A new study says that an EU ban on the trade in wild birds has helped reduce the global business by 90%.
Prior to the 2005 regulation that limited the market, European countries were the foremost importers of birds, mainly from West Africa.
These imported creatures often escaped and posed threats to local populations and ecosystems.
Latin America has now become the main bird source, and is now responsible for 50% of the much smaller global market.
Flu sparks ban
It was in response to concerns about the spread of avian influenza that the EU imposed a temporary ban on wild bird imports in October 2005. This was made permanent two years later.
Prior to the ban, the global trade saw around 1.3 million birds bought and sold every year, according to the Convention on the Trade in Endangered Species (CITES).
The EU was the world's biggest importer of birds at the time with Belgium, Italy, the Netherlands, Portugal and Spain accounting for two thirds of all wild birds sold on the global market.
About 70% of them came from West Africa, mainly from Guinea, Mali and Senegal.
"There is some redirection of trade to other areas and some may have gone underground, but the global drop is so massive that those cannot account for it on their own," author Dr Diederik Strubbe, from the University of Copenhagen, told BBC News.
"By implementing this ban the trade has effectively eliminated a lot of demand from the market and the main picture that emerges is that the trade has largely collapsed."
Latin America has replaced Africa as the main source according to this study, supplying demand in Mexico and the United States. However the overall number of birds being traded has reduced to around 130,000 every year.
What's also changed is the type of birds being bought and sold.
Songbirds from Africa once dominated the market - now parrots are in the ascendant.
"The songbirds like canaries are only a fraction of what they were before, only 20% of the former level," said Dr Strubbe.
"The other popular birds are parakeets they have also declined a bit, not to the extent of the songbirds. Despite the ban they have remained rather popular on the global market and they have found new destinations."
Other researchers in the field welcomed the new study.
"What was really elegant about this paper was that they brought a number of datasets together and they showed us that to some extent the supply chains reconfigure but to some extent they don't. So that this policy had a beneficial impact," said Dr Paul Jepson from the University of Oxford, who wasn't involved in the research.
"For me, it's one of the big issues in wildlife trade governance, understanding the dynamics of supply chains."
The wild bird trade has long caused problems both in the country of origin and the importing nation.
Europe has seen large numbers of invasive parrots causing damage to local ecosystems, out competing local birds and damaging crops. More than 100 cities across the continent have seen parakeets establish.
So serious is the issue that a research group called Parrotnet was funded to assess the scale of the problem. In the UK, ring-necked parrots, descended from pets and aviary birds which have escaped or were deliberately released, have become so plentiful that they pose a threat to vineyards and fruit farms.
There are also impacts on the countries where the birds are captured with a loss of biodiversity and a loss of income for those involved in the trade.
The authors say that over time, the EU ban will likely end the ongoing problem of invasive birds.
"Among invasive species, birds are quite prevalent but our results suggest that the emergence of these, such as the parakeets living in Europe, are largely a phenomenon of the past," said Dr Strubbe.
"We do expect that invasions of new bird species will be become much rarer than before."
The research has been published in the journal Science Advances.