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The head of the fish is the first part to smell.

[Ἰχθὺς ἐκ τῆς κεφαλῆς ὄζειν ἄρχεται: ἐπὶ τῶν ἐπιστάτας φαύλους ἐχόντων]

Michael Apostolius (c. 1420 - c. 1480) Greek teacher, writer, copyist [Apostolius Paroemiographus, i.e., Apostolius the proverb-writer]

Apostolius 9.18.12, Tilley F 304
    (Source)

See Erasmus, Adages, Book 4, ch. 2, #97 [tr. Drysdall], who cites Apostolius, who appears to have been the first to record the proverb:

"The head of a fish begins to stink first." Used of bad rulers, whose contagion poisons the rest of the people. The expression seems to derive from the language of common people.

[Piscis primum a capite foetet ... Piscis a capite primum incipit putere. Dictum in malos principes, quorum contagione reliquum vulgus inficitur. Apparet ab idiotarum vulgo sumptum.]

Alt. trans.:

• "Fish start to stink at the top: [this is a proverb] applied to people who have scoundrels for leaders." [tr. @sentantiq]
• "The fish always stinks from the head downwards: The freshness of a dead fish can be judged from the condition of its head. Thus, when the responsible part (as the leaders of a country, etc.) is rotten, the rest will soon follow. ἰχθὺς ἐκ τῆς κεφαλῆς ὄζειν ἄρχεται, a fish begins to stink from the head." -- Jennifer Speake, ed., Oxford Dictionary of Proverbs (2015) [Source]