The two departments work independently of each other.

这两个部门独立运作。

《牛津词典》

There are two main groups of bats, which are believed to have evolved independently of each other, but both from a common ancestor.

蝙蝠主要有两大类，人们认为它们是各自独立进化的，但都来自同一个祖先。

youdao

It does not allow get and put access to be granted independently of each other.

它不允许彼此相互授予获取或放置权限。

youdao

They also tried to manage their exchange rates and their monetary policies independently of each other.

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They are groups of eleven or fewer people engaging in violent disorder entirely independently of each other.

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I'm saying both could have existed independently of each other and been used.

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