You can copy and paste the SpeciesAlias to another model, but not all the data will be carried to the target model.
When you paste the SpeciesAlias to another model, the current relationships between the Species would be no longer maintained. The SpeciesAliases and Reactions pasted to the new model would be treated as a newly created components, and establish the new relationships in the model.
If there is a SpeciesAlias of the same contents existed in the model, it will become a new alias of the Species that the SpeciesAlias belongs to.
If there is no SpeciesAlias of the same contents existed in the model, new Species will be added to a model and will become the first alias.
However, the SpeciesAlias pasted from the other mode, unlike the ones newly created in the model, carries the copy of the contents of Species referred to in the original model. Therefore, it will carries the ID of the Species as well as the attributes specified by the users along with it.
Reactions associated with the SpeciesAlias would also be copied and pasted to the new model. The attributes associated with the Reactions would be pasted simultaneously, but the Reaction ID would always be re-numbered.
Caution: There may be the cases when the Species ID of the pasted SpeciesAlias conflicts with the existing Species ID. In such case, the Species ID would be re-registered automatically.
The "notes" associated with the components would be passed to the target model.
When the Species ID or name of the pasted SpeciesAlias conflicts with the existing Species ID or name, the "Duplicate�notes" dialog will appear and the notes will not be copied. (new in 4.0)

