ABC's new horror series "The River" may have finished on top of the genre heap this week, but that doesn't mean this show isn't in some serious trouble out the gate.

The series, starring Bruce Greenwood from "Star Trek" fame, averaged a 4.7 rating/8 share, according to Fast National overnight ratings from The Nielsen Co. That would have tied it with ABC's comedy "Last Man Standing," which is produced with a far smaller budget than the location-heavy "River."

Although "The River" did beat competition from NBC ("The Biggest Loser," "Parenthood") and Fox ("New Girl," "Raising Hope"), it didn't even have a chance against CBS, which aired "NCIS: Los Angeles" and "Unforgettable."

In what would be even worse news, audiences abandoned the show by the time its second hour started. The first hour picked up a respectable 5.1/8, but then audiences started to tune out, and 16 percent of the audience checked out by the time the next hour aired.

That could suggest there would be an even bigger fall for the series this coming week, and if that does happen, don't expect to see "The River" beyond this season.

"Alcatraz" is still slipping for Fox, once again losing a sizable piece of audience from the week before. This time, its 4.1 household rating was down 16 percent from the week before, and is 31 percent off its premiere. It's 5.1/7 average, however, is still giving Fox better numbers than the 3.8/6 it earned there last year. Also, at least for now, it's still doing better than the 4.6/7 "House" did in that timeslot earlier this season.

That wasn't the only Fox show getting bad news this week. "Fringe" finished behind "Vampire Diaries" on The CW for the second time this year (last time it happened was on Nov. 6, although the two shows did tie Jan. 8). Fox has not announced whether this would be the last season for that show, but it becomes more and more likely with each passing week.

For complete television ratings analysis from the past week, check out our sister site Inside Blip.

Top Network Genre Shows, Week of Feb. 5 -- [Audience Loyalty Index rating]

Fast Nationals usually provide a snapshot of what Americans are watching by pulling numbers from the top urban markets that include both live viewing and same-day timeshifted viewing. A rating point generally represents more than 1.1 million households while the share indicates the percentage of televisions turned on that was tuned to the specific program. These numbers typically shift when final ratings are issued.

Data collected from The Nielsen Co., as distributed by Zap2it. GenreNexus tracks non-news, non-event programming, and figures for this story reflect airing of new episodes only. For more information on the Audience Loyalty Index, click here.