# Weights, Heights, Dry Matter Intake, Body Condition Score

## Weights, general

Weight is modelled by the Von Bertalanfy function which has three parameters, A, B, and K.

Weight = A*(1 - B*exp(-Kt))**3

where the mean values are A = 633.3 kg, B = 0.601, and K = 0.0036, and t is the age of the cow.

Weights are for non-pregnant, non-lactating cows under healthy conditions. The fetus weight is calculated as

Log10(fetus wt) = 2.932 - 3.347*exp(-0.00406*g)

where g is the number of days pregnant.

Adjustments for diseases are specific to each disease and are described in that section of the website.

Adjustments for cold and heat stress are described in the section on Weather Simulation.

## Weights, within lactation

Weights change within lactation due to milk production early in the lactation. Weight at the start of lactation is given by the function in the previous section. Relative changes are given by the factors in the following table, which differ depending on first or later parities.

 Week of Lactation Parity 1 Later parities 1 1.00 1.00 4 0.981 0.968 7 0.981 0.952 10 0.983 0.950 13 0.998 0.952 16 1.002 0.960 19 1.009 0.968 22 1.022 0.976 25 1.031 0.984 28 1.037 0.992 31 1.046 1.000 34 1.056 1.006 37 1.065 1.013 40 1.074 1.024 43 1.087 1.032 46 1.102 1.048

Weight varies from day to day, due to unknown effects. The standard deviation of these fluctuations is assumed to be 1.5 kg per day. This noise is added to the expected weight.

## Heights

Height is modelled by the Von Bertalanfy function which has three parameters, A, B, and K.

Height = A*(1 - B*exp(-Kt))**3

where the mean values are A = 150 cm, B = 0.211, and K = 0.0041, and t is the age of the cow.

Heights do not vary day to day due to environment. Height never decreases until older ages. Before that time the cow will most likely have been culled. Cows will differ in their growth rate. Height is highly correlated to stature.

Heights do not affect diseases, feed intake, milk production, or any financial aspects of the simulation, at this time.

## Dry Matter Intake, to first calving

For animals from birth to first calving, dry matter intake can be determined by the following exponential function with two parameters, A and K.

Intake = A*(1 - B*exp(-Kw))

where the mean values are A = 15.36 kg, and K = 0.0022, and w is the body weight of the animal. The standard deviation of intakes from day to day is 1.45 kg.

## Dry Matter Intake, within lactations

Within a lactation, dry matter intake is determined from body weight and protein yield with the following formulas.

Intake = (4.6 + 0.011*BW + 12.4*PY)*LAG, for first lactations, and

Intake = (8.4 + 0.006*BW + 12.2*PY)*LAG, for later lactations.

where LAG accounts for a delay due to energy balancing. LAG depends on week of lactation and month of peak milk yield. A table of LAG values is given below.

 Week of Lactation Peak 1 Peak 2 Peak 3 1 .77 .65 .59 2 .85 .75 .66 3 .90 .81 .72 4 .94 .87 .77 5 .96 .90 .81 6 .97 .92 .84 7 .99 .95 .87 8 1.00 .96 .89 9 .97 .91 10 .98 .93 11 .98 .94 12 .99 .95 13 1.00 .96 14 .97 15 .98 16 .99

Adjustments for pregnancy, diseases, and cold or heat stress are given in other sections.

## Body Condition Scores

An initial BCS will be genetically determined at the beginning of each lactation. BCS will then change relative to calving date similar to the changes in body weight. BCS is measured on a 1 to 9 scale with a genetic variance of 0.864 and a residual variance of 1.16.

 Week of Lactation Parity 1 Later parities 1 1.00 1.00 4 0.943 0.943 7 0.876 0.876 10 0.810 0.810 13 0.820 0.820 16 0.830 0.830 19 0.841 0.841 22 0.849 0.849 25 0.857 0.857 28 0.865 0.865 31 0.873 0.873 34 0.881 0.881 37 0.889 0.889 40 0.897 0.897 43 0.905 0.905 46 0.913 0.913