The breeding of new strains of edible mushrooms is very important to the industry and many new strains are created every year from home hobbyists. With my knowledge of line breeding which is more patience than science I will try to explain different techniques to you which is very much the same as the way I used to breed different strains of Fancy Guppies over many years. I also worked with orchids but found that with guppies the same as mushrooms I could go through 4-5 generations in a year giving me faster results compared to orchids where with some species it could be several years. With mushrooms it could be possible to go through 6-10 generations per year depending on what characteristics you are looking for and how much space you have.
Always try to keep within the species you are working with. If you start trying to cross closely related species you will run into all kinds of problems especially if you loose any parent species you are working with not to mention having them escape into the wild although many hybrids are incapable of breeding themselves, I will have to do some more research myself to find out if fungi responed more to plant or animal breeding, plants can handle more anomolies than animals even having 2-3 extra chromosomes that would just not work in animals. It is workable in the very long term but you will need a lot of workspace, separation area's and all kinds of anomalies to work through.
When line breeding it is very important to have 2 or more lines set up as early as possible in your breeding program for outcrossing later on and keeping accurate records is essential.
Although it is possible to get very high P(agar transfer/generation) ratings and still have good results you will inevitably run into problems. Many mushroom varieties that have been made are actually F1 hybrids and not great to even cross with themselves to get any consistency from their offspring.
The easiest way for the home hobbyist to hybridise is to choose a variety you like the general characteristics off and just keep taking spore prints off every generation and keep inbreeding without introducing new genetic material. Over the generations you can take the best of every generation and by best I mean it is what you are looking to put into your strain. What you’re looking for in your strain may be different to someone else’s idea of what they want. Every couple of generations do some spore work on Agar to see how your breeding program is progressing. You should notice sectoring of new varieties and also alot of differences but over a few generations you should notice still sectoring but each sector will start to become more and more alike. Condensing the genes like this so as many of the offspring as possible resembling the parent gives you more flexability not having to rely completely on cloning.
When you start to notice most of the sectors have clear/visible similarities it is time to start your new lines. Make sure you fruit all of your potential parent lines and save a few on agar slants in case things go wrong, this ensures you don't have to go back to the total start if there are problems. At this stage you will also start to see recessive traits expressed. Recessive does not necessarily mean bad, it just means that a few traits that were hidden by dominent genes are starting to express themselves and they are incredibly easy to work with if you can isolate them, you wouldn't say someone with blue or green eyes had something wrong with them, the trait is just less dominant than brown eyes. When I was line breeding guppies for different characteristics I always got excited when I saw ressesive genes popping out of my strains because they were so easy to fix into a strain, sometimes only requiring a generation or 2 to get over 80% of the offspring looking like the parents.
Another option for beginners is to go with an actual species that was found in the wild. They should breed true to type if they are naturalized.
P ratings are very species specific, some species can only be cloned a handful of times and others can be cloned many times. As long as the cultures are kept healthy it is the mushrooms ability to clone itself that means mushrooms like oysters and shiitake can be cloned dozens of times before senesence kicks in. My shiitake straw strain has a P rating of 21 and it is still going strong. I will however be line breeding all of my varieties over time, eventually I will be able to take more true to type spore prints without having to rely completely on cloning. I still have the original cultures and can get replacements with the original "P" ratings from liquid nitrogen storage. It is unlikely you will find a top mushroom producer less than "P" 7 or so, simply because it has to prove itself before it ends up known at all.