Compatibility of running and climbing

[Deleted User]

Evening guys,

I am looking for any advice on the compatibility of running and climbing (of the indoor variety).

My thinking is that as climbing uses and tones the upper body, that would be of benefit to running and holding yourself upright, such as in the latter stages of a race.

Are there any specific physical reasons that they are perhaps non-complimentary, other than if you injured yourself in either discipline of course.

Thank you!

Mark