In my experience the birds are very fond of the berries and do a good job of spreading it!
The marbled vein ones are not such thugs and loved by flower arrangers. They have them on sale at Marjorie Fish's garden in Somerset.
I've a similar growing spot as you, semi shaded under shrubs, and it's been well behaved for the last 10 years. I spend more time getting rid of the neighbour's ordinary arum which keeps spreading through, just pull out the leaves as soon as you see any seedlings you don't want.
The berries are poisonous so if you have little ones around make sure you teach them not to touch them.
Gardening on the wild, windy west side of Dartmoor.
A great array of comments and advice.
You have eased my worried brow.
Many thanks all
Just another day at the plant...