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To understand the violent criminal, says Richard E. Tremblay, imagine a 2-year-old boy doing the things that make the terrible twos terrible — grabbing, kicking, pushing, punching, biting.

Now imagine him doing all this with the body and resources of an 18-year-old.

You have just pictured both a perfectly normal toddler and a typical violent criminal as Dr. Tremblay, a developmental psychologist at University College Dublin in Ireland, sees them — the toddler as a creature who reflexively uses physical aggression to get what he wants; the criminal as the rare person who has never learned to do otherwise.

In other words, dangerous criminals don’t turn violent. They just stay that way.

These findings have been replicated in multiple large studies by several researchers on several continents.

“It’s highly reliable,” said Brad J. Bushman, a psychology professor at Ohio State University and an expert on child violence, who noted that toddlers use physical aggression even more than people in violent youth gangs do. “Thank God toddlers don’t carry weapons.”

The son of a professional football player, Dr. Tremblay played football himself and was fascinated with its regulated version of extreme physical aggression. After college he did social work in a prison and saw firsthand how seldom such programs changed violent criminals. By the time the violent child gets big, it’s often too late.

So he trained his focus earlier and earlier, and learned that the younger the children, the more they whacked each other. With adolescents, physically aggressive acts can be counted in incidents per month; with toddlers, he said, “you count the number per hour.”

In most children, though, this is as bad as it gets. The rate of violence peaks at 24 months, declines steadily through adolescence and plunges in early adulthood. But as Dr. Tremblay and Daniel S. Nagin, a criminologist at Carnegie Mellon University, found in a pivotal 1999 study, a troublesome few do not follow this pattern.

The study tracked behavior in 1,037 mostly disadvantaged Quebec schoolboys from kindergarten through age 18. The boys fell into four distinct trajectories of physical aggression.

The most peaceable 20 percent, a “no problem” group, showed little physical aggression at any age; two larger groups showed moderate and high rates of aggression as preschoolers. In these three groups violence fell through childhood and adolescence, and dropped to almost nothing when the boys reached their 20s.

A fourth group, about 5 percent, peaked higher during toddlerhood and declined far more slowly. Their curve was more plateau than hill.

As they moved into late adolescence and young adulthood, their aggression grew ever more dangerous, and it tailed off late. At age 17 they were four times as physically aggressive as the moderate group and committed 14 times as many criminal infractions. It’s these chronically violent individuals, Dr. Tremblay says, who are responsible for most violent crime.

(These numbers are all for boys and young men; girls’ physical aggression declines in arcs similar to those of boys, but at sharply lower levels.) The results were surprising. At first glance, they seemed at odds with one of criminology’s oldest tenets — the age-crime curve, first graphed in 1831 by the Belgian statistician Adolphe Quetelet.

Mining French crime records, Quetelet found that arrest rates soared in the midteens before falling in the 20s. His famous curve was later replicated in studies of criminal records going back to the 16th century. By contrast, the Tremblay-Nagin findings suggested that violent behavior peaked much earlier than the teen years.

But as Janette B. Benson and Marshall M. Haith noted in a 2010 child development textbook, the two sets of curves are not contradictory: Quetelet’s curve reflects not violence, but the rate at which we “start arresting and convicting individuals who have been physically aggressive toward others at least since kindergarten.”

In 2006, Dr. Tremblay and Dr. Nagin published a larger study tracking 10 groups of about 1,000 Canadians between ages 2 and 11 for periods of six years. The research echoed the 1999 study. A third of the children were peaceable throughout; about half used physical aggression often as toddlers, but rarely as preadolescents; and about a sixth remained physically aggressive as 11-year-olds. This last group matched groups in other studies that ran in the 5 percent to 15 percent range.

To Dr. Tremblay, the findings suggest cause for optimism: that humans more readily learn civility than they do cruelty.

We start as toddlers. We learn through conditioning, as we heed requests not to hit others but to use our words. We learn self-control. Beginning in our third year, we learn social strategies like bargaining and charm. Perhaps most vital, we use a developing brain to read situations and choose among these learned tactics and strategies.

But what of the relative few who remain physically aggressive? If it’s possible to spot this cohort as early as kindergarten, why can’t we bend their arc downward? Here, says Dr. Tremblay, “the entire field is stumped.”

Programs that provide comprehensive support, including parent training, do seem to help, though they are difficult to deliver to the deeply troubled families that need them most.

Child development experts increasingly say such services are crucial — starting “as close as possible to conception,” as Dr. Tremblay put it in one recent paper, and continuing through early childhood.

Similarly, his research is going further back in the life span. He and some colleagues are planning to capture data in mothers and newborns, and then to follow them for two decades, to determine whether environment shapes the chemical wrappings of the children’s genes, and thus perhaps their activities, in ways that correlate to behavior.

When I remarked to Dr. Tremblay, now 69, that this seemed like an awfully long time to wait for answers, he laughed. Science is slow, he said, and behavior is hard to measure. We may never completely crack this nut. But we have to try.