Learn Russian

No, I figured it out, I think. It's по-(relative adjective), meaning "in the manner of whatever it is the relative adjective is relative to". Relative adjectives in -ский (русский, пиратский) decline like ordinary adjectives, subject to the normal rule that и replaces ы after к. But "soft" relative adjectives from the names of animals go like третий, with a soft sign added in declension: русского, горячего but лисьего, волчьего. That's where the soft sign in по-волчьи etc. comes from.