Hi again, Gayle and thanks so much for waiting!
The behavior you described from your 1 year old male, is not uncommon. He's trying to assert his dominance over your female, even though she's older and might be bigger. For him, this may also be a form of play. He's bored, wants her attention, so he bothers/attacks her. It's possible that he was taken away from his mom-cat and siblings when he was too young and was never taught by mom, how to be sociable with other cats. He will most likely outgrow this behavior, but for the time-being, there are several things you can do to deter him.
First, I would get some Feliway plug in diffusers; these emit cat calming pheromones that cut down on stress/anxiety. You can find them in major pet stores, vet offices, and/or online. Here is more information: http://www.feliway.com/ca_en
If you should see him getting ready to attack her, stand out of site and shake a can of coins or pebbles to stop him in his tracks. You want to stand out of sight, so he associates the sound with his actions, not with you. Keep a few cans around the house, so they are conveniently located, for any room you're in.
You can also make sure that he's not bored (well, that both of them are not bored), but having a tall kitty condo or cat tree for them to play on (and even sleep) and a bunch of exciting toys they can play with. The list below contains many toys, manufacturers and even a cat dvd they will enjoy. I think the foraging toy will be great for him to play 'stalk/hunt prey,' instead of stalking your female. I love the toys made by 'Fat Cat,' so check them out at your pet supply stores or even Walmart.
There are other over the counter calming treatments, to settle him down, if he's too wild, going after her:
Note: don't use the oral products at the same time; just use one, in conjunction with the Feliway.
I don't like to recommend prescription medication, only as a last resort, so give these ideas above, a chance to work and if you see no improvement in a couple of weeks, discuss with your vet, if a prescription medication would be good for your male. There are many to choose from. Clomicalm is well-recommended:
I hope things will improve for both your kitties!
Please be so kind as to rate my answer with positive feedback, as that is the only way I receive recognition from the website for my assistance. Thank you very much!
Providing a positive rating will not end our conversation, should you need me for any follow-up. Simply click 'Reply to Expert' for clarification or additional information, if needed.