A close look at the tweeting patterns of the entire Republican field during the primaries, however, reveals that Trump’s pattern is an outlier.

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Are these Twitter fights different from the usual negative campaigning?

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It is easy to forget that this is the first presidential contest in which candidates have used Twitter to engage one another directly. As David McCabe noted in The Hill in August 2015, “social media has even doubled as a virtual debate stage, with candidates sparring in a manner inconceivable just a few election cycles ago.”

In research for our newly published article “Twitter Taunts and Tirades: Negative Campaigning in the Age of Trump,” we examined every tweet issued by each of the 17 candidates for the Republican presidential nomination mentioning another candidate. Our goal was to see whether the embrace of social media is altering the tone of campaigning — in particular, by making it easier for all candidates to attack a number of opponents.

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We noted the tone of each tweet (positive, negative, or neutral) to see whether dynamics among the candidates were like the dynamics that political scientists have predicted or found in previous studies. Specifically, if Twitter is used as negative campaigning usually occurs, (1) attacks should increase as the end of a campaign approaches, and (2) candidates should only attack opponents who are ahead of them in the polls, although the leading candidate may strike back at their closest competitor.

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Republican primary candidates’ tweets changed abruptly after Trump entered the race

Of the candidates’ approximately 2,000 mentions of their Republican opponents’ names or Twitter handles, we focused on 1,069 that were clearly either positive or negative. (We excluded retweets of others’ tweets.) Not surprisingly, over the course of the primary, candidates became more acrimonious.

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At the start of the campaign, GOP candidates’ tweeted mentions of one another were positive 19 times for every one negative tweet. However, during 10 days in early July 2015 — soon after Trump entered the race — that ratio changed to one positive for every four negative tweets.

By the last few months before Trump’s nomination, the Republican candidates hardly ever tweeted anything positive at one another. They issued just one positive tweet for every 20 negative. In the rare instance of a positive tweet, candidates were mostly bidding farewell to opponents as they dropped out.

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Seventeen candidates punched ‘up,’ and one punched ‘down’

Is negative campaigning helpful or harmful? According to research, the answer is mixed.

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Attacking other candidates can help educate voters and draw attention to the attacking candidate. But sometimes the attacker loses standing, as voters lose faith in mean-spirited candidates. Candidates trailing in the polls have a greater incentive to lash out, while those in the lead usually resist.

It’s hardly surprising, then, that Trump received far more negative tweets from opponents than he hurled at them, getting around seven incoming attacks for every four outgoing. If we consider all 17 candidates’ negative tweets about one another, only 28 percent (252 of 911) are instances of “punching downward.” (We define that as a negative tweet from a candidate who has been ahead of the candidate he’s attacking in an average of the previous five major polls.)

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But here’s the surprise: Of the 252 tweets in which a candidate hits a weaker opponent, Trump accounts for all but 10. Trump is by far the candidate most likely to punch downward.

It’s not that the other candidates don’t engage one another. In 340 affect-laden (either positive or negative) tweets, Trump was neither sender nor receiver. Ninety-two were aimed at a poorer-performing candidate; of these, fully 89 percent were positive. More than twice as many, 248 tweets, were directed upward at better performers, and as is the norm, 79 percent of these were negative.

In other words, most candidates attacked their better-performing rivals. A few avoided negative comments, except for occasional criticism of Trump. Trump alone used Twitter to insult his many opponents with abandon. Only two of 16 opponents — Rick Santorum and Jim Gilmore — completely avoided his barbs.

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Trump would also trade punches with his closest competitors. At times he started fights, repeatedly needling Sen. Ted Cruz of Texas, who turned the other cheek — until Trump finally provoked a response by insulting his wife. Trump hit Sen. Marco Rubio of Florida with nearly twice as many negative tweets as he received from Rubio. Ben Carson issued just a single tweet that was mildly critical of Trump, and got eight harsh Trump tweets; not once did he retaliate, and only addressed Trump again to endorse him.

When he was attacked, Trump struck back hard at even some of the most poorly performing candidates, often mocking their poor poll performance. For instance:

Why did Trump go on the attack so indiscriminately?

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Some see it as indicating a man who cannot let go of a grudge.

Others portray Trump’s behavior as the mark of a thin-skinned campaigner who just can’t resist lashing out, even upstaging one of his own policy speeches by attacking the several women who accused him of sexual assault when he tweeted, “All of these liars will be sued after the election is over.”

Still others see a master of new media, a P.T. Barnum for the Twitter age, who knows that conflict sells and the more conflict, the better.