Unnatural as it seems, parents who kill their own children are seen by domestic violence workers as just the extreme tip of a very big iceberg of largely hidden threats of violence.
"Threats to do it are extremely common, and they are often what keeps women in relationships," says Jill Proudfoot of Auckland-based agency Safer Homes in New Zealand Everyday (Shine).
And parents who act on those threats are more common than you might think. Social Development Ministry researchers found an average of three cases of "filicide" a year between 2002 and 2006, where one or both parents killed their own children deliberately. Another four children a year died from physical assaults and punishments where their parents did not intend to kill.
The latest report of the official Family Violence Death Review Committee found three more children died in murder-suicides during parental separations in the two years 2010-11.
"My impression is that it happens more often than we hear about in the paper," Ms Proudfoot says.
"I get the arrest files every morning from the police and very often it's reported that he has made threats to kill, threats against the children, that he has deliberately harmed a child or an animal and made threats that if she leaves him he will kill her."
The death review committee found 22 children and 50 adults died from family violence in 2010-11, while police attended 94,000 family violence incidents in 2011 alone. "As the visible tip of the iceberg, family violence deaths are not only a measure of lethality but also an important barometer of the incidence of family violence," said committee head Dr Julia Tolmie of Auckland University.
The report found no discernible trend in the death rate. Thirty people died in family violence in 2002 and 27 in 2010, and the numbers in between fluctuated apparently randomly between a low of 17 in 2003 and a peak of 45 in 2009.
The report does not break down the subset of deliberate "filicides" by gender, but other evidence suggests mothers and fathers are almost equally likely to kill their children. An Australian study of all 291 children killed by filicide there between 1997 and 2008 found 140 were killed by their fathers, 127 by their mothers, and the rest by both parents.
A sixth of the parents - 24 mothers and 16 fathers - killed themselves after killing their children.
An earlier study by Waikato University sociologist Dr Jo Barnes found 24 cases of parents deliberately killing their own children and themselves in four Australian states between 1973 and 1992. Twelve killers were fathers and 12 were mothers.
But Dr Barnes found the reasons for the killings were quite different for men and women.
With fathers, she found a common theme of "possessiveness and control".
"Mostly when they kill their children, they have lost a custody battle or are unable to see their children for whatever reason," she says.
"It's often just spite: 'If I can't have them, you're not going to have them either, I'll fix you, you'll feel bad for the rest of your life."'
In one case, a father who killed his children and himself wrote a letter to his estranged wife saying he didn't want his children brought up by her because she was "a bad mother",
Another left a note saying, "I want you to suffer."
The Social Development Ministry researchers found six of the 15 NZ cases of deliberate filicide between 2002 and 2006 were associated with the parents separating, and all six killers were fathers. Three of the six fathers killed themselves too and one other tried to do so.
"In three of the six cases custody of the children was in dispute, while in the other cases it appears more likely that the murder of the children was in retaliation for the mother's leaving," the researchers found.
"In all six of these events there were other co-occurring factors associated with the death. These included mental illness, substance abuse and major stressors such as threatened loss of NZ residency."
In contrast, with mothers, Dr Barnes found that in most cases the mothers' "prime objective" was suicide, but they killed their children as well because they saw their children as almost part of themselves and feared leaving them alone.
One woman who was depressed after her baby suffered brain damage in a car accident wrote to her parents: "I don't feel I am murdering my children but saving them from sorrow and pain without their father ... I have tried very hard, I cannot leave my children behind."
The Social Development Ministry study found that five of the nine NZ filicides between 2002 and 2006 that were not due to separation were due to "major mental health" issues or "mercy killing". The other four involved babies or very young infants.
The death review committee found that 55 per cent of children killed by parents or other family members in 2010-11 were in homes where there was either intimate partner violence or the parents were separating.
Men were 76 per cent of the killers of adult partners, and the committee found that seven out of eight women who killed their male partners had actually been the "primary victims" of domestic violence in the relationship.
In Dr Barnes' study, one woman who killed her 3-year-old daughter and then suicided was reported to have "been depressed over the fact that she suspected her ex-defacto had been sexually abusing the child".
Another "had had a number of arguments with her husband over money and his drinking habits and was feeling harassed by her children".
"There were stories of women saying, 'Who's going to look after my children when I'm gone, and the children will never forgive me if I leave them,"' Dr Barnes says.
A common feature in all the studies is that most parents who kill their children deliberately were already known to police and other agencies. Fourteen of the 22 NZ children killed in 2010-11 were known to Child, Youth and Family Services (CYFS), and six of the 24 women killed by their partners had protection orders in place against the offenders.
Dr Tolmie says a protection order "should only ever be part of a multi-agency safety plan, it should never be the plan."
Although agencies such as Shine and CYFS already share information with the police at regular meetings, Dr Tolmie's committee wants high-risk cases channelled into more intensive multi-agency management bringing in all agencies involved with the family, such as doctors and addiction services, to make sure women and children are safe.
Shine's "Safe at Home" programme has provided more intensive protection for 500 homes so far in central and south Auckland, Tauranga and Christchurch. The Government has given it $500,000 a year up to June this year to install new locks, lighting, wooden doors to replace glass doors and other security features, with alarms linked to police systems which bring up the full history of the offender.
The programme is being evaluated and a positive evaluation may encourage the Government to roll out the programme nationally. "It's been astonishingly successful," Ms Proudfoot says. "As long as that safety plan has been followed, none of those women have been harmed."
The tragic roll call
• 1984: Philip Colin Money, 36, Auckland, threw his daughter Vanessa, 5, and son Haydon, 3, off the harbour bridge; he jumped too but survived and was found to have been legally insane at the time. He had believed he was Jesus Christ.
• 1992: Brian Schlaepfer, 64, Pukekohe, shot or stabbed his wife, three adult sons, his son's wife and child, then himself. He had been depressed after arguments with his wife and sons, who worked on the family farm.
• 1994: Alan Bristol, Wanganui, killed his daughters Tiffany, 7, Holly, 3, and Claudia, 18 months, then himself, after a long court battle with his estranged wife Christine over custody of the girls.
• 2000: Rosemary Perkin, 35, Nelson, killed daughters Alice, 8, Maria, 6, and Cherie, almost 2, then herself, a few months after separating from her husband.
• 2001: Frank Hingston, 44, Riwaka (Nelson), strangled daughters Dominique, 6 and Nikkita, 5, then killed himself, three weeks after separating from his wife.
• 2004: Brenda Fielding, 40, Onaero (Taranaki), killed her son Cameron,10, and daughter Krystal, 8, then herself. Her husband worked overseas in the oil industry but came home regularly.
• 2004: Lapana Seve, 45, Auckland, killed his daughter Storm Apera-Seve, 4, then left her body in back seat of car and stepped out in front of truck on the northwestern motorway. He had had Storm for the weekend but his estranged wife had been granted primary custody.
• 2004: Bronson O'Carroll, 30, Otaki Beach, stabbed his son TeHau TeHoro, 10, and daughter Ngamata, 8, then stabbed himself, a few months after his 10-year relationship with the children's mother ended.
• 2004: Kelvin Mercer, 32, Dunedin, killed his estranged wife and baby son Will, then burnt down his wife's house with himself inside it. He had been told that he had to sort out his drug problem if he wanted access to his children.
• 2007: Garth Abbott, 29, Auckland, drove off the Mt Wellington summit road killing his daughter Britney, 9, while arguing on his cellphone with his wife, who had talked to him about a divorce. Police said he intended to kill himself and his two daughters, who both suffered from a rare genetic disorder, but he said the crash was an accident. He was jailed for four and a half years for manslaughter.
• 2008: Graeme Dore, 67, Western Southland, killed his adult special-needs daughter Sarah-Jane Dore, 27, then himself.
• 2009: Melissa Dorward, 31, Haumoana (Hawkes Bay), suffocated her daughters Keira, 4, and Ellah, 2, then killed herself. She was pregnant but separated from the children's father.
• 2009: Kim Flowers, 47, West Auckland, killed her son Dominic, 8, then herself. She was married but speakers at her funeral said she was depressed and had tried to take her life twice before.
• 2010: Sung Eun Cho, 43, Christchurch, killed her daughters Holly, 17, and Kelly, 13, then herself. Her husband Young Jin Baek had returned to Korea to support the family financially, and committed suicide himself four days after his family died. The family was reported to be lonely and had financial and immigration difficulties.
• 2011: Kataraina Matthews, 33, Auckland, killed her baby daughter Kororia and died with her in a Salvation Army flat after attending treatment for alcohol addiction.