Species distribution models are scarcely applicable to invasive species because of their breaking of the models’ assumptions. So far, few mechanistic, semi-mechanistic or statistical solutions like dispersal constraints or propagule limitation have been applied. We evaluated a novel quasi-semi-mechanistic approach for regional scale models, using historical proximity variables (HPV) representing a state of the population in a given moment in the past. Our aim was to test the effects of addition of HPV sets of different minimal recentness, information capacity and the total number of variables on the quality of the species distribution model for Heracleum mantegazzianum on 116000 km2 in Poland. As environmental predictors, we used fragments of 103 1×1 km, world- wide, free-access rasters from WorldGrids.org. Single and ensemble models were computed using BIOMOD2 package 3.1.47 working in R environment 3.1.0. The addition of HPV improved the quality of single and ensemble models from poor to good and excellent. The quality was the highest for the variants with HPVs based on the distance from the most recent past occurrences. It was mostly affected by the algorithm type, but all HPV traits (minimal recentness, information capacity, model type or the number of the time periods) were significantly important determinants. The addition of HPVs improved the quality of current projections, raising the occurrence probability in regions where the species had occurred before. We conclude that HPV addition enables semi-realistic estimation of the rate of spread and can be applied to the short-term forecasting of invasive or declining species, which also break equal-dispersal probability assumptions.