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Lactation curve

Definition

Section titled “Definition”

The lactation curve is the pattern of daily milk yield across a cow’s lactation, plotted against days in milk (DIM). Milk rises quickly after calving, reaches a peak, then declines slowly until dry-off.

Its key features:

  • Peak milk: the highest daily (or test-day) yield in the lactation.
  • DIM at peak: when the peak occurs.
  • Persistency: how slowly milk declines after peak, usually expressed as the month-to-month ratio (e.g. 94% means each month yields 94% of the month before) or as % decline per month.
  • Shape by parity: first-lactation cows peak lower and later and are more persistent; mature cows peak higher and earlier and decline faster.

Peak milk drives total lactation yield: a common rule of thumb is that each extra 1 lb of peak milk adds about 200–250 lb to the lactation.

A herd or pen-level curve (average milk by DIM band) is the basis for expected milk: what a pen should be producing given its DIM and parity mix. Comparing pens on raw milk per cow is misleading when their DIM differ.

Formula

Section titled “Formula”

Wood’s (1967) incomplete gamma model, the classic curve fit:

y(t) = a × t^b × e^(−c × t)


y = daily milk at DIM t
a = scale (overall yield level)
b = rate of rise to peak
c = rate of decline after peak


DIM at peak  = b / c
Peak milk    = a × (b / c)^b × e^(−b)
y(t) = a\,t^{b}\,e^{-ct}, \qquad
t_{\text{peak}} = \frac{b}{c}, \qquad
y_{\text{peak}} = a\left(\frac{b}{c}\right)^{b} e^{-b}

Persistency, as a month-to-month ratio:

persistency (%) = milk in month n+1 / milk in month n × 100   (after peak)
P = \frac{\bar{y}_{n+1}}{\bar{y}_{n}} \times 100

Pen performance against expected:

expected pen milk = Σ over cows of herd-average milk for that cow's DIM band and parity
pen index (%)     = actual pen milk / expected pen milk × 100

How to pull it in DC305

Section titled “How to pull it in DC305”

PLOT draws milk against DIM; SUM ... BY with a DIM grouping gives a table.

PLOT MILK FOR LACT=1                 first-lactation curve (PLOT graphs against DIM)
PLOT MILK FOR LACT>1                 mature curve
PLOT MILK FOR LACT=1 WITH LACT>1     both curves on one graph
SUM MILK BY LACT FOR DIM<60          early-lactation milk by parity
LIST ID LACT DIM MILK PEAKM FOR LACT>0

PEAKM is DC305’s peak test-day milk for the current lactation. It is calculated from test-day records, not stored in the cow file.

PLOT takes test-day items only and groups by DIM by default (\R groups by test date instead); WITH acts as a second FOR for an overlay.

Test-day data is monthly, so peak from PEAKM is the highest test, not the true daily peak. Herds with daily parlor meters can build a daily curve outside DC305. Pen and group naming varies by herd; check the herd’s private dc305-vocab mapping.

Typical range

Section titled “Typical range”

Herd context: US Holsteins, freestall or dry-lot, milked 3x, herd averaging about 85–95 lb/cow/day.

Measure 1st lactation 2nd+ lactation
DIM at peak 60–90 40–60
Peak milk (lb) 85–100 110–130
Persistency (month-to-month) 94–96% 90–93%
  • Peak ratio: first-lactation peak ≈ 75–80% of mature-cow peak. Well below that suggests heifer growth, transition or grouping problems; well above it suggests mature cows are under-performing.

Expected milk by DIM band, as a share of the herd’s mature-cow peak (shape only; scale to the herd):

DIM band 1st lactation 2nd+ lactation
0–30 65–75% 80–90%
31–60 75–80% 95–100%
61–100 75–80% 90–97%
101–200 68–75% 75–88%
201–305 60–68% 60–72%
> 305 55–62% 50–60%

Common mistakes

Section titled “Common mistakes”
  • Comparing pens on milk per cow without adjusting for DIM and parity. A fresh pen and a late-lactation pen will never match. Compare actual against expected for the pen’s mix.
  • Reading a herd curve built from a snapshot as a cow’s lifetime curve. A cross-sectional plot of today’s cows by DIM mixes calving seasons and heat-stress months.
  • Treating PEAKM as true peak. Monthly tests miss the real peak; cows tested once before peak look like early peakers.
  • Early-lactation noise. Fresh-cow yields in the first 5–10 DIM are unstable and partly colostrum/withheld milk. Don’t fit or rank on them.
  • Ignoring parity. Mixing first-lactation and mature cows flattens the curve and hides problems in either group.
  • Ignoring milking frequency and pen moves. A change from 3x to 2x, or a pen move, causes a step drop that is not a persistency problem.
Section titled “Related”