Just because Tolkien didn't mention them doesn't mean they didn't exist. Tolkien didn't mention female eagles or female Haradrim either, as far as I know, but no one is suggesting
they were dug out of the ground.
Yes, eagles and Haradrim are "natural" creatures, whereas orcs are something a bit off-center, but my point is not bothering to talk about something doesn't mean it doesn't exist. I don't think Tolkien would have cared enough about the mechanics of orc reproduction to include it in LotR. He probably felt our imaginations were horrid enough without going into graphic detail.
"Breed" (the transitive verb) can mean several things:
"1. To cause to reproduce, especially by controlled mating and selection: the Rohirrim breed horses.
2. To develop new or improved strains in (organisms), chiefly through controlled mating and selection of offspring for desirable traits.
3. To inseminate or impregnate; mate with."
I certainly hope Saruman was doing 1 & 2 and not 3!
Getting up sufficient numbers of orcs in 50 odd years is possible depending on starting numbers, when orcs become adults/sexually mature, and how many offspring they have at one time. Let's say time of gestation is a year. So, if you start with 400 orcs (200 of which are female), and orcs become adults at the age of 10 years, and they always have quadruplets:
Year 1: 200 adult female orcs (and 200 male orcs to fertilize them)
Year 2: 200 female, 200 male and 800 baby orcs (400 female, 400 male). The 200 original females breed again.
Year 3: 200 female, 200 male and 1600 baby orcs
Year 4: 200 female, 200 male and 2400 baby orcs
Year 5: etc.
Year 10: 200 female, 200 male and 7200 immature orcs
Year 11: The first crop of 800 baby orcs are now adults and ready to breed.
600 female, 600 male and 7200 immature orcs (the original adults made new babies to make up for the ones transitioning to adulthood)
Year 12: The second crop of baby orcs become adults. 1000 female, 1000 male and 8800 immature orcs (7200 from the original adults and 1600 from the new breeders)
Year 13: The third crop of babies matures. 1400 female, 1400 male and 12,000 immature orcs (7200 from the original orcs, 3200 from the first set of babies and 1600 from the second set of babies.)
Year 14: The fourth crop of babies matures. 1800 female, 1800 male and 16,800 immature orcs (7200 + 4800 + 3200 + 1600)
You can see things are going to rapidly increase from here, especially once the offspring of the original baby orcs start to breed. Even if we stopped after Year 14 and waited another 10 for all the babies to reach fighting age, we'd have 20,400 adult orcs (10,200 male) after 23 years. Under these hypothetical conditions, Saruman would have no trouble building up an army of massive proportions in 47 years (although some orcs might be geriatric). Of course, the timeline changes if orcs mature more slowly or have fewer offspring, but increasing starting numbers can make up for that a bit. If any computer savvy people want to build an "Orc breed-o-meter" so we could play with the parameters, that would be entertaining.
-Lily