I don't know, I've seen nibble marks in the Papaya but I'm sure the birds join in as well. However it would be a brave squirrel to run up a solitary papaya tree with four dogs roaming round the garden.
One thing I have noticed is that whenever I've tried growing European runner beans the bloody sparrows eat all the red flowers and we get no crop. Seems strange - back in the UK the sparrows never touched the bean flowers.