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Recently, there has been much debate whether niche based models (NBM) can predict biological invasions into new areas. These studies have chiefly focused on the type of occurrence data to use for model calibration. Additionally, pseudo-absences are also known to cause uncertainty in NBM, but are rarely tested for predicting invasiveness. Here we test the implications of using different calibration sets for building worldwide invasiveness models for four major problematic decapods: Cherax destructor, Eriocheir sinensis, Pacifastacus leniusculus and Procambarus clarkii. Using Artificial Neural Networks models we compared predictions containing either native range occurrences (NRO), native and invasive occurrences (NIO) and invasive only (IRO) coupled with three types of pseudo-absences – based on sampling only 1) the native range (NRA), 2) native and invasive ranges (NIA), and 3) worldwide random (WRA). We further analysed the potential gains in accuracy obtained through averaging across multiple models. Our results showed that NRO and IRO provided the best predictions for native and invaded ranges, respectively. Still, NIO provided the best balance in predicting both ranges. Pseudo-absences had a large influence on the predictive performance of the models, and were more important for predictiveness than types of occurrences. Specifically, WRA performed the best and NRA and NIA performed poorly. We also found little benefit in combining predictions since best performing single-models showed consistently higher accuracies. We conclude that NBM can provide useful information in forecasting invasiveness but are largely dependent on the type of initial information used and more efforts should be placed on recognizing its implications. Our results also show extensive areas which are highly suitable for the studied species worldwide. In total these areas reach from three to nine times the species current ranges and large portions of them are contiguous with currently invasive populations.