Drift lambing was a pain for all involved (sheep and man) ---used it once or twice but sheep are best left alone at lambing
GO---you just need to improve your sheep a bit so they don't need tailing
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Regarding breeding no or bare tails; yes great, but the trade off in introgressing these genes and diminishing those traits that pay the bills would really hurt.
Drift lambing---having a set of fields for lambing in and drifting the sheep around them
So, start with 100 ewes in field #1 , after a couple of days when say 15 have lambed you open the gates and let the un-lambed ewes drift through to field # 2, when 15 of them have lambed you let the un lambed ewes through to field # 3 etc
The idea being that you have less mis-mothering due to the lambed ewes being left with lots of room ---tried this and found it to be more hassle than it was worth. You end up with plenty of mis mothering when you 'drift' the ewes
Some people do it with success
Removing tails is only one part of the exercise, ear marking, maybe Pulpy Kidney vaccinating, long acting vit B12 injection, DNA blood sampling for many breeders, etc.
Regarding breeding no or bare tails; yes great, but the trade off in introgressing these genes and diminishing those traits that pay the bills would really hurt.
I hadn't realised that kiwi breeders give a prophylactic shot of B12 - why not breed sheep that can tolerate lower levels of it?
To answer your specific question: there are two things.
1) It depends on whether there is genetic variation for the trait and to the extent of this variation
2) It probably isn't cost-effective to select for genetic differences. Each time you put selection pressure on one trait you have to reduce it for another. Where the traits have high economic worth then it is viable to put selection pressure on it. For example, for some disease traits it is worth looking at a genetic approach but when there are cheap prevention/treatment options then it is not cost-effective to use a genetic approach.
I think I've made sense!
It might be, but it also might be that those animals you are selecting for have better traits in a number of areas. What I'm saying is that it doesnt nescessarily follow that selecting for multiple traits is slower, it might be, but it isn't nescessarily a logical step to assume it will.