The prevalence of gun violence in top PG-13 movies has more than tripled since the rating was introduced in the mid-1980s, and last year it eclipsed even the amount in R-rated movies, according to findings to be published Monday in the journal Pediatrics.

“I think most parents would be surprised to learn that,” said Brad Bushman, a professor of communication and psychology at Ohio State University and one of the study’s authors. “We were pretty shocked.”

The authors said their findings are particularly troubling given considerable research into what has been called the “weapons effect,” which suggests that depiction of gun violence in media could lead to more aggressive behavior in the real world.

“We know that movies teach children how adults behave, and they make gun use appear exciting and attractive,” said Dan Romer, another co-author and the director of the Adolescent Communication Institute of the Annenberg Public Policy Center in Pennsylvania.

To determine how violence — and specifically gun violence — has changed in films over time, researchers chose 945 films sampled from the 30 top-grossing releases each year from 1950 to 2012. Coders sifted through the movies, noting violent sequences.

Researchers said they excluded violence not intended to harm anyone, such as accidents and run-of-the-mill sports aggression. They also excluded activities such as hunting and the use of large-scale weapons such as rocket-propelled grenades and military artillery.

In the end, they found that violence in films had more than doubled since 1950, and that violence had tripled in PG-13 films over the past quarter-century. In addition, while PG-13 movies initially had only about as much violence as G- and PG-rated films, since 2009 they have contained as much violence as R-rated films, or more.

Romer said even though some of the most popular PG-13 films in recent years, such as “The Hunger Games,” “The Dark Knight Rises” and “Snow White and the Huntsman,” are based on comic-book heroes or other fantasy characters, “these films have a lot of violence in them.”

“We think that the PG-13 rating is no longer very helpful,” he said. “If they’re going to allow content like that in PG-13 movies . . . it sort of goes against the grain of how they define the difference” compared with an R-rated movie, he added.

The PG-13 rating, introduced in 1984 after an uproar over violence in “Indiana Jones and the Temple of Doom,” indicates that parents should be “strongly cautioned” that some material may not be appropriate for children not yet teenagers. The R rating means anyone under 17 must be accompanied by a parent or adult guardian.

According to the Motion Picture Association of America’s rating system, “there may be depictions of violence in a PG-13 movie, but generally not both realistic and extreme or persistent violence.” By comparison, an R-rated movie could contain “intense or persistent violence.”

An MPAA spokeswoman declined to comment on Monday’s study but referred to information about how the group determines ratings at the Web site The site says that while the ratings are meant to help guide parents about a movie’s content, “it’s ultimately up to you to decide whether a movie is suitable for your family.”

The findings in Monday’s study, the authors write, are “troubling given the large body of research evidence showing that violent media can have harmful effects on children and youth.”

While many scholars agree with that conclusion, others have questioned the link between media violence and real-world violence. Christopher J. Ferguson, chairman of the psychology department at Stetson University, has written that the weight of evidence so far does not merit drawing hard conclusions. “If you are curious whether media violence contributes to violent crime,” Ferguson wrote in 2009, “the simple answer to that is we really don’t know.”

Meanwhile, two California economists, Gordon Dahl and Stefano DellaVigna, found in 2008 that attendance at violent movies actually reduced violent crime in the short term, possibly because they were keeping some at-risk individuals out of bars and off the streets for several hours. But both men said in e-mails that deciphering the long-term effects of media violence is trickier.

Monday’s study “does a good job showing that gun use has increased over time in movies, especially in PG-13 movies,” Dahl said. “But the more important question is whether repeated exposure to media violence increases violent behavior in the long run. This is a difficult question to answer, and not one that I’ve seen a convincing answer to.”

Romer and Bushman emphasized that their findings are not intended to pin violent behavior in young people on increased violence at the movies. But they said the MPAA should at least reevaluate how it rates films with growing amounts of guns and gore.

“I’m not a policymaker. I don’t really care what adults see,” Bushman said. “What I do care about is children exposed to age-inappropriate media. . . . Maybe films that contain excessive gun violence should have an R rating.”

Added Romer: “We think that’s pretty reasonable.”