Repeatability of Milk Production

Repeatability is the concept that what happened in the past is going to happen in the future, given similar conditions. For example, if a cow had an above average lactation yield, is she expected to remain above average in the next lactation? Some traits and events are more repeatable than others. It is documented in the scientific literature that people are not very good at estimating the repeatability of events. We often believe some biological events are highly repeatable, when in fact they are not. For example, when a cow fails to conceive in 3 breedings, we believe there must be something wrong with the cow, even though the herd average conception risk is, say, 30%. Or, in other words, we may believe that the chance she will conceive on the 4th breeding is a lot smaller than 30%, when in fact studies show it remains close to 30%. The number of breedings it took to get a cow pregnant in one lactation is not very repeatable. When something is not repeatable, our best estimate for the future is the herd or group average. What happened to the cow in the past does not matter much.

Milk production is more repeatable than the number of breedings for individual cows. Higher producing cows in the past are correctly expected to be higher producing cows in the future. To make milk production between lactations more comparable, it makes sense to first adjust milk production for the age of the cow and some other factors. Mature equivalent (ME) milk is the predicted amount of milk produced in 305 days as if the cow were a mature cow. ME milk is calculated by applying adjustment factors to the actual amount of milk produced in 305 days for every cow in the herd. These factors adjust for days in milk, milking frequency, season of calving, location, and age. Projected 305 day ME milk is database item 013 in PCDART. The ME milk in the previous lactation is database item 227.

It turns out that the repeatability of ME milk production between lactations is about 50%. In the figure, I plotted the ME milk in the first lactation against the ME milk in the second lactation for a random sample of 1% of all cows on DHIA in Florida between 2001 and 2007. On average, if a cow had a higher ME milk in the first lactation, she had a higher ME milk in the second lactation. But this was not necessarily true for all cows as the cloud of observations shows. A repeatability of 50% means that half of extra milk in the first lactation compared to the average is expected in the second lactation. For example, a cow that produced +1000 lbs more than her herd mates in the first lactation is expected to be 50% x 1000 = 500 lbs better in her second lactation. The repeatability of ME milk between any two consecutive lactations (e.g. second and third) was also about 50% in the Florida data. Between first and third it was about 37%.

When we have the ME milk from several completed lactations, the expected ME milk in the next lactation can be estimated based on the ME milk yields in all previous lactations using the formula [N / (N+1)] x [average herd mate deviation] where N is the number of lactations available on a cow and the average herd mate deviation is based on all previous lactation records of the cow. After one lactation, the repeatability of the average herd mate deviation, [N / (N + 1)], is 1/2 = 50%. We see this in the figure as well. After two lactations, it is 2/3 = 67% etc. So if a cow had a milk production of +1000 lbs in the first lactation and +600 lbs in the second lactation, then her expected milk production compared to herd mates is 2/3 x (+1000 +600)/2 = 0.67 x 800 = +536 lbs. This +536 lbs is a measure of the cow's estimated relative producing ability (ERPA). ERPA milk is PCDART database item 014.

These repeatabilities mean that above average cows for milk yield are expected to be above average in the next lactation, although the difference is regressed downward toward the herd mate average. Similarly, below average cows for milk yield are expected to be below average in the next lactation, but the difference with the average herd mate is expected to be smaller.