That the parks are operating on a shoestring comes as no surprise to those working to preserve Africa’s wilderness, said Peter Fearnhead, chief executive officer and co-founder of African Parks, a nonprofit that manages 15 protected areas on the continent.

“What’s very helpful about this paper is that it actually puts a number to the problem,” said Mr. Fearnhead, who was not involved in the study.

In the new analysis, the authors used wild lions as a proxy for how Africa’s national parks are faring. Because of their place at the top of the food chain, lions are considered an umbrella species — a bellwether of an ecosystem’s health.

“If lions are doing well, everything else — with the exception of rhinos — is also doing well,” said Peter Lindsey, director of the lion recovery fund at the Wildlife Conservation Network and co-author of the new paper. (Rhinos are an exception because of poaching to meet the extreme demand for rhino horn.)

Throughout much of Africa, lions are not doing well. Their numbers have dropped 43 percent over the past two decades to as few as 20,000 in the wild. They now occupy just 8 percent of their historic habitat.