And among those who work in research and development — the engine of discovery and innovation for the industry — immigrants made up one-third of the labor force, according to the 2014 report. Foreign-born scientists made up 43 percent of medical and life scientists, the study found.

“In general, intellectual endeavors in the U.S. -- education, research — they rely on immigrants,” Lowry said. “It’s important to have innovation, and innovation comes from diversity. A difference in perspective allows for a difference in approach.”

Yet in the run-up to a big meeting Tuesday morning with Trump, the pharmaceutical industry was muted compared with other big businesses responding to the ban.

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Pharmaceutical Research and Manufacturers of America (PhRMA), the trade group that represents the industry and usually speaks on its behalf, said it didn't have a comment about the ban. Neither did Pfizer, one of the world's largest pharmaceutical companies. And those that did have a response to the ban often struck a neutral tone and focused on its employees.

“We are working to fully understand the implications of the Executive Order on our business and our employees,” AstraZeneca said in a statement.

“Upholding our steadfast commitment to associates of all nationalities and religions is core to our values as we work to address society's most pressing healthcare challenges,” a Novartis statement said, noting that to date there had been no disruption to Novartis employees as a result of the order.

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Leaders in the biotech industry, on the other hand, were more vocal.

“The travel ban is causing confusion among several of my company's associates and I have been told by other biotech CEOs of similar responses across the industry,” Ron Cohen, a chief executive of Acorda Therapeutics, said in an email. “This is a difficult situation for scientists, doctors and other professionals whom we rely on to help invent and develop new treatments and cures for disease. If we restrict travel excessively, they will go elsewhere and their talents will enrich other countries.”

It's not necessarily surprising that pharmaceutical leaders didn't take a vocal public stand on Trump's policy ahead of such a high-profile meeting. The industry has been hammered by Trump and accused of “getting away with murder” on pricing. The trade group launched a major ad campaign last week aimed at changing its image after a year of blistering congressional hearings and news stories about rising drug prices. The industry has been trying to fend off any government intervention on pricing.

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After the meeting at the White House, Merck chief executive Kenneth Frazier answered a reporter's question about the ban.

“We have employees from around the world; we have to get the best scientists, the best employees around the world, so having access to those employees and having an environment in our companies that stimulates diversity and inclusion is very important to us,” Frazier said.

But the George Mason researchers said that the industry's competitive edge going forward may depend in large part on keeping and attracting its immigrant workforce for a reason none of those leaders brought up. Immigrants tend to come from countries that have fast-growing pharmaceutical markets — places where U.S. companies would like to sell drugs. In other words, if those immigrant workers are deterred, they could easily become part of the competition.

“Given that the majority of immigrants within the pharmaceutical industry are from the world’s fastest growing pharmaceutical markets, the U.S. may benefit from the continued encouragement of immigration from those regions,” the authors said. “Failing to do so carries the risk that those individuals will use their skills and talents to build the pharmaceutical industries in the very countries that are emerging as the leading competitors to the U.S. pharmaceutical industry.”