Before I give you my impression on manx rats I want to give you a good link to look at just in case I miss something that they cover :
Taillessness in rats is a mutation as opposed to a deformity or a single easily identifiable dominant or recessive gene. By definition, a deformity is something that impacts an animal in a negative way and impairs the way the animal lives its life; whereas a mutation can be beneficial and non-hindering. Taillessness in rats doesn't hinder them in any way, nor does it affect them negatively. They are agile, even more agile than some tailed rats I have seen. Because they are born without a tail they never learn how to use and depend on one, and instead find ways to balance themselves by positioning their legs more centrally underneath them should they be put in to a situation where balance is paramount. In day-to-day life though there is no difference between them and their tailed brethren. They will climb, monkey hang from bars, walk the ceilings of their cage, run, jump, buck, and play just like any other rat.
They are able to regulate their temperature through the pads of their feet, just like all rats, and as such do not require a tail to be able to release heat. Only in extremely hot situations (temps 90 degrees Fahrenheit and above) would you see a problem with a tailless rat, but you would also see it with the tailed ones. There is no reason that a domesticated rat should ever be exposed to high temperatures, but should it happen the tailless rat has ways to adjust for it. If they were in the wild and it became too hot to regulate they would go underground or in to a heavily shaded area to cool down, just like a tailed rat would. In a domestic setting though, if they have no way to escape the extreme heat they may suffer from it, but the tailed rats that were with them would as well.
A lot of people don't understand how the manx mutation works. It's not a deformity that we are compounding negatively upon by breeding, nor is it a simple gene that can be easily predicted and replicated. It's just like any evolutionary advancement in animals that we would consider to be a mutation, but it's a totally benign mutation if bred correctly. Because it can present itself in many different forms by the length of the remaining tail if there is one, it's crucial that people never breed them unsafely. An unsafe pairing for example would be breeding incompletely formed manx (which can be felt through palpation, or seen through x-ray) or breeding two unrelated manx from unknown lines and with no known background. From what I have read and seen from other ratteries it is then, and only then that you run into problems such as partially formed musculature around the anus and vagina, or splayed pelvises. But again, it is a rarity to see those problems anymore as more and more knowledgeable breeders are starting to work with the manx, opposed to people who just want to make more so they can make money or have bragging rights to be working with a rare variety. If you are breeding them right you should see 1-3 manx in a litter; more than one is actually somewhat rare.
These are all just my opinions and my experiences while working with the manx mutation. I don't advise any breeder who is unfamiliar with the manx mutation to take them on and start a breeding program from them without doing as much research as you possibly can. I would also contact other manx breeders and see what their experiences with the mutation have been. We all experience things and learn things differently so you may learn something from them you couldn't have found out any other way.
Because most people learn visually, here is a short video of my manx girl Hazel from a few years ago, showing a bit of how agile and capable manx rats are. They are in no way deformed, like many uneducated people would lead you to believe.
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