Call it the arrow of cancer. Like the arrow of time, it was supposed to point in one direction. Cancers grew and worsened.

But as a paper in The Journal of the American Medical Association noted last week, data from more than two decades of screening for breast and prostate cancer call that view into question. Besides finding tumors that would be lethal if left untreated, screening appears to be finding many small tumors that would not be a problem if they were left alone, undiscovered by screening. They were destined to stop growing on their own or shrink, or even, at least in the case of some breast cancers, disappear.

“The old view is that cancer is a linear process,” said Dr. Barnett Kramer, associate director for disease prevention at the National Institutes of Health. “A cell acquired a mutation, and little by little it acquired more and more mutations. Mutations are not supposed to revert spontaneously.”

So, Dr. Kramer said, the image was “an arrow that moved in one direction.” But now, he added, it is becoming increasingly clear that cancers require more than mutations to progress. They need the cooperation of surrounding cells and even, he said, “the whole organism, the person,” whose immune system or hormone levels, for example, can squelch or fuel a tumor.