Murders and suicides are individually so common as to rarely merit reporting in the press. Combined murder-suicides are much more rare, but, like simple homicides and suicides, occur with clockwork regularity.
It can be difficult to understand why suicides happen. Is it insanity? Impulse? Crippling despair? If so, why that particular impulse, and why that particular self-destructive despair?
Suicide seems like the most irrational of acts, if not in personal terms than at least in terms of evolutionary fitness. Doesn't suicide cut off one's chance to survive and reproduce?
There are, however, reasons to think that the impulse to self-destruction is often one that is conducive to inclusive fitness, or would have been conducive to fitness in recent environments of evolutionary adaptedness.
Murder is somewhat more understandable without doing genetic math. Despite the modern state prohibition on murder and murder's consequent fitness costs, there is every reason to suspect that most murders are fitness-promoting.
Some murders, however, are not in themselves fitness-promoting, but nevertheless appear to occur as the most extreme effects of a generally fitness-promoting drive. Male violence against women, for instance, seems to be commonly motivated by actual or suspected infidelity,† and is of course an effective tool for controlling women and discouraging fitness-damaging adultery. As Johan van der Dennen puts it in his review of David Buss' The Murderer Next Door: Why the Mind is Designed to Kill,
Traits that have been subjected to natural selection often overshoot and undershoot the exact optimum in terms of their reproductive advantage. [Emphasis mine.]
By far, the most common victims of a murder-suicide are one's spouse and/or children. Why would anyone commit such a fitness-damaging act? If they are truly inexplicable flukes, why do murder-suicides happen with such regularity? The Violence Policy Center reports that
Medical studies estimate that between 1,000 and 1,500 deaths per year in the United States are the result of murder-suicide. [Violence Policy Center] analysis reveals that, in the first half of 2005, there were 591 murder-suicide deaths, of which 264 were suicides and 327 were homicides. Using these figures, more than 10 murder-suicide events occur in the United States each week.
There are many factors that indicate that the presumed fitness-promoting motives for murder are not present in homicide-suicides. Children killed in murder-suicides are significantly older than children killed in simple filicides. Infants are the most frequent victims of simple filicide, with rates of filicides falling for preschool children and reaching a low point among elementary school children; child victims of murder-suicide, however, are most likely to be elementary school children and least likely to be infants. An infant is much less valuable in fitness terms than an older child; the murder-suicides therefore seem paradoxical.
In addition, biological children are significantly more highly represented among murder-suicide victims than among simple filicide victims. This is especially remarkable, note the authors of one study, because
the familicide victims’ ages averaged substantially older; this age difference should have had an opposing effect since 12-year-olds (the mean age of familicide victims) are much more likely to have had stepfathers than 4-year-olds (the mean age of other filicide victims). 
Of course, killing a biological child is likely to be fitness-threatening, whereas killing a stepchild is likely to be fitness-enhancing; again, the murder-suicide data is perplexing in evolutionary terms.
Another data point is the extreme underrepresentation of women among perpetrators of homicide-suicide, as compared to simple homicide and suicide. Women commit suicide at about a quarter the rate of men in the United States, and kill their spouses at about 75% of the rate at which men kill their spouses. But out of 264 murder-suicide perpetrators in the first half of 2005, only 16 were female. (In contrast, of the 327 murder-suicide victims in the same period, 255 victims were female and 72 victims were male.) Females are particularly underrepresented among perpetrators of familicide, a variety of murder-suicide in which a perpetrator kills both a spouse and one or more children. One study of filicide-suicides  found that half as many women as men commit filicide-suicide, but that
[s]ixty-five percent of the fathers attempted to kill their wives as well as their children, whereas no mothers attempted to kill their husbands. In all, 55 percent of the fathers, but none of the mothers, attempted familicide, that is, annihilation of the entire family. [Emphasis mine.]
In simple spousal homicides, as noted above, jealousy is the typical motive. But jealousy is rare as a motive in murder-suicides. Bossarte et al. (2006), using data from the National Violent Death Reporting System, found that only 1.9% of murder-suicides during the study period were associated with jealousy. *
Yet another salient difference between murder-suicides and simple homicides is the victim-offender relationship. Homicide-suicides differ from homicides in that a significant majority of homicide-suicides - ranging from 66% to 84% in various studies - involve killings of "intimate partners."  (As noted above, almost all these victims are women.) In contrast, only between 5.2% and 19.2% of simple homicides are wife killings. 
The correlation works in both directions. Not only are homicide-suicides more likely to involve intimate partners than simple homicides; intimate partner killers are much more likely to commit suicide than killers of other victims. One study found that only 5% of all homicides were followed by a suicide attempt, but "among men who killed their female intimate partner with a firearm, 59% also took their own life." Another study found that "among male perpetrators, nearly one third (30.6%) of those who killed their intimate partner (n = 438) also ended their own lives, while only 1.7% of those who killed a non-intimate (n = 3459) also killed themselves."
The mental state of perpetrators also varies between homicides and homicide-suicides. Homicide-suicide perpetrators are much less likely to be psychopathic than are those who commit simple homicide. A Swedish study reported that
'Psychopathic' perpetrators, who generally are over-represented in most violent criminality, were comparatively uncommon. Only seven (4%) in the study group [of 164] met the diagnostic criteria for psychopathy . . . 
And homicide-suicides are much more likely than ordinary homicides to be premeditated.
To summarize the differences, homicide-suicides are
- characterized by older (and therefore more valuable) child victims
- more likely to include biological (and therefore more valuable) children
- unlikely to be perpetrated by women (especially murder-suicides that include spousal homicide)
- unlikely to be motivated by sexual jealousy
- likely to be wife killings
- unlikely to be perpetrated by 'psychopathic' people
- likely to be premeditated.
What explains the differences?
One hypothesis is that murder-suicide is motivated by altruism or caring. There is little evidence to support this claim. In one study that reported motive, only seven out of 65 murder-suicides were "mercy killings" - and in six out of seven cases, the victim was over age 55. In addition, a person determined to commit suicide may wish to spare his or her spouse the suffering associated with his or her loss. In fact, men are particularly affected by a spouse's suicide. The male suicide rate, already high compared to that of women, rises by a factor of 46.2 after the suicide of a partner. (The suicide rate for women, already lower than that of men, rose by a factor of 15.8%.) If altruistically preventing suffering were a major motive in murder-suicides, one would expect women to commit spousal murder-suicide and/or familicide at a rate closer to that of men (or, at least, closer to the rate at which women commit simple suicide or homicide).
Vengeance as a motive is belied by the low rate of jealousy-related homicide-suicides, as noted above, and by the high rate of inclusion of biological children.
I propose a model for homicide-suicide as follows. Homicide-suicide is the result of the unfortunate juxtaposition of two ordinarily fitness-promoting drives. On their own, each drive is evolutionarily adaptive; together, they spell disaster. However, the relatively low rate of murder-suicide indicates that this juxtaposition is rare enough as to not counteract the beneficial selective effects of the two drives individually.
The first drive is the drive to self-destruction under conditions of (a) perceived burdensomeness and (b) failed belonging, as described by Thomas Joiner (though he does not concede that this drive is selective). In selection terms, it is reasonable to commit suicide when the burden one's continued existence places on one's genetic kin exceeds one's prospects for future genetic contribution via creating new offspring (or caring for existing offspring). It is therefore reasonable to conclude that the drive to commit suicide under these conditions would be subject to positive selection. In fact, one study found that perpetrators of homicide-suicide were likely to have experienced "recent legal problems (25.3%) [or] a job or financial problem (9.3%)," both indicating perceived burdensomeness and/or failed belonging.
The second drive is proprietariness. Perceiving one's children as one's property is generally fitness-promoting; one protects one's children from harm, utilizes their labor, benefits from their breeding capacity, and directs their life choices. Proprietariness toward children promotes both the nurturing and protection of children and the parental side of parent-offspring competition.
Proprietariness is the explanation that Daly & Wilson  propose to explain the enormous overrepresentation of men as perpetrators of spousal homicide-suicide and familicide-suicide as compared to women.‡ It makes evolutionary sense for a man to be proprietary toward a woman; exclusive sexual access is extremely important for a man in fitness terms. It makes much less sense, evolutionarily, for a woman to be proprietary toward her husband. His sexual dalliances make little fitness difference for her, as long as they do not threaten his continued investment in her children. Purdah and related behaviors are relatively common in societies toward women; nowhere do they exist toward men.
Proprietariness tidily explains the relatively high representation of women among filicide-suicides as compared to familicide-suicides and spousal homicide-suicides; women would be expected to feel proprietary toward their children, but much less so toward their husbands.
Murder-suicide, according to my model, occurs when (a) a perpetrator experiences extreme despair as a result of perceived burdensomeness and/or failed belonging, and therefore wishes to commit suicide; but (b) proprietary feelings toward a spouse and/or children lead the perpetrator to take others with him, as if they were tomb ornaments.
†It is probably more psychologically comfortable to assume that men are violent toward women because of suspected infidelity, rather than actual infidelity. However, the violent responses of men, while certainly not morally justified, seem to at least reflect genuine female infidelity most of the time. Daly & Wilson  cite a study at p. 201 that found that, in eleven out of eleven non-psychotic spousal homicides studied, "the victim was engaged in an affair with another man or had led the offender to believe that she was being unfaithful to him. In 10 of the cases, the victim made no attempt to conceal her other relationships." Another study, cited by Daly & Wilson at 208, found that 47% of women who had been raped and beaten by their husbands admitted to adultery, compared to 23% of those who were battered but not raped, and only 10% of women who were not victimized.
*Bossarte et al. (2006) note that their results contradict a 2005 study) on "intimate femicide" using data from the province of Ontario, Canada, from 1974-1994, which found that intimate partner suicide-homicides were significantly more likely to be motivated by jealousy than simple intimate partner homicides (55% versus 42% respectively). The Ontario study also found a higher percentage of de facto unions versus registered marriages in simple murders than in murder-suicides, which contradicts both the Wilson et al. (1995) data and the Banks et al. (2008) data. What do we make of this?
There is circumstantial evidence that makes the Bossarte et al. result more convincing than the Dawson result. First, married people are highly represented among intimate partner murder-suicides compared to unmarried cohabiting couples; unmarried cohabiting couples, on the other hand, are drastically overrepresented among ordinary intimate partner homicides. Why does this matter? Daly & Wilson (1988)  at p. 213 think that male investment is low in couples living "common law" (compared to married couples). They say: "Perhaps the material investment of men in common-law unions is relatively low, and the women are therefore more likely to be on the lookout for alternatives, inspiring a more coercive proprietariness in their mates."
Second, a huge proportion of men who kill their estranged wives or wife-equivalents commit suicide. The proportion of men who kill non-estranged adulterous wives are much less likely to also kill themselves (Daly & Wilson (1988)  at p. 219). That estrangement is such a trigger fits better with proprietariness than jealousy; losing a female mate, while costly in fitness terms, is nowhere near as costly for the male as potentially supporting non-biological children.
Third, victims of intimate partner murder-suicide are significantly older than victims of simple intimate partner homicide. Barber et al.  found a mean age difference of 9.4 years between the two groups. Young wives (who are most valuable and fertile) are extremely highly represented among simple homicide victims; a reasonable interpretation of this is that more valuable women trigger more violent sexual jealousy. Wives who are victims of murder-suicide tend to be older and hence, in evolutionary terms, less valuable (see Daly & Wilson (1988)  at p. 206), and so less likely to trigger violent sexual jealousy.
‡Daly & Wilson  (at 219) also dismiss the "remorse" hypothesis (that women rarely commit murder suicide because they lack the highly developed moral sense of men - which assumes that suicides following homicides are committed out of remorse). In fact, murder-suicides often leave evidence of premeditation. In addition, if a murder-suicide is to take place, the suicide generally happens contemporaneously with the homicide; a suicide days or weeks after a homicide, when remorse would be expected to set in, is extremely rare. Daly & Wilson cite a study that found that "whereas 192 homicidal Canadian husbands killed themselves immediately after the homicide, only another 3 committed suicide days or weeks later. Indeed, in the total sample of 6559 Canadian homicides, there were just 8 killers who committed suicide after a delay that might reflect remorseful brooding."
1. Agerbo, E. "Midlife suicide risk, partner's psychiatric illness, spouse and child bereavement by suicide or other modes of death: a gender specific study." J Epidemiol Community Health. 59(5):407–412 (2005).
2. Banks, Laura, Cameron Crandall, David Sklar and Michael Bauer. "A Comparison of Intimate Partner Homicide to Intimate Partner Homicide-Suicide: One Hundred and Twenty-Four New Mexico Cases." Violence Against Women 14:1065 (2008).
3. Barber, Catherine W., Deborah Azrael, David Hemenway, Lenora M. Olson, Carrie Nie, Judy Schaechter and Sabrina Walsh. "Suicides and Suicide Attempts Following Homicide: Victim-Suspect Relationship, Weapon Type, and Presence of Antidepressants." Homicide Studies 2008:12:285.
4. Belfrage, Henrik, and Mikael Rying. "Characteristics of spousal homicide perpetrators: a study of all cases of spousal homicide in Sweden 1990-1999." Criminal Behavior and Mental Health 14:2:121-133 (2006).
5. Bossarte, R M, T R Simon and L Barker. "Homicide-Suicide: Characteristics of homicide followed by suicide incidents in multiple states, 2003–04." Injury Prevention 2006:12(Supplement 2 ):ii33-ii38.
6. Buss, David M. The Dangerous Passion. Bloomsbury, 2000.
7. Daly, Martin, and Margo Wilson. Homicide. New York: Aldine de Gruyter, 1988.
8. -------- Risk-taking, Intrasexual Competition, and Homicide. Nebraska Symposium on Motivation 47: 1-36(2001).
9. Hatters Friedman, Susan, MD, Debra R. Hrouda, MSSA, Carol E. Holden, PhD, Stephen G. Noffsinger, MD and Phillip J. Resnick, MD. "Filicide-Suicide: Common Factors in Parents Who Kill Their Children and Themselves." J Am Acad Psychiatry Law 33:4:496-504 (2005).
10. van der Dennen, Johan M. G. "Review Essay: The Murderer Next Door: Why the Mind is Designed to Kill." Homicide Studies 2006:10:320.
11. Violence Policy Center. "American Roulette: Murder-Suicide in the United States." (2006).
12. Wilson, M. I. & Daly, M. "Who kills whom in spouse killings? On the exceptional sex ratio of spousal homicides in the United States." Criminology 30:189-215 (1992).
13. Wilson, Margo, Martin Daly, and Antonietta Daniele. "Familicide: The Killing of Spouse and Children." Aggressive Behavior 21:275-291 (1995).
14. Dawson, Myrna. "Intimate Femicide Followed by Suicide: Examining the Role of Premeditation." Suicide and Life-Threatening Behavior 35(1) (2005).