So long, solitude: The world's biggest cruise ships are getting more crowded by the week

The world's biggest cruise ships are back to sailing mostly full.

Royal Caribbean CEO Michael Bayley on Thursday said occupancy levels on the line's five giant Oasis Class ships — the five biggest cruise vessels ever built — had been running above 80% in recent weeks. Other vessels in the megaship brand's fleet also have been seeing high occupancies as of late, he said.

"We've had ships sailing at 100% into the Caribbean market on our short [cruise] product," Bayley said during a conference call with Wall Street analysts. "And as we head toward Memorial Day weekend, we are going to see a significant percentage of our ships sailing at 100% and greater."

Bayley's comments came after Royal Caribbean's parent company, Royal Caribbean Group, reported that occupancy levels on its ships had been growing month-by-month since the start of the year. Occupancy averaged about 57% during the first quarter of the year but rose to 68% by the end of March, the company said.

The company said it expected occupancy levels to average 75% to 80% in the current quarter across all of its brands.

Royal Caribbean Group is the parent company of its namesake Royal Caribbean brand as well as Celebrity Cruises and Silversea Cruises. It also owns a partial stake in Europe-based TUI Cruises and Hapag-Lloyd Cruises.

Royal Caribbean Group's report on occupancy levels, which came as the company reported first quarter earnings, was the latest sign that the days of sailing on unusually uncrowded ships are coming to an end.

Related: Loving the uncrowded ships? Get ready for a change

Historically, most cruise ships operated by major cruise companies such as Royal Caribbean Group have sailed at occupancies close to 100%. The industry has traditionally followed a business model built around managing bookings to ensure ships are always full.

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But occupancy rates on cruise ships have been far below normal over the past year as the industry slowly bounced back from a months-long, COVID-19-related shutdown.

Some ships initially sailed with just 20% or 30% of normal passenger loads, as TPG reporters saw first hand while covering the restart of cruising over the past year.

Royal Caribbean Group and other major cruise companies such as Carnival Corporation and Norwegian Cruise Line Holdings initially capped occupancy on ships as part of a strategy to reduce COVID-19 transmission between passengers. Cruise ship occupancy subsequently remained lower than normal in part due to the hesitancy of some consumers to book cruises during the various waves of the COVID-19 pandemic.

Related: The ultimate guide to picking a cruise line

As consumers have become more confident in booking cruises, occupancy has risen.

Royal Caribbean executives on Thursday suggested that occupancy levels had been bouncing back most strongly for sailings to the Caribbean but less strongly for sailings in Europe.

Cruises departing from ports that North Americans can reach by car (sometimes called "drive-to cruises" in the industry) are in particularly high demand — a sign that cruisers are still looking to stay somewhat local as they begin traveling again.

"What we've seen in terms of demand in the American market for the drive-to products ... has been really strong," Bayley said.

Demand for cruises in Europe in recent months, by contrast, have been hurt by customer worries about getting trapped overseas if they test positive for COVID-19. The U.S. government requires that anyone flying into the country, even American citizens, test negative for COVID-19 before being allowed to enter.

"It is our expectation in Europe for our load factors [for the summer] to be lower," Royal Caribbean Group CEO Jason Liberty said during the conference call. "Some of it is very much related to [trying to hold the line on prices], but some of it also relates to the testing requirement to come back into the U.S. for Americans ... those things weigh on the consumer in terms of their travel expectations."

Liberty and other executives also said the war in Ukraine had had an effect on demand for European travel.

Liberty said he expected occupancy across the line's ships to remain below 100% during the third quarter of the year — traditionally the most profitable time of year for the cruise industry.

Still, Liberty said occupancy overall was likely to continue to build month-by-month throughout the year, and he said he expected ships to run more than 100% full by the end of the year — something possible when more than two people stay in some cabins.

Cruise companies consider a ship to be 100% occupied when two people are staying in every cabin. Most cabins on cruise ships have two main "berths," as cruise companies call bed spaces. Some cabins also have pull-down bunks or sofa beds that allow for more occupants.

"We're going to be building up through the back half of this year to that triple digit [occupancy percentage] mark," Liberty said.

Liberty noted that the company was seeing more close-in bookings than normal, and he suggested the long-term outlook for travel is strong. People want to get back to traveling.

"We continue to see strong demand for leisure travel and cruising," Liberty said. "The robust, secular trend of experiences over things that propelled our business in the past years is now recovering toward pre-COVID levels."

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