Implications
A literature review was conducted on different ways of defining traits and considering relationships among them in the calculation of economic values (EVs) in livestock breeding. Diversity among trait definitions makes it difficult to compare EVs from different investigations and individual authors. It was shown that, for the EV of a trait to be correctly interpreted, it is necessary to know exactly how the trait was defined, how its relationships with other traits were accounted for and what assumptions were made in the model for the calculation of EVs.
Introduction
Hazel (Reference Hazel1943) proposed the breeding objective or aggregate genotype of an animal to be defined as ‘the sum of its several genotypes (assuming a distinct genotype for each economic trait), each genotype being weighted according to the relative economic value (EV) of that trait’. Since this landmark publication, increasingly sophisticated methods have been proposed for combining information on multiple traits into selection criteria, which maximise improvement of economic merit through definition of multiple-trait breeding objectives and selection indices (Dekkers and Gibson, Reference Dekkers and Gibson1998). Reviews on these methods are found, for example, in the papers by Goddard (Reference Goddard1983), Harris and Newman (Reference Harris and Newman1994), Kluyts et al. (Reference Kluyts, Neser and Bradfield2003) and Amer (Reference Amer2006).
Since the 1950s, many papers have been published dealing with the estimation of economic importance of traits (EVs) in different livestock species. These EVs may be strongly influenced by the definition of the traits, by the whole complex of traits considered for selection purposes and by assumptions made on inter-relationships among traits in the algorithm for the calculation of EVs (Wolfová et al., Reference Wolfová, Wolf, Kvapilík and Kica2007).
The objective of the present review is to point to consequences of different trait definitions (characterising the same animal productive or functional ability) used by distinct authors in the calculation of EVs. The advantages and disadvantages of these trait definitions will be discussed. Furthermore, different approaches for choosing the trait complexes for which EVs are calculated and for considering the relationships among traits within and outside those complexes will be critically reviewed.
Main problems in selecting and defining traits for breeding objectives
Breeding objectives of different livestock species generally include several trait complexes (e.g. milk production, growth and carcass traits). For each trait complex, one or more traits can be defined that influence the net merit of breeding animals and that can be improved through selection on the trait itself or through selection on one or more indicator traits correlated with that trait.
There are only a small number of traits whose definition is straightforward, for example, milk fat and milk protein content or birth weight. Mostly, the ability of an animal to produce milk, meat, wool or eggs with high economic efficiency can be described by alternative traits defined in different ways. The main questions arising when choosing and defining a trait are: (i) How to define growth ability of animals; (ii) How to define a trait that can be but is not necessarily expressed repeatedly during the animal's life, mainly in connection with reproductive cycles of breeding females; (iii) How to define a trait that differs in average value between sexes or among animal groups; (iv) How to determine what is crucial when selecting one or several traits from a number of alternative traits to characterise a specific biological potential of an animal; and (v) Which relationships or dependencies among traits should be taken into account when computing the EV of a specific trait.
In the following sections, approaches for solving these problems are discussed from investigations dealing with the calculation of EVs of traits in livestock, mainly in cattle and sheep as well as in pigs and poultry.
Definition of traits characterising the growth potential of animals
Various mathematical expressions have been used to describe the growth of animals. For example, the Gompertz function (Gompertz, Reference Gompertz1825), the Von Bertalanffy function (Von Bertalanffy, Reference Von Bertalanffy1934) and the Brody function (Brody, Reference Brody1945) have been applied to describe growth in sheep, cattle and poultry. These functions can be written in the following form:
$$)(--><$$>\matrix{ {y(t) = a\times \exp ({\rm{ - }}b\times \exp ({\rm{ - }}ct))} \hfill & {{\rm{Gompertz}} \ {\rm{function}}} \hfill \\ {y(t) = a{{{(1{\rm{ - }}b\times \exp ({\rm{ - }}ct))}}^3} } \hfill & {{\rm{Von}} \ {\rm{Bertalanffy}} \ {\rm{function}}} \hfill \\ {y(t) = \left\{ {<!\begin{array}{*{20}c}>\matrix{ {\exp (ct)} & {{\rm{for }} \ t \,\lt\, T} \\ {a(1{\rm{ - }}b\times \exp ({\rm{ - }}ct))} & {{\rm{for }} \ t \,\geq \,T} \\\end{array}}} \right.} \hfill & {{\rm{Brody}} \ {\rm{function}}} \hfill (1)<$$><!--$$
where y(t) is body weight at time t; a, b and c are parameters of the functions; T is the time at which the inflexion point of the Brody curve is achieved; and exp is the exponential function. In the literature, different modifications of these functions have been used. For example, Miesenberger (Reference Miesenberger1997) also included a factor for birth weight in the Brody function.
Initially, growth curves were derived assuming that animals were grown under non-limiting conditions. When limiting conditions prevented growth potential from being fully realised, some authors added an additional multiplier to the original growth functions, for example, Amer et al. (Reference Amer, Emmans and Simm1997) for beef cattle, Conington et al. (Reference Conington, Bishop, Waterhouse and Simm2004) for meat sheep in extensive pasture systems and Menge et al. (Reference Menge, Kosgey and Kahi2005) for indigenous chickens.
Distinct types of growth curves were applied in fattening v. breeding animals by Miesenberger (Reference Miesenberger1997), who used the Gompertz function for the growth of fattened bulls and the Brody function for the growth of replacement heifers. Fuerst-Waltl and Baumung (Reference Fuerst-Waltl and Baumung2009) proceeded in a similar manner for the growth of lambs in fattening and of breeding females from birth till slaughter or mature weight, respectively.
In studies by Hirooka et al. (Reference Hirooka, Groen and Hillers1998a), Koots and Gibson (Reference Koots and Gibson1998), Amer et al. (Reference Amer, Simm, Keane, Diskin and Wickham2001), Albera et al. (Reference Albera, Carnier and Groen2004), Fernández-Perea and Jiménez (Reference Fernández-Perea and Jiménez2004) and Rewe et al. (Reference Rewe, Indetie, Ojango and Kahi2006), growth of young animals till weaning and during the fattening period was assumed to be linear, whereas growth curves were applied for breeding animals from weaning to culling or to mature weight. This non-linearity of growth was approximated by piecewise linear functions in the studies by de Vries (Reference De Vries1989), Bekman and van Arendonk (Reference Bekman and van Arendonk1993) and Wolfová et al. (Reference Wolfová, Wolf, Krupová and Kica2009).
Four main approaches that have been used for choosing and evaluating traits, which characterise animal growth described by one of the above-mentioned non-linear functions or by a linear function, are reviewed and commented in the following paragraphs.
Mature weight as the main or only growth trait
When calculating the EV of a trait, the trait level must be varied (increased and/or decreased) to get the appropriate changes in profit or another efficiency criterion. Mature weight (asymptotic weight, parameter a) is a growth trait, the level of which can be varied easily in all three growth curves shown in equation (1); therefore, the EV for this trait can be calculated from the growth curve. In the Von Bertalanffy or Brody curves, birth weight may also be varied to calculate its EV. The weight of animals at different ages or the average growth rate in a certain time period may then be calculated as a function of mature weight and eventually of birth weight. The EV of mature weight includes changes in the growth pattern of all animal groups, the growth of which was described by the growth curves. Almahdy et al. (Reference Almahdy, Tess, El-Tawil, Shehata and Mansour2000) used mature weight as the sole trait to describe the economic impact of growth ability in sheep. The EV was expressed per kg weight change in females born as singles, but considered the economic impact of growth changes in lambs born in multiple litters as well. In the calculation of the EV for mature weight in cattle, Koenen et al. (Reference Koenen, Berentsen and Groen2000) only considered changes in the live weight of breeding females. A small number of authors (Groen, Reference Groen1988; Hirooka et al., Reference Hirooka, Groen and Hillers1998a and Reference Hirooka, Groen and Hillers1998b) used growth curves to estimate the EV for birth weight, in addition to the EV for mature weight.
A certain disadvantage of the above approach is that breeders normally do not select on mature weight or birth weight but rather on growth rates (or only one growth rate) during specific periods of life. For example, breeders may be interested in increasing the growth rate of progeny till weaning and during fattening. However, exclusive selection on increased growth rates will often result in higher mature weight as well (Taylor et al., Reference Taylor, Thiessen and Murray1986). As a consequence, selection of bulls for a high growth rate in a performance test has resulted in increased mature weight of dairy and beef cows in recent decades.
However, increased growth rate in certain phases of life does not have to be necessarily connected with higher mature weight. Current long-term selection experiments with the Japanese quail have shown that it is possible to change the shape of the growth curve, keeping mature weight (asymptotic weight) nearly constant (Hyánková et al., Reference Hyánková, Knížetová, Dědková and Hort2001). However, according to these authors, mature weight must be a selection criterion next to growth rate to achieve this result. A problem with this approach is that in practical situations, animals are mostly selected before they reach mature weight. Information from parents (e.g. bull dams) and other relatives has to be used then or indirect selection on conformation traits connected with mature weight has to be applied to stabilise mature weight.
On the other hand, treating mature weight as the only trait for growth ability and assuming a priori higher growth rates for animals with higher mature weight may prevent changes in animal growth patterns, which could be economically favourable.
Parameters of the growth curve as primary traits
Applying the Gompertz curve (see equation (1)) to bulls during fattening, Miesenberger (Reference Miesenberger1997) altered parameters b and c, while keeping parameter a (mature weight) constant to calculate the EV of growth rate. The same procedure was used by Fuerst-Waltl and Baumung (Reference Fuerst-Waltl and Baumung2009) for growth rate of lambs from birth to slaughter and by Lind (Reference Lind2007) for net daily gain of bulls during fattening.
However, Fuerst-Waltl and Baumung (Reference Fuerst-Waltl and Baumung2009) showed that the EV of the growth rate of lambs was sensitive to different changes of the parameters of the Gompertz growth curve. Generally it seems to be very difficult to find arguments that justify a particular way of changing the parameters of the growth curve. There is a certain danger from unconsciously manipulating the function parameters until an expected EV is achieved.
Changing only parameter a (mature weight) in the growth function is straightforward and easy to interpret. However, Miesenberger (Reference Miesenberger1997) and Fuerst-Waltl and Baumung (Reference Fuerst-Waltl and Baumung2009) assumed that changing mature weight would have an impact on the growth curve of only replacement females and cows or ewes. That would mean that growth of animals intended for fattening and growth of breeding females were different traits. This is a questionable assumption, because both sexes are generally kept under the same feeding conditions till weaning (or till the end of rearing of dairy calves), and both sexes are used for fattening (especially in sheep). Vargas et al. (Reference Vargas, Groen, Herrero and Van Arendonk2002) changed the mature body weight parameter a in the Brody growth curve, causing a shift in the entire growth curve; moreover, they expressed the EV for the growth potential per change in body weight of heifers at 28 month of age (the only growth trait evaluated).
Linear approximations of parts of the growth curve
The third approach for the calculation of EVs for growth traits uses the growth curve to estimate animal weight at specified ages. On the basis of these weights, linear daily gains for the sequential age intervals are calculated. These are considered as traits for which EVs are calculated, either separately for each segment or jointly. This procedure has been applied to broiler chickens and geese (Shalev and Pasternak, Reference Shalev and Pasternak1983 and Reference Shalev and Pasternak1999) and to cattle (Albera et al., Reference Albera, Carnier and Groen2004; Fernández-Perea and Jiménez, Reference Fernández-Perea and Jiménez2004).
Albera et al. (Reference Albera, Carnier and Groen2004) predicted weights of breeding heifers and cows at different ages using the Von Bertalanffy curve. Post-weaning linear daily gains between two ages were then calculated for females and expressed as proportions of the growth rate of young bulls during fattening, which was the only growth trait for which EVs were calculated. Proportional changes in daily gain of heifers in fattening, and replacement heifers and cows in all growth periods after weaning, were assumed and the effects of these changes were included into this EV. Therefore, mature weight was assumed to increase with increasing post-weaning growth rate and was not evaluated as a separate trait.
Generally, the assumption of an inter-relationship among the growth rates of different animal groups seems to be more comprehensible from the biological point of view than the assumption of no connection among them. An exception to this principle was applied by Albera et al. (Reference Albera, Carnier and Groen2004) to growth of calves up to weaning, which was considered fixed within each sex and unrelated to growth after weaning. This can be a realistic assumption in beef cattle kept on pasture without supplementary feeding of calves till weaning, in which case growth of calves could be limited by the milk production of cows. However, on good pasture, calves with high growth potential can compensate for low cow milk production by eating more pasture. The growth rate of calves till weaning itself can also have an important EV and should be, in our opinion, evaluated as an additional trait.
A combination of a non-linear growth curve with a linear growth curve was applied by Hirooka et al. (Reference Hirooka, Groen and Hillers1998a and Reference Hirooka, Groen and Hillers1998b), Fernández-Perea and Jiménez (Reference Fernández-Perea and Jiménez2004) and Rewe et al. (Reference Rewe, Indetie, Ojango and Kahi2006) for beef cattle in a pasture system with intensive fattening of surplus calves. In fattening, linear growth was assumed from birth to weaning and from weaning to slaughter. The growth of replacement heifers and cows was described by the Brody curve (Hirooka et al., Reference Hirooka, Groen and Hillers1998a and Reference Hirooka, Groen and Hillers1998b; Rewe et al., Reference Rewe, Indetie, Ojango and Kahi2006) or the Von Bertalanffy curve (Fernández-Perea and Jiménez, Reference Fernández-Perea and Jiménez2004). These authors frequently considered weight at different ages and not growth rate as the trait of interest when calculating EVs for growth.
When changing growth rates till weaning or in fattening of male calves, proportionately lower growth rates in female calves during the same time intervals were assumed by Hirooka et al. (Reference Hirooka, Groen and Hillers1998a and Reference Hirooka, Groen and Hillers1998b), whereas Fernández-Perea and Jiménez (Reference Fernández-Perea and Jiménez2004) assumed fattening of male calves only. In both investigations, post-weaning growth of breeding females was assumed to be independent of growth of animals in fattening. Hirooka et al. (Reference Hirooka, Groen and Hillers1998a and Reference Hirooka, Groen and Hillers1998b) stated that growth of animals in feedlot under unrestricted feeding followed a different growth function than that of breeding animals under pasture conditions. It was shown by Bond et al. (Reference Bond, Warwick, Olejen, Putnam, Hiner, Kotula and Weiland1982) that market weight of fattened animals can exceed asymptotic mature weight under pasture conditions.
As mentioned above, differences in the genetic growth potential of calves (lambs) till weaning cannot be fully expressed when milk is the main source of nutriment for calves (lambs) and milk production of cows (ewes) is insufficient. Koots and Gibson (Reference Koots and Gibson1998) therefore expressed the weaning weight of beef calves, not only as a function of mature weight but also of peak milk yield. The EV of mature weight then included the effect of changes in mature weight on cow weight at different ages, weaning weight, post-weaning gain and optimal slaughter weight in fattening. Moreover, these authors defined post-weaning growth rate of young animals in fattening as a separate trait independent of mature size and called this trait ‘residual post-weaning growth rate’. In that case, the possibility to change the shape of the growth curve while keeping mature weight constant was assumed. This approach is in accordance with the finding of Hyánková et al. (Reference Hyánková, Knížetová, Dědková and Hort2001), as mentioned before.
Separate traits for different growth periods without applying a growth curve
In livestock populations, weights of animals are most commonly available at certain times in the management cycle, at birth and weaning for example. Such measurements can serve for calculating growth rates for the intervals between two adjacent weighings, in which case growth between weighings would be assumed to be linear. This approach allows taking into account different management and feeding strategies in different life periods of animals intended for selling, breeding or fattening.
Wolfová et al. (2005, Reference Wolfová, Wolf, Kvapilík and Kica2007 and 2009) divided the growth period of young animals of both sexes in cattle and sheep into segments, which were consistent with management calendar and feeding practices, and then used the population means for weights at the start and end of each segment to calculate the average growth rate for that segment (e.g. growth rate till weaning, post-weaning growth rate for animals fattened or reared as replacements). Mature weight of animals was considered to be a separate trait, which could be altered by selection independently of growth rate at younger ages. This approach allows adjusting the EVs of different growth rates for feeding rations, labour and other costs, which can differ among growth periods and which make the addition of a multiplier for correcting the general growth curve for limited feeding conditions unnecessary.
Linear growth rates from birth to slaughter were also assumed by Bekman and van Arendonk (Reference Bekman and van Arendonk1993) who considered only birth weight and daily gain from birth to slaughter in dairy and dual purpose cattle. De Vries (Reference De Vries1989) divided the growth period of pigs into three stages, assumed linear growth within each segment (growth of piglets till weaning, in rearing and during fattening) and considered mature weight of sows to be a separate trait. These same growth periods were utilised by Houška et al. (Reference Houška, Wolfová and Fiedler2004), but they defined weight gain from birth to slaughter as the only growth trait in the breeding objective for pigs.
The EVs of growth rate in a specific time period can easily be converted to EVs for alternative traits to characterise growth ability, for example, animal weight at a certain age or animal age at a fixed weight (Coopman et al., Reference Coopman, Krafft and Gengler1999; Bett et al., Reference Bett, Kosgey, Bebe and Kahi2007; Byrne et al., Reference Byrne, Amer, Fennessy, Cromie, Keady, Hanrahan, McHugh and Wickham2010; Houška et al., Reference Houška, Wolfová, Nagy, Csornyei and Komlosi2010).
As shown in this section, growth ability of animals can be described by many different traits. The approaches and assumptions used for the calculation of the EV for a specific growth trait (in particular for mature weight) by different authors are highly variable, having a material impact on the EV of this trait. Each approach has certain advantages and disadvantages so that a general recommendation for choosing one of them is impossible because of differences among breeding programmes caused by specific economic, production and management conditions. However, as a rule, the choice of the growth traits, for which the EVs are calculated, should be tightly linked to the choice of growth traits for genetic evaluation. For example, treating mature weight as the solely growth trait and as a driving variable affecting other partial growth traits might be appropriate only in situations where other measurements (growth rates in different parts of animal life and in different sexes) are not available and mature weight is the only growth trait of interest in the breeding goal. If performance data for growth in different segments of animal life are available, the evaluation of the economic impact (EVs) of changes in growth rates (or weights) in each segment separately seems to be preferable. Such EVs are easily interpretable to farmers and may be mostly combined in an easy way to a selection index, taking into account the genetic correlations between the different segments of the growth curve.
Definition of traits characterising repeated animal performance
Many important traits in livestock occur repeatedly in the lifetime of an animal, most prominently those connected with oestrus and reproductive cycles of breeding females. Examples are milk yield per lactation in dairy cattle, egg production per laying period in laying hens and litter size in pigs. Furthermore, functional traits such as conception rate, calving (farrowing, lambing) interval, survival rate and calving performance belong to this group. Traits such as conception rate even show a twofold (nested) repetition: for reproductive cycles and, within each reproductive cycle, for oestrus cycles. In the following paragraphs, the main approaches applied for defining traits expressed repeatedly in the lifetime of an animal are reviewed.
Defining the average of repeatedly expressed performance as trait of interest
A common approach in the literature has been to consider only the mean value of the repeated trait averaged over all repetitions (reproductive cycles, oestrus cycles) in the calculation of EVs. For example, Bekman and van Arendonk (Reference Bekman and van Arendonk1993) and Legarra et al. (Reference Legarra, Ramón, Ugarte and Pérez-Guzmán2007) calculated the EVs of milk production traits from the annual production of milk carrier, fat and protein. This approach is suitable in situations where milk production traits were the only traits included in breeding goals for dairy cattle. However, when reproductive and health traits have been added and their EVs should be simultaneously estimated next to the EVs for milk production traits, the definition of milk (fat, protein) as average annual yield per cow may cause an underestimation of the EVs for reproductive and health traits. As a case in point, a prolonged service period of dairy cows (an indicator of inability to conceive) generally prolongs the length of lactation and influences the average milk yield per cow per year; although the genetic potential for milk production is not affected. Similarly, cow survival influences the age structure of cow herds that again has a material impact on the average annual milk yield. Keeping average annual milk yield per cow constant when estimating the EVs of conception rate or cow survival means that the non-genetic effect of the changes in those traits on annual milk production cannot be included in their EVs. Furthermore, in current breeding programmes, hardly anyone would suggest using the average unadjusted annual milk production of a cow as selection criterion, and therefore there is little justification to calculate the EV for this trait.
An underestimation of the impact of reproductive traits, particularly conception rate, on economic efficiency also occurs, when conception rate is defined as the average over different numbers of inseminations (in dairy cattle) or oestrus cycles (in beef cattle). When changing the value of conception rate in the calculation of the EV of this trait, it is often assumed that this change only has an impact on the culling rate of barren cows. The effect of conception rate on a prolonged lactation or on calving date in systems with seasonal calving is omitted in this case.
Survival, conception or mortality rates of breeding females may also be defined as averages over all reproductive cycles when calculating EVs for these traits (Stewart et al., Reference Stewart, Bache, Harris, Einstein, Lofgren and Schinckel1990; Tolone et al., Reference Tolone, Riggio, Maizon and Portolano2011). Menge et al. (Reference Menge, Kosgey and Kahi2005) defined laying capacity as average number of eggs laid per hen per clutch over different laying periods. Similarly, Shalev and Pasternak (Reference Shalev and Pasternak1999) defined egg production for geese as the average annual egg number. Houška et al. (Reference Houška, Wolfová and Fiedler2004) characterised sow fertility by conception rates averaged over all reproductive cycles, but distinguished conception rates after the first, second and third inseminations.
Treating repeated performance as repeated expressions of the same trait
In more recent papers, repeated animal performances have been assumed to be only different expressions of the same trait. When calculating the EV for such a trait, the average values of all repeated trait expressions were changed simultaneously. Some authors applied changes by the same absolute value for all trait components, whereas other authors applied proportional changes. The EVs for those traits were mostly related to the average values of the repeated expressions. Some examples will be given.
Miesenberger (Reference Miesenberger1997) increased the daily milk production of cows in each lactation by the same absolute value and expressed the resulting change in profit per kg change in the average annual herd milk production per cow. The same approach was applied by Fuerst-Waltl and Baumung (Reference Fuerst-Waltl and Baumung2009) when calculating the EV for milk production of dairy sheep. De Vries (Reference De Vries1989) or von Rohr (Reference Von Rohr1998) increased litter size and culling rate of sows in all reproductive cycles by 0.1 piglets per litter and by 1%, respectively, when calculating the EVs for those traits. Reinsch and Dempfle (Reference Reinsch and Dempfle1998) changed the losses of calves, conception rates, dystocia and health traits in all lactations by the same percentage, assuming a correlation of one among expressions of the corresponding traits in all lactations. Similarly, Dekkers (Reference Dekkers1991) and Veerkamp et al. (Reference Veerkamp, Dillon, Kelly, Cromie and Groen2002) increased the involuntary culling rate and conception rate of cows in each lactation and the lactation month proportionally by the same relative factor, when calculating the EVs of those traits. Wolfová et al. (2007 and 2009) changed the daily milk production of dairy cows and ewes during the entire milking period in all lactations proportionally by 0.5% and expressed the resulting change in profit per kg change in the average standardised milk production per 305 days in cows and per 150 days in sheep.
In our opinion, proportional changes of all repeated trait expressions (e.g. among milk production or litter size in different parities) when calculating EV seem to be more appropriate and more close to the biological reality than changes by the same absolute value. However, the choice of multiplicative v. additive changes of the trait levels has no impact on the EV of the trait, if the EV is presented per unit change in the average of all repeated trait expressions, but it has a meaningful impact on the EV if it is presented per unit of a reference quantity for a repeatedly expressed trait (see next section).
Defining a reference quantity for repeatedly expressed traits
This approach is similar to the previous one, except that calculated EVs of the repeatedly expressed trait are not given per unit change of the average trait value over all repeated performances, but rather per unit change in a reference trait that must be defined for each specific situation. Groen (Reference Groen1988), for example, characterised productive ability for milk traits in cattle by 305-day first lactation yields of milk carrier, fat and protein as the reference traits. However, the EVs of these traits also included the impact of changes in milk, fat and protein production on profit in the following lactations by transmitting the changes in the first lactation via adjustment factors to all subsequent lactations. A similar approach was used by Wolfová et al. (Reference Wolfová, Přibyl and Wolf2001) for the estimation of the EV for first parity milk yield, the reference trait.
Groen and Korver (Reference Groen and Korver1989) defined dry matter intake of a cow weighing 600 kg, yielding 6000 kg of milk and being in the 2nd month of the first lactation as the reference quantity for dry matter intake as such. Multiplicative factors were used to calculate dry matter intake in the remaining months of the first lactation and in subsequent lactations. Nielsen et al. (Reference Nielsen, Groen, Ostergaard and Berg2006) defined a base risk of disease incidence for a specific life cycle stage of cows. To include the effect of a change in this base risk on other cow stages (different lactations), the authors used odds ratios calculated for those stages.
Roughsedge et al. (Reference Roughsedge, Amer, Thompson and Simm2005) related the effect of changes in the calving interval in all lactations to the appropriate change in the first calving interval. Vargas et al. (Reference Vargas, Groen, Herrero and Van Arendonk2002) chose the average performance of a heifer with an age at first calving of 28 months and with a calving interval of 12 months as reference value for milk production traits, and then applied multiplicative factors to adjust for different ages, parities and calving intervals. For conception rate, the reference trait was the value obtained for a single insemination at the 2nd month of the first lactation. Houška et al. (Reference Houška, Wolfová and Fiedler2004) chose the number of piglets born alive in the first farrowing as reference trait for litter size and applied multiplicative factors for higher parities.
Referring the EV of a repeatedly expressed trait to one unit of a reference quantity could be appropriate in situations where breeding value estimation for such a trait is also based on a specific trait definition, for example, on 305-day milk yield in the first lactation only or on conception rate of females after the first insemination.
Defining repeated trait expressions as different traits
Another approach is to handle the expressions of the same biological trait in different reproductive cycles as if they were distinct traits. Dekkers (Reference Dekkers1994) and Albera et al. (Reference Albera, Carnier and Groen2004) defined calving ease in the first lactation as a trait different from calving ease in later lactations. Wolfová et al. (2005 and 2007) evaluated conception rates separately of heifers and cows, in accordance with breeding value estimation procedures for this trait in the Czech Republic. Wolfová et al. (Reference Wolfová, Wolf, Krupová and Kica2009) used this same approach for conception rate in sheep. Reinsch and Dempfle (Reference Reinsch and Dempfle1998) calculated the EVs for milk production traits separately for parities 1, 2 and ⩾3 in accordance with the multi-trait breeding value estimation procedure used at that time in Germany.
Definition of traits expressed in different sexes or animal groups
Growth and carcass traits, fleece weight and survival rate may be measured in both sexes and in different age groups or management groups (animals in fattening, breeding animals). Though breeding values for growth and carcass traits are often estimated on the basis of testing one sex during a specific life period only, it is expected that an improvement in the trait as measured would be achieved in all sexes and at different ages. Therefore, when calculating the EVs for these traits, the impact of improved genetic potential in all sexes and in different animal categories or groups (e.g. young and adult animals) on the economic efficiency of the production system should be taken into account. Some approaches to this problem for growth traits were mentioned in the foregoing section. Other approaches encountered in the literature for the calculation of EVs of traits expressed in different sexes or animal groups are summarised and discussed in the following paragraphs.
Defining a specific trait for only the most important animal group
The EV for the trait of interest would be estimated on the basis of changing the average performance for this trait only in a specific sex or specific category of animals, typically the group that is expected to be the most important in the evaluated production system. This procedure was used by Munoz-Luna et al. (Reference Munoz-Luna, Yadav and Dempfle1988) and by Bekman and van Arendonk (Reference Bekman and van Arendonk1993) when calculating the EVs for growth rate or carcass traits during fattening; only bulls were included because very few heifers are fattened in production systems with dairy cattle. Kahi and Nitter (Reference Kahi and Nitter2004) considered only heifers when estimating the EVs for pre-weaning and post-weaning daily gain and survival rate in dairy cattle, because their model did not involve fattening of male calves.
Defining a trait separately for each sex or animal group
The EV of a trait may be estimated separately for each sex (females, males, castrates) or animal group, a procedure used by many authors. In sheep, Ponzoni (Reference Ponzoni1988) and Jones et al. (Reference Jones, Amer, Lewis and Emmans2004) applied this approach for wool, growth and carcass traits. Byrne et al. (Reference Byrne, Amer, Fennessy, Cromie, Keady, Hanrahan, McHugh and Wickham2010) evaluated lambing difficulty separately for single-bearing and multiple-bearing ewes.
In cattle, Newman et al. (Reference Newman, Morris, Baker and Nicoll1992), Wolfová et al. (Reference Wolfová, Wolf and Hyánek1995), Phocas et al. (Reference Phocas, Bloch, Chapelle, Bécherel, Renand and Ménissier1998), Van der Werf et al. (Reference Van der Werf, van der Waaij, Groen and de Jong1998), Fernández-Perea and Jiménez (Reference Fernández-Perea and Jiménez2004) and Rewe et al. (Reference Rewe, Indetie, Ojango and Kahi2006) estimated the EVs for fattening and carcass traits separately for some of the following categories: calves, heifers, cows, bulls and castrates. Koots and Gibson (Reference Koots and Gibson1998) evaluated calving ease separately for heifers and cows.
Groen et al. (Reference Groen, Jiang, Emmerson and Vereijken1998) and Jiang et al. (Reference Jiang, Groen and Brascamp1998) defined finishing weight, feed consumption, mortality and carcass traits separately for females and males when calculating the EVs for these traits in broiler production systems. Wood (Reference Wood2009) proceeded similarly when estimating EVs for fattening and carcass traits separately for hens and toms in turkey production.
Combining EVs calculated separately for different animal groups into a joint EV for the given trait has mostly been accomplished by weighting the partial EVs by the number of animals in each group per reference unit (e.g. per cow per year or per lambing ewe per year; Wolfová et al., Reference Wolfová, Wolf and Hyánek1995; Phocas et al., Reference Phocas, Bloch, Chapelle, Bécherel, Renand and Ménissier1998; Fernández-Perea and Jiménez, Reference Fernández-Perea and Jiménez2004) or by weighting the partial EVs by the number of gene expressions of the selected parents in each animal group (Amer et al., Reference Amer, Simm, Keane, Diskin and Wickham2001; Conington et al., Reference Conington, Bishop, Waterhouse and Simm2004; Wolfová et al., Reference Wolfová, Wolf, Přibyl, Zahrádková and Kica2005; Berry et al., Reference Berry, Madalena, Cromie and Amer2006). Using this approach, the authors assumed that a change in the genetic potential for a trait would result in the same changes in the phenotypic means in both sexes and in all animal groups. Consequently, sex- and age-specific differences in the phenotypic trait means were not reflected when changing the means for the calculation of EVs, which may therefore fail to account for all economic effects of the modelled selection.
If this problem was judged to be sufficiently serious, it could be overcome by treating each trait expressed in different sexes as a separate trait with a separate EV and using genetic and phenotypic correlations among those traits when constructing a selection index, as done by Ponzoni and Newman (Reference Ponzoni and Newman1989). Rewe et al. (Reference Rewe, Indetie, Ojango and Kahi2006) distinguished between the expressions of the same trait in progeny and in cows when developing selection indices, but the expression of that trait in bulls and heifers was assumed to be equivalent.
Defining a trait as average over sexes
The effect of sex is frequently neglected when calculating the EV for a trait. This is especially common for traits measured in early growth phases and during fattening. This policy becomes necessary when data for the EV estimation of a trait are not available separately for sexes. Munoz-Luna et al. (Reference Munoz-Luna, Yadav and Dempfle1988), Bekman and Van Arendonk (Reference Bekman and van Arendonk1993) and Fuerst-Waltl and Baumung (Reference Fuerst-Waltl and Baumung2009) applied this procedure to growth and carcass traits of calves, and Koots and Gibson (Reference Koots and Gibson1998) and Coopman et al. (Reference Coopman, Krafft and Gengler1999) calculated the EV of survival rate of calves till 6 months or till weaning in this way.
Growth and carcass traits as well as survival rates of lambs were averaged over sexes and litter sizes by Kosgey et al. (Reference Kosgey, van Arendonk and Baker2003), Conington et al. (Reference Conington, Bishop, Waterhouse and Simm2004), Haghdoost et al. (Reference Haghdoost, Shadparvar, Nasiri and Fayazi2008) and Tolone et al. (Reference Tolone, Riggio, Maizon and Portolano2011). Similarly, averages over sexes were used by De Vries (Reference De Vries1989) and Houška et al. (Reference Houška, Wolfová, Nagy, Csornyei and Komlosi2010) for fattening and carcass traits of pigs, and by Bett et al. (Reference Bett, Kosgey, Bebe and Kahi2007) for pre-weaning survival of kids.
If there are substantial differences in the trait level between males and females, and if profit (or another efficiency criterion) is a non-linear function of the evaluated trait, the EV will depend on the proportions of males and females in the population under consideration. This can lead to a bias in the estimate of the EV if only measurements from farm samples and not performance data from the whole population are available. EVs, which are calculated knowing the proportions of sexes in the whole population in all animal groups, may be the most appropriate for weighting traits for which the breeding values were estimated from models adjusting for sex as a fixed effect.
Defining reference groups for a trait expressed in different sexes or animal groups
The EV of a trait that occurs in different sexes may be expressed per unit of the trait in one sex, or in one sex within a specified animal group. The animals of this sex and group may then be designated as the reference group. Although such EVs refer to a certain group of animals, they normally include the economic effect of proportional (or additive) changes in the same trait in other sexes and animal groups. Some examples will be given. Albera et al. (Reference Albera, Carnier and Groen2004) referred the EV of post-weaning daily gain in Piemontese cattle to daily gain of fattened bulls, taking into account proportional changes in the growth rates of fattened heifers and reared breeding heifers. Wolfová et al. (Reference Wolfová, Wolf, Přibyl, Zahrádková and Kica2005) expressed the EV for growth rate till weaning or during fattening of beef cattle per daily gain of female calves.
Almahdy et al. (Reference Almahdy, Tess, El-Tawil, Shehata and Mansour2000) used mature weight of single-born female sheep as the reference trait, assuming that changes in mature weight of this animal group would cause proportional changes in mature weight of females born in litters of a different size and of males born in litters of any size. Krupová et al. (Reference Krupová, Wolfová, Wolf, Oravcová, Margetín, Peškovičová, Krupa and Dańo2009) expressed the EV for growth rate of lambs till weaning per daily gain of female lambs born as singles. Borg et al. (Reference Borg, Notter, Kuehn and Kott2007) chose ewe lambs born as singles and weaned at an age of 120 days as the reference category for the calculation of the EVs for birth and weaning weight.
Groen (Reference Groen1988) defined a female calf born in a cow's first parturition as the reference category for the calculation of the EV for birth weight; cows were the reference category for mature weight. Birth weight in the remaining categories was related to the reference categories via adding or subtracting an appropriate constant. A disadvantage of this method is that relative differences among categories may not be reflected when changing the trait value of the reference group in the calculation of EVs.
Combining different approaches when defining traits
Various approaches described above may be combined, as the following examples illustrate. Rewe et al. (Reference Rewe, Indetie, Ojango and Kahi2006) calculated the EVs for sale weight and feed intake separately for bulls and heifers; while dressing percentage, consumable meat percentage and post-weaning survival rate were defined as averages over sexes (male and female calves) and animal groups (cows, heifers and bulls). Lôbo et al. (Reference Lôbo, Pereira, Facó and McManus2011) defined dressing percentage and mortality of lambs and yearlings as averages over sexes; however, mortality of adult animals, weight at slaughter and mature weight were treated separately for females and males.
Hirooka et al. (Reference Hirooka, Groen and Hillers1998b) changed the genetic levels of growth and carcass traits in beef cattle proportionally in different sexes and divided the change in biological and economical efficiency by the total change (weighted sum across all categories) of the evaluated trait in the defined system. Wolfová et al. (Reference Wolfová, Wolf, Krupová and Kica2009) and Byrne et al. (Reference Byrne, Amer, Fennessy, Cromie, Keady, Hanrahan, McHugh and Wickham2010) used average survival rates of female and male lambs at birth or till weaning, taking into account the proportions of singles, twins and so on.
In this section, many different approaches for treating repeated performances when calculating the EV of a trait were discussed. The availability of performance records for a trait expressed in different sexes, oestrus cycles or parities and the effects in the model for breeding value estimation for this trait should be decisive when searching for the appropriate definition of repeatedly expressed trait and for a correct approach when calculating its EV. For instance, assume that weaning weight is measured in both sexes and the model for breeding values estimation adjusts for sex effects. Then, in our opinion, the economic impact of increased genetic potential for weaning weight should include the economic effect of the increase in weaning weight of both male and female calves, whereas the sex-specific relative difference in weaning weights should be kept constant. As a further example, assume that the breeding value for milk yield is calculated on the basis of first lactation yield only. Then, the EV for this trait should include the economic effect of changes in milk yield in all lactations, while keeping the relative differences in milk yield among parities constant.
Choice of a trait from a group of traits characterising a specific biological potential of animals
The genetic potential of an animal to produce a specific product of a certain quality, or the genetic potential for reproductive ability and health can be often described by alternative traits. The choice of the most appropriate trait for a certain biological potential is not always straightforward. Before making a decision for a trait or a group of traits, the availability of data for breeding value estimation and for the calculation of EVs as well as the direct and indirect impact of candidate traits on revenues and costs in the evaluated production system should be assessed first. When the relationship is known between two potential traits to describe the same biological potential of animals, a conversion of the EV for the first trait to an EV for the second trait generally is possible. In the following paragraphs, some problems arising in this context will be presented, and approaches described in the literature to solve the problems will be discussed.
Traits characterising the (productive) lifetime of breeding females
In the literature, the term ‘longevity’ is often used, although not all cows have a long life. Probably ‘(productive) lifetime’ is a better identification of the trait. The definition of ‘longevity’ of breeding females is perhaps the most controversial among traits included in the breeding goals of livestock species. ‘Longevity’ is mostly defined as average productive lifetime of breeding females, that is, average time between first calving (lambing, farrowing, etc.) and culling. In some cases, lifespan, that is, the age of breeding females at culling, is taken as the trait of interest (Van Arendonk, Reference Van Arendonk1991; Roughsedge et al., Reference Roughsedge, Amer, Thompson and Simm2005). Assumptions made in the calculations of the EV for lifespan differ substantially among authors, which causes substantial differences among the absolute as well as relative EVs for this trait. One reason for the high variability among the estimated EVs for lifespan of breeding females is that it is a composite trait. The EV of lifespan depends predominantly on which of the component traits were changed during the calculation. For illustration, an example for cattle will be given.
Lifespan, defined as average lifespan of breeding females (LS), can be split into heifer rearing and cow productive lifetime components:
$$ LS\, = \,AGE1\, + \,PLT $$
where AGE1 is the age of heifers at first calving and PLT is the average productive lifetime of cows (interval between first calving and culling). Age of heifers at first calving is highly dependent on reproductive management but is also influenced by reproductive ability of young females. It can be expressed as a function of the following variables:
$$ AGE1\, = \,AGEM1\, + \,INT1LH\, + \,LP $$
where AGEM1 is the age of heifers at first mating, INT1LH is the interval between the first insemination and actual conception of heifers (which is a function of heifer conception rate, length of the oestrus cycle and the oestrus detection rate) and LP is the length of pregnancy. The average productive lifetime of cows in time units (years or days) can be expressed in a simplified form in the following way:
$$ no{ PLT\, = \,(NL\, - \,1)\,\times \,CI\, + \,DC \cr CI\, = \,IC1M\, + \,INT1LC\, + \,LP \cr NL\, = \,1/p $$
where NL is the average number of lactations, CI is the average calving interval, DC is the average interval between calving and culling after the last lactation, IC1M is the average interval from calving to first insemination (which is determined by the ability of cows to express oestrus and by the voluntary waiting period), INT1LC is the interval between the first and the last (successful) insemination of cows (which is again a function of conception rate, length of the oestrus cycle and oestrus detection rate), LP is the length of pregnancy and p is the total culling rate of cows per lactation, which is equal to the fraction of cows in the first lactation when the cow population is in the stationary state. The total culling rate (or average survival rate) takes into account death of cows and culling for any reason (failure to conceive, culling for adverse health and also voluntary culling, e.g. for low milk production).
Reproductive traits of heifers and cows are often handled as different traits in breeding value estimation. In this case, the age at first calving should not be included in the calculation of the EV for cow longevity. Cow longevity should then be defined as productive lifetime PLT as given in equation (4).
It follows from equation (4) that a change in PLT can be achieved through variations in at least four variables characterising reproductive ability and health status of cows (IC1M, INT1LC, LP and p), resulting in different EVs to characterise productive lifetime. Therefore, it should always be clearly stated which variables are the basis for calculating the EV of productive lifetime.
When choosing traits for breeding objectives to increase lifetime, it is important to recognise the separate impacts of reproductive ability of breeding females and their disease resistance. Productive lifetime of breeding females in itself should be defined as a trait characterising exclusively the health status of animals (Reinsch and Dempfle, Reference Reinsch and Dempfle1998), and the EV of this trait should only include the impact of changes in the culling rate for adverse health and female mortality rate on the economics of the evaluated production system (Conington et al., Reference Conington, Bishop, Waterhouse and Simm2004; Roughsedge et al., Reference Roughsedge, Amer, Thompson and Simm2005; Legarra et al., Reference Legarra, Ramón, Ugarte and Pérez-Guzmán2007).
When productive lifetime is defined in this way, average survival rate may be used as an alternative trait. However, care must be taken to change only culling for health problems and mortality rate and to keep culling for failure to conceive and voluntary culling (e.g. for low milk production) constant when calculating the EV for survival rate.
Some authors, however, propose to optimise voluntary culling strategy and reproductive management when improving survival rate without concern as to whether results are achieved through better health or better reproductive ability. This approach is implemented mostly through dynamic modelling (e.g. Dekkers, Reference Dekkers1991; Stott, Reference Stott1994; Dekkers et al., Reference Dekkers, Ten Hag and Weersink1998). The EVs of productive lifetime (survival rate) or conception rate then include the economic effect of changes in voluntary culling and/or of changes in the voluntary waiting period and the maximal number of services before culling a female. Such an approach assumes an immediate management response to a change in trait levels at each combination of states animals could be in during the time interval considered. The problem with this approach is that in practice the reaction of management to genetic changes may be often slow and that the farmer's response to the genetic change may be restricted to several farms or years only and not necessarily transferred to further generations. A further problem of using dynamic programming is adding a substantial level of complexity to the derivation of EVs. When applying dynamic programming, the actual management response to the genetic change should be always clearly explained, because it can have a material impact on the EVs of some traits. The economic impact of improved survival of cows, for example, will be very different if farmers react to this improvement with more voluntary culling, keeping the same number of replacements or with the same level of voluntary culling, and keeping a lower number of replacements (see Wolfová and Wolf, Reference Wolfová and Wolf1997).
Systematic changes in management and marketing conditions over time, whether caused by changes in trait levels, by technical improvement or political decisions, may be better considered in a new calculation of the EVs and in the adaptation of the breeding objective. An exception is when there is a clear indication that farmers could extract more profit from their farming system, if they make management changes in conjunction with the specific trait change of interest.
Traits characterising reproductive performance
The abilities to express oestrus, as well as to conceive and bear progeny (embryonic mortality rate) are primary reproductive traits of females influencing revenues and costs. However, there are practical problems in acquiring data for EV and breeding value estimation for these components of female reproductive ability. Therefore, calving (lambing, farrowing) interval as a composite trait was chosen by several authors (Albera et al., Reference Albera, Carnier and Groen2004; Kahi and Nitter, Reference Kahi and Nitter2004).
The calving interval is influenced by the interval from calving to first mating, the conception rate and the length of pregnancy. These three components have distinct patterns of inheritance and different impacts on the economics of the evaluated production system. For this reason, which of the three components are changed should always be implicitly described when calculating the EV for calving interval. Fuerst-Waltl and Baumung (Reference Fuerst-Waltl and Baumung2009), for example, calculated the EV for lambing interval by reducing days to first service rather than improving conception rate. González-Recio et al. (Reference González-Recio, Pérez-Cabal and Alenda2004) included only the effect of prolonged days dry into the EV of calving interval. In a study by Pärna et al. (Reference Pärna, Kiiman, Vallas, Viinalass, Saveli and Pärna2007), calving interval reflected the ability of cows to conceive. The change in calving interval was caused by a change in the interval between first service and conception. A similar definition was applied by Reinsch and Dempfle (Reference Reinsch and Dempfle1998), who changed the service period of cows when calculating the EV of calving interval.
In replacement females (heifers, ewe lambs, gilts), age at first parturition is sometimes used to characterise reproductive ability. This trait can also serve as an easily recorded proxy for conception rate, but again it is a composite trait of age of replacement females at first service, conception rate and length of pregnancy. Therefore, a clear description of the assumptions made when calculating the EV of age at first parturition as a reproductive trait should be given (González-Recio et al., Reference González-Recio, Pérez-Cabal and Alenda2004; Kahi and Nitter, Reference Kahi and Nitter2004; Roughsedge et al. Reference Roughsedge, Amer, Thompson and Simm2005).
Some authors have assumed that replacement females are first mated at the optimal weight for the evaluated breed and have expressed age at first service as a function of the growth rate. The economic impact of the change in age at first mating (and therefore also in the age at first parturition) is then included in the EV of growth rate (Wolfová et al., 2007 and 2009).
The number of inseminations per conception is another alternative trait to characterise reproductive ability. However, the economic importance of reproductive ability can be underestimated, if this trait alone, or together with calving interval, is included in the breeding goal, and if the costs for insemination of cows culled because of failure to conceive are not considered. González-Recio et al. (2004) avoided this underestimation by expressing the costs for culling heifers and cows for failure to conceive as a function of the number of inseminations. The EV for the number of inseminations can be transformed to the EV for the trait ‘inverse of the number of inseminations to conception’, which was proposed as an alternative trait for the estimation of the breeding value for female fertility in dairy cattle by Weller and Ezra (Reference Weller and Ezra1997).
Traits characterising dairy production ability
In papers dealing with the estimation of EVs, the ability of a cow to produce a certain amount of milk with a specific composition is defined in different ways. For example, Du Plessis and Roux (Reference Du Plessis and Roux1999), Veerkamp et al. (Reference Veerkamp, Dillon, Kelly, Cromie and Groen2002) and Rovere et al. (Reference Rovere, Astigarraga and Urioste2010) presented EVs for milk, fat and protein yields. In their calculations, increasing percentages of fat and protein were used to increase the output of fat and protein at constant milk yield. Increasing milk yield, the fat and protein contents were decreased not to change fat and protein yields. In this case, milk yield was actually defined as carrier yield (without fat and protein). This definition was in accordance with the milk pricing system in the authors’ countries in which only fat and protein were included in the milk payment system, but milk volume had a zero price and was only connected with costs.
However, when breeding values for milk, fat and protein yields have been estimated simultaneously with a multi-trait animal model, the correlation between milk yield, on one side, and fat and protein yields (contents), on the other, have already been taken into account. Then the a priori assumption of a negative correlation between milk volume and milk components in the calculation of the EV for milk yield hides the risk of double counting.
Dairy industries today often specify a base milk price for reference fat and/or protein percentages and pricing systems are based on fat and/or protein differentials. Under these market conditions, it is economically important whether fat (protein) yield is increased by changing milk yield with constant fat (protein) content or by changing fat (protein) content at constant milk yield. Wolfová et al. (Reference Wolfová, Přibyl and Wolf2001) showed in an example that the change in profit per cow per year (EV) owing to increasing fat yield would be €2.12/kg fat when increasing fat content at constant milk yield, but €4.84/kg fat when increasing milk yield at constant fat content.
Milk yield in kg (including all components) is mostly the trait recorded for cows at each test day and used for breeding value estimation. The further recorded traits are fat and protein (possibly also lactose) contents, whereas fat or protein yields are calculated from these data and sometimes used as the only milk production traits in selection indices. Therefore, in the case of pricing systems on the basis of milk component differentials, we recommend to calculate the EV for milk yield with fixed fat and protein content and to include this trait in the breeding objective, irrespective of whether fat and protein contents or fat and protein yields are defined as further traits (Wolfová et al., Reference Wolfová, Wolf, Kvapilík and Kica2007; Krupová et al., Reference Krupová, Wolfová, Wolf, Oravcová, Margetín, Peškovičová, Krupa and Dańo2009). Then fat and protein contents should be always the primary traits for which levels are to be changed, when calculating EVs for fat and protein production and the levels of which are to be held constant when calculating EV for milk yield. Then, the transformation of the EVs for fat and protein contents to EVs for fat and protein yields is straightforward (Kahi and Nitter, Reference Kahi and Nitter2004; Pärna et al., Reference Pärna, Kiiman, Vallas, Viinalass, Saveli and Pärna2007; see also discussion on this topic by Dekkers and Gibson, Reference Dekkers and Gibson1998).
Adjusting the EV of a trait for dependencies among traits
According to James (Reference James1982), all traits that have an economic impact and that are expected to be improved by selection should be included in the breeding objective. In addition, their EVs should be evaluated simultaneously, without taking into account any correlations among those traits. Genetic and phenotypic correlations among the traits in the breeding objective or among the selection criteria (which do not need to be the same as traits in the breeding objective) should play a role when constructing selection indices (Dekkers and Gibson, Reference Dekkers and Gibson1998). However, Koots and Gibson (Reference Koots and Gibson1998) pointed out that selection indices are linear, meaning that non-linear interdependencies among traits cannot be accounted for in the derivation of selection indices and should be accommodated directly by incorporating them in the model for the calculation of EVs.
Many authors dealing with the estimation of EVs evaluated only selected groups of traits that have been included in breeding value estimation or in selection indices in a particular situation and have handled the above-mentioned problems of relationships among traits in different ways. Examples have been provided below.
Including relationships among traits through system optimisation
Dynamic optimisation models to estimate the EV for a specific trait were presented by Boichard et al. (Reference Boichard1990) for cow conception rate, Dekkers (Reference Dekkers1991) for involuntary culling rate, conception rate and 305-day milk yield, Stott (Reference Stott1994) and Brandts et al. (Reference Brandts, Canavesi and Cassandro1996) for cow functional longevity and Dekkers et al. (Reference Dekkers, Ten Hag and Weersink1998) for lactation persistency. Vargas et al. (Reference Vargas, Groen, Herrero and Van Arendonk2002) used a stochastic simulation model in which the EV of each trait was calculated on the basis of changing the genetic level of that trait; however, the final phenotypic changes could affect more than one trait as a result of interactions between feeding, production, health and fertility in the dynamic model of digestion. The predicted phenotypic performance of cows was then entered into a dynamic programming model to optimise voluntary culling and insemination policies at the herd level.
In these models, a change in the trait average altered the optimal mating and voluntary culling policy of farmers, which in turn resulted in changes in the length of the calving interval, productive lifetime of cows and total milk production. However, the question arises to what extent real production systems can be optimised. The papers cited above considered only certain aspects of optimisation of production systems (optimisation for culling and insemination decisions). In the calculated EVs, the economic effects of the genetic changes in trait levels and of changes in management actions are confounded and their interpretation for breeders is difficult. Furthermore, Dekkers (Reference Dekkers1991) showed that the EVs of traits can be rather robust to the degrees and types of sub-optimality of culling and mating decisions.
Including relationships among traits without optimisation
In most papers, optimisation has not been used. If the parameters in the models for the estimation of EVs are estimated from field data, they can be expected to reflect the farmers’ perception of the optimal management of at least the group of animals as an average, and for some traits (e.g. feeding in response to milk production potential) optimisation at the individual animal level. Therefore, a number of authors have assumed that the production system already was optimised before changing the trait levels, and then did not optimise the system after the trait changes. They did, however, include some relationships among traits. Most of these authors included only such relationships that were caused by non-genetic factors and assumed that any change at the genetic level of a trait would be fully expressed at the phenotypic level as well.
To further consider this issue, two groups of papers, one group using stochastic simulation, and the other group using multiple regression models, will be considered separately before discussing the remaining papers that used different procedures.
Including relationships among traits through stochastic simulation of phenotypes
Nielsen et al. (Reference Nielsen, Groen, Ostergaard and Berg2006) used complex stochastic simulation models for the estimation of EVs for a number of traits. A change in the genetic level of a trait did not cause an identical change at the phenotypic level owing to the stochastic nature of the model. Furthermore, the non-linear relationships among milk production, body weight and feed intake capacity included in the model caused correlated phenotypic changes in all three traits when the genetic level of any one of them was altered. An increase in mature weight of cows, for example, led to a decrease in milk yield owing to an insufficient increase in feed intake. The EV of mature weight estimated by these authors included therefore not only the direct impact of cow weight on feed costs for maintenance and growth and on revenues from culled cows, but also an indirect impact on income from milk.
However, this approach is not in accordance with the common practice in breeding value estimation for milk yield. To the best of our knowledge, models used for breeding value estimation for milk production do not include cow weight at the time of collection of test-day records. If a cow has lower daily milk production because she needs more energy for higher body weight than a smaller cow with the same genetic potential for milk production, then the heavier cow would have a lower breeding value for milk yield than the lighter cow. In other words, the relationship between milk and body weight is already implicitly included in the breeding value for milk, and should not be included in the EV for body weight.
Including relationships among traits using multiple regression
St-Onge et al. (Reference St-Onge, Hayes and Cue2002) used a different approach that may be highly appropriate for inclusion of the relationships among traits when estimating EVs of traits. They estimated the EVs of traits included in the selection index as regression coefficients of farm profit (calculated from field recorded data) on estimated breeding values for these traits. A disadvantage of these EVs is the fact that they were estimated on the basis of past and not (as recommended) future production, marketing and economic conditions. Furthermore, economic data from farms can be very difficult to acquire and subject to inaccuracy.
Further methods for including relationships among traits
Hirooka et al. (Reference Hirooka, Groen and Hillers1998a) took the economic impact of changes in dystocia occurrence into account when calculating the EVs of birth, weaning and mature weight in beef cattle, because dystocia was not part of the breeding objective.
Albera et al. (Reference Albera, Carnier and Groen2004) included the negative effect of dystocia on the length of calving interval in the EV of calving ease, although calving interval was a separate trait that characterised cow pregnancy rate. However, the reference trait for calving interval was calving interval of cows with no calving difficulty. For conception rate and calf survival, Wolfová et al. (2005 and 2007) defined the expression of those traits in cows with easy calving as the reference traits. When calculating the EV for dystocia (defined as average calving score), the effects of dystocia on conception rate and calf survival were taken into account. Koots and Gibson (Reference Koots and Gibson1998) proceeded similarly; they related conception rate and survival rate of calves or cows to a fixed rate of calving ease and included the economic effects of dystocia-caused changes of conception rate and cow survival in the EV of calving ease.
The EV of conception rate as calculated by Miesenberger (Reference Miesenberger1997) and by Wolfová et al. (2005 and 2007) included the economic impact of changes in milk production caused by the effect of conception rate on lactation length and cow productive lifetime. The EV of conception rate presented by Koots and Gibson (Reference Koots and Gibson1998) included economic effects from related changes in cow culling rate (changes in calving score, milk yield and calf weaning weight caused by changes in herd structure). Similarly, the EVs of reproductive and health traits calculated by Wolfová et al. (Reference Wolfová, Wolf, Kvapilík and Kica2007) reflected changes in the age structure of the cow herd and included changes in the total milk yield, even though the genetic potential for milk production was held constant.
The EV of growth rate of replacement females calculated by Wolfová et al. (Reference Wolfová, Wolf, Přibyl, Zahrádková and Kica2005) included the economic impact of the change in average age of heifers at calving, because heifers were assumed to be mated at fixed (optimal) weight. On the other hand, the EV of cow mature weight included the correlated effect of an increase in age at first mating of heifers (Wolfová et al., Reference Wolfová, Přibyl and Wolf2001), because the weight at first mating was expressed as a proportion of mature weight. Groen (Reference Groen1988) took the change in dry matter intake capacity of cows into account when calculating EVs for milk and growth traits, although dry matter intake was evaluated as a separate trait. In our opinion, these approaches are relevant, because related changes in other traits are assumed not to be caused by a genetic correlation between traits, but by changes in the age structure of the cow herds.
Conclusions
Great diversity exists in the definitions of traits thought to describe the same biological potential (growth, for example) of animals. Traits expressed in separate time periods of an animal's life and in different sexes have been treated in different ways in the estimation of EVs of traits for the breeding objective in livestock species. Contrasting trait definitions have advantages, disadvantages and limitations, and therefore unambiguous recommendations for or against a certain type can rarely be given.
However, for achieving better comparability and interpretability of estimated EVs reported in the literature, clear and unique definitions of the traits, complete information on assumptions used in the models for the calculation of EVs and details on the accommodation of inter-relationships between traits should be given. Care should be taken not to consider the relationships between traits twice in EV estimation and selection processes. The method and the model used for the breeding value estimation of a specific trait should determine which relationships to include in the calculation of the EV of the trait. Furthermore, the EVs for all traits should be estimated simultaneously.
Acknowledgements
The authors thank E. Krupa and R. Prošková (Prague Uhříněves, Czech Republic) for helpful discussions and for excellent technical assistance, respectively, W.D. Hohenboken (Philomath, Oregon, USA) and an unknown reviewer for editing the English of the paper and for valuable comments. The research was supported by the project MZE 0002701404 of the Ministry for Agriculture of the Czech Republic.
