TOKYO — President Trump has put a hard-line trade agenda at the center of his 12-day trip to Asia, which begins here on Sunday. Yet Mr. Trump is leaving his two most senior economic advisers back home, as well as the White House economist whose anti-China views inform much of Mr. Trump’s thinking on the subject.

He is also not taking his daughter Ivanka, who accompanied him to a summit meeting in Germany in July and raised eyebrows after she took his empty seat during a session with other world leaders. Her husband, Jared Kushner, a senior adviser who once laid claim to the China portfolio, will return to Washington after the president’s stop in Beijing.

The staffing of any major presidential trip is an exercise in internal politics — sometimes byzantine — as the White House parcels out coveted seats on Air Force One. But the Trump administration’s staffing of this trip is drawing particular scrutiny from those seeking clues about who’s up or down, and what message the president is trying to send to allies and adversaries.

In some cases, the administration’s staffing decisions have been driven by straightforward domestic politics. White House officials said Treasury Secretary Steven Mnuchin and Gary D. Cohn, the director of the National Economic Council, both needed to stay in Washington to lobby Congress for Mr. Trump’s proposed overhaul of the tax code.