The sensitivity of predicted financial and genetic gains in Holsteins to changes in the economic value of traits

Summary

The objective of this study was to assess the impact of using different relative economic values (REVs) in selection indices on predicted financial and trait gains from selection of sires of cows and on the choice of leading Holstein bulls available in the UK dairy industry. Breeding objective traits were milk yield, fat yield, protein yield, lifespan, mastitis, non-return rate, calving interval and lameness. Relative importance of a trait, as estimated by a.h², was only moderately related to the rate of financial loss or total economic merit (ΔTEM) per percentage under- or overestimation of REV (r = 0.38 and 0.29, respectively) as a result of the variance–covariance structure of traits. The effects on TEM of under- or overestimating trait REVs were non-symmetrical. TEM was most sensitive to incorrect REVs for protein, fat, milk and lifespan and least sensitive to incorrect calving interval, lameness, non-return and mastitis REVs. A guide to deciding which dairy traits require the most rigorous analysis in the calculation of their REVs is given. Varying the REVs within a fairly wide range resulted in different bulls being selected by index and their differing predicted transmitting abilities would result in the herds moving in different directions in the long term (20 years). It is suggested that customized indices, where the farmer creates rankings of bulls tailored to their specific farm circumstances, can be worthwhile.

Introduction

Genetic selection goals for dairy cattle, originally aimed at production traits only, have been expanded in stages over the past 30 years in most countries to include more target traits covering production, functionality and health and fertility. Each addition to the selection goal often involves the use of additional measured phenotypic traits (Cunningham & Tauebert 2009) and requires knowledge of the correlations between the new traits and those already in the breeding goal. In the UK and the US Holstein dairy industries, typical selection criteria traits include milk, fat and protein yield, productive lifespan, somatic cell count (SCC), udder composite score, feet/legs composite score, non-return rate, calving difficulty and interval (Norman et al. 2010). Multi-trait selection is carried out by the calculation of selection indices that require genetic parameters and relative economic values (REVs) for all breeding goal traits.

Several authors have concluded that the efficiency of index selection is not very sensitive to changes in the REVs used in the index. The robustness of a method to derive REVs was investigated by Visscher et al. (1994) by calculating 11 different sets of Australian herd parameters, varying production levels, average herd life, costs and returns. Protein yield had the highest relative REV, followed by survival and mature body size. The latter traits were approximately half as important as protein yield, with the REV for body size being negative. Fat and milk yield were approximately equally important as each other and 40% as important as protein yield. Milk (volume) yield had a negative REV. Milk protein can be expected to be worth more than fat or milk volume where there is decreased demand for fluid milk and increased consumption of cheese and export of dairy products. REVs were fairly robust to changes in herd parameters, implying that they can be used across a wide range of farm environments.

However, in an earlier reappraisal of the problem, using large changes in the REVs, Smith (1983) showed that considerable losses in efficiency can be incurred in some instances. Smith stated that if one trait, or a few traits, dominates the index as measured by the product of the economic value (a) and the heritability (h²) for the trait, the efficiency will be sensitive mainly to changes in those traits. If there is a balance among traits (i.e. similar a.h² values), then moderate losses in efficiency may be incurred through changes in the REVs. A better measure of relative importance should be the economic value and the genetic variance (a.σ_g), to take into account the variance of traits. Smith also reported that large losses in efficiency can occur when (i) important traits are omitted or unimportant traits are given importance, (ii) when the direction of selection is reversed for an important trait or (iii) when assumptions in the model that produces the economic values are inappropriate or subject to fluctuation. Thus, long-term predictions of the outcomes of selection on an overall index are subject to errors from a variety of sources – the SE of the correlation between traits, the SE of the estimate of heritability and the stability of assumptions used to calculate the economic values used. The implications for a comprehensive definition of breeding goals, and the effects of unexpected changes in requirements, from husbandry or market changes, were considered by Smith (1983).

Feed costs continue to be the major costs of milk production in dairy cattle (Ramsden et al. 1999). Therefore, it is important to optimize the level and source of nutrient intake (e.g. energy). Economic values for dry matter intake capacity (DMIC) ranged from 18 to 40/kg/cow/year in Danish production systems and depended on the difference between marginal costs of roughage and concentrates (Koenen et al. 2000). In the USA, Dado et al. (1994) estimated the feed costs per kilogram of milk component, expressed as kilograms of standardized milk with equivalent value, as 1.00 for lactose, 1.89 for fat and 3.49 for protein. This approach was used as the national averages for ratio of shelled corn to milk price and soybean meal to milk price were stable over time, permitting estimation of feed costs from milk price as prices inflate.

Multiple trait selection indexes should account for different markets and production systems. Breeding programmes should estimate future, rather than current, costs and prices (Van Raden 2004). The REVs for some traits or trait components of dairy sires differ substantially between purebred and crossbred dairy systems. There are also differences among the REVs of traits for beef sires, depending on whether these bulls are used for terminal crossing with F1 females in the cow–calf pasture system (backcrossing), for crossing in dairy herds producing slaughter animals, or for crossing in dairy herds producing F1 females for the cow–calf pasture system (Wolfova et al. 2007).

Hoekstra et al. (1994) found that phenotypic correlations between milk production traits and fertility traits were negative (−0.05 to −0.18), with genetic correlations being more negative (−0.14 to −0.62). High correlations have been found among production levels across different lactations. Genetic correlations between second and third lactations are close to one, indicating that these can be considered as repeated observations of the same trait. Genetic correlations between yield on days within lactation are high except between extreme parts of the lactation (Druet et al. 2005). In the UK, lactation persistency is defined as the rate of decline in daily yield after the peak within lactation and is often defined as a ratio of yield at 2 points in lactation. The lower the rate of decline after the peak, the higher the lactation persistency. A cow with a higher lactation persistency can make better use of inexpensive forage depending on season of calving, may suffer less stress from high peak yield, is more resistant to disease, shows an increased conception rate and probability of pregnancy and is therefore more likely to be profitable. Sensitivity analyses have shown that an increased probability of pregnancy, an increased persistency of milk yield and a smaller replacement heifer cost greatly reduce the average cost of a pregnancy (De Vries 2006). Appuhamy et al. (2007) found that increased lactation persistency (uncorrelated with 305-day yield) was associated with lower levels of mastitis. Despite these effects, most selection indices treat protein yield as the main trait of interest without reference to increased lactation persistency, as the impact of persistency on total economic merit (TEM) is usually relatively minor (Togashi & Lin 2009).

The objective of this study was to assess the impact of the use of different REVs in a multi-trait index on predicted financial and trait gains from selection of sires of cows and on the choice of leading Holstein bulls available in the UK.

Methodology

The selection index program MTIndex, used by Cottle (2011) to study the sensitivity of genetic gains to variations in genetic parameters, was modified to also allow trait REV (a_i) variance. The breeding objective traits studied were milk yield, fat yield, protein yield, lifespan, mastitis, non-return rate, calving interval and lameness. Mammary composite score and SCC were included as selection index traits for mastitis, and the feet and leg composite score was the selection index trait for lameness. These are standard traits used by the national genetic evaluation system for dairy cattle in the UK. The sires of dams (SD) pathway was modelled assuming there were 75 progeny records for each bull for the eight selection index traits. The SD pathway is the most important pathway for commercial dairy producers.

Genetic standard deviations and correlations (Tables 1 and 2) were obtained from an analysis of the predicted transmitting abilities (PTAs) of 712 (as of June 2010) available Holstein bulls in the UK. Heritability and phenotypic parameters were derived from the literature (Stott et al. 2005; Wall et al. 2005), the Interbull website (http://www-interbull.slu.se/national_ges_info2/framesida-ges.htm) and unpublished dairy data analyses. The ‘true’a_i values were derived from the bio-economic modelling approach described by Santarossa et al. (2004). These values are used in the computation of the UK national index Profitable Lifetime Index (£PLI).

Table 1. Parameters used in calculating the index standard deviation or total economic merit (TEM)

	Trait	Units	Genetic σ	Heritability (h^2)	Economic Value (£)
1.	Milk	kg	553.17	0.40	−0.03
2.	Fat	kg	17.48	0.39	0.80
3.	Protein	kg	14.89	0.39	1.71
4.	Lifespan	no. lactations	0.41	0.06	25.40
5.	SCC	log cells/ml	20.93	0.12	−
6.	Mammary	score	2.25	0.27	–
7.	Mastitis	cases per lactation	0.06	0.05	−100.00
8.	Non-return	%	4.03	0.02	2.16
9.	Calving Interval	days	7.50	0.03	−0.35
10.	Feet and Legs	score	1.95	0.15	–
11.	Lameness	cases per lactation	0.03	0.02	−100.00

Table 2. Correlations used in modelling index standard deviation or TEM. Phenotypic correlations above diagonal, genetic below diagonal

Trait	1	2	3	4	5	6	7	8	9	10	11
Traits: 1. Milk, 2. Fat, 3. Protein, 4. Lifespan, 5. SCC, 6. Mammary, 7. Mastitis, 8. Non-return, 9. Calving Interval, 10. Feet and Legs, 11. Lameness.
1		0.46	0.82	0.00	−0.12	0.00	0.00	0.00	0.20	0.00	0.02
2	0.46		0.85	0.00	−0.11	0.00	−0.02	−0.12	0.18	0.16	0.02
3	0.82	0.62		0.00	−0.11	0.00	0.00	−0.14	0.18	0.09	0.01
4	−0.08	−0.01	−0.10		−0.06	0.11	0.40	0.00	−0.51	0.22	−0.10
5	−0.10	−0.09	0.00	−0.35		−0.06	0.20	−0.08	0.12	−0.21	0.10
6	0.34	0.17	0.15	0.13	−0.01		−0.05	0.00	0.04	0.29	−0.15
7	0.36	0.19	0.31	−0.22	0.7	−0.28		−0.02	0.03	−0.01	0.01
8	−0.40	−0.24	−0.41	0.22	0.04	−0.24	−0.21		−0.34	−0.13	0.10
9	0.34	0.29	0.30	−0.38	0.17	0.25	0.28	−0.33		0.00	0.00
10	0.19	0.16	0.09	0.22	−0.21	0.45	−0.20	−0.13	−0.01		−0.80
11	0.27	0.32	0.37	0.25	0.10	−0.30	0.26	0.05	0.00	−0.98

The a_i of each trait was varied trait by trait by small equal increments within the range −a_i to 3*a_i so that percentage (or relative) REV inaccuracy (PEVI) varied from −200 to +200% when the program was run separately for each trait. When the a_i values were all varied together, their standard errors were set at a_i/2 and these were multiplied by a Box & Muller (1958) transformation, (−2log_eU₁)^1/2.sin2πU₂, where U₁ and U₂ are independent random variables from a density function on the interval (0,1). This produced normally distributed REVs for each trait. Responses to index selection (SDIndex) were then calculated using the generated a_i values using 100 iterations for each trait in turn or 1000 iterations when all a_j values were allowed to vary together. The a_i values resulting in the index with the largest TEM gain from the 1000 random iterations (opt a_i) were used to focus in on the combination of a_i’s that resulted in the highest TEM. The program calculated indexes with REVs stepping through the range (opt a_i + a_i)/2 up to 2*opt a_i − (opt a_i + a_i) in five equal increments so that all combinations of a_i values were used (>37 000 iterations) within these ranges. The a_i values that resulted from the ‘true’ REVs, and from the largest SDIndex value from the random sampling and from the best three indexes from the structured iterations were then used to create ‘new’ index values for the 712 Holstein sires from their PTA values for all traits, except mastitis and lameness which were not available. The five new calculated index values for each bull were compared with their existing £PLI value by estimating the correlations between index values and determining the top 10 bulls on each of the six indexes. The high value indexes had ‘incorrect’ REVs, but they were within the normal distribution of possible a_i values.

To determine the sensitivity of total economic response (or TEM) to a_i values, the financial losses of using incorrect versus ‘true’ economic values were calculated for a single trait as follows:

Firstly, an index_t with assumed true REVs (a_1t, a_2t, …) was calculated with g_1t, g_2t, …g_11t being the predicted trait (physical) genetic gains (per standardized selection differential per generation interval) for traits 1–11.

SDIndex_t = g_1t.a_1t + g_2t.a_2t + g_3t.a_3t + …

Then the 100 normally distributed REVs for trait j (a_j) were used in the calculation of index_f, with the ‘false’ REV for a trait (a_f) = a_t (true) + Δa, so when Δa > 0, a_f was an overestimate of a_t.

Let g_1f, g_2f, …g_10f be the predicted trait gains using index_f, and

SDIndex_f = g_1f.a_1f + g_2f.a_2t + g_3f.a_3t + …

• For trait 1, SDIndex_t − SDIndex_f = g_1t.a_t − g_1f.a_f + (g_2t − g_2f).a_2t + (g_3t − g_3f).a_3t + …

• = g_1t.a_1t − g_1f (a_1t + Δa₁) + (g_2t − g_2f).a_2t + (g_3t − g_3f).a_3t + …

• = g_1t.a_1t − g_1f.a_1t − g_1f.Δa₁ + (g_2t − g_2f).a_2t + (g_3t −g_3f).a_3t + …

• = − g_1f.Δa₁ + (g_1t − g_1f).a_1t + (g_2t − g_2f).a_2t + (g_3t −g_3f).a_3t + …

Financial loss (−ΔTEM) from using a_1f instead of a_1t

• = (g_1t − g_1f).a_1t + (g_2t − g_2f).a_2t + (g_3t − g_3f).a_3t + …

Therefore, −ΔTEM = SDindex_t − SDIndex_f + g_1f.Δa₁,

where g_1f = genetic gain in trait 1 on index_f

Δa₁ (inaccuracy) = false REV − true REV

PEVI = 100*Δa₁/a_1t.

All values for TEM, −ΔTEM, and g_i were converted to a 10-year basis for the SD pathway by multiplying them by 0.5 * 1.76 (i)/6.5 (L) * 10 (Dekkers 1992). The −ΔTEM values are zero when Δa is zero and were asymmetrically positive for all other Δa and PEVI values. Thus, a polynomial was fitted for −ΔTEM versus the full range of Δa and PEVI values, but a linear regression with zero intercept was fitted for −ΔTEM versus all negative Δa and PEVI values, and similarly for all positive Δa and PEVI values. The regression coefficients enabled a quantitative comparison of the relative sensitivities of financial loss to changes in the ten trait REVs.

Linear regressions of TEM and g_i values versus a_i values with non-zero intercepts were also calculated with or without genetic parameters being allocated non-zero SE values. This enabled the sensitivity of TEM and g_i to variations in genetic parameters to be assessed (Table 3). The typical SE values for non-zero correlations were set lower for milk production traits than fertility traits (Hoekstra et al. 1994).

Table 3. Regression coefficients: annual TEM (£) and trait gain (units) versus EV (£) from DS selection when a trait EV changes, with and without genetic parameter estimate variance

Trait (T) with varying EV	EV range (£)	TEM (£)/year		Trait gain (units)/year
		SE = 0	SE, Non-zero	SE = 0	SE, Non-zero
^aHigh value because of a very low true EV.
Milk (kg)	−0.08 to 0.03	4.02 (0.075) +8.70 (1.814)*T, r^2 = 0.18	4.02 (0.081) +7.37 (1.956)*T, r^2 = 0.12	38.8 (0.68) +1171.1^a (16.38)*T, r^2 = 0.98	38.7 (0.96) +1199.4^a (23.29)*T, r^2 = 0.96
Fat (kg)	−1.17 to 2.08	2.54 (0.055) +1.26 (0.045)*T, r^2 = 0.89	2.53 (0.060) +1.23 (0.049)*T, r^2 = 0.88	0.30 (0.050) +1.02 (0.041)*T, r^2 = 0.87	0.29 (0.058) +1.05 (0.048)*T, r^2 = 0.83
Protein (kg)	−1.71 to 5.06	3.63 (0.169) +0.56 (0.065)*T, r^2 = 0.43	3.62 (0.169) +0.57 (0.064)*T, r^2 = 0.44	−0.062 (0.050) +0.63 (0.019)*T, r^2 = 0.92	−0.62 (0.050) +0.63 (0.019)*T, r^2 = 0.92
Lifespan (lactations)	−25.40 to 75.18	2.94 (0.024) +0.02 (0.001)*T, r^2 = 0.87	3.00 (0.047) +0.02 (0.001)*T, r^2 = 0.64	0.004 (0.0003) +0.0004 (0.00008)*T, r^2 = 0.97	0.004 (0.0008) +0.0005 (0.00002)*T, r^2 = 0.83
Mastitis (cases)	−300 to 100	3.11 (0.012) −0.001 (0.0001)*T, r^2 = 0.74	3.11 (0.030) −0.002 (0.0001)*T, r^2 = 0.40	0.0002 (0.00001) +0.00001 (0.00000009)*T, r^2 = 0.97	0.0002 (0.0001) +0.00002 (0.0000007)*T, r^2 = 0.85
Non-return (%)	−2.16 to 6.39	3.29 (0.013) −0.017 (0.004)*T, r^2 = 0.15	3.28 (0.034) +0.003 (0.0104)*T, r^2 = 0.01	−0.09 (0.0003) +0.03 (0.0001)*T, r^2 = 0.99	−0.08 (0.008) +0.04 (0.003)*T, r^2 = 0.72
Calving interval (days)	−1.04 to 0.35	3.16 (0.001) +0.01 (0.0026)*T, r^2 = 0.02	3.16 (0.027) −0.04 (0.050)*T, r^2 = 0.01	0.05 (0.00002) +0.14 (0.00004)*T, r^2 = 0.99	0.04 (0.010) +0.17 (0.019)*T, r^2 = 0.43
Lameness (cases)	−300 to 100	3.25 (0.004) +0.001 (0.0002)*T, r^2 = 0.91	3.24 (0.026) +0.001 (0.0002)*T, r^2 = 0.08	0.001 (0.000004) +0.000004 (0.00000002)*T, r^2 = 0.99	0.001 (0.00004)*T +0.000004 (0.0000003), r^2 = 0.71

Results

The change in TEM and trait response to selection with varying REVs for the three sensitive traits, milk, fat and protein, when the REV was assumed to have actually changed, is shown for parameters that were given a zero SE (Figure 1) or were allowed to vary within a normal distribution with a non-zero SE value (Figure 2). These results for all other traits are shown in Appendix 1 (zero SE) and Appendix 2 (non-zero SE).

Figure 1.  Change in annual total economic merit (TEM) and genetic gain (kg) with actual REV changes with no variation in correlations. (a) Milk, (b) fat, (c) protein.

Figure 2.  Change in TEM and genetic gain (kg) with actual EV changes with variations in correlations. (a) Milk, (b) fat, (c) protein.

The annual financial losses due to under- or overestimating the true REV are shown in Figure 3 and 4 and Table 4 on a percentage or absolute basis. The losses were not symmetrical when the REV used was an underestimate versus an overestimate of the true REV. The rate of financial loss (£ per percentage or absolute difference of the incorrect REV from the true REV) for each trait was not closely related to the a.σ_g value for each trait.

Figure 3.  Loss of returns with use of inaccurate REVs per unit change in REV. (a) Milk (kg), (b) fat (kg), (c) protein (kg), (d) lifespan (lactations), (e) mastitis (cases), (f) non-return (%), (g) calving interval (days), (h) lameness (cases).

Figure 4.  Loss of returns with use of inaccurate REVs per percentage change in REV. (a) Milk (kg), (b) fat (kg), (c) protein (kg), (d) lifespan (lactations), (e) mastitis (cases), (f) non-return (%), (g) calving interval (days), (h) lameness (cases).

Table 4. Financial loss/year from use of incorrect EVs. Linear regression coefficients (£ per unit or 100% change in EV) with zero genetic parameter estimate variance

Trait	ai*σg	EV underestimated		EV overestimated
		100%	Per unit	100%	Per unit
^aHigh value because of a very low true EV.
Milk (kg)	−£0.01	−0.44(0.007), r^2 = 0.97	16.13^a(0.278), r^2 = 0.97	0.62(0.014), r^2 = 0.96	−23.11^a(0.507), r^2 = 0.96
Fat (kg)	£0.31	−0.92(0.039). r^2 = 0.90	−1.15(0.049), r^2 = 0.90	0.13(0.002), r^2 = 0.97	0.17(0.002), r^2 = 0.97
Protein (kg)	£0.67	−1.70(0.027), r^2 = 0.97	−1.00(0.016), r^2 = 0.97	0.39(0.003), r^2 = 0.98	0.23(0.002), r^2 = 0.98
Lifespan (lactations)	£1.52	−0.29(0.011), r^2 = 0.91	−0.01(0.0004), r^2 = 0.91	0.13(0.003), r^2 = 0.95	0.01(0.0001), r^2 = 0.95
Mastitis (cases)	−£6.20	−0.12(0.004), r^2 = 0.92	0.001(0.0004), r^2 = 0.92	0.09(0.003), r^2 = 0.94	−0.001(0.00003), r^2 = 0.94
Non-return (%)	£0.04	−0.11(0.004), r^2 = 0.93	−0.05(0.002), r^2 = 0.93	0.12(0.004), r^2 = 0.93	0.05(0.002), r^2 = 0.93
Calving interval (days)	−£0.01	−0.01(0.001), r^2 = 0.92	0.04(0.001), r^2 = 0.92	0.01(0.001), r^2 = 0.92	−0.04(0.001), r^2 = 0.92
Lameness (cases)	−£2.69	−0.03(0.001), r^2 = 0.92	0.0003(0.00001), r^2 = 0.92	0.04(0.001), r^2 = 0.92	−0.00004(0.00001), r^2 = 0.92

The a_i values for the highest TEM index for the eight breeding objectives traits were −0.012, 2.468, 5.300, 45.556, −74.466, 1.698, −0.532, −110.059 and 93.354 respectively, with an SD index value of 93.35. This value was much higher than the true a_i index gain (23.21), but it is artificially high if the true REVs are indeed the true REVs. The incorrect REVs within the normal distribution were used to assess the sensitivity of bull selection to the use of incorrect REVs.

The correlations of the five indexes are shown in Table 5. The £PLI and true index were highly correlated (0.96), whereas the top artificial indexes had correlations of 1 with each other and lower correlations with the £PLI and true indexes of 0.83 and 0.96. The top 10 bulls selected by the five indexes are shown in Table 6, with their trait PTAs in Table 7. Although the correlations are high, the group of bulls selected varied considerably between indexes. The £PLI and true index had seven out of 10 bulls in common, whereas the other indexes only had two bulls in common with the true index and three in common with the £PLI index. This suggests that choice of bull is sensitive to choice of REVs. However, the different 10 bulls selected were relatively high up the rank on all indexes; therefore, the trait response from their use would be similar overall. However, such differences may be particularly important for specific herds and peculiar circumstances, e.g. an organic herd selecting against mastitis and where the chosen bulls are especially good or bad for this trait.

Table 5. Correlation between the index values of 712 bulls

	PLI	Random	Index 1	Index 2	Index 3	True
PLI	1
Random	0.847	1
Index 1	0.834	0.997	1
Index 2	0.827	0.997	1	1
Index 3	0.835	0.997	1	1	1
True	0.963	0.855	0.835	0.829	0.836	1

Table 6. Top 10 bulls (of 712) ranked on indices calculated using the ‘true’ REVs and the largest SDIndex value from random sampling and the best three indexes from structured iterations. The top ten bulls in common with the indices based on ‘true’ REVs or the PLI index are designated (A–K)

PLI	Random	Index 1	Index 2	Index 3	True
O-bee Manfred Justice (A)	O-bee Manfred Justice (A)	O-bee Manfred Justice (A)	O-bee Manfred Justice (A)	O-bee Manfred Justice (A)	O-bee Manfred Justice (A)
Mascol (J)	Delta Canvas	Delta Canvas	Delta Canvas	Delta Canvas	Wizzard (B)
Wizzard (B)	Ruskenn	Ruskenn	Ruskenn	Ruskenn	Ljsselvliedt Breakout (C)
Ljsselvliedt Breakout (C)	Wizzard (B)	Wizzard (B)	Wizzard (B)	Wizzard (B)	Lancelot (D)
Urnieta Zelati ii (I)	Vanzetti Valentein Raul	Vanzetti Valentein Raul	Vanzetti Valentein Raul	Vanzetti Valentein Raul	Jardin (E)
Burlane Tennyson (K)	Jobess	Jobess	Jobess	Jobess	Alta Tucano (F)
Laudan	Skalsumer Jorryn	Careca	Careca	Careca	Bilsrow Jock (G)
Lancelot (D)	Burlane Tennyson (K)	Burlane Tennyson (K)	Skalsumer Jorryn	Skalsumer Jorryn	Klassic Merrill Lynch (H)
Ramos	Careca	Skalsumer Jorryn	Netherside Dynamo	Burlane Tennyson (K)	Urnieta Zelati ii (I)
Bilsrow Jock (G)	Ensenada Taboo Planetet	Netherside Dynamo	Burlane Tennyson (K)	Netherside Dynamo	Mascol (J)

Table 7. The predicted transmitting abilities (PTAs) for the main traits of the top ten index bulls listed in Table 6

Bull	PTAs
	Milk	Fat	Protein	Lifespan	Calving Interval Index	Non-return Index
O-bee Manfred Justice (A)	680	31.2	25.7	0.6	−2.94	0.0
Wizzard (B)	593	42.5	22.9	0.2	2.27	−0.8
Ljsselvliedt Breakout (C)	12	26.2	10.6	0.4	−4.34	2.6
Lancelot (D)	415	20.3	22.7	0.6	5.35	−1.4
Jardin (E)	422	20.8	24.2	0.2	2.07	0.6
Alta Tucano (F)	121	25.8	13.7	0.4	−6.55	−0.5
BilsrowJock (G)	528	32.4	23.4	0.1	5.91	−0.3
Klassic Merrill Lynch (H)	291	20.5	14.7	0.4	−0.05	3.4
Urnieta Zelati ii (I)	271	37.1	12.8	0.4	3.79	−1.0
Mascol (J)	553	27.9	23.4	0.2	−1.52	−1.1
Burlane Tennyson (K)	810	30.0	24.1	0.3	6.87	0.3
Laudan	535	16.3	17.7	0.8	3.77	0.6
Jobess	737	32.9	26	0.1	4.1	−1.4
Skalsumer Jorryn	672	26.0	28.3	0.0	2.54	−1.4
Ruskenn	945	29.8	32.1	0.0	4.89	−2.2
Delta Canvas	1041	32.1	31.7	0.2	9.76	−4.1
Ramos	296	12.7	9.5	0.9	−6.24	0.4
Vanzetti Valentein Raul	844	30.0	30.8	−0.1	6.64	−3.6
Careca	543	38.3	26.3	−0.3	4.34	−3.7
SkalsumerJorryn	672	26.0	28.3	0.0	2.54	−1.4
Netherside Dynamo	849	32.6	28.2	−0.1	10.95	−4.5

Discussion

The loss in profit (−ΔTEM) by use of an incorrect REV, when the REV inaccuracy is expressed as a percentage (or proportion) of the true REV, is only approximately proportional to the relative importance of a trait, as measured by a.h² or a.σ_g. That is, the most important traits based on this measure, mastitis, lameness, lifespan, protein and fat, tended to have the highest −ΔTEM values, but the correlation between a.σ_g and the rate of financial loss per percentage of under- or overestimation of REV was only 0.38 and 0.29 respectively. Thus, a.h² or a.σ_g is an imperfect measure of sensitivity of REVs for multi-trait dairy cattle selection indexes because of the variance–covariance structure of traits.

The sensitivity of the TEM response differs depending on whether the REV has been under- or overestimated, i.e. is asymmetric. The correlation between the rate of change in TEM and trait REV when under- or overestimated was only 0.50 overall for all traits. The calculations here, the first such analysis for UK Holsteins, suggest that TEM is most sensitive to proportional underestimates and overestimates of the REV of protein, fat, milk and lifespan and least sensitive to calving interval, lameness, non-return and mastitis REVs. Non-linear and non-symmetrical bias effects on TEM were also found in the earlier study of Vandepitte & Hazel (1977), who simulated a vector of biased REVs for seven breeding objective traits in pigs, as well as studied single trait bias. They found that feed efficiency had the largest percentage effect when REVs were underestimated, whereas dressing percentage had the highest effect when REVs were overestimated, REV overestimates being lower in TEM effect generally. They also found that the effects of errors in REV on TEM increased rapidly as the level of error in the REV increased. The variance of estimated gain in the false aggregate genotype resulting from selection on a false index increased at a much faster rate than the variance of gain in the true genotype resulting from using the false index as REV error level increased. In contrast, Gibson & Dekkers (2011) stated that the effects of negative or positive REV bias on financial gain were symmetrical.

The relative loss of TEM as a result of inaccuracy per unit of REV is more difficult to compare between traits as its value depends on the trait’s unit of measurement. The correlation between a.σ_g and the rate of loss per unit under- or overestimation of REV was only 0.10 and 0.12 respectively. The sensitivity of loss of TEM per unit under- or overestimation of REV was highest for milk, fat and protein, and lowest for lameness, mastitis, lifespan and calving interval. This list of traits differs slightly from the proportional REV change results and is affected by the different units used for each trait.

The loss of income from the use of an incorrect REV is more significant for some traits and depends on the level of over- or underestimation. For example if the protein REV is underestimated by 10%, the loss of financial genetic gain is ∼£0.17/cow/year. For a 100 cow herd, this loss would accumulate over a period of 30 years to produce a non-discounted loss value of £8432 or a discounted value of £5400 (5% discount rate). If the protein REV was overestimated by 10%, the loss of financial genetic gain is lower at ∼£0.039/cow/year, with a 100 cow herd losing £1934 (non-discounted) or £1238 (discounted) over 30 years. In contrast, the loss of income from the use of an incorrect REV for some traits is very minor. For example an REV underestimate of 10% for calving interval results in a loss of only £0.001/cow/year or £0.12/100 cows/year, which is only worth £60 (non-discounted) or £38 (discounted) after 30 years of selection. These levels of financial loss are relatively small at the individual farm level but are additive and significant at the national industry level. The regression slope values in Table 4 provide a valuable guide in deciding which traits require the most rigorous analysis in the calculation of their REVs.

Previous studies of dairy trait REVs in various countries have suggested that trait REVs are important, can be calculated in different ways and can be difficult to estimate. Brascamp et al. (1985) found that the REVs derived from profit equations depended on the base used for the evaluation. Thus different REVs are obtained per unit of investment, per breeding female, per individual or per unit of product. This has led to uncertainty and confusion about appropriate REVs in livestock improvement, and to apparent differences in interests between the investor, the farmer and the consumer. Brascamp et al. found that if the profit equation has a zero outcome, or the profit equation is transformed by setting its outcome to zero by considering profit as a cost of production (so-called normal profit in economics), then the REVs are the same for all bases of evaluation.

Amer & Fox (1992) subsequently reported that disparities between estimates of REVs calculated in different ways disappear when REVs are calculated using a neoclassical model based on the theory of a firm. This is the approach used by Santarossa et al. (2004) and the UK Profitable Lifetime Index (£PLI). The conventional approach to the derivation of REVs by rescaling the production enterprise to a fixed input, output or profit implicitly makes unreasonable assumptions about the behaviour of farmers. They found that when the demand for farm output is elastic, a significant proportion of the benefits from genetic improvement is accrued to producers, whereas when the demand is inelastic, the majority of benefits is accrued to consumers. REVs calculated from the perspective of all producers can thus be different from those calculated from the perspective of an individual farmer or society as a whole, i.e. producers and consumers. Breeding decisions are usually individual producer decisions made to maximize profit or producer utility and can, therefore, differ between producers.

Different markets for milk will impact on the REVs, but our study was based on the approach of Santarossa et al. (2004) who used one set of milk prices based on the published averages paid by UK milk buyers, where a premium is paid for protein. Dairy sire selection tools published by USDA have three separate indexes: Net Merit is designed for producers who ship to milk manufacturing markets where protein premiums are paid; Fluid Merit is designed for producers who ship to fluid milk markets with no protein premiums and Cheese Merit is for producers who ship milk exclusively to cheese plants (Cole et al. 2010). Beard (1987) studied a breeding objective for Australian dairy cattle where milk is sold on three separate markets: liquid milk, domestic manufacture and export manufacture. REVs varied widely when subject to errors in the price of milk components within markets, errors in the export price for milk and errors in feed cost.

The impact of UK milk quotas on REVs was not considered in this study. Beard (1987) found that selection indexes were quite insensitive to variation in the size of quotas on Australian domestic markets. However, some studies suggest that quotas can have a significant impact on REVs. Groen (1989) calculated REVs in situations with and without output limitations, with roughage input limitations and with simple product output limitations. The imposition of milk output limitations resulted in a decrease in milk carrier REVs. Simple product output limitations strongly influenced REVs of production traits. In situations with limitations, REVs were sensitive to product and production-factor prices, milk production level and level of mature weight.

Veerkamp et al. (2002) calculated REVs for milk, fat and protein yields, survival and calving interval using a farm model for pasture-based systems in Ireland. Three scenarios were simulated as follows: (S1) milk and fat% quota with a fixed number of cows per farm and quota leasing; (S2) non-quota scenario with a fixed number of cows per farm and (S3) milk and fat% quota with a fixed output per farm. Sensitivity analysis showed that with high quota costs and/or lower fat prices, the weighting of fat yield was close to becoming negative in the quota leasing scenario (S1). There were major re-rankings among the top 1000 bulls because of a negative weighting on fat.

The REVs used for functional traits would change if welfare is weighted more highly. Groen et al. (1997) reported that genetically and socio-economically balanced selection on production (milk and beef) and functional traits (health, fertility, efficiency of feed utilization and milkability) in dairy cattle requires physiological modelling of animal production, farm economics and social aspects, and appropriate assumptions on future production circumstances. This working group considered the inclusion of social aspects in deriving REVs for functional traits to be a major challenge for animal breeders. Nielsen et al. (2005) subsequently suggested increasing the REVs for the functional traits, mastitis resistance and conception rate, and lowering the REV for milk yield as a method for placing a non-market value representing animal welfare and societal influences for animal production to achieve sustainable breeding goals. Functional traits had the lowest sensitivity to inaccurate REVs in our study.

Despite the problems in estimating dairy trait REVs discussed above, most studies of dairy selection indices have focused on genetic parameter values and varying the inclusion of different traits in the index. Few studies have focused on the assumed REVs, as has been done in this study.

Varying the REVs within a wide range (±200%) in the current studies resulted in different top bulls being selected and their differing PTAs would result in the herds moving in different directions in the long term (20 years). However, the choice of top bulls is essentially dictated by the breeding companies that make the top bull portfolio available in the first place. Thus, farmers are effectively choosing from within the list, rather than making wide ranging selection decisions. Nonetheless, this has led to spectacular gains in productivity over the last 30 years, indicating that most of the top bulls are good overall. Any slight re-ranking is unlikely to have a major effect on breeding or financial outcomes. However, this may not hold true when the breeding goal gets broader by including more traits. As noted, the highest heritability traits affect the index most, but when the index has a larger number of lower heritability traits, their value to the user may be more specific, e.g. a farmer may be specifically interested in fertility, so all other traits being equal, the bull with good fertility would be favoured. The PLI rankings may not reflect this objective, leading to the option of customized indices where the farmer creates rankings of bulls tailored to specific farm circumstances. The proposition of Santarossa et al. (2004) that genetic indices should be customized to herd circumstances using herd-derived REVs remains pertinent.

Acknowledgements

We acknowledge helpful discussions with Prof. Julius van der Werf.

Appendices

Appendix 1

Change in annual total economic merit (TEM) and genetic gain with actual REV changes with no variation in correlations: (a) lifespan (lactations), (b) mastitis (cases), (c) non-return (%), (d) calving interval (days), (e) lameness (cases).

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Appendix 2

Change in TEM and genetic gain with actual EV changes with variations in correlations; (a) lifespan (lactations), (b) mastitis (cases), (c) non-return (%), (d) calving interval (days), (e) lameness (cases)

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