New iphone- deleting apps on old phone?

Just got the new iPhone. I'm still using my old iPhone as an iPod touch. I came up with a question. I have my share of virtual pets on my phone, and decided I didn't want to take care of the originals on my old phone in addition to the exact copies on my new phone. If I delete the apps on my old phone, will anything happen to the apps on my new phone? I don't plan on syncing my old phone anymore, if that helps with anything at all.
Thanks!