq. [2], an average LGR function can be derived for each trait by integrating Eq. [1] over the distribution of the trait for a range of population means. The biological values of days from birth to 113.5 kg, backfat thickness, and loin eye area are then obtained from Eq. [4] as the first derivatives of Eq. [2] by substituting the appropriate f(x) and g(x/mu;). Integrals in all equations were solved numerically using Matlab 5.2 (The Math Works, Inc., Natick, MA).
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Footnotes
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1 Journal paper No. J-19804 of the Iowa Agric. and Home Econ. Exp. Stn., Ames, Project No. 3456, and supported by Hatch Act and State of Iowa funds. 
Received for publication April 5, 2002.
Accepted for publication January 6, 2003.
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Abstract
Introduction
