Two other kittens born in 2012 were produced by the same mother and father, he said.
Over the years, researchers have found seven mountain lions that were the products of inbreeding, Riley said.
Riley says the kittens were healthy but there's concern that without new blood, eventually inbreeding could cause physical defects, such as heart problems and sterility.
The lions live in a patchwork of local, state and federal parkland that stretches westward from Los Angeles into Ventura County.
About a dozen pumas roam the area, but it's a tight squeeze when adult male pumas typically each have huge territories, Riley said.
The area is surrounded by densely populated areas and is bounded by such major highways as U.S. 101, which is heavily developed along most of its length.
"There's almost no place left where there's natural habitat (along the route) ... it's just a huge barrier for all animals," Riley said.
Young male mountain lions that typically would seek their own territories have been unable to leave and have been killed by an older male, Riley said.
"Their movements are totally circumscribed by the freeway," he said, noting that one young male was struck and killed by a car in October. The animal crossed eight lanes of roadway but couldn't jump a 10-foot-high retaining wall topped with chain-link fencing.
"That makes this inbreeding more likely than it might otherwise be because the young animals can't get elsewhere," he said.
In addition, other animals cannot easily move into the area from Los Padres National Forest and other neighboring wilderness areas, contributing to low genetic diversity, Riley said.
Research on the local puma population "shows that conflict with other lions, rodenticide poisoning and vehicle collisions are the top causes of death among more than 30 lions studied," the recreation area statement said.
The recreation area, state parks, the Santa Monica Mountains Conservancy, the California Department of Transportation and others have long sought about $10 million in funding to create a wildlife corridor in the Agoura Hills area — essentially, a tunnel that would allow the mountain lions and other animals to cross under U.S. 101.
There are plenty of mountain lions in California, but Riley said he thinks it's "amazingly cool" that a population still survives in the Santa Monica Mountains, in the midst of the urban sprawl.
It would be a shame if they disappeared, he said.
"It would be an ecological loss and even a cultural loss," Riley said. "These wild places that we spend millions of dollars to preserve — they would be a bit less wild."