Carlos Lois, whose lecture I recently attended at Children's Hospital, has been studying this question for some time and presented some interesting evidence in favor of the idea that new neurons integrate into existing adult circuits in much the same way that the brain develops during adolescence. This is to say that more neurons than are actually needed are birthed and migrate to the region of interest (in his case, the olfactory bulb). There they attempt to integrate into the existing circuitry. Those that succeed survive and become functional; those that do not integrate well die. On the particular topic of survival, he presented an interesting experiment.
His lab introduced one of two proteins into the subventrical zone of mice using a viral expression technique. The first protein, called NachBac, is an excitatory ion channel that tends to polarize the voltage of the cell's membrane towards a positive potential. The second protein was a potassium channel that has the opposite effect, making the cell's membrane potential more negative. Interestingly, both proteins increased the apparent activity of the neuron, as assessed by the number of times it fired an action potential at rest (action potentials are the electrical impulses that transmit information along nerves and allow neurons to communicate). Despite the increase in activity under both conditions, the cells with a more negative resting membrane potential died more than normal neurons, while those that were more skewed towards positive potentials survived more readily. This makes the argument that the only deciding factor in the survival of new neurons is the resting membrane potential. This likely means that spontaneous activity is not important for neuron surival, but coordinated or responsive activity is, as the neurons expressing NachBac would be more responsive to incoming signals.
This is another step along the way to understanding how we might one day be able to replace regions of the brain lost to stroke, disease, or injury.