Quantifying the essential aspects of the lactation curve in an
efficient and consistent way enables use of statistical methods in the
study of many interesting and economically important questions, and
increases our power to to detect and analyze factors influencing dairy
productivity. MilkBot^{® }models milk production as an
equation with four parameters, each with a distinct meaning. These
parameter values encapsulate the unique shape of a lactation curve, so
that by observing parameter values we can make inferences about health
and productivity. Alternatively, MilkBot can calculate such traditional
attributes as time and magnitude of peak production, persistence of
production, and cumulative or projected production.

Each MilkBot^{®} parameter describes an aspect of the
shape of the lactation curve, and is independent of other parameter
values. It is reasonable to hypothesize that particular
environmental factors, or particular interventions, will have
characteristic effects on parameter values. This remains to be
proven, but it is important to understand the individual meanings of
the four MilkBot^{®}parameters.

"**Milkbot.Scale**" (or "**Scale**") calculates an
abstract overall capacity to produce milk, and can be expressed in
units like pounds, kilograms, or liters. It can be calculated at any
point in the lactation, from one or more milkweights. It is a
theoretical maximum that is never quite reached in normal conditions,
somewhat higher than actual peak daily milk. If the Milkbot.Scale
increases by 10%, then predicted production increases by 10% for each
day of the lactation. Peak milk and cumulative milk yield are also
influenced by the shape of the curve, which is controlled by the other
three parameters .

**Milkbot.Ramp**" (or "**Ramp**") measures how steeply
milk production rises after calving, and is expressed in "days". If a
cow comes into milk slowly, she will have a high Ramp value. Ramp
values are useful in exploring transition management.

**Milkbot.Offset**" (or "**Offset**") measures the
time between the day of calving and the beginning of lactation in a
physiological sense. Changes in offset shift the curve to the left or
right, and are measured in days. Without daily milk weights or large
data sets, it is difficult to differentiate between the effects of
offset and ramp parameters. For this reason, we often prefer the
reduced parameter, **peak day**, a statistic influenced by both
ramp and offset values. Both Ramp and Offset have their largest
influence in the pre-peak portion of the lactation curve.

**Milkbot.Persistence**" (or "**persistence**") is a
measure of the natural decline in production, expressed as a half-life.
If a cow had persistence of 300 days, then she would be expected to
drop in milk by 50% every 300 days. Infinite persistence would mean no
drop at all. The effect of Milkbot.persistence in early lactation is
obscured by the larger effects of ramp and offset parameters, but it
dominates in late lactation. It also has a small effect on the peak day
statistic.

Actual milk production on a given day is predicted by these four parameter values. Because each parameter has a known effect on the shape of the curve, it is easy to understand what changes in parameter values mean in terms of their effect on milk production. It is also straightforward to hypothesize what effect a given intervention might have on individual parameter values.

In many circumstances, understanding of parameters can be simplified by use of "reduced parameters" such as "Day of Peak Milk", a calculated value mainly influenced by Ramp and Offset values, but also slightly influenced by Persistence. Since Day of Peak Milk is also directly observable, it is a more natural expression of lactation curve shape than the primary parameter values which underlie it, and sufficiently precise for most applications.