For body maintenance, to restore body protein losses from the gastro-intestinal tract (GIT) and the integument (i.e. skin and hair), the SID lysine requirement (in g/d) is:

For the numerator, “basal endogenous lysine losses recovered at the terminal ileum have been estimated at 0.417 g per kg of feed dry matter intake; these losses have been related to feed intake, assuming 88 % feed dry matter, and to whole-GIT losses, assuming that large intestinal losses represent 10 % of GIT losses recovered at the ileum […]. Integument lysine losses have been estimated at 4.5 mg per kg of BW^0.75.”

For the denominator, “inevitable plus minimum lysine catabolism is assumed to be 25 % of SID lysine intake, equivalent to a 0.75 efficiency of SID lysine utilization to support [these] losses. This efficiency […] increases with improvements in pig performance potential. For every [gram per day] increase in PD_max, relative to the typical mean value for gilts and barrows [which was set at PD_max = 147.7 g/d], the rate of […] catabolism is reduced by 0.002” (i.e. by 0.2 %).

This 2012 approach replaces the one of NRC (1998) that quantified these maintenance requirements (g/d) as 0.036 × BW^0.75. In the new approach, “by specifically identifying the maintenance amino acid requirements associated with skin and hair losses and endogenous intestinal losses, the substantial contribution of [the latter] is represented more explicitly”.

For whole-body protein deposition (PD, in g/d), the SID lysine requirement (in g/d) is:

The denominator is the same as that in Equation 1. For the numerator, “it is assumed that PD contains 7.10% lysine. [… ] The marginal efficiency of lysine utilization declines with BW.” This declining efficiency was estimated as 0.682 and 0.568 at 20 and 120 kg BW, respectively — equivalent to a proportional increase in the lysine requirement of 0.0990 and 0.3205, respectively. The term 0.0547 + 0.002215 × BW in Equation 2 is the linear regression through these values.

This 2012 approach replaces the one of NRC (1998) that quantified these deposition requirements (g/d) as 0.12 × PD; in Equation 2, this would hold, for example, for a pig with PD_max = 150 g/d and BW = 99.6 kg.

In our target nutritional environment, protein deposition is never constrained, so that the pig’s genetic potential is always fully expressed; PD across the 20–120 kg body weight trajectory would then be a function of PD_max. Supplementary Material S1 shows that the average PD across that growing period is 87% of PD_max, or vice versa PD_max = 1.155 × average PD. The total SID lysine requirement (in g/d) of a growing pig between 20 and 120 kg body weight is then as follows:

In this 20 to120 kg body weight trajectory, the average BW is 70 kg, the average BW^0.75 (following Foster et al., 1983) is 120 1.75 − 20 1.75 1.75 × ( 120 − 20 ) = 23.8  kg 0.75 , and the average DFI is typically approximately 2.5 kg/d. With that, Equation 3 works out as:

The next step is to quantify PD (and more specifically, its genetic trend) in real-life pigs. Outside laboratory conditions, actual large-scale measurement of PD is prohibitively difficult; a more realistic alternative is to estimate it from lean tissue growth rate (LTGR) – which in turn will be derived from body growth rate and from backfat and loin muscle depth.

Mohrmann et al. (2006, their Figure 2) relate lean mass (in kg) to protein mass in the soft tissue (P_soft, in kg; “soft tissue” is the whole body including skin and excluding bones, blood and the thoracic and abdominal viscera) of growing pigs from 20 to 120 kg body weight as lean = 5.07 × P soft 0.954 (r=0.98; conversely, P_soft = 0.202 × lean^1.019). Using the same data, Landgraf et al. (2006, their Table 2) listed the weights and protein contents of soft tissue, viscera and bones; whole-body protein mass (P, in kg) can be calculated from these weights and can then be related to lean mass, as estimated from P_soft with Mohrmann’s prediction equation described above. This gives

The ratio between lifetime whole-body protein deposition (PD, in kg/d) and the lifetime lean tissue growth rate (LTGR, in kg/d) is then as follows:

…with age at slaughter in days, carcass weight CWT in kg, lifetime carcass growth rate CGR in kg/d, and lean in kg; leanprop is lean as a proportion of carcass weight.

Equation 6 can be rearranged to relate PD to LTGR. With age = 155 d this gives

These pigs had an average MRI-estimated LTGR of 0.380 kg/d from 20 to 120 kg BW; on the basis of data from Mitchell et al. (2012) on the body weight and body composition of neonate piglets, the LTGR from 2 to 120 kg BW of Mohrmann & Landgraf’s pigs can then be extrapolated as 0.252 kg/d, i.e., 0.663 times the 20 to 120 kg value.

Schinckel et al. (1996) related whole-body protein deposition (PD, in kg/d) to body weight (BW, in kg) and fat-free lean deposition (FFLD, in kg/d) in growing pigs from 25 to 152 kg body weight via an extension of Kanis and Koops (1990) nonlinear statistical model:

This can be rearranged as a convoluted main-effects-and-interaction model with eight parameters to be estimated:

…with f 1 ( FFLD ) = ln ( a + b × FFLD ) ,  f 2 ( BW ) = c × BW + e BW +  g × BW 2

and f 3 ( BW ) = d × BW + f BW + h × BW 2

Averaged across a 20 to 120 kg BW trajectory and across female and castrated male pigs, Schinckel’s [a, b, c, d, e, f, g, h] estimates work out as

Schinckel’s pigs had an average FFLD of 0.283 kg/d from 20 to 120 kg BW; with the 0.663 extrapolation factor derived from Mohrmann & Landgraf’s data this translates as LTGR = 0.188 kg/d from 2 to 120 kg BW.

We used backfat and loin muscle depth (BFX and LDX, as measured in mm on the carcass by equipment such as FOM) records from 62,434 pigs slaughtered after 2020 to calculate the carcass lean content as predicted by the commercial prediction equations used routinely in each of ten countries (Pig Improvement Company (PIC), 2022, their Table 3.1). These ten predicted lean content values were then averaged by animal, and the average was regressed on BFX and LDX. This gives our average “worldwide” prediction equation to convert carcass backfat and loin muscle depth (in mm) to carcass lean content (in %):

…and from there, in terms of estimated breeding values (EBVs):

This can then be combined with the EBV for the lifetime carcass growth rate (EBV_CGR, in kg/d) to derive the EBV for the LTGR (in kg/d), as follows:

…where the μ _… terms are the phenotypic population means (i.e., line means) of the traits, calculated across a useful period such as the most recent 12 months. EBV_CGR, EBV_BFX and EBV_LDX have zero population means, whereas EBV_LTGR does not.

The commercial prediction equations that led to our Equations 9 and 10 were derived by regressing dissected lean mass on backfat and loin muscle depth. This dissected lean mass includes intramuscular fat (IMF), which raises the question of the extent to which the carcass lean elements in our Equations 5 and 7 (due to Mohrmann & Landgraf) and (8) (due to Schinckel) may be biased because IMF was excluded there but is implicitly included in our Equation 11.

Mohrmann et al. (2006) estimated the lean content of their pigs via in vivo IMR. Kongsro and Gjerlaug-Enger (2013) used a similar technique (computer tomography: CT) on pigs with 0.44 to 3.23% chemically determined IMF in the loin muscle (a very wide range) and concluded that “CT is not a feasible method for in vivo prediction of intramuscular content”, mainly because their pigs, although sedated for the scan, still moved enough to make the equipment’s resolution inadequate for detecting the IMF. Therefore, Mohrmann’s lean tissue readings most likely include the IMF and there is no bias to adjust for in Equation 7.

Schinckel’s “carcass fat-free lean mass” was obtained as the sum of the fat-free lean masses of (i) ham, (ii) loin, (iii) butt, (iv) picnic, and (v) the combined rest of the carcass. In this respect, “fat-free lean” means that the actually dissected gross lean mass of components (i) to (iv), and the actually dissected lean plus adipose tissue mass of component (v), were adjusted for their respective adipose tissue content, which was due to imperfect dissection of the lean tissue, especially in component (v), where this was deliberate. For this adjustment, (vi) the chemically determined lipid mass in the dissected gross lean parts of components (i) to (iv), and in the dissected lean plus adipose tissue part of component (v), were divided by (vii) the chemically determined lipid proportion of all the dissected subcutaneous plus intermuscular adipose tissue; this gives estimates of adipose tissue mass, which were then subtracted from (viii) the dissected gross lean (or lean plus adipose) mass of each component: (viii) – (vi) / (vii). Unfortunately, none of these intermediate values are reported in the Schinckel et al. (1996) article. This dissection separated the gross lean of components (i) to (iv) from subcutaneous and intermuscular adipose tissue; any such adipose residue missed by the dissection (and the large amount of adipose tissue that was deliberately retained in component (v)) would have been dealt with by the abovementioned “fat-free” adjustment. This adjustment will also have subtracted the IMF content, which is typically approximately 2% in the ham and loin muscles, 4% in the shoulder muscles (D’Souza et al., 2002; Font i Furnols et al., 2019) and much higher than that in the muscles of component (v). Assuming 2, 2, 4 and 7% IMF in those muscle groups, respectively, and applying lean distribution values from Pulkrábek et al. (2006, their Tables 1, 2), the overall (adjusted-out) IMF content of the dissected carcass lean in Schinckel’s pigs would have been approximately 4%. Hence, the application of Equation 7 to LTGR values based on a lean prediction that was not adjusted for the IMF (as in Equation 8) would overestimate the PD, so the regression coefficient of Equation 8 should be reduced to 0.365 / 1.04 = 0.351:

This leads to the following steps:

For body maintenance, to restore body protein losses from the gastrointestinal tract (GIT) and the integument (i.e., skin and hair), the SID lysine requirement of sows is given by NRC (2012, p. 139) as a simplification of our Equation 1 for growing-finishing pigs:

Across a 200 to 300 kg body weight trajectory, the average BW^0.75 (following Foster et al., 1983) is 300 1.75 − 200 1.75 1.75 × ( 300 − 200 ) = 62.8  kg 0.75 , and the average DFI is typically approximately 2.75 kg/d (PIC, 2016, Table J1 and Figure I7; Lavery et al., 2019). With that, Equation 13 works out as lysreq_maint = 2.2 g/d.

In general terms, the SID lysine requirements for protein deposition (PD) in the nonreproductive parts of the sow’s body, in the uterus and the mammary glands (not the milk), in the fetus, and in the placenta and amniotic fluid are given by NRC (2012, p. 139) as a simplification of our Equation 2 for growing-finishing pigs:

To calculate the lysine retention for each tissue, the lysine content of the tissue’s protein can be combined with that tissue’s PD. Tables 2–11 of NRC (2012) gives lysine contents of 6.74% of body protein, 6.92% of uterine protein, 6.55% of mammary gland protein, 4.99% of fetal protein, and 6.39% of placental and abdominal fluid protein.

As in growing-finishing pigs, body protein deposition in sows can be quantified in terms of the lean tissue growth rate (LTGR, in kg/d). Equations 6, 7 and 12 for growing-finishing pigs can be scaled to the sow level as follows.

Miller et al. (2017) measured whole-body PD during gestation (days 31 to 112) in Canadian Yorkshire sows of parities 1, 2 and 3 at 0.110, 0.078 and 0.102 kg/d, respectively. This can be converted to the LTGR, following Supplementary Material S2 ; this gives the LTGR of Miller’s sows during gestation (days 31 to 112) in parities 1, 2 and 3 as 0.185, 0.156 and 0.178 kg/d, respectively.

Routine recording of the traits that constitute LTGR in pigs takes place during performance testing, typically at 100 to 130 kg liveweight, but the PD (or LTGR) of Miller’s sows at that stage was not reported (and was probably not recorded). This is unfortunate because it would have made it possible to relate the gestational LTGR to the performance test LTGR in Miller’s animals and, from there, to other genotypes. Therefore, we need an approximation, following Supplementary Material S3 .

Canadian Yorkshire gilts that were performance tested (at 100 kg liveweight) in 2015 had an average lifetime liveweight growth rate (LWGR) at 0.613 kg/d and 10.2 and 62.5 mm BFP and LDP, respectively (Appendix 7 of CCSI, 2016). Substituting those values into equation (B4) of Supplementary Material S3 gives a 100-kg lifetime LTGR of 0.265 kg/d. The momentary LTGR on the day of first mating at approximately 125 kg live weight can be estimated from this value (following Supplementary Material S1 ) as 1.17 × 0.265 = 0.309 kg/d. Taking this as the base level (100%) on day 1 of parity-1 gestation, the abovementioned gestational LTGR levels (days 31 to 112 in parities 1, 2 and 3) of Miller’s sows work out as 0.185 kg/d = 60%, 0.156 kg/d = 50% (increasing from zero on day 1), and 0.178 kg/d = 58% (increasing from 0.01 kg/d = 3% on day 1) of the first-mating base level, respectively. This pattern is illustrated, with some rounding errors, in Figure 3 . The average value of the red trendline, from the first mating at 249 days of age to the third mating at 683 days, represents 41.4% of the base-level LTGR.

The realized genetic trend of LTGR during the grower−finisher stage in Camborough is shown in Figure 4 : a stable linear increase in dLTGR = 0.00267 kg/d per year since 2017. To work back from the LTGR to the whole-body PD, we use the equation of above: PD = 0.00486 + 0.3194 × LTGR. This indicates a genetic trend in Camborough’s whole-body protein deposition rate of dPD = 0.00486 + 0.3194 × 0.00267 = 0.0057 kg/d additional protein deposition in the grower-finisher stage per year. Adopting the PD pattern of Figure 3 and its percentwise consequences for Camborough sows, this gives an annual increase in the parity-1 to parity-3 (434 days) body protein deposition rate of dPD_sowbody = 0.414 × 0.0057 = 0.00237 kg/d: that is the annual increase in the average daily protein deposition rate in the nonreproductive parts of the sow's body due to the current genetic trends in the grower-finisher LTGR in PIC-L02 and PIC-L03.

The average daily body lysine retention (lysretn, in g/d) across multiple parities is then 0.0674 × PD_sowbody, and the associated SID lysine requirement follows from substitution into Equation 14 as

Fetal protein mass is predicted by Equations 8-56 and 8-58 of NRC (2012) as follows:

…where TNB is litter size (total number born), PBWT is individual piglet birth weight (in kg), and D_gest is the number of days in lactation, from 1 to 116.

The average daily fetal lysine retention (lysretn, in g/d) throughout gestation can then be estimated by evaluating Equation 16 for D_gest=116 (ignoring the D_gest=1 entry because it is so much smaller than the D_gest=116 one), dividing through 116, and multiplying by the lysine content of 0.0499. This gives:

The protein mass in the placenta and amniotic fluid (P_placenta) can usefully be related to the fetal protein mass P_fetus of Equation 17. Equation 8-57 of NRC (2012) goes back to Noblet et al. (1985) who measured both these pools and analyzed their course over time with the number of viable fetuses and the sow’s energy intake as covariables. The regression equations below their Table 6 can be used to predict P_fetus at 116 days of gestation (P_fetus,116) and the associated P_placenta,116 for variable values of TNB; these two predictions relate linearly to each other as in Equation 18:

The associated average daily lysine retention throughout gestation can then be estimated in a similar way as lysretn_fetus by dividing P_placenta,116 through 116, and multiplying by the lysine content of 0.0639. In terms of P_fetus,116 this gives:

Uterine protein mass is predicted by Equation 8-59 of NRC (2012) as follows:

The average daily uterine lysine retention throughout gestation can then be estimated via Equation 20 for D_gest=1 and D_gest=116, subtracting, dividing through 116, and multiplying by the lysine content of 0.0692. This gives:

The parenchymal protein mass in the mammary glands at D_gest days in gestation can be estimated from Table 2 of Ji et al. (2006):

…where TTN is the number of functional teats.

The average daily lysine retention in the mammary glands throughout gestation can then be estimated by evaluating Equation 22 for D_gest=1 and D_gest=116, subtracting, dividing through 116, and multiplying by the lysine content of 0.0655. This gives:

The parenchymal protein mass in the mammary glands during lactation can be estimated as follows. Kim et al. (1999, their Figure 3B) reported the protein mass (g) in the aggregated suckled mammary glands at 21 days in lactation, dependent on how many teats are actually suckled which is determined by litter size during lactation (LSL): P_{suckledglands} = 132.8 + 37.8 × LSL (R² = 0.88), where LSL = NBA × (1 – PWM), NBA is the litter size (number born alive) and PWM is the preweaning mortality rate. A nonsuckled gland goes into regression and retains 10 g of protein at the end of lactation (Kim et al., 2001, their Table 2). Their effective number is TTN – LSL. The protein mass of the whole udder at 21 days of lactation is then 132.8 + 37.8 × LSL + 10 × (TTN – LSL) = 132.8 + 27.8 × LSL + 10 × TTN. According to Kim et al. (1999, their Table 1), the corresponding protein mass at the start of lactation (due to the gestational deposition of our Equations 22, 23) is 44 g per gland. Subtracting 44 × TTN, dividing through 21, and multiplying by the lysine content of 0.0655 gives the average daily lysine retention in the mammary glands throughout lactation:

…which may be negative as well as positive.

Substituting Equations 17, 19, 21, 23 and 24 into Equation 14 gives the average daily SID lysine requirements associated with these protein deposition processes, as in Equations 25 to 29:

The equivalent of Equation 2 for colostrum or milk production follows from Equation 8-76 of NRC (2012):

…where matmob is the amount of body protein mobilized during lactation (g/d); we ignore it here because we are ultimately interested only in the effects of trends in the reproduction traits, and such effects on body protein mobilization are very difficult to model. Hence, Equation 30 overestimates the true lysreq_col/milk; at the same time, any mobilized body protein will have to be replenished during the subsequent gestation, which will increase lysreq_sowbody as in Equation 15.

To calculate lysine retention, the lysine content of each protein can be combined with the PD. Table 2 of Yao et al. (2023) gives 7.85% lysine in milk protein and 7.50% lysine in colostrum protein.

Colostrum protein synthesis can be predicted from Tables 1 and 7 of Vadmand et al. (2015): colostrum yield (kg/d) = 1.10 + 0.20 × LBWT, where LBWT is the litter birth weight in kg, calculated as NBA × PBWT. Colostrum contains 16.5% protein; a large proportion of this consists of immunoglobulins, which are synthesized outside the mammary glands during the week before farrowing. Therefore, P_colostrum (kg) = 0.165 × (1.10 + 0.20 × NBA × PBWT) = 0.1815 + 0.033 × NBA × PBWT. Assuming that this takes place during the final 7 days of gestation, the average daily colostrum protein synthesis in g/d is as follows:

Milk protein synthesis follows from Hansen et al. (2012): milk production at D_lact days in lactation (D_lact ≥ 2) can be described with a Wood lactation curve (often used for dairy cows: M_Dlact = α × D_lact ^β × e ^{–λ × Dlact}); its parameters α, β and λ can be quantified in terms of litter size and litter weight gain; Supplementary Material S4 provides more detail. The milk protein content (%) is 4.71 + 4.43 / D_lact + 0.07 × (CP_feed – 15.9); CP_feed is the CP content of the feed (%). Assuming a feed with CP_feed = 15.9 %, the resulting patterns are illustrated in Figure 5 ; the associated prediction equation for total sow milk protein synthesis from day 2 in lactation to weaning at 22 days is P_milk (kg) = 2.086 + 0.371 × LSL + (0.183 × LSL – 0.264) × LWG. The final term LWG = (LWWT – NBA × PBWT) / 22 is the average litter weight gain (kg/d), with LWWT as the litter weaning weight (kg/d). The average daily milk protein synthesis (in g/d) from days 2 to 22 of lactation is then

Substituting Equations 31 and 32 into Equation 30 gives the average daily SID lysine requirements associated with these protein synthesis processes:

…where LSL = NBA × (1 – PWM) and LWG = (LWWT – NBA × PBWT) / 22.