Greetings x44,
I feel honor bound to answer you as best I can.
Although, I have had some experience in farming mice and chickens, it was some time ago. My knowledge of inducing mutations is only from what I read and is extremely limited.
The point that some of the other people who have posted are that the study of mutation is often done in living things that have very short reproductive life cycles. Fruit flies and bacteria cycles are days or hours. On these, mutations can be induced with simple processes like exposure to UV light or some chemical under controlled conditions.
Studying induced mutations in mice and chickens would be somewhat more difficult, time consuming and arduous. Instead of days and months it would take years to get results. Also, inducing mutations using chemicals or possibly X-rays in mice and chickens would be harder to control. Additionally, the offspring may be not able to reproduce by virtue of the effects of the mutations. If I recollect correctly, mice will eat their stillborn young.
Never the less let us do a few scenarios. Please note that I have not done anything of this nature and am only guessing.
You inject a female mouse with a mutagenic compound and she survives (which may be rare). Then we mate her with a male and offspring result. Some of these offspring in rare cases has the trait you want to propagate. You separate out these offspring and try to mate them (which may not happen). By the way the trait you are looking for may not happen in the first generation and may be recessive.
You take fertilized eggs and subject them to doses of X-rays. Assuming they hatch from incubation (which may be rare) and they have a trait that you want to propagate, you can continue with the process of trying to select for this trait.
Well, good luck and let us know how you make out in a few years.
Regards,
Bill