The enigmatic title may be “Bird Box,” but in the first flashback of this occasionally riveting sci-fi thriller, the banter between the sisters Malorie (Sandra Bullock) and Jessica (Sarah Paulson) keeps returning to horses. Jessica, a breeder, chats enthusiastically about her stud as she drops by to visit Malorie, a pregnant recluse who spends her days painting in her studio. During Malorie’s checkup at the hospital, Jessica even imagines how great it would be if she herself existed in equine form.

There’s probably a would-be metaphor waiting to reveal itself in these scenes — maybe it is the screenwriter Eric Heisserer’s way of clearly contrasting Jessica as the free-spirited sibling and Malorie as the cynical one who harbors zero desire to become a mother. (Malorie grumpily describes her own pregnancy as having a “condition.”) But like much of the characterization found in this movie from the Danish filmmaker Susanne Bier (“After the Wedding”), the horse-related theme is severely undercooked.

“Bird Box,” an adaptation of Josh Malerman’s novel, jumps between two timelines under the premise “What if M. Night Shyamalan’s ‘The Happening,’ in which people mysteriously begin killing themselves, had blindfolds?” The opening scene is the present, with Malorie brusquely instructing two children, Boy (Julian Edwards) and Girl (Vivien Lyra Blair), about the treacherous journey on which they are about to embark down a river in a canoe. Once outside, they must never take off their blindfolds, or They. Will. Die.