The limits and difficulties related to the tools currently in use for palaeosynecological comparisons of faunas or floras of different geological periods are discussed. The new method of the Wagner parsimony Applied to Palaeosynecology Using Morphology (WAPUM method), is defined and tested on morphological characters gathered from two insect groups Odonatoptera and Thripida. The difficulties related to the monophyly of the taxonomic groups used in the more traditional approaches are no longer a problem when using the WAPUM method. In the WAPUM a character is ‘presence versus absence of species bearing a morphological structure’. The results obtained from use of the WAPUM minimize the number of changes among character states. Application of the WAPUM could reveal signals to confirm or object the currently available scenarios for the global changes in the evolution of past diversity and disparity of organisms (major changes or global crises of diversity).