RESUMEN
We carried out a six-year study aimed at evaluating if and how a Brazilian Atlantic Forest small mammal community responded to the presence of the invasive exotic species Artocarpus heterophyllus, the jackfruit tree. In the surroundings of Vila Dois Rios, Ilha Grande, RJ, 18 grids were established, 10 where the jackfruit tree was present and eight were it was absent. Previous results indicated that the composition and abundance of this small mammal community were altered by the presence and density of A. heterophyllus. One observed effect was the increased population size of the spiny-rat Trinomys dimidiatus within the grids where the jackfruit trees were present. Therefore we decided to create a mathematical model for this species, based on the Verhulst-Pearl logistic equation. Our objectives were i) to calculate the carrying capacity K based on real data of the involved species and the environment; ii) propose and evaluate a mathematical model to estimate the population size of T. dimidiatus based on the monthly seed production of jackfruit tree, Artocarpus heterophyllus and iii) determinate the minimum jackfruit tree seed production to maintain at least two T. dimidiatus individuals in one study grid. Our results indicated that the predicted values by the model for the carrying capacity K were significantly correlated with real data. The best fit was found considering 20~35% energy transfer efficiency between trophic levels. Within the scope of assumed premises, our model showed itself to be an adequate simulator for Trinomys dimidiatus populations where the invasive jackfruit tree is present.