The body of Moira Jones was found in Queen's Park in May 2008
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The Moria Jones murder trial has heard that DNA taken from the businesswoman's body matched the DNA profile of the accused.
Forensic scientist Carol Weston told High Court in Glasgow that the chances of someone else having the same DNA profile was more than one in a billion.
She also said she believed Marek Harcar had sex with Miss Jones.
The 33-year-old Slovakian denies raping and murdering Ms Jones in Queen's Park in Glasgow last May.
Ms Weston who works for the Scottish Police Services Authority told the court she took swabs from Miss Jones body.
She later carried out tests on a duvet cover taken from the Glasgow bedsit where Mr Harcar lived. Two stains on the cover were analysed and DNA was found.
Miss Weston told the jury: "The probability of this profile originating from another male unrelated to Marek Harcar is one in a more than a billion."
Miss Weston also analysed the swabs taken from Miss Jones body. Semen found on the swabs matched the previous DNA profile.
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I can only tell this was invented. It was not me, I did not do it
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She said this "supported" the assertion that Mr Harcar had sexual intercourse with Miss Jones.
Ms Weston agreed with the Lord Advocate that "in her opinion" Miss Jones did not get up after sex had taken place.
Earlier the court heard evidence from Det Sgt Brian Foster who helped extradite Harcar back to Scotland last July.
The jury was read parts of a police interview with Mr Harcar, carried out when he was brought back to Glasgow.
In relation to the murder charge, he said: "Well, I can only tell this was invented. It was not me, I did not do it.
Mr Harcar claimed: "I heard that something happened. I was walking round about there because that is where I used to stay."
"But, I would not have even imagined in my dreams that this could happen in relation to me."
Special defences
It is claimed that Mr Harcar forced Ms Jones across the park against her will before he repeatedly punched, kicked and stamped on her head and body.
He is then said to have repeatedly struck her on the ground, forcibly removed her clothes, compressed her neck, pinned her to the ground and raped her.
Mr Harcar is also alleged to have murdered the businesswoman, who is originally from Staffordshire, and stolen from her.
He is then accused of attempting to defeat the ends of justice by fleeing to the Czech Republic and Slovakia between 1 and 18 June last year.
Mr Harcar has lodged defences of incrimination and alibi, blaming three others for the murder of Ms Jones.
The trial, before Lord Bracadale, continues.
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