Apple on Thursday fought back against the arguments that its controlling policies over the iPhone and iPad App Store hurt innovation and competition, releasing a report from economists it hired who said the tech giant's apps and services such as Apple Maps, Apple Music and iMessage are not as popular as their peers.

In the US, for example, Apple's Maps app represented 36% of usage, and its iMessage represented less than half. In music streaming and video streaming, it's far lower, at 21% and 3%, respectively. The Analysis Group report mostly relied on data collected by Data.ai, formerly known as App Annie, though Apple representatives indicated the company didn't dispute its findings.

"For many countries and app types, the Apple app accounts for 20 to 30% of total app usage," the study's authors at Analysis Group wrote, adding that Apple's apps are "eclipsed" in popularity by third-party apps in nearly every country. "This reflects that while the Apple apps are widely used, third-party apps are used more frequently."

Apple has hired Analysis Group economists to publish reports about its App Store over the years, including one released in July 2020, just before a Capitol Hill hearing on the tech industry, that argued its 15% to 30% commission rates for many in-app purchases wasn't anticompetitive.

The newly published research comes as Apple faces pressure from lawmakers, regulators and competitors around the world about how it manages and controls its iPhones and iPads, two of its most important products that together made up more than half of its $123.9 billion in revenue during the holiday shopping season last year. 

On the policy front, the company is preparing to comply with a new set of rules in the European Union, known as the Digital Markets Act, which would require more interoperability among messaging apps, the ability for users to uninstall preinstalled software and apps, and better analytics data, among other things. The new rules governing the tech industry are still being finalized, but could force many powerful companies including Apple and Google to upend the way they do business today.

"What we want is simple: Fair markets also in digital," European Competition Commissioner Margethe Vestager said in a statement last month when announcing the rules, which haven't yet been approved by EU governing bodies, including the European Parliament. "We are now taking a huge step forward to get there -- that markets are fair, open and contestable."

Meanwhile, other countries, including South Korea, have passed laws requiring app store operators like Apple and Google to allow developers more flexibility, something both companies have historically resisted.

Apple is also under considerable pressure in the US, where it faces potential new antitrust laws and regulatory investigations. It's also fighting a high-profile lawsuit brought by Epic Games, maker of the hit online title Fortnite, which is winding its way through the appeals process.

Google, for its part, has responded to the pressure by announcing a landmark deal with music streaming giant Spotify to loosen its grip on the Google Play app store. Google said it will allow Spotify to collect payments for its service directly from customers, avoiding the typical 15% to 30% commissions Google charges many app developers. Google has suggested more deals may be on the way.

Apple, too, has loosened some of rules. Last month it began allowing "reader apps," which connect to subscription services for music, books, movies and television shows, to direct customers to their website outside the App Store for payment. Until that point, Apple didn't allow such moves, something it received criticism for from a US District Judge last year.