Mark Lundy claims his murder convictions were based on unreliable science, and an unsympathetic public who saw him as a "fat so-and-so" who faked his grief.

Lundy's team, led by Jonathan Eaton QC, laid out their case in the Court of Appeal today, fighting to overturn his murder convictions from the 2015 High Court trial.

Lundy was not in court despite initially being set to watch the appeal by AVL.

The hearing is being streamed live on the Herald and Newstalk ZB sites, in a first for New Zealand media access. The stream stops when suppressed matters are discussed.

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The appeal is focused on the infamous two spots on his polo shirt, which prosecutors argued was Lundy's wife Christine's brain tissue.

Eaton said the jury at the 2015 retrial should never have heard the mRNA evidence, as the analysis was too new and unproven to be relied upon.

He said Lundy became a "guinea pig" for a brand-new method of analysis, which in the 16 years since the first court case had never again been used to identify unknown material.

"When you've got that level of complexity, this is an issue that should have been thrashed out by the experts, through peer review and conferences," Eaton told the court.

Christine Lundy, Mark Lundy and Amber Lundy in happier times. Photo / File
Christine Lundy, Mark Lundy and Amber Lundy in happier times. Photo / File

"Not in front of a jury, saying 'right well there's our conflicting views, you work out if it's reliable or not'."

Eaton argued the Court of Appeal justices had a duty to make sure all evidence submitted in court could be relied upon.

"The courts are dropping the ball on the admissibility of new science.

"And hence we have the UK Law Commission expressing their concerns in reports before you.

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"We have the lengthy 2009 report from the Nation Research Council in the United States, which presents all sorts of concerns.

"And then in September last yet, post Mr Lundy's conviction, we have the PCAST report to Mr Obama regarding the presentation of science in criminal courts.

"And when one reads those reports and sees the climate of concern in relation to forensic science in criminal justice, it is instructive to this court in regards to what the standard ought to be in New Zealand.

"And it all comes back to the issue of scientific validity."

Eaton said that part of the problem was the public perception of Lundy. He said there was an "elephant in the room" in terms of the effect of the widely-seen video of Lundy at the funeral of Christine and Amber.

"There is this view that he is a big fat so-and-so, who was with a prostitute on the night, and people saying 'did you see the unconvincing performance at the funeral? Of course he is guilty'.

"He has engendered no public sympathy."

Mark Lundy being supported after the funeral of his wife Christine and daughter Amber in the year 2000. Photo / Mark Mitchell
Mark Lundy being supported after the funeral of his wife Christine and daughter Amber in the year 2000. Photo / Mark Mitchell

The appeal hearing is set to continue tomorrow, with the defence team presenting further arguments on the reliability of the mRNA analysis, as well as evidence the jury judged Lundy based on his demeanour in court and at the funeral.

The Crown legal team, led by Philip Morgan QC, has not yet presented its rebuttal arguments.

The appeal is the latest in a long-running legal saga since Christine and Amber Lundy were found dead in their Palmerston North home in August 2000.

Mark Lundy was first convicted of their murders in 2002, and his first appeal attempt resulted in the court increasing his prison sentence to 20 years.

His conviction was quashed by the Privy Council in 2013, with a ruling that there were problems with the analysis of the brain tissue, as well as time of death.

Lundy and his lawyers tried to have the mRNA evidence of brain tissue on his shirt thrown out before his 2015 High Court retrial, but his team failed to convince both the Court of Appeal and Supreme Court.

The appeal hearing is expected to continue until Thursday.