In order to further educate myself regarding the term 'Invasive Species', I turned to the Society for Conservation Biology and came across : Misconception and mismanagement of invasive species: "The paradoxical case of an alien ungulate in Spain" by Jorge Cassinello. First published:15 February 2018 https://doi.org/10.1111/conl.12440 

“The aoudad (Ammotragus larvae) is a North African ungulate /introduced in Spain, which was labeled “invasive” by Spanish authorities due to misreading of the term used by early studies. Indeed, to date, there are no conclusive empirical data showing negative effects of the aoudad on native flora and fauna.”

I encourage everyone to read this article for a clearer vision of the term “Invasive species”, and under what conditions and terms it could be applied, and how it can also go dreadfully wrong, and either lead to complete eradication or open-season / permitted hunting of the animal, in its area of residence. 

There are 16 birds on the Spanish Ministry of Agricultural, Food & Environment’s list of Invasive bird species (Page 22); and our parrot friends are on there. Two other parrot species not on the invasive species list (yet), can also be found living free range in the area of the Maria Luisa park in Seville, Some Blue-crowned Parakeets and Senegal parrots, (not in great numbers), cohabit the park (also because of accidental or intentional release) ; along with the Monks and RNPs who were once both the cheapest and most traded parrots in Spain. More than 190,000 Monk parakeets have been imported from Uruguay and Argentina into Spain and almost 63,000 Ring-necked parakeets from Pakistan and Senegal, These birds continued to be imported legally since the mid 70’s until the temporary, (2005) and permanent, (2007) EU bans. After that they continued to be sold in pet shops as cheap pets until the new regulations of 2013.

For reasons of clarity I will argue my case for each bird separately, based on my perception of the Ministry’s criteria of serious harm to other fauna, flora, environment by introduced species. If anyone is interested in reading up on the lists and laws; here is the Translated English link:  https://translate.google.com/translate?hl=en&sl=es&u=https://www.boe.es/boe/dias/2013/08/03/pdfs/BOE-A-2013-8565.pdf&prev=search

You will also find the aoudad (Ammotragus larvae) the ungulate referred to earlier, on the list of invasive mammals. 

And here is the original Spanish: https://www.boe.es/boe/dias/2013/08/03/pdfs/BOE-A-2013-8565.pdf

Incidentally, while reading various Spanish newspaper articles, I was horrified to discover that there are certain times of the year, where hunters are allowed to shoot down the Argentinian ( Myiopsitta monachus) and the Kramer (Psittacula krameri) parrots.