I have a copy of the study (it's behind the Science subscription wall, sadly), which states that the "wild" populations are the protected populations in Amboseli National Park and Asian elephants in the Burmese logging industry. I don't know about the Burmese observational practice, but Cynthia Moss (who is one of the authors of the study) and Joyce Poole run a project at Amboseli which definitely tracks infant mortality; the gestation period of an elephant is 22 months, so it's a simple matter to track who's pregnant, who's given birth, and who's lost a baby.