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Journal of Animal Science - Animal Genetics

Towards an improved estimation of the biological components of residual feed intake in growing cattle1


This article in JAS

  1. Vol. 92 No. 2, p. 467-476
    Received: July 12, 2013
    Accepted: Nov 20, 2013
    Published: November 24, 2014

    2 Corresponding author(s):

  1. D. Savietto*†‡§,
  2. D. P. Berry 2 and
  3. N. C. Friggens‡§
  1. Institute for Animal Science and Technology, Universitat Politècnica de València, Camino de Vera s/n 46022 Valencia, Spain
    Animal & Grassland Research and Innovation Centre, Teagasc, Moorepark, Co. Cork, Ireland
    INRA, UMR0791 Modélisation Systémique Appliqué aux Ruminants, 16 rue Claude Bernard 75231 Paris, France; and
    AgroParisTech, UMR0791 Modélisation Systémique Appliqué aux Ruminants, 16 rue Claude Bernard 75231 Paris, France


Residual feed intake (RFI) is the difference between observed and predicted feed intake. It is calculated as the residuals from a multiple regression model of DMI on the various energy expenditures (e.g., maintenance, growth, activity). Residual feed intake is often cited to be indicative of feed efficiency differences among animals. However, explaining a large proportion of the (phenotypic and genetic) interanimal variation in RFI remains difficult. Here we first describe a biological framework for RFI dwelling on similarities between RFI and energy balance. Alternative phenotypic and genetic statistical models are subsequently applied to a dataset of 1,963 growing bulls of 2 British and 3 Continental breeds. The novel aspect of this study was the use of a mixed model framework to quantify the heritable interanimal variation in the partial regression coefficients on the energy expenditure traits within the RFI equation. Heritable genetic variation in individual animal regression coefficients for metabolic live weight existed. No significant genetic variation in animal-level regression coefficients for growth or body fat level, however, existed in the study population. The presence of genetic variation in the partial regression coefficient of maintenance suggests the existence of interanimal variation in maintenance efficiency. However, it could also simply reflect interanimal genetic variation in correlated energy expenditure traits not included in the statistical model. Estimated breeding values for the random regression coefficient could be useful phenotypes in themselves for studies wishing to elucidate the underlying mechanisms governing differences among animals in RFI.


Improving animal feed efficiency is of great interest for increasing profitability in the Agri-Food industry as well as reducing the environmental footprint of animal production systems. Many alternative definitions of feed efficiency exist, each with their advantages and disadvantages (Berry and Crowley, 2013). Residual feed intake (RFI) is increasing in popularity as a measure of animal-level feed efficiency (Berry, 2008). Originally proposed by Byerly (1941) in poultry and later developed by Koch et al. (1963) in growing cattle, RFI is the difference between actual feed intake (usually expressed on a dry matter basis; DMI) and the expected DMI based on observed performance and the associated energy coefficients. These coefficients are usually estimated by least squares regression of DMI on selected energy expenditures (e.g., ADG, metabolic live weight).

Irrespective of the definition, the estimate of feed efficiency used should account for different functions involved in resource usage. For instance, 2 animals with a similar intake could have different growth rates because of differences in their maintenance and other functional partitioning of intake energy. If all functions are considered, if the coefficients can be precisely estimated, and if all measurements are error free, then the residual must equal zero for all animals. Such a model is unlikely, however, for 4 reasons: 1) the measurement of traits will always contain some error, 2) it is difficult to directly measure and thus include all functions, 3) the precise estimation of coefficients relies on a clear separation of functions according to their energy costs; growth, for example, comprises both protein and lipid deposition, which have different energy costs (Pullar and Webster, 1977), and 4) individual animal energy coefficients may deviate from the population mean reflecting differences in the efficiency of energy conversion into body functions. Speculation on individual animal differences in the efficiencies of conversion of feed to different body functions exists (Meyer and Garret, 1967; Johnson et al., 2003; Van Milgen and Noblet, 2003). We hypothesized that such interanimal variation could be quantified in a mixed model framework modeling both the (fixed) population average conversion efficiency and (random) animal deviations from this population average. However, this will only hold if all relevant energy expenditures are included in the equation to generate RFI. Therefore, the aims of this study were 1) to evaluate alternative models for including different energy expenditures in the RFI equation and 2) investigate if individual differences in the partial regression coefficients on energy expenditure exist.


The RFI approach was defined by Koch et al. (1963), who accounted for maintenance costs on efficiency by regressing DMI (kg/d) on mid-test weight (MW) as well as on BW gain (kg/d):in which µ is the model intercept, b0, b1, b2, and b3 and the partial regression coefficients and e is the model residual.

This regression of feed intake (FI) on performance has been extensively used to compute the residuals and subsequently interpret these residuals as a measure of feed efficiency (Berry, 2008; Berry and Crowley, 2013). It is, however, worth noting that the regression of FI (kg of DM/d) on production (i.e., the RFI equation) is, in principle, the same as the equation for energy balance (EB; MJ/d):in which Fec is the feed energy content and Emaint and Egain are the energy costs of maintenance and BW gain (kg/d), respectively.

This is useful because research on separating biological components of performance according to their energy costs has mainly been undertaken in the context of EB and predicting energy requirements (Emmans, 1994, 1997).

It has been long known that the major factor influencing maintenance energy requirements is BW0.75 (Kleiber, 1947), and most RFI equations include this term. However, this ignores the fact that differences in maintenance energy requirements for different body components exist because there is substantial turnover of protein but little, if any, turnover of lipid (Kirkland et al., 2002). Pullar and Webster (1977), for example, estimated a higher increment of heat production per kilojoule of protein (1.25 kJ/d) than per kilojoule of fat (0.36 kJ/d) deposited. Therefore, the energy requirements for maintenance should be a function of BW adjusted to constant body fatness (Emmans, 1997). Attempts have been made to make this correction by including a (ultrasound) measure of body fat in the RFI equation (Basarab et al., 2003). However, such an approach does not properly account for the energy demand because of the multiplicative effect between body size and body fat content (Friggens et al., 2007). This phenomenon can be appropriately accounted for by including an interaction between body size and fat depth (i.e., fat mass) in the RFI equation or by adjusting BW for fat content before its inclusion in the RFI equation. Zygoyiannis et al. (1997) documented a generalized method to estimate kilograms mass per unit of BCS adjusted for mature size of sheep, extended to cattle data. Other methods also exist (NRC, 2000; Thorup et al., 2012).

With respect to growth, the vast majority of variation in composition of growth is between protein and lipid (Moulton, 1923; Owens et al., 1995), which are the 2 major energy depots in growth. It has been shown that the energy cost of depositing protein is approximately 1.64 times greater than the cost of depositing fat (Pullar and Webster, 1977) and that 1 kg of protein translates to approximately 4.5 kg lean tissue whereas 1 kg lipid equates to 1.3 kg adipose tissue. Therefore, properly accounting for differences in composition of growth in RFI estimation requires that the energy demand for growth should consider protein accretion and fat deposition separately. Thorup et al. (2012) developed this argument based on the fact that body lipid content can be estimated from BCS (Wright and Russel, 1984). Given this, empty BW, body lipid, and body protein masses can be estimated (details in Thorup et al., 2012).

Many energy system incorporate animal activity within the definition of maintenance (i.e., the energy used when both protein and lipid changes are zero; Emmans, 1994). The inclusion of activity as a maintenance cost is based on some arbitrary and constant level of activity (Emmans, 1997). However, animals show considerable differences in activity levels (Ramseyer et al., 2009), especially in grazing production systems (Wesley et al., 2012). The development of accelerometer- and global positioning system–based technologies for individual monitoring offer the opportunity to reliably measure activity (Moreau et al., 2009), allowing the separation of this component from maintenance.

Another issue is the effect of intake level on the energy value of the feed. This effect, related to the rate of passage of the feed through the digestive tract, challenges the implicit assumption of linearity in most RFI equations.

Any factor contributing to the individual variability in FI not included in the model or assumed to be constant among individuals will contribute to inaccurate feed efficiency estimations. This is also a shortcoming of the model proposed in the present study. In the following, within the limits of the dataset available, we attempt to incorporate these considerations, derived from the biological assumptions made primarily in the construction of the EB equation, into the development of a multiple regression model to estimate expected FI, and subsequently derive RFI.


Data Editing

Performance data from 3,724 purebred beef bulls tested at the national bull performance centre at Tully, Kildare, Ireland, between September 1983 and September 2011 were available. Details of the test station practices, the criteria used to select bulls, and the feed composition during the performance test program was described in detail by Crowley et al. (2010). Over the years, the feed offered was composed of forage (1.5 kg/animal per d) and ad libitum concentrate. Because forage orts were not weighed back, only the concentrate intake (CI; kg/d) was used as the measure of FI. Individual CI was recorded as the average of daily CI in 14-d periods between years 1983 and 1991, 21-d periods between years 1992 and 2005, and 7-d periods between years 2005 and 2011. All CI data used in the present study was on a fresh, as-fed basis. Animal BW was also measured every 14, 21, and 7 d between the years 1983 and 1991, 1992 and 2005, and 2005 and 2011, respectively. Therefore, during a 70-d test period, a minimum of 4 CI average records and 4 BW measures were available. Differences in mean energy density of the diet between the years were accounted for through the inclusion of batches of animals as contemporary group in the statistical model (described later).

From the original data, 161 bulls with less than 4 BW and CI records during the test period (last 70 d on test) were discarded. Bulls enter the performance station in batches, with up to 3 batches per year. The 3,563 bulls represented 106 different batches (i.e., contemporary groups) and 5 breeds (Angus [AN] = 263, Charolais [CH] = 880, Hereford [HE] = 164, Limousin [LI] = 1,311, and Simmental [SI] = 945). Several breeds were represented in each batch, hereafter referred to as contemporary group.

Performance Traits

Average daily gain was calculated for each animal by regressing BW on days in test, considering all the BW records available for each animal within 96 d before the end of the test as described by Crowley et al. (2010). Bulls where the linear regression explained less than 95% of the BW variability (n = 303) were discarded, thereby avoiding animals having an abnormal growth during the 96-d test period. Mid-test metabolic BW (MTW; kg0.75) was calculated from the intercept and regression coefficient estimated by a linear regression of BW0.75 on days in test. Mean CI was calculated as the arithmetic mean of the CI records from the last 70 d on test. Fat depth (FAT; cm) measurements, available on 2,008 bulls, were recorded around the middle of the performance test; FAT in the present study was the average values of 3 measures made at the third lumbar vertebra plus the 13th thoracic vertebra (Conroy et al., 2009). A total of 45 bulls (AN = 5, CH = 16, HE = 0, LI = 18, and SI = 6) with a FAT greater than 3 standard deviations from the breed group mean were considered as outliers and excluded. Only 1,963 bulls (AN = 183, CH = 485, HE = 100, LI = 821, and SI = 374) belonging to 69 contemporary groups with information on CI, MTW, ADG, and FAT remained after edits.

Phenotypic Regression Models

Alternative multiple regression models for feed efficiency were progressively built up following the biological framework presented previously. All analyses were performed using the GLM procedure of SAS (SAS Inst. Inc., Cary, NC). All phenotypic models included both contemporary group (69 levels) and breed (5 levels) as fixed effects. The phenotypic models investigated werein which b0, b1, and b2 represent the partial regression coefficients of CI on MTW, ADG, and FAT, respectively, b3 represents the partial regression coefficient for the different 2-way interactions between MTW, ADG, and FAT, and e represents the residual from the model. The goodness of fit (R2, adjusted R2, and Akaike information criteria [AIC]) as well as the correlation between the residuals from the different models were used to compare models. Model [P2] was that originally proposed by Koch et al. (1963). An additional series of analyses tested the significance of the interactions between breed and the regressor variables.

Genetic Regression Models

Variance components were estimated using model [P3] described previously but fitting alternative random components. All models were fit using mixed model methodology in ASREML (VSN Int. Ltd., Hemel Hempstead, UK) and included contemporary group and breed as fixed effects. In all instances, relationships among animals were considered by tracing the pedigree of each animal back to founder animals (i.e., animals with no known parents); up to 16 ancestral generations were used in the generation of the relationship matrix. The genetic models fitted werein which b0, b1, and b2 represents the fixed (i.e., population average) partial regression coefficients of CI on MTW, ADG, and FAT, respectively, b0A, b1A, and b2A represent the random (i.e., individual animal) partial regression coefficients for MTW, ADG, and FAT, respectively, Animal represents the individual animal direct additive genetic effects for the intercept term, and e represents the model residual. The covariances between the random intercept and random regression coefficients were also estimated. In a separate analysis, the heritability of the residuals from model [P3] (i.e., RFI as traditionally defined) was estimated using a mixed model that included breed as a fixed effect and animal as a random effect as undertaken by Crowley et al. (2010).


Data Description

Summary statistics for initial and final age as well as performance measures for the 1,963 beef bulls included in the study are in Table 1. No breed differences existed for either initial or final age. Charolais and SI bulls were heavier than the other breeds both at the start and end of test. Charolais and LI bulls had the lowest CI (11.38 and 10.19 kg/d) and FAT (0.256 and 0.249 cm). Hereford, SI, and CH bulls grew fastest (1.74, 1.74, and 1.75 kg/d, respectively). Angus and SI bulls were ranked as high RFI (0.332 and 0.443 kg/d, respectively) and LI as low RFI (–0.205 kg/d).

View Full Table | Close Full ViewTable 1.

Overall mean and least square means from the statistical model for initial and final age, initial and final BW, concentrate intake (CI), mid-test metabolic BW (MTW), ADG, fat depth (FAT), and residual feed intake (RFI) across breeds

Trait Mean, n = 1,963 AN, n = 183 CH, n = 485 HE, n = 100 LI, n = 821 SI, n = 374 Pooled SEM P-value for breed effect
Initial age, d 314 334 320 307 306 305 31 0.4551
Final age, d 399 418 404 392 390 390 29 0.3857
Initial BW, kg 456.3 436.0a 487.2b 427.9a 437.1a 493.1b 9.12 <0.0001
Final BW, kg 599.2 574.1a 635.5b 574.5a 572.2a 640.0b 9.62 <0.0001
CI, kg/d 10.94 11.71c 11.38b 11.56bc 10.19a 12.24d 0.19 <0.0001
MTW, kg 0.75 113.2 108.4a 117.2b 107.8a 108.3a 118.1b 1.42 <0.0001
ADG, kg/d 1.70 1.63a 1.75b 1.74b 1.60a 1.74b 0.04 <0.0001
FAT, cm 0.309 0.552c 0.256a 0.559c 0.249a 0.316b 0.015 <0.0001
RFI,2 kg/d 0 0.332c –0.124ab 0.025b –0.205a 0.443c 0.12 <0.0001
a,b,c,dLeast square means within a row with different superscripts differ (P < 0.05).
1AN = Angus; CH = Charolais; HE = Hereford; LI = Limousin; SI = Simmental.
2Residuals from the multiple regressions of CI, corrected for contemporary group, on MTW, ADG, and FAT.

Phenotypic Models

The partial regression coefficients of CI on MTW, ADG, FAT, and their interactions (all corrected for the systematic effects of both contemporary group and breed) for the different models evaluated are in Table 2. The partial regression coefficient of CI on MTW (i.e., an approximation for animal size) ranged from 0.080 to 0.093 (kg/d) per kg0.75 of MTW when no interaction term was included in the model. Mid-test metabolic BW, contemporary group, and breed explained 69% of the total variability in CI. Average daily gain explained an additional 7 percentage units of the variance in CI over and above that explained by MTW, contemporary group, and breed. The partial regression coefficients of CI on ADG ranged from 1.808 to 1.900 (kg/d) per (kg/d) of ADG when no interaction term was included in the model. Including FAT with contemporary group, breed, MTW, and ADG in the model increased the R2 and the adjusted R2 by only 0.004 and 0.005 percentage units, respectively. The partial regression coefficient of CI on FAT was 1.132 (kg/d) per cm of FAT when other factors (contemporary group, breed, MTW, and ADG) were also in the model. The R2 of all models with the main effects only ranged between 0.691 and 0.765.

View Full Table | Close Full ViewTable 2.

Partial regression coefficients of concentrate intake (CI) on mid-test metabolic BW (MTW), ADG, fat depth (FAT), and their interactions for the phenotypic models that did not contain any genetic effects

Model1 MTW ADG FAT MTW × ADG MTW × FAT ADG × FAT R2 Adjusted R2 2 AIC3
[P1] 0.093 0.691 0.679 –497.3
[P2] 0.081 1.887 0.760 0.750 –991.0
[P3] 0.080 1.899 1.132 0.764 0.755 –1,026.5
[P4] 0.104 3.471 1.167 –0.014 0.765 0.756 –1,034.2
[P5] 0.080 1.900 1.254 NS4 –0.001 NS 0.764 0.755 –1,024.5
[P6] 0.080 1.831 0.758 NS 0.213 NS 0.764 0.755 –1,025.0
1Models included the contemporary group (n = 69) and breed (n = 5) as systematic effects.
2Adjusted R2 = 1 – [SSE × (n – 1)]/[SST – (nv)], in which SST is the total sum of squares, SSE is the error sums of squares, n is the number of individuals, and v is the residual degrees of freedom.
3AIC = Akaike information criteria: n × ln (SSE/n) + 2 × k, in which SSE is the error sum of squares and k is the number of independent variables. Lower is the best.
4NS = non-significant (i.e., regression coefficients do not different (P < 0.05) from zero).

None of the interactions between the continuous regressor variables improved the fit to the data with the exception of the interaction between MTW and ADG. This term explained an additional 0.15 percentage units of the variability for CI. The correlation between residuals of models [P3] (i.e., no interaction term in the model) and [P4] (i.e., interaction between MTW and ADG in the model) was 0.998.

Only the association between CI and MTW was curvilinear (P = 0.005). The linear and quadratic regression coefficients of CI on MTW were 0.140 (kg/d) per kg0.75 of MTW and –0.0003 (kg/d) per (kg0.75)2 of MTW, respectively. However, only an additional 0.10 percentage units of the variance in CI was explained by the quadratic term and the correlation between the residuals from a model with just a linear term for MTW or with both a linear and quadratic term for MTW was 0.998; hence, the quadratic effect was not further considered since the fit of the model did not improve substantially by accounting for the curvilinear effect and therefore was essentially equivalent to the model with just linear coefficients. The correlation between the residuals of models [P1] to [P6] ranged from 0.87 to 1.00. In all instances, the residuals from model [P1] had a correlation with the residuals from the other models lower than 0.882. The correlations among the residuals of models [P2] to [P6] were greater than 0.988.

In a separate analysis, with only contemporary group included as a fixed effect, the association between MTW and CI differed (P = 0.016) by breed. However, when ADG was also included in the model the interaction between breed and MTW was no longer significant. No significant interaction with breed existed for either ADG (P = 0.760) or FAT (P = 0.781).

Genetic Models

Variance components for the alternative random effects in the genetic models are in Table 3. When the residuals from model [P3] (i.e., RFI as traditionally defined) was fitted as the dependent variable, the heritability was 0.41 ± 0.08. The genetic and residual variance for the simplest model (i.e., model [G1]) with a random animal intercept term was 0.317 and 0.315 (kg/d)2, respectively. The heritability was 0.50 ± 0.08. The fixed and random terms in both models were identical except that for the former model, a 2-step approach was taken (i.e., RFI was first calculated using a phenotypic model and then the genetic parameters estimated for RFI) while the latter model estimated the systematic environmental effects and genetic effects simultaneously. The correlation between the estimated breeding values for RFI from the single- and 2-step approach was 0.991.

View Full Table | Close Full ViewTable 3.

Additive genetic variance for animal-specific random regression on the intercept, mid-test metabolic BW (MTW), ADG, and fat depth (FAT) as well as the residual variance, heritability (h2), and model fit statistics for the genetic models across breeds, which included relationships among animals

Additive genetic variance
Residual variance, (kg/d)2 h2 2 Log (likelihood) AIC3
Model1 Intercept, (kg/d)2 MTW, (× 10–4 kg0.75)2 ADG, (kg/d)2 FAT, (cm)2
[G1] 0.317 0.315 0.50 –581.30 1,174.6
[G2] 0 0.4 0.178 0.72 –561.63 1,137.3
[G3] 0.222 0.035 0.306 0.52 –579.41 1,172.8
[G4] 0.299 0.212 0.308 0.51 –580.59 1,175.2
[G5] 0 0.4 0 0.178 0.72 –561.63 1,139.3
[G6] 0 0.4 0.173 0.170 0.73 –561.03 1,138.1
[G7] 0.218 0.032 0.137 0.302 0.52 –579.11 1,174.2
[G8] 0 0.4 0 0.173 0.170 0.73 –561.03 1,140.1
1All models included the contemporary group and breed as systematic effects as well as random animal effects (with relationships) for the intercept, MWT, ADG, and FAT where appropriate.
2Heritability for models [G2] to [G8] were calculated using the phenotypic variance from model [G1] and the residual variance from the tested models.
3AIC = Akaike information criteria: –2 × Log (likelihood) + 2 × k, in which k is the number of parameters in the model. Lower is the best.

When individual animal deviations in the regression of CI on MTW were included as a random effect, the residual variance reduced to 0.178 (kg/d)2; no genetic variance in the random intercept term existed. Using the phenotypic variance of CI from the base model (i.e., model [G1]) and the residual variances estimated in each of the subsequently tested models, a pseudoheritability was calculated. The pseudoheritability of the RFI model that included a random animal deviation in the regression coefficient of CI on MTW was 0.72. Using exactly the same random terms in a model without FAT gave a pseudoheritability of 0.74. The pseudoheritability obtained from this model but using the original larger dataset (3,260 bulls) was 0.57.

Relative to the base model (i.e., model [G1]) with just a random animal intercept term, small reductions in the residual variance of the model were observed when random regression terms on both ADG and FAT were separately considered. The residual variance of the model was lowest when individual animal deviations from the fixed regression on both MTW and FAT were included in the model. The AIC of this model, however, indicated that it was not superior to the model with just random deviations from the fixed regression on MTW (i.e., model [G2]).

The correlation between the animal intercept term and the individual animal deviation in regression coefficient for MTW in model [G2] was –0.96 ± 0.02. The new variance components were 2.012 (kg/d)2, 0.0003 (kg/d)/(kg0.75)2, and 0.239 (kg/d)2 for the animal intercept, the animal slope on MTW, and the residual, respectively. The pseudoheritability was 0.62; including the covariance between intercept and the random regression on MTW improved the AIC from 1,137.3 to 1,121.5. Therefore, the most parsimonious model, as determined by the AIC, was that containing a random intercept, a random deviation from fixed regression on MTW, and a covariance between them.


Several studies have used RFI as the basis for attempting to identify biological predictors (Herd et al., 2004; Richardson and Herd, 2004; Herd and Arthur, 2009), genomic variation (Nkrumah et al., 2004; Barendse et al., 2007; Nkrumah et al., 2007; Sherman et al., 2008; Snelling et al., 2011), candidate genes (Karisa et al., 2013), or gene expression patterns (Chen et al., 2011) contributing to differences in feed efficiency among animals. However, the success of such approaches depends heavily on the components included in equation used to generate RFI. For example, if the RFI model only includes MTW, then individual animal differences in ADG will contribute to differences in RFI and any biological or genomic markers detected to predict these differences in RFI will, to a large extent, simply reflect growth rate rather than differences in true efficiency. Furthermore, if growth is included but modeled incorrectly, that is, not taking into account the different energy-using components (lipid and protein), then the problem remains; the quantification of the true efficiency phenotype is biased. One aim of this study was to explore the issue of how to extend the RFI equation to minimize this shortcoming.

If relevant energy expenditures are included in the equation to generate RFI (e.g., maintenance, lean growth), it is pertinent to ask the question whether there is individual variation in the partial efficiencies (i.e., the energy coefficients) associated with these components. One way to detect (heritable) differences in these partial efficiencies would be to allow individual animal (random) deviations from the fixed regression coefficients. Therefore, the second aim of this study was to investigate if animal differences in the partial efficiencies exist. These in themselves would be useful phenotypes for further, in-depth analysis to detect biological predictors or better understand the underlying biological mechanisms or genomic variation. The two aims of this study are interrelated because the interpretation of animal differences for specific energy expenditures (explored using the genetic models) depends on which energy components are considered in the model (explored using the phenotypic models).

Phenotypic Models

The proposed phenotypic models explained more than 69% of the phenotypic variance in CI, resulting in residual variances (i.e., RFI) less than 31%. The partial contribution of ADG to the phenotypic variance of CI was 6.9% when the model already included MTW, contemporary group and breed and is at the lower end of the documented 7 to 16% in other populations (Nieuwhof et al., 1992; Arthur et al., 2001; Robinson and Oddy, 2004; Hoque et al., 2006). In the present study, when FAT, a measure of body lipid content, was added to the multiple regression model already containing both MTW and ADG, the residual variability was reduced by only 0.4%, which is less than documented in most other populations of growing animals (up to 7% as reviewed by Berry and Crowley, 2013). Hoque et al. (2006) reported an even greater marginal contribution of fat measures (13%) to differences in FI in Japanese Black cattle, a breed genetically predisposed to greater marbling. In agreement with the present study, Schenkel et al. (2004) reported a low contribution of fat measures to FI variability in growing bulls having a backfat depth between 0.258 and 0.606 cm. Despite the low contribution of FAT measures to variability in CI, considering body composition in the RFI equation is still important (Basarab et al., 2003).

Several studies have described a direct relationship between maintenance requirements and body composition (i.e., body mass of fat and protein; Moe et al., 1971; Noblet et al., 1999; Kirkland and Gordon, 1999). There is good evidence that protein and fat mass have very different maintenance requirements (Webster, 1981; Birnie et al., 2000) and that there is a multiplicative effect between maintenance and body composition (Van Milgen and Noblet, 2003). In other words, maintenance requirements are related to protein mass, which means adjusting BW for fat mass, that is, body fat content (approximated by subcutaneous FAT × BW). The interaction between MTW (a proxy for body size) and FAT was not, however, significant in the present study. We also considered the interaction between ADG and FAT because, in addition to an effect on maintenance, the energy costs of synthesizing protein and lipid differs (Pullar and Webster, 1977). In the present study this interaction was also not significant. The nonsignificance of these two interaction terms probably reflects the limitations of the FAT measure available and also the fact that the animals were in the linear phase of growth, a period where relatively little changes in the proportion of protein and fat are observed (Owens et al., 1995). We suggest that the inclusion of these effects would be more important in the calculation of RFI on animals at ages close to maturity (i.e., greater variation in body composition; Owens et al., 1995) or in feedlot cattle on a high energy diet (e.g., 80 to 90% grain plus concentrates). These effects should also be considered when defining long-term feed efficiency in mature animals because body condition changes are an important feature of their productive life (Veerkamp et al., 1995).

In the present study, the interaction between MTW and ADG was significant, increasing the model R2 by only 0.0015. This interaction indicated heavier faster growing animals ate less than predicted by MTW, ADG, and FAT alone. Conversely but to a lesser extent, lighter faster growing animals ate more than predicted. In biological terms these contrasting effects are difficult to explain. However, this interaction should be interpreted with caution because including this interaction term in the model considerably affected the coefficients of both MTW and ADG probably suggesting an overparameterized model.

Genetic Models

Genetic differences in RFI are normally quantified using a two-step approach: 1) retain the residuals from a regression of intake on the various energy-using components (e.g., maintenance, growth, activity) and 2) estimate the additive genetic variance of these residuals. In the present study a single-step approach was used; the animal (random) effect was included in the multiple regression of CI on MTW, ADG, and FAT after accounting for contemporary group and breed effects. Although the breeding values estimated using either the single- or the two-step approach were strongly correlated (r = 0.991), the single-step approach had the advantage of simultaneously estimating all parameters. The heritability for RFI using the single-step approach (0.50 ± 0.08) was not different to the heritability estimated using the two-step approach (0.41 ± 0.08) and was within the range of heritability estimates for RFI estimated in growing animals using a two-step approach (0.07 to 0.68) reported in the literature (Berry and Crowley, 2013). Although not substantial, the heritability of RFI was reduced when FAT was included in the multiple regression model along with MTW and ADG; the small decrease in heritability is likely due to the weak marginal relationship observed in the present study between FAT and CI (adjusted for the other effects in the model). This decrease in heritability nonetheless does suggest that as the multiple regression equation to derive RFI becomes more complete (i.e., more energy expenditures are included in model), what remains in the residual term is increasingly random noise, which should not be heritable. However, the residual component may still contain heritable differences in conversion efficiencies for biological functions not accounted for in the regression.

In the present study, the genetic analysis was extended to investigate if animal differences in the partial efficiencies of the energy expenditures exist. This approach was intended to provide further information on which components of the efficiency complex (e.g., maintenance, protein deposition) exhibit heritable variation. Accordingly, individual deviations from the partial regression coefficients were sequentially included in the models. The existence of significant genetic variation in the random regression coefficients on MTW suggest that (heritable) differences in the partial efficiency of maintenance may indeed exist. This result should nonetheless be interpreted in the context of the available data and RFI equation used. For example, when FAT was omitted from the mixed model, the genetic variance of the partial regression coefficient of CI on MTW increased by 6 percentage units because MTW and FAT are to some extent correlated; a meta-analysis of 5 studies indicated a genetic correlation of 0.21 between FAT and MTW (Berry and Crowley, 2013). Therefore, the interanimal variation on the energy coefficient of CI on MTW partly reflected differences in body composition.

Pathway analysis of structural genomic variations (Nkrumah et al., 2004; Barendse et al., 2007; Sherman et al., 2008) and differences in gene expression patterns (Chen et al., 2011) in animals divergently selected for RFI suggest that a large proportion of the variation in RFI among animals can be attributable to maintenance. This hypothesis has been substantiated by physiological evidence (Richardson and Herd, 2004; Herd and Arthur, 2009; Kolath et al., 2006; Bottje and Carstens, 2009; Grubbs et al., 2013; Ramos and Kerley, 2013). The existence, in the present study, of individual (heritable) deviations from the partial regression coefficient of CI on MTW, a proxy for maintenance, supports this hypothesis. The breeding values for these random regression coefficients generated in the present study may help molecular geneticists to focus on the biological mechanisms contributing to the additive variation in maintenance requirements. Elucidation of the underlying biological mechanisms may also aid in deciding what energy expenditures (or alternative statistical modeling) should be used to reduce further the variation in RFI providing a more direct strategy to improve feed efficiency. If the interanimal variation in energy coefficients truly reflect differences in energetic efficiencies, they may actually be less prone to genotype × environment (e.g., feed system, maturity) influences, which are known to exist for RFI (Durunna et al., 2011; Berry and Crowley, 2013).

Understanding the genetic or physiological components contributing to variation in complex phenotypes such as FI or efficiency can be best achieved by decomposing the phenotype into its likely contributing components. Here we propose that if studies attempting to understand contributing factors to RFI are to be successful, the variation in contributing factors to RFI should be removed in the RFI equation thereby reducing the complexity of the RFI phenotype. Moreover, such an approach facilitates selection on the individual components of FI. Here we used an alternative approach by quantifying the extent of heritable genetic variation in animal deviations from the population average energy coefficients on the energy expenditures. As well as reducing the variation (and therefore probably the complexity) of RFI, breeding values for the random regression coefficients themselves could be very useful to help elucidate the relative importance of the various components that are likely to contribute to interanimal variation in maintenance efficiency or the factors correlated with maintenance that should be included in the RFI equation.




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