Mating rituals are various behaviours, serving as a precursor to copulation in almost all animal species. In general these serve to aid the females of the species to pick out a mate. They can be interpreted as tests or demonstrations of the male's (mental and/or physical) fitness.
Now one example of a mating ritual, practiced by many animals including deer and elephants, is chasing. It consists of the male chasing the female for sometimes several hours until the female allows the male to "catch" her. It's important to note that this "chase" is typically entered/initiated willingly by the female, she's not simply trying to get rid of unwanted attention.
Now my question is if it would be possible for an animal species to do the opposite. Could, there be an animal species where the female chases the male?
I want to make it very clear at this point that my question isn't about whether the inversion of sexual selection roles (in where females instead of males compete for the latter) is possible: indeed it is, for instance it's the dominant model undertaken by spotted hyenas, and it often happens in human beings.
My question is about whether there could be an arrangement where the females of a species chase the males as a test of the males vigour. Or in other words a mating ritual in which the male attempts to outrun the female as a demonstration of his stamina/agility.
So to conclude my main question broken down would be:
- In what way (if any) could this inverted chase ritual be beneficial?
- Is it a behaviour that could have plausibly evolved?