Gabrielle Union and Chris Rock in a scene from "Top Five." That movie and civil rights drama “Selma” struggled to find financing from the biggest movie studios. (Ali Paige Goldstein/AP)

With critical praise for the civil rights drama “Selma,” Chris Rock’s comedy “Top Five,” and the social satire “Dear White People,” it looks like Hollywood has been on a roll this year producing movies showcasing black casts and black directors.

Yet all these films — much like “12 Years a Slave” and “The Butler” from last year — have another thing in common: The films struggled to find financing from the biggest movie studios, relying instead on independent producers, black investors and even crowdfunding to get made.

Despite America’s changing demographics, Hollywood’s most powerful industry leaders have been slow to respond to a demand for movies that reflect cultural and racial shifts that have long been underway.

In the five decades since Harlem-based Rep. Adam Clayton Powell held congressional hearings on discrimination in Hollywood, a persistent racial gap exists between what’s viewed on screen and reality. Minorities make up more than 36 percent of the U.S. population but represented only 10 percent of lead characters in movies and sat in 12 percent of director’s chairs in 2011, the last year for which data is available.

To explain why big movie studios rarely invest in films starring and made by minorities, many point to the lack of diversity among the decision-makers — the executives who ultimately choose which movies are most widely distributed to the world. Aside from Warner Bros. Entertainment’s chief executive Kevin Tsujihara, the top leaders of the five biggest movie studios in the country are white.

The problem was highlighted recently when private e-mails exchanged between Amy Pascal, co-chair of Sony Pictures Entertainment, and movie producer Scott Rudin were made public after an illegal hack of the company’s data. In the e-mails, the two jokingly speculated about President Obama’s taste in films and rattled off titles Obama might like — all movies with leading black men.

The casual stereotyping by Hollywood heavyweights set off a wave of anger from moviemakers and civil rights leaders.

“It’s devastating is the truth,” said Dede Gardner in a panel earlier this month after the Washington premiere of “Selma,” which she co-produced. “There are no grades of racism. There’s just racism.”

On Thursday morning, Pascal met in New York with the Rev. Al Sharpton of National Action Network and Marc Morial of the National Urban League to apologize for the e-mails and to seek their counsel on improving diversity in Hollywood. Sony declined to comment for this story.

Faced with declining box office sales in this country, Hollywood executives sometimes argue privately that movies starring minorities or that confront racial issues are a tougher sell in foreign markets, where they see the biggest growth for their industry. But “12 Years a Slave,” for instance, was a hit overseas with 70 percent of sales in foreign countries, according to Box Office Mojo.

“Part of the problem is it’s an incredibly insular industry,” said Darnell Hunt, director of the Ralph J. Bunche Center for African American Studies at UCLA. “The people who make decisions, who green-light projects, tend to surround themselves with people pretty much like themselves.”

But for these executives, he added, “it’s becoming harder and harder to bury their heads in the sand and pretend there’s not this demographic earthquake happening. At some point, it’s not going to be sustainable. They’re going to have to start making movies that people of all colors will want to see.”

Hollywood’s reluctance

“Selma,” set to be released on Christmas, has already received a Golden Globe nomination for best picture and best director. But the movie — the first to dramatize on the big screen the Rev. Martin Luther King Jr.’s work organizing the seminal 1965 march from Selma to Montgomery, Ala. — almost didn’t get made.

The original script was passed around in 2007, but no major studio was willing to fund it. Brad Pitt’s small production company Plan B Entertainment and French investors financed it in 2008 with a modest budget. For years, it struggled with financing and changes in its director. It wasn’t until Oprah Winfrey stepped in this year that the project turned into a major motion picture event. With her financial backing, Paramount jumped in to distribute the film.

“It’s been 50 years since the events that we chronicle occurred,” said “Selma” director Ava DuVernay at the recent panel discussion. “The fact that there hasn’t been any theatrical portrayal of who he was and what he did is — I think — criminal.”

Other new movies this year directed and written by African Americans also had to secure funding sources outside the large Hollywood studios. Rock’s “Top Five” was produced by Barry Diller’s IAC Films. Director and writer Justin Simien turned to crowdfunding Web site Indiegogo to raise more than $41,000 in initial funds to jumpstart the making of his movie, “Dear White People.” Independent producers filled out the rest of the movie’s small budget, estimated by Simien to be roughly $1 million.

The makers of “The Butler” say they also struggled to get support in Hollywood for their movie, directed by Lee Daniels and based on Washington Post writer Wil Haygood’s article about a White House butler who witnesses three decades of history while serving occupants of the Oval Office.

Daniels had won praise for directing “Precious” and producing “Monster’s Ball.” The script was by Danny Strong, who had success writing the HBO movie “Recount.”

But when producers approached the biggest movie studios to fund it, the studios passed, saying they were afraid the movie wouldn’t bring profits overseas, according to producer Pam Williams. She said the implication was clear: Black casts and films that deal with race don’t resonate with foreign audiences.

“It was shocking how no one in Hollywood wanted to step up and make the movie,” said Williams, who co-produced the movie with Laura Ziskin. “There was such a universal story at its core.”

When Williams was searching for investors, she said a couple of investors even asked if the lead characters could have a white friend. “Those conversations ended very quickly,” she said.

That’s around when Ziskin, who was dying from breast cancer, sought out Sheila Johnson, a wealthy, black female financier. Johnson had made her fortune after selling Black Entertainment Television, the company she co-founded with her ex-husband, Robert Johnson.

After reading the script, Johnson quickly became the driving force behind the movie’s funding. She flew across the country several times to meet with investors and eventually rounded up 20 funders, Williams said.

Starring Forrest Whitaker, with Winfrey in a supporting role, the movie was a box office hit, grossing about $180 million in more than 50 countries with a budget of $30 million.

It’s not that foreign movie watchers don’t want films with black stars, said Brickson Diamond, chief operating officer of the Executive Leadership Council, an organization for global black leaders. The onus, he said, is on companies to invest in marketing their actors to make them more popular overseas.

He noted that the National Basketball Association, with a majority of black players, is hugely popular overseas, especially in China, and that actors Kevin Hart and Will Smith are also global A-listers.

The pressure to change

The gap between Hollywood and the general population is growing bigger as the country becomes more diverse.

Movies with 31 percent to 40 percent minority casts — the share closest to how America looks — accounted for just 2 percent of the top films from 2011 examined for the 2014 report by the UCLA’s Ralph J. Bunch Center for African American Studies. People of color wrote only 7.6 percent of the 172 movies examined.

“We’re not even making progress, we’re not even churning water, we’re actually going backward in certain ways,” said Hunt at UCLA.

And yet minorities — particularly Latinos — are the fastest growing movie audience and make up 44 percent of the nation’s most avid theatergoers, according to the Motion Picture Association of America.

Black moviegoers are also a huge market, accounting for 195 million visits to movie theaters in 2011, a report from BET Networks said. African Americans also make an average 13.4 visits a year to the movies, compared to 11 times for the general market.

To respond to the growing demand, the major studios have taken steps to appeal to diverse audiences.

Sony Pictures Entertainment has heavily marketed its weekend release of “Annie,” starring Quvenzhané Wallis and Jamie Foxx. Warner Bros.’ success with the horror film “Annabelle” was due in large part to its popularity among Latino audiences. The studio targeted those audiences with Spanish-language promotion in border towns and gimmicks like “Annabelle”-branded holy water. The “Fast and Furious” franchise is cast and marketed to bring in racially diverse, young audiences, too.

Meanwhile, there are some changes apparent in the TV world.

In 1999, the NAACP reported that no actor of color was cast in a leading role on prime-time television that season. But that has changed, with several shows this season with Latino, black and Asian lead stars.

There’s ABC’s “Cristela,” starring Mexican American Cristela Alonzo, about a Dallas-based law student who moves back home with her family. ABC also has the new family comedy “Fresh Off the Boat,” based on celebrity chef Eddie Huang’s best-selling memoir, about a Chinese American family.

One of the most celebrated new prime-time comedies this fall is ABC’s “Black-ish,” with more than 7 million viewers each week. The show features the first all-black family seen on prime-time television in several years.

The slow emergence of movies and TV shows made by black directors and writers means that plots illustrating the everyday experiences of African Americans mirror examples in real life, sometimes unfortunately.

“Dear White People,” a satire set at a fictional Ivy League campus where a fraternity threw a tacky black-themed bash, was awarded as a “Breakthrough Talent” at this year’s Sundance Film Festival. That same week, Arizona State University students were suspended for hosting a Martin Luther King Jr. Day frat party where attendees mocked black people by wearing basketball jerseys and bandannas and posting photos online with hashtags like #blackoutmlk.