In the last year, I’ve completed Green Belt certification, which is a portion of Lean Six Sigma training. I loved the coursework, and though it was for work and surely I’ll apply these skills to engineering, I couldn’t help but relish the fact that they are also really useful for sheep! Open-mouthed smileAnd supposedly, Lean Six Sigma credits some of its origin to Agriculture, and it’s early use of statistical analysis in breeding improvements. So here is some fun tinkering with statistical analysis of factors which may affect birth weight in my lambs.

Birth weight in pasture lambing operations is a big deal. Tiny lambs risk chilling, big lambs risk birthing problems. So the holy grail is to have a narrow distribution of birth weights that is in the range of good. I’m not thrilled about lambs under seven pounds or over eleven. Those are arbitrary limits just based on my sense of what’s tiny and what’s huge.

Different people have different preferences and thresholds. I happened to notice recently that Susan Schoenian, small ruminant expert whom I respect who also breeds Katahdins, specifies her goal on her website: 8 – 8.5 pounds. That’s a very narrow spread, but she must have reasons why she feels that is the ideal weight range for her operation. I’ve heard other breeders who prefer to have larger lambs in the 10-12 pound range.

I have data from 95 lambs over the last three years, and three main sires. Here’s a summary distribution of all their birth weights.

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So I don’t have much of a problem on the big end right now, but I do have too many on the small end. I would like to narrow the spread; and also raise the mean, which is now at 7.7 pounds, to more like 9 pounds. So what factors play into small birth weights, I wondered?

I am using a tool called Minitab, which can do statistical analysis calculations. One thing that bugs me is hearing how often people assume an observed correlation and act on it, without any math to back that up. Of course we’re humans, and we make assumptions every day about cause and effect, and most of the time it doesn’t matter much even if our assumptions are wrong. But before we take business actions on these guesses, we should make sure that statistics back up our theories first. Otherwise, the results we think we’re seeing could be just due to random chance, or some variable of which we’re not aware. And we could waste money on an improvement effort that doesn’t actually work.

Ewe Feeding Schedule

This year, I felt like I noticed that the earlier births were smaller. I wondered if this could be caused by my feeding schedule, and whether I should start ramping up intake a week earlier, to make sure those early-borns got enough support in their last month of gestation. Here’s a time series plot of birth weights across birth dates for just this year:

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Minitab calculates a “p-value” when testing a theory. This number gives you a sense for how likely it is that you are right or wrong to assume a relationship. A p-value below 0.05 is good, this is the generic threshold most people use when basing statistical conclusions. It means there is a very low probability that data will fall outside of the extremes of the data you already have. But it’s ok to use a higher threshold, it all depends on how much you are willing to gamble by possibly taking action on incorrect assumptions.

So I tested to see if there is a relationship between birth weight and conception date (this test used 2011 data only). Sure enough, there is, with a p-value of 0.003, but it’s a negative correlation- the later the breeding, the smaller the lamb. The same is true of the correlation between birth weight and birth date, though the p-value is less confident on that one, at 0.121. These are variations on the same theme, as generally the ewes that breed earlier lamb earlier, but not always. So huh, I don’t know what to make of that, other than to know that increasing feed earlier in the gestation cycle likely won’t help, so I shouldn’t waste my money there. Good to know.

Gestation Period

The next thing I wondered was whether birth size was related to gestation period. Here is the spread of gestations over those 95 lambs. My sheep definitely seem to stack  up on the low side, given the various published ranges of 144-152, or 140-159 days. My mean is 146 days.

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The p-value for this positive correlation is 0.014. So it’s true that the longer the babies stay in the cooker, the bigger they are at birth. And that would be what you’d expect, after all. I presume this is partly genetic, partly chance, and I believe that others have proven a correlation between twins and triplets and shorter gestations.

Sire

So next I tested whether the sire choice had anything to do with it. This is a little bit different of a statistical test. The above tests were done using numeric or “continuous” data, and you can get more accurate conclusions with smaller data sets using this kind of data. But sire choice is considered “attribute” data (kind of like true/false outcomes as opposed to decimal outcomes), so usually larger data sets are required to make a definitive conclusion. But 95 lambs should be plenty for this test. The p-value is 0.003, so definitive evidence that my sires are having a (genetic) impact on birth weight. Their data spreads look like this (ear tag #s in the left hand column):

Sires

The dashed lines indicate the 95% confidence interval for the mean: a wide spread means the data is inconsistent (or there’s not enough), and therefor we can’t make tighter predictions on future outcomes in that category. #0024 is a first year ram and I didn’t use him much, so that’s why there is less confidence in his predictions, there is insufficient data. The asterisk is the current mean value for the sire.

This does not come as a shock to me, because my NSIP data has been telling me the same thing: Liberace (#900) though he looks like an awesome stud and he has a great pedigree, so far is not panning out so well for me in this area. Hershey (BLM417) and Lefty (#0024), though looks-wise seem in the same league or not as good, are much stronger in this metric. But it’s important to not throw the baby out with the bathwater: this is only one metric, and one goal. So Lee isn’t as strong here, but he’s better elsewhere. Just something to factor into the equation when making breeding decisions.

Gender

So surely males are born bigger than females, right? Trick question! Nope. P-value is 0.37. SmileThough the mean for the females is lower, and their 95% confidence spread is shifted lower, the spreads between males and females are too big and overlapping. So we can’t mathematically conclude that boys have a better chance of being born heavier than girls.

Gender

Birth Type

Are twins and triplets smaller than singles? P-value here is 0.018, so yes, definitely. Here are the spreads on this factor.

BirthType

Interesting that twins and triplets have similar groupings, that the twins don’t seem to have an advantage over triplets. In fact, this is really interesting to me, because the Katahdin community really debates over triplets. Some feel they are a by-product of selecting for twins, and are actually not desirable because they theoretically increase risk and don’t grow as well. So some people view them as something to tolerate, or even select against. But my data set would imply that the triplets are at least not disadvantaged at birth when compared to twins. That is, if they make it out of the womb alive! Winking smile

Dam Age

Do mature ewes have larger lambs? Now this one I woulda’ thought for sure would be the case. I breed my ewes to lamb as yearlings, and the ewes themselves are not really finished growing- they’ll still fill out a lot before age two. And it sure seems like they often have some wee-sized lambs. But the math isn’t there: I cannot make a statistical claim that the ewelambs have smaller babies, no matter which way I slice it. I tried with both categorizing by yearling, two, and older; and also just by yearling and older.  The means are very close, and the spreads very wide. So it seems pretty random!

DamAge

There are some fancier things I could do to analyze multiple variables at once, for example, do younger ewes who have twins have smaller lambs than older ewes with twins? But I couldn’t think of any interesting tests that would be “action-able” so I didn’t go further in analyzing this path.

Conclusions

So what does this tell me? Well, not a whole lot! Open-mouthed smile But it’s interesting anyway. I’m glad it prevented me from wasting a few hundred bucks on extra grain in late gestation- now I know making that change won’t likely help. And I think it makes me worry less about triplets. What we do know is that birth weight is genetic, and I should select for it. NSIP can help me with this, because it can do similar math to this; but with further iterations on relationships between siblings, cousins and generations and across multiple farms’ data.

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