Placing emphasis on 'noticing vs running' is just confusing you. Noticing helps the rabbit run just as much as it helps it look in the right direction.

Sorry I wasn't being clear, previously I had always meant noticing=='showing the fox you have noticed it'.

If average rabbit speed become slower then there will be a commensurate change in the threshold at which foxes chase rabbits even when they have been spotted.

What threshold? I'm guessing other factors such as the fox's independent assessment of the rabbit's speed?

It will remain useful to show the fox that it has been spotted in all cases in which about 200ms of extra head start is worth sacrificing so that a chase may potentially be avoided.

I didnt consider the fact that signaling having noticed required that sacrifice. Does it affect the analysis?

consider a situation in which rabbits and foxes always become aware of each other's presence at a distance of precisely 250m. Would anyone suggest that rabbits would freeload and not bother to be fast themselves in that circumstance?

I don't understand this part.