Land management for cattle farming affects the persistence of an important fruit tree in the Brazilian Savanna

•Annona crassiflora populations had low fit to the negative exponential distribution model even in preserved sites.•Structure of populations showed recruitment gaps, mainly of small size plants where vegetation thinning and cattle farming were practiced.•Recruitment gaps caused by land use and management may lead local populations to extinction.•Local extinction of Annona will impact availability of food and a source of income for small farmers.