Data

A model used in Australia to calculate economic values for dairy breeding objectives (Visscher et al. Reference Visscher, Bowman and Goddard1994; Pryce et al. Reference Pryce, van der Werf, Haile-Mariam, Malcolm and Goddard2009) was adapted and developed by Bell et al. (Reference Bell, Eckard, Haile-Mariam and Pryce2013a ) to model GHG emissions from a dairy herd. For a full description of the Breeding Objectives Model see Bell et al. (Reference Bell, Eckard, Haile-Mariam and Pryce2013a ). Briefly, the model was constructed in Microsoft Excel to calculate changes in profit per cow in response to changes in biological traits. For the present study, the model was extended to include changes in GHG emissions per cow and per kg MS due to a management or genetic change. Responses were quantified by calculating differences between the current state (baseline situation) and a positive or negative change in a biological trait (adjusted situation). The extended model was used in the present study to dynamically represent the average milk-recorded UK dairy herd (referred to as the average herd) and to assess effects of changes in biological traits.

Herd structure

A total of 13 age groups were modelled, which included the period between birth and first calving for herd replacements, and 12 lactations. Replacement animals were assumed to calve at 2 years of age, with cows surviving for an average of 2·9 lactations which is in accordance with recent UK estimates (Table 1). It was assumed that all births resulted in a single live calf, and that 0·50 of calves were male and 0·50 female. The only animals to leave the system were cull cows, male calves and surplus female calves. All calves sold were assumed to leave the system immediately after birth (and contribute no GHG emissions to the system). This assumption ignores the effect of calf mortality, which was assumed to be the same in both the baseline and altered situations.

Table 1.

Production values included in the model for an average cow in the UK

* From CDI (http://ukcows.com/thecdi, accessed 21 February 2013).

Herd structure was derived using a Markov chain approach. A Markov chain can be used to describe the herd as a vector of states (s) that cows occupy at a given point in time (Stott et al. Reference Stott, Veerkamp and Wassell1999), which in the present study was each age group. The vector of states at time t is multiplied by a matrix of transition probabilities (s×s) to give the vector of states at time t+1. The probability of a cow progressing to the next lactation (from lactation n to n+1 and from lactation 1 to n) was dependent on the chance of a cow being culled during the current lactation (Table 2). If the transition matrix is constant for all stages; that is, the model is stationary, then repeated matrix multiplication will produce a fixed long-run vector (steady-state), which is independent of the initial state vector. This long-run steady-state vector provides a useful basis for comparative assessment of alternative herd structures, i.e. a change in the number of cows in each age group, as shown in Table 2. The number of replacements required to maintain the average herd structure was 34·4 animals per lactation in a 100 cow herd. For simplicity individual cow values were multiplied by 100 to represent a herd of 100 cows.

Table 2.

Modelled average milk fat yield, milk protein yield, DM intake, SCC, calving interval, mastitis incidence, lameness incidence, survival and long-run steady state for a 100 cow herd from the Markov chain for an average herd in the baseline situation for a heifer replacement and lactations 1–12

* From CDI (http://ukcows.com/thecdi, accessed 21 February 2013).

† Heifers assumed to enter the milking herd at 730 days of age, with calving intervals obtained from CDI (http://ukcows.com/thecdi, accessed 21 February 2013).

Energy requirements, feed intake and live weight

It was assumed that energy requirements (of milking cows and herd replacements) for maintenance, growth, pregnancy, activity and lactation were achieved and that feed intake was always sufficient to achieve energy requirements in the baseline situation.

The diet composition of a lactating cow was calculated based on the average animal (Table 1) using the FeedByte^® rationing model version 3.78 (available at http://www.sruc.ac.uk/info/120110/dairy/354/dairy_services-key_features), which calculates a least-cost ration that meets the energy, protein and mineral requirements of the animal. The ration was formulated from pasture, grass silage and dairy concentrate based on their nutrient composition (Table 3) and cost (Table 4). The diet was constrained to a maximum of 500 g pasture per kilogram of fresh feed. The lactating cow diet consisted of 340 g pasture, 320  grass silage and 340 g dairy concentrate per kilogram dry matter (DM) intake per lactation (Table 3), at an estimated cost of £0·086 per litre of milk. This diet was considered representative of a typical UK feeding system (Wilkinson & Audsley Reference Wilkinson and Audsley2013). A milking herd replacement (growing heifer) was assumed to be fed a diet of 500 g pasture and 500 g grass silage per kilogram of fresh feed. The cost of feed consumed by each age group was estimated by multiplying total DM intake by metabolizable energy (ME) content and cost per unit ME of the diet (Table 4). A unit reduction in DM intake assumed that ME requirement of the animal remained constant in the baseline and adjusted situations, but ME intake and associated cost of consumed feed were lower to represent an improvement in residual feed intake.

Table 3.

Assumed nutrient composition of pasture, grass silage and dairy concentrate

* Using equation of Minson & McDonald (Reference Minson and McDonald1987).

† Estimated from Rowett Feedingstuffs Evaluation Unit Third Report data (Wainman et al. Reference Wainman, Dewy and Boyne1981) as: OMD_m=0·1436+1·0183×(ME/GE).

‡ From Bell et al. (Reference Bell, Wall, Russell, Simm and Stott2011), except for ether extract from FeedByte^® model.

§ Digestible CP (g/kg DM)=CP−(((0·3×(1−(DMDm+0·1)))×CP)+(0·105×ME×0·008)+0·0152); Non-fibre carbohydrate=1000−(NDF+ash+crude protein+ether extract); undigested organic matter=reciprocal of undigested organic matter plus ash content (g/kg DM) of feed at maintenance intake level.

Table 4.

Assumed income and costs associated with production for an average herd obtained from Redman (Reference Redman2012)

* Based on milk compositions for milk fat and protein in Table 1 and an average price of 24 pence per litre of milk.

† Feed costs were deducted to give a non-feed cost associated with a milking herd replacement in the model.

‡ Herd test, animal health, housing and dairy supplies.

§ Assumed cost of 30 min per artificial insemination, 50 min per case of severe and fatal clinical mastitis (P. Down, The University of Nottingham, Sutton Bonington, UK, personal communication) and 15 min for digital lameness, 12 min for interdigital lameness and 20 min per case of sole ulcer lameness (Kossaibati & Esslemont Reference Kossaibati and Esslemont1997).

Metabolizable energy (ME, MJ/day) required for maintenance (E _maint), gain or loss of body protein (E _p) and lipid (E _l), pregnancy (E _preg), activity (E _act) and lactation (E _lact) for the average cow are presented in Table 5. The effective energy system proposed by Emmans (Reference Emmans1994) was used to estimate feed intake. Feed intake of an animal was calculated from total ME requirement and the net energy supplied by the food consumed:

where ME, GE, FE and E _CH4 is the metabolizable, gross, faecal and enteric CH₄ energy (all MJ/kg DM). The values of 0·616 and 3·8 are the heat increments associated with fermentation and faeces production, and energy lost in faeces was assumed to be 20 MJ/kg faeces DM. Excretion of urine leads to a loss of digestible crude protein (DCP) (Emmans Reference Emmans1994). Residual feed intake (RFI) is defined as the difference between actual and predicted feed intake. Residual feed intake represents variation in efficiency of metabolic processes, which is independent of the animal's body size and production level; which for example, can be estimated from regression of DM intake against mean body weight and growth rate in heifers (Williams et al. Reference Williams, Pryce, Grainger, Wales, Linden, Porker and Hayes2011). The economic value for RFI is the cost of increasing marginal feed costs by one unit whereas all other traits are held constant. So, even if feed intake is sufficient, an animal that eats less will be more profitable at the same level of milk production and fitness.

Table 5.

Percentage of total energy (% of ME) for a heifer replacement and the average lactating dairy cow for maintenance (E_maint), protein growth (E_p), lipid growth (E_l), pregnancy (E_preg), activity (E_act) and milk production (E_lact) over a lifetime

The animal's live weight was assumed to be its empty body weight (kg of protein, lipid, water and ash) plus gut fill. Figure 1 shows the live weight and body composition of the average cow assumed in this study with a mature empty body weight of 550 kg. The body condition score of the cow was estimated from body lipid using the equation of Wright (Reference Wright1982) and converted to a 1 to 9 point scale (NRC 2001) for the present study using the following formula:

Fig. 1.

Average mass of protein, lipid, ash, water and gut fill in the live weight of an average heifer replacement and a dairy cow from lactations 1–12 with a mature empty body weight of 550 kg.

The average live weight of a cow was estimated to be 632 kg, with a body condition score of 4·5 on a 9-point scale (Table 6). Gut fill was assumed to equate to the water held by dietary fibre content and estimated as 13·2 times the intake of neutral-detergent fibre (NDF) (kg/day) (Takeda & Kiriyama Reference Takeda and Kiriyama1979).

Table 6.

Average values per cow for production and fitness traits, and N excretion, enteric and manure CH₄ and N₂O emissions for a long-run steady state herd

* Includes contribution from herd replacements.

Calculation of yields per cow lactation

Data for average number of days for each lactation, milk production at maturity and milk composition were obtained for the year 2011/12 from the Centre for Dairy Information (http://ukcows.com/thecdi, accessed 21 February 2013), which collates data from recorded dairy cows in all regions of the UK (Table 1).

The total amount of milk produced during each lactation was estimated by multiplying the milk production at maturity from the CDI data by the proportion of mature productivity for each lactation. The proportion of mature productivity was calculated to be E _maint−(E _p+E _l)/maximum of E _maint−(E _p+E _l) across lactations (Bell et al. Reference Bell, Eckard, Haile-Mariam and Pryce2013a ). Mature productivity of milk was reached at four lactations for the average cow (information obtained from CDI, http://ukcows.com/thecdi, accessed 21 February 2013). Amounts of milk protein, fat and lactose produced were calculated based on milk fat and protein content (Table 1) and an assumed milk content of 0·05 lactose. Average yields per lactation were 8965 litres of milk, 358 kg of fat and 290 kg of protein (Table 6).

Greenhouse gas emissions

Sources of GHG emissions were from enteric and manure CH₄, and direct (from stored manure and application of dung, urine and manure) and indirect N₂O from storage and application of manure to land (from leaching and atmospheric deposition of nitrogen from nitrogen oxides (NOx) and ammonia (NH₃)) as attributed in the UK National GHG Inventory for agricultural production (Brown et al. Reference Brown, Cardenas, MacCarthy, Murrells, Pang, Passant, Thistlethwaite, Thomson and Webb2010). Emissions were expressed as carbon dioxide equivalent (CO₂-eq.) emissions per cow, and per kilogram of MS; the functional units as defined by Guinée et al. (Reference Guinée, Gorree, Heijungs, Huppes, Kleijn, de Koning, van Oers, Wegener Sleeswijk, Suh, Udo de Haes, de Bruijn, van Duin, Huijbregts, Lindeijer, Roorda, van der Ven and Weidema2002). Kilograms of CO₂-eq. emissions for a 100-years time horizon were calculated using conversion factors from CH₄ to CO₂-eq of 25 and from N₂O to CO₂-eq of 298 (Forster et al. Reference Forster, Ramaswamy, Artaxo, Berntsen, Betts, Fahey, Haywood, Lean, Lowe, Myhre, Nganga, Prinn, Raga, Schulz, Van Dorland, Solomon, Qin, Manning, Chen, Marquis, Averyt, Tignor and Miller2007).

Enteric CH₄ emissions were estimated per kg DM intake by the equation (Bell et al. Reference Bell, Eckard, Moate, Craigon and Garnsworthy2013b ) based on the composition of the diet (Table 3) as:

where DOMD_p and DOMD_m are digestible organic matter at the production and maintenance intake levels, EE is ether extract, and NFC non-fibre carbohydrate (all g/kg DM). The DOMD_p and DOMD_m contents were estimated from the organic matter concentration of the diet (g/kg DM) multiplied by digestibility of organic matter at the production (OMD_p) and maintenance intake level (OMD_m). The OMD_p was estimated by the equation of Huhtanen et al. (Reference Huhtanen, Rinne and Nousiainen2009) as:

where OMD_m is the digestibility of organic matter at the maintenance intake level. The CH₄ emissions per kg DM intake were converted to emissions as a proportion of feed GE in the model, which meant CH₄ emissions were c. 0·068 of GE for the pasture/silage diet fed to a herd replacement and 0·056 of GE for the pasture/silage/concentrate diet of a lactating cow. This corresponds well with the loss of CH₄ per % of feed GE of 6·5±1% proposed by IPCC (Reference Eggleston, Buendia, Miwa, Ngara and Tanabe2006) for high to low forage diets for dairy cows and UK GHG inventory values (Brown et al. Reference Brown, Cardenas, MacCarthy, Murrells, Pang, Passant, Thistlethwaite, Thomson and Webb2010). Estimated annual emissions (from Table 6) for CH₄ (144 kg/year for enteric and 42 kg/year for manure) and N₂O (8 kg/year) were higher than in the UK GHG inventory. Data in the present study were from recorded cows, which are typically selected for improved production. Losses of CH₄ and N₂O emissions were estimated using linear relationships for all biological traits except survival (a curvilinear relationship with survival is generated by the Markov chain).

The IPCC (Reference Eggleston, Buendia, Miwa, Ngara and Tanabe2006) Tier II methodology was used to predict manure CH₄ and N₂O emissions (from N excretion) for manure handling systems, as well as manure deposited on pasture. The N excreted by the animal was partitioned into dung (N intake−digested N intake) and urine (N intake−(N retained+N in dung)). Emission factors for manure CH₄ and N₂O are shown in Table 7. Based on UK GHG inventory values the following were fixed in the calculations: CH₄ conversion factor of 0·662 m³/kg CH₄ and CH₄ producing capacity of manure of 0·24 m³/kg volatile solids (Brown et al. Reference Brown, Cardenas, MacCarthy, Murrells, Pang, Passant, Thistlethwaite, Thomson and Webb2010). Volatile solids in manure were calculated from the undigested organic matter (1−digestible organic matter kg/kg).

Table 7.

Assumed percentage of manure produced by management system for a herd replacement and lactating cow for an average system, and emission factors used to calculate the GHG emissions (Brown et al. Reference Brown, Cardenas, MacCarthy, Murrells, Pang, Passant, Thistlethwaite, Thomson and Webb2010)

Fertility

All cows were assumed to be artificially inseminated. The average number of inseminations per cow was calculated as:

where the start of an oestrous cycle was assumed to be 426 days after birth for a replacement heifer and 82 days after calving for a lactating cow. Gestation length was assumed to be constant at 283 days (Table 1). This allows for a replacement to enter the herd at 730 days of age and a milking cow to have a 365 day calving interval. Calving interval was determined from the average lactation length plus the drying off period (Table 2). The cost of poor fertility was calculated from the cost of each insemination (labour cost per h/2+semen straw cost; Table 4), the additional feed consumed by a milking cow and the cost of a milking herd replacement per extra day required.

Mastitis and lameness

Along with poor fertility, mastitis and lameness are considered to be two of the most costly health problems in dairy cattle and are therefore included in the model. The proportion of cows in each lactation that had mastitis (Table 2) was calculated using a cumulative normal distribution with a mean log transformed SCC of 400 000 somatic cells/ml (de Haas et al. Reference de Haas, Veerkamp, Barkema, Gröhn and Schukken2004). A linear extrapolation of the data of Rutherford et al. (Reference Rutherford, Langford, Jack, Sherwood, Lawrence and Haskell2009) provided the increase in incidence of lameness with parity (Table 2). A cow with mastitis and lameness had an associated cost for treatment and loss of milk (Appendix). For mastitis, 0·3 incidences were assumed to be clinical cases; for lameness, 0·25 were assumed to be clinical cases; the remainder were assumed to be subclinical cases. A case of clinical mastitis was assumed to cost £206 per incidence and subclinical £54, which is consistent with costs reported by Heikkilä et al. (Reference Heikkilä, Nousiainen and Pyörälä2012). A case of clinical lameness was assumed to cost £305 per incidence and subclinical £40, which is consistent with costs reported by Willshire & Bell (Reference Willshire and Bell2009). The costs of mastitis and lameness are shown in the Appendix (Table A).

Change in profit

The model included a partial budget calculation to determine the change in profit (e.g. income−variable costs=profit or loss) per cow for each age group in the herd for a change in a trait; this is often referred to as the economic value of the trait. The change in income corresponds to the maximum amount of money that could be made by a change of one unit in each trait (e.g. 1 kg milk or 1% mastitis incidence). Economic value of a trait is over a lifetime, but breeding values are expressed in lactating cows, so feed costs of growing heifers and lactating cows are shared among lactating cows. Variable costs and income that correspond to the traits of interest were included in the analysis in pounds sterling (Table 4). The average values for milk, feed and livestock prices were obtained from Redman (Reference Redman2012).

Improved efficiencies of production

The change in profit, CO₂-eq. emissions per cow and per kg MS by a single unit change in each of 11 biological traits was assessed. The 11 traits represent a range of production traits and fitness traits. An increment of one unit increase in each trait was investigated while keeping all other traits constant. The traits assessed were: production traits of milk volume (litres/lactation), fat and protein yield (both kg/lactation), live weight (kg), body condition score (1 to 9 point scale), survival (%/lactation), and feed efficiency and fitness traits of residual feed intake (kg/day), SCC (‘000 cells/ml), mastitis and lameness incidence (both %/lactation) and calving interval (days/lactation). The average value and unit for each trait per cow assumed in the modelled average herd is shown in Table 6.

A multi-trait selection index, as described by Pryce et al. (Reference Pryce, van der Werf, Haile-Mariam, Malcolm and Goddard2009) and Hayes et al. (Reference Hayes, van der Werf and Pryce2011), was used to estimate the annual change in the 11 traits and the economic change, with an estimate of annual change in profit per cow from selection on multiple traits. A multi-trait selection index takes into account the economic values of the traits included, their heritabilities, and genetic and phenotypic correlations between traits in order to calculate optimal index weights for each trait (Pryce et al. Reference Pryce, van der Werf, Haile-Mariam, Malcolm and Goddard2009). Phenotypic and genetic correlations between traits were mostly obtained from Pritchard et al. (Reference Pritchard, Coffey, Mrode and Wall2013), except for live weight, condition score (both Pryce et al. Reference Pryce, van der Werf, Haile-Mariam, Malcolm and Goddard2009), and DM intake and residual feed intake (Veerkamp et al. Reference Veerkamp, Emmans, Cromie and Simm1995; Vallimont et al. Reference Vallimont, Dechow, Daubert, Dekleva, Blum, Barlieb, Liu, Varga, Heinrichs and Baumrucker2010, Reference Vallimont, Dechow, Daubert, Dekleva, Blum, Liu, Varga, Heinrichs and Baumrucker2013). Economic values were derived using the Breeding Objectives Model described earlier.