They are the fluffy-tailed invaders that, as the seasons change, can often be seen busy rummaging on the forest floor seeking out their winter food stash.

But while grey squirrels may have a degree of cuteness appeal, the deadly risk they pose to Scotland’s dwindling numbers of red squirrels have made them among the least welcome of woodland creatures.

Now there are worrying signs that the pesky grey invaders are encroaching even further into territories previously regarded as strongholds for their red-haired distant cousins.

In recent days, grey squirrels have been spotted in areas north of Perth and Dundee, in locations seen as being at the very frontline of red squirrel protection.

It’s raised concerns that without serious action the grey intruders, which not only out-compete the smaller red squirrels for food but can also carry deadly squirrelpox virus, will continue to push ever further north.

There are now calls for people enjoying the autumn colours of Perthshire and Tayside to help spot and report sightings of the grey invaders.

Ann-Marie MacMaster, Saving Scotland’s Red Squirrels’ Conservation Officer for Tayside, said: “There have been several grey sightings in areas that we would normally consider red squirrel strongholds – Aberfeldy, Strathbraan and Glenalmond.

“At this time of year, it’s not uncommon to see grey squirrels in unexpected places, because the young squirrels that were born over summer will be dispersing “What we really want to know is whether these squirrels are simply passing through or are part of a resident population, which would be much more concerning for the local reds.”

Grey squirrels have been spotted at Strathbraan in Perthshire, close to the Dunkeld and Birnam woods, and the Hermitage, areas which are considered a ‘paradise’ for red squirrels.

As well as providing ample food and shelter for the squirrels, the Perthshire woods are particularly popular at this time of year among visitors, due to their colourful mix of conifers, broadleaf, evergeen and deciduous trees which transform into a riot of autumn colour.

There have also been reports of grey squirrels being seen at Millhaugh Bridge in Glenalmond, Tayside, and unconfirmed sightings at locations from Luncarty in Perth and Kinross to Arbroath, and further north to Friockheim in Angus.

She added: “Public sightings are so important to our conservation work because they help us build a better picture of what’s happening on the ground, and take appropriate action. If anyone in these areas sees a grey squirrel they can help by reporting it on our website.”

Saving Scotland’s Red Squirrels, a National Lottery-funded partnership project led by the Scottish Wildlife Trust, works across Scotland to reduce the spread of grey squirrels. In Tayside, it focuses on what is known as the ‘Highland Line’ – a 10km-wide strip which runs from Montrose, through Kirriemuir, Dunkeld, Crieff and beyond to the west.

A key concern is that incoming grey squirrels in the northeast might connect with an existing ‘island’ population in Aberdeen which was introduced in the 1970s, with devastating implications for neighbouring reds.

Grey squirrels are native to the oak-hickory woodlands of the eastern states of America and were brought to the UK in the early 19th century as pets. When their popularity waned, they were released to the wild, quickly overwhelming populations of smaller red squirrels.

The first grey squirrels in Scotland were released on the shore of Loch Long in Argyll and Bute in 1892. Within two decades, greys had covered an area of around 800 sq-km and arrived on the east side of Loch Lomond.

At around the same tim, red squirrel hunting was at a peak. Between 1903 and 1929, the Highland Squirrel Club culled 82,000 red squirrels.

The destruction of native woodland, habitat fragmentation and changing land use has also affected red squirrel numbers. There are now thought to be just 120,000 red squirrels in Scotland, which makes up 75% of the entire UK population.

However, efforts are being made to reintroduce red squirrels in areas where numbers have disappeared. Since 2016, Findhorn-based charity Trees for Life has relocated 204 red squirrels from areas with thriving populations to nine woodlands across the Highlands.

Seven sites in the Wester Ross area - Ben Shieldaig, Coulin Estate, Inverewe Gardens, Attadale, Plockton, Letterewe and the Reraig peninsula – have seen red squirrels re-introduced.

The charity has also released red squirrels at Spinningdale on the shore of Dornoch Firth in Sutherland, and the Ardtornish Estate at Lochaline on the Morvern peninsula. Young squirrels have been sighted at every site following the breeding season.

Richard Bunting of Trees for Life, said: “"Many Highland woodlands offer the reds excellent habitat far from disease-carrying grey squirrels – but because reds travel between trees and avoid crossing large areas of open ground, they can’t return to isolated woodlands without our help.

“This project shows the positive difference that rewilding can make for nature, wildlife and people.

“We are giving red squirrels a helping hand to return to some of their long-lost forest homes – so they can flourish again in the woodlands where they belong for the first time in decades.

“This is leading to significant new populations of this much-loved species. It's offering real hope for the long-term survival of Scotland's precious red squirrels.”

However, it’s been argued that without more drastic conservation measures, red squirrels could disappear from the UK by 2030.

And there are also concerns that grey squirrel damage to young trees could hinder efforts to ‘rewild’ woodlands and efforts to plant new forests to help with carbon capture targets. Damage caused by squirrels costs the forestry sector £40m per year.

Targeting grey squirrels with contraceptives to control the population and gene technology are both being explored as alternatives to culling.

Andrew Kendall of the European Squirrel Initiative, said: “Planting millions of trees is a futile waste of money, because unless grey squirrels are controlled, these trees will not grow to achieve their full ability to sequester carbon. They will never be fully grown trees, they will be destroyed and all the money spent will be wasted.”

The ESI is working with Roslin Institute in Edinburgh to develop gene engineering technology which would drive sterility in female grey squirrels – potentially eradicating the UK population over a 20-year period.

The technology is expected to be in place within five years but will face a range of hurdles to overcome before it might be introduced.

However, Mr Kendall does not anticipate any public outcry over the potential loss of the grey squirrel.

“We have conducted many opinion polls on attitudes towards controlling grey squirrels using a non-lethal method of control, and over 70% say they would support that,” he said.

“We have no concerns over gaining public support - they know unless grey squirrels are removed, there will be no red squirrels.”