The Sunday Herald said the figures were official government statistics. It listed a table of losses farmers had suffered in both 2013 and 2016.
Marine Harvest suffered the heaviest mortalities last year, losing 7,609 tonnes of Atlantic salmon, compared to 2,224 tonnes in 2013. It harvested 45,046 tonnes last year, as opposed to 50,144 in 2015.
The Scottish Salmon Company lost 5,873 tonnes, up from 2,436 tonnes in 2013. It reported "unprecedented mortalities" for 2016 in its annual report.
Niche producer Wester Ross Fisheries lost 33 tonnes of salmon (86 tonnes 2013), and not the 3,142 tonnes originally reported in the Herald, and mistakenly repeated here.
Significant mortalities in Western Isles
Other 'mort' figures listed by the Herald were: Scottish Sea Farms 1,678 tonnes (1,897t 2013); Grieg Seafood Shetland 611 tonnes (Zero t 2013); Loch Duart 33 tonnes (581t 2013). Two trout farmers, Kames - 2,854 tonnes (51t 2013) - and Dawnfresh - 200 tonnes (122t 2013) - were also listed.
The Herald also reported that this year there had been 7,700 tonnes of morts up to June, and that there had been significant mortalities in the Western Isles since then.
Comparing the number of smolts put to sea with the 6-10 million mortalities, the percentage of unwanted fish deaths in Scottish farms is between 14-23 per cent. By comparison, Norway's mortality rate in 2016 was 18 per cent. Both countries fare poorly in comparison to the Faroe Islands, where losses have been around 5-10 per cent for several years.
AGD a big problem
Scott Landsburgh, chief executive of the Scottish Salmon Producers' Organisation (SSPO) said: "AGD (amoebic gill disease) has been a big problem, on top of the lice burden. Lice numbers did rise at the beginning of last year, but we spent significantly last year to bring them back under control.
"But gill disease is a problem, there's no doubt about it, and it's not just pertinent to Scotland, it's all over the world: Norway, Canada, Chile, we're all having challenges with gill disease. If in any way your fish gills are compromised and you try to treat them for other things such as the lice burden - and we have to abide by the low number management on lice - it's a compromise, you could well get mortality and that's what's happened.
"You need to work hard to make sure the fish have the least stress as possible in the welfare management of them, which is where we are at now, and I think we are in a better place now. There have been problems in the Western Isles, and I think that is in a turnaround situation now.
"We absolutely do not want high mortality and we are doing all we can to turn that around, and I think we are beginning to see a turnaround. But it's not easy, there are all sorts of gill irritants coming through in the water bodies just now. AGD is a serious challenge and nobody has the perfect answer yet, and we're all working hard to deliver a management regime that causes the least stress possible to the fish. By doing that hopefully we will reduce mortalities quite significantly."
Critics of the salmon farming industry used news of the mortalities to press their case for change, and call for a switch from net pens to closed-containment facilities.
But Landsburgh said: "It's just nonsense. It's like saying 'I think we should have 100 per cent electric cars as of next year because we are polluting the streets of Edinburgh and Aberdeen and Glasgow and Dundee - in fact, I think we should make everyone drive electric cars tomorrow'. It's the same thing (with closed containment). This is not tried, not tested, it is not commercially worked yet anywhere in the world, and so it's a pipe-dream. It's easy for people to say, but they've no idea what they're talking about."
Steve Bracken, business development manager for Marine Harvest Scotland, said: "Fish welfare is paramount but sometimes you are hit with something like AGD and that can give you a big problem."
He said salmon farming was still a young industry and "we are still learning".
Despite the mortalities, and a claim in the Herald by fish farming opponent Don Staniford that the industry was "haemorrhaging cash", high prices mean farmers have been making money. Marine Harvest Scotland made an operating profit of €41.1 million last year, while the Scottish Salmon Company made net earnings of nearly £9 million.