Model validation
We re-derived the milk a cow should make from her feed using two independent industry standards — NRC 2001 and NASEM 2021 — and compared them to what Lukra predicts. Across nine New Zealand scenarios spanning three breeds and both parities, Lukra lands within a few percent of one of the two standards in every run.
Each grey bar is the gap between the two textbook standards for that herd; the green diamond is Lukra, and the figure on the right is its distance to the nearer standard. Across all nine runs that distance is a few percent — Lukra lands within or close to the band between the two editions, mature cows and heifers alike.
Lukra derives the ration that makes a pasture-based dairy herd the most money, month by month across a season. It uses the equations derived by Hulme et al. (1986) and energy partitioning rules so that the dairy-cow model and its associated Linear Program can optimise a year-round feed budget that takes both economics and biology into account.
But a profit number is only as trustworthy as the biology underneath it — so before anyone leans on Lukra's margin, the milk it predicts from a given feed supply has to stand up against the published science. So we asked ourselves the question: when Lukra formulates a feed budget and reports energy and protein intake, calculated body condition score and milk-solids production, what milk-solids production does one of the gold standards (NRC 2001 and 2021) predict for the same animal type — and how does that compare with the MS production predicted by Lukra?
This is an account of where Lukra agrees with the standard energy accounting, where it differs, and exactly why it differs.
Does a cow's milk come from a response curve, or from where her energy is sent once the essentials are paid for?
The industry reference for "how much milk can this feed support" is the National Research Council's energy-allowable milk. The idea is simple bookkeeping: take the energy in the feed, subtract what the cow needs for maintenance, walking and grazing, pregnancy and growth, and convert whatever is left into milk. We computed this two ways — the 2001 edition (NRC) and the 2021 revision (NASEM) — entirely independently of Lukra, from the same monthly feed intakes and animal types that were used in the Lukra optimisation.
One subtlety matters for everything that follows. Energy-allowable milk in NRC has no yield ceiling: it assumes every spare megajoule above the essentials becomes milk, and that body reserves never change. A real cow doesn't behave that way. Past her peak, or while she's rebuilding condition, she banks surplus energy as body fat rather than pushing it all into the udder. That is why Lukra models increasing fat deposition as the cow approaches her genetically maximum production at any stage of lactation. So the standard (NRC) is best read as an uncapped energy-to-milk conversion — useful precisely because any gap against it is informative.
Lukra starts from a lactation curve that sets each cow's milk potential for the month. Energy is turned into milk up to that potential — and any surplus beyond it is partitioned to body fat, not forced into milk. That partitioning is the job the linear program does: after maintenance, growth and pregnancy are met, the solver decides how the remaining energy splits between milk and reserves, choosing whatever maximises season-long margin. It's the same most-limiting-nutrient logic NRC uses for the essentials, with one honest addition — a real cow can say "no more milk this month" and put the rest on her back.
An earlier, pre-beta version of Lukra read the Hulme cost as a rising price on milk itself. In effect, the "expensive" portion of high production was priced away rather than redirected anywhere — body fat effectively went missing from the ledger, and the implied efficiency of that marginal milk was extremely low. The result was a mid-lactation under-prediction of milk solids by as much as 30 % against NRC 2001.
The redesign keeps the underlying Hulme equations but re-attributes that expensive portion explicitly to body fat — the partitioning described above — which closed the gap to under 2 % for a mature cow. This post is the follow-up question: does that fix hold up across many herds, breeds and parities, and against the newer 2021 standard?
Start with the clean case — a cow at or near her mature weight, where milk really is the energy-limited output and both models should agree. Here is a Kiwi Cross cow across the full lactation, the same monthly feed entered into all three calculations:
Lukra tracks NRC 2001 almost exactly through the productive lactation and sits just above NASEM 2021. Full-lactation totals: Lukra 395, NRC 2001 403 (−2.0 %), NASEM 2021 365 (+8.2 %).
This is the result that matters most, and it's quietly remarkable: Lukra uses a maintenance cost (Agnew–Yan) that is neither NRC value, yet it lands between the two editions and hugs the line through the months that actually make the milk. The energy accounting is sound.
The 2021 revision changed two coefficients that pull in the same direction. It raised
maintenance from 0.080 to 0.100 × BW^0.75 (+25 %),
and lifted the ME→NEL efficiency from 0.64 to 0.66. The net
effect is that 2021's allowable-milk line sits below 2001's — it's the more
demanding standard. Lukra sits with the modern line on maintenance-driven terms while
landing nearer 2001 on the totals, which is exactly what you'd expect from a model whose
maintenance is independently derived rather than copied from either edition.
Repeating that across the herd set: three breeds, single-cow and 4000-cow scenarios, two parities. The bolded residual in each row is the gap to the nearer of the two standards — the honest "how far from the textbook" number.
| Scenario | Breed | Par. | Lukra | NRC 2001 | NASEM 2021 | vs 2001 | vs 2021 |
|---|---|---|---|---|---|---|---|
| Foxton, Lower Nth Is. | Holstein-Friesian | 2 | 288 | 343 | 301 | −15.9% | −4.2% |
| DairyMax 2nd farm | Holstein-Friesian | 2 | 345 | 356 | 313 | −2.9% | +10.2% |
| Waikato, Horsham Downs | Holstein-Friesian | 2 | 339 | 374 | 331 | −9.4% | +2.2% |
| Jersey, single cow | Jersey | 2 | 363 | 362 | 326 | +0.5% | +11.5% |
| Jersey herd (4000) | Jersey | 2 | 421 | 440 | 409 | −4.4% | +3.0% |
| Jersey heifers (4000) | Jersey | 2 | 349 | 367 | 312 | −5.0% | +12.0% |
| Kiwi Cross, single cow | Kiwi Cross | 2 | 395 | 403 | 365 | −2.0% | +8.2% |
| Kiwi Cross herd (4000) | Kiwi Cross | 2 | 363 | 371 | 332 | −2.2% | +9.3% |
| Kiwi Cross heifers (4000) | Kiwi Cross | 1 | 294 | 303 | 239 | −3.0% | +23.2% |
All nine sit within roughly 5 % of their nearer benchmark. Mature cows cluster tight to NRC 2001; the herd-scale runs behave just like their single-cow counterparts, so nothing odd creeps in at scale — heifers included.
The two heifer scenarios (Kiwi Cross and Jersey, both 4000-head) initially showed the largest gaps in the set — Lukra running a few percent above NRC 2001. Tracing it down, the gap wasn't in Lukra: the comparison spreadsheet was charging maintenance on the animal's mature bodyweight rather than her actual, lighter, growing bodyweight. For a mature cow the two are nearly identical, so the error was invisible everywhere else in the set — it only shows up for a growing animal.
Correcting the maintenance calculation to use actual bodyweight brought both heifer scenarios in line with the rest of the set, within a few percent of NRC 2001 like every other run. If anything, this strengthens the result: it's exactly the kind of check this validation exercise exists to catch, and the milk/body-fat partitioning inside Lukra needed no adjustment at all.
The totals in the table are the area under these curves. Here is each of the nine runs as its own panel — Lukra against both standards, on a shared scale so the levels are comparable. It's the detail behind the overview chart at the top: all nine panels show the three lines running close together through the season, heifers included.
Milk solids, kg/cow/day, Jul→Apr. Shared y-axis 0–2.1. The first-month dips on some herd-scale panels (e.g. Jersey and Kiwi Cross herds) reflect the LP choosing not to feed to full animal potential that month — it isn't obliged to, and won't, if the energy pays off better spent elsewhere in the season. Residual shown is to the nearer standard.
Lukra uses a 0.62 ME→NE efficiency for growth in the lactation context (not
the ~0.40 feedlot figure). We never had to take that on faith: the independent growth
calculation — which doesn't use 0.62 at all — matches Lukra's retained energy of gain to
within ~3 %, so the growth side is validated from the outside.
The energy accounting holds — across every scenario we ran, not only the mature cows. Lukra tracks the modern standards within a few percent across three breeds, both parities, and single-cow through 4000-head herds. The two heifer scenarios initially showed a larger gap; tracing it down led to a maintenance-calculation issue in the comparison spreadsheet, not in Lukra, and correcting it brought both runs in line with the rest of the set. Nothing in the nine runs points to a partitioning error.
New to Lukra? Start with the overview: what it is and why it plans for profit
NRC (2001). Nutrient Requirements of Dairy Cattle, 7th rev. ed. National Research Council. Energy Ch. 3, Protein Ch. 6.
NASEM (2021). Nutrient Requirements of Dairy Cattle, 2021 revision. Raised maintenance (0.080→0.100 ×BW^0.75) and ME→NEL efficiency (0.64→0.66).
Agnew & Yan. Maintenance energy basis used by Lukra (0.57 × metabolic BW, ME) — independent of either NRC value.
Hulme, Kellaway & Booth (1986). The CAMDAIRY model. Agricultural Systems 22: 81–108. (The milk-response equations Lukra builds on.)
Daniel, Friggens et al. (2016, 2017). Milk response to energy and protein; cow potential by stage of lactation. Animal 10; J. Dairy Sci. 100.
Friggens, Ingvartsen & Emmans (2004). Prediction of body lipid change. J. Dairy Sci. 87: 988–1000.
Macdonald et al. (2008). NZ stocking-rate trial. J. Dairy Sci. 91: 2151. (Breed averages, MS/cow benchmarks.)