The greatest challenge faced when breeding populations of forest species is to achieve the right equilibrium among genetic gain and no loss of the effective population size. Thus this study aims to define the best thinning strategy to compose a seed orchard of Eucalyptus benthamii to obtain genetic gain maintaining the effective population size. The population of E. benthamii studied consisted of 28 open-pollinated progenies. The diameter at breast height (DBH) and height (H) parameters were determined three years after planting. Measurement data were analyzed and compared using four different mathematical models (with and without competition effect and spatial variation). Strategies considering genetic gain and effective population size were simulated considering the number of families, the number of individuals between families, and the total number of individuals. The mathematical model accounting for the competition effect had the best fit for DBH whereas the model accounting for the environmental variation effect presented the best fit for H. The ranking of BLUPs grouped the families into three clusters (best, intermediate/average, worst/poor families). The strategy that maintains 40 % of the individuals, generates a genetic gain of 13 % in DBH and 8 % in total height while maintaining an effective population size greater than 92 for booth traits.
