According to the Janzen-Connell hypothesis, seedling recruitment around tropical trees is more likely away from parent trees because of density- or distance-dependent predation or pathogen attack on seeds and seedlings. This was expected to lead to a more regular distribution of conspecific adults than would be expected by chance, and to favour coexistence. We first show theoretically that, even if yearly survival increases only slightly with distance to parent trees, an outward shift of seedling recruitment curves with time is very likely simply because seedlings live more than one year before recruiting to the juvenile stage. We tested this hypothesis for a humid savanna, dioecious palm tree, Borassus aethiopum, for which three discrete stages were defined by clear morphological traits. We found that (1) individuals of the second seedling stage are found on average further from their mother than individuals of the first seedling stage, and juveniles are found even further away (relative outward shifts between the three successive stages), and that (2) the older a female is, the further away its seedlings are (temporal outward shifts of distributions of seedlings). Both yearly recruitment (transition between two stages) and survival of seedlings are distance dependent and not density dependent. A matrix population model was used to demonstrate that, during the reproductive part of female palm life cycle, the cumulative effects of these distance-dependent variations in yearly recruitment and survival rates are sufficient to explain qualitatively the observed outward shifts.