Each group is only linked to one checkbox right? You should just need to use the answer from above the way I read this.
${invasivetypes} = 'Birdvetch'
That fails when your lists becomes 'Birdcetch, anytexthere', now the strings don't match.
selected(${select_multiple_species}, 'birdvetch') instead asks if that list (the data saved in the field for the select_multiple) contains your item, which is does so relevant is flagged and your group should show.
If it's not working try the other variation of label or name, check the capitilization. It'll be that.