A woman – believed to be the boy’s mum – was being held by police last night.
According to reports the mother is understood to be from Botswana and another child, believed to be the boy’s sister, was said to be safe and well.
Speaking about the boy’s mother, neighbour Victoria Thomson told the Daily Record: “She moved there a wee while ago, maybe last year. They haven’t been there long.
“She lived there with her two children. The other one was a wee girl. The wee boy was five but that is all I know.
“I don’t think she had a partner. She was a really quiet lady. She always had her curtains shut as well.”
She added: “The only time I saw her was when she went up to the school and back.”
Crew members are being offered counselling after being traumatised by the gory scene.
Scottish Police Chief Inspector Stephen Sneddon said: “On arrival, police officers found the child with a significant injury to his body and he was later pronounced dead at the scene by the Scottish Ambulance Service.
“Enquiries into the full circumstances surrounding this incident are ongoing and a woman is currently detained in connection with the investigation. We are not currently looking for anyone else and I want to reassure the local community that there is no risk to them.”
The local police commander described the area as “quiet”.
He said: “I would emphasise that this is a very unusual incident which poses no risk to others.”
Tributes have been left near the house where the boy was discovered.