Lambing began mid-March. By the time lambing finished on April 10th, we had 29 lambs ... 18 rams and 11 ewes. Of those, there are 9 white ram lambs, 1 white ewe lamb, 1 black ram, 2 black ewes, 8 moorit rams, and 8 moorit ewes. Last year we also had 29 lambs, with 20 of them being rams and 9 being ewes.
I had begun to think this thing of having more rams than ewes was an unhappy trend, so I asked Keith about the significance over all. He has tried to explain this mathematically, so this may not be of much interest to some?
Ariel and her twins
Poppy and her twins
Given 29 lambs, what are the chances that you will have delivered the following number of rams (or ewes)? You can reverse the rams or ewes in any case. We are just looking at rams produced ... you could as easily look at ewes produced.
As an aside ...
There is much speculation about WHY an animal might produce more rams than ewes? (or vice versa?)
I think that in most mammal species there is agreement that it is the pH of the uterus that determines the sex of the offspring. One could speculate that a particular female animal has a chronically more acid or more basic uterus as a function of that animal's body chemistry.
In times of harsh conditions ... drought, poor food, predator pressure, disease, extreme heat, etc. ... it is a somewhat common thing for a ewe, who would normally produce twins, to absorb (not a true abortion) one or both of the fetuses. This may also be a factor in the number of lambs and their sexes produced.
* 6 or fewer rams out of 29 births = essentially 0
* 7 rams out of 29 births = 0.04%
* 8 rams out of 29 births = 0.8%
* 9 rams out of 29 births = 1.9%
* 10 rams out of 29 births = 3.7%
* 11 rams out of 29 births = 6.4%
* 12 rams out of 29 births = 9.7%
* 13 rams out of 29 births = 12.6%
* 14 rams out of 29 births = 14.4%
In each case these are the odds of getting EXACTLY that specified number of rams. The probabilities are symmetrical about the average (14.5 rams out of a possible 29) so the probability for getting, say, exactly 18 rams (which is the same as getting exactly 11 ewes) will be 6.4%.
But with many births, the odds of getting a specific exact number ... any specifically prescribed number at all ... goes down as the number of births go up. We want to find out how UNUSUAL it is to get some certain distribution, such as *AS FEW AS* 11 rams out of 29 births. Thus we have to add up the probabilities of the cumulative chances of getting 11 or less rams: 0.00% +0.04%+ 0.8% + 1.9% + 3.7% + 6.4% = 12.8%. But the oddness could have skewed the other way as well - it's just as odd to get 11 or fewer ewes as it is to get 11 or fewer rams, so the odds for getting 11 or fewer ANYTHING (of one gender) is twice that amount: 12.8% x 2 = 25.6%
Thus, to answer the question "out of 29 births, how often will I get somewhere between only 0 to 11 animals of one gender (and hence between 18 and 29 animals of the other gender?", the answer is 25.6% of the time (or about 1 chance in 4). A little unusual, but not much.
On the other hand, "out of 29 births, how often will I get 10 or fewer animals of one gender (and hence 19 or more animals of the other gender?", the answer is 12.8% (or about 1 chance in 8). Getting a bit more rare.
And "out of 29 births, how often will I get 9 or fewer animals of one gender (and hence 20 or more animals of the other gender?", the answer is 5.4% (about 1 chance in 19). Getting somewhat unusual.
But "out of 29 births, how often will I get 8 or fewer animals of one gender (and hence 21 or more animals of the other gender?", the answer is 1.6% (about 1 chance in 63). Should probably make you sit up and notice.
And "out of 29 births, how often will I get 7 or fewer animals of one gender (and hence 22 or more animals of the other gender?", the answer is 0.08% (about 1 chance in 63). Only once in about 1,250 times. Starting to be a blinkin' miracle, or at least evidence that there is something more afoot than a 50-50 chance of one particular gender being born!
We went over our flock records back to the year 2000, and totalled up the number of rams and ewes born. The larger the sample of animals, the more even the distribution becomes. So given enough time and animals it does even out. We are actually (over all) up a few ewe births at this time. WHEW!!!!
We have many of his rams and ewes ... his rams in particular have his face. I have only to look at Starbuck and I can see James' face, but somehow its not the same. I miss him.
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