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LOS ANGELES — TV's Asian-American characters are so frequently slighted that even programs set in the biggest, most diverse cities leave them out of the picture, a new study found.

For "Tokens on the Small Screen," professors and scholars at six California universities looked at 242 broadcast, cable and digital platform shows that aired during the 2015-16 season and tallied the numbers, screen time and portrayals of characters of Asian or Pacific Islander descent among 2,000 TV characters.

The report released Tuesday, a follow-up to broadcast TV studies done in 2005 and 2006, found increasing opportunities for Asian-American actors but concluded they are still underrepresented and "their characters remain marginalized and tokenized on screen."

There was a sense of optimism with the emergence of ABC's "Fresh Off the Boat" and "Dr. Ken" and Netflix's "Master of None," all starring and focused on Asian-Americans, said Nancy Wang Yuen, a Biola University associate professor and one of the study's authors.

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"It felt like, 'Oh, we're finally making it,'" Yuen said in an interview. "But even ("Dr. Ken" star) Ken Jeong said, "Of this many shows, we only have three?'"

The cancellations of Jeong's sitcom and the Netflix historical drama "Marco Polo," which featured a hefty number of Asian characters, showed how tenuous the hold on representation is, the study said.

Ken Jeong, left, and Danny Pudi attend the "Community" panel on Day 5 of Comic-Con International. Jordan Strauss / Jordan Strauss/Invision/AP

A third (34.5 percent) of all Asian or Asian-American characters were found to be on just 11 shows - with the 14 characters on "Marco Polo" alone making up 10 percent of the total — which sets up a "risk of greater decimation when networks decide to cancel even one show," according to the report.

The concentration of characters on a few shows also means that many viewers never see an Asian-American on screen, which the study says "effectively erases" them from a large part of the TV landscape.

There are 155 shows that lack a single Asian-American character, including 63 of broadcast and basic cable series and 74 percent of premium cable shows, the study found.

The exclusion is startling on shows set in urban areas. Among all New York-based shows, which has an Asian-American population of 13 percent, 70 percent of shows lacked a single series regular of that ethnicity. More than 50 percent of shows set in Los Angeles, with a population that's 14 percent Asian, lacked any such characters.

Other study findings:

Among all series regulars, white characters represent 69.5 percent; African-Americans 14 percent; Latinos, 5.9 percent, and Asian and Pacific Islanders were 4.3 percent. Their numbers among the U.S. populations: white, 61.3 percent; black, 13.3 percent; Latino, 17.8 percent, Asian-Americans, 5.9 percent.

Four Pacific Islanders were found to be series regulars, including Dwayne Johnson of "Ballers"; Uli Latukefu of "Marco Polo"; Keisha Castle-Hughes of "Roadies," and Cliff Curtis of "Fear the Walking Dead." That represents 0.2 percent, or half of their slice of the U.S. population, the report said.

Eighty-seven percent of Asian-American series regulars are on screen for less than half an episode, with white series regulars on screen three times longer than their Asian-American counterparts.

Besides Biola, the study included participants from California State University, Fullerton; University of California, Los Angeles; Thomas Jefferson School of Law; San Jose State University, and the University of San Francisco.

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