Long-term potentiation of synapse strength requires enlargement of dendritic spines on cerebral pyramidal neurons. Long-term depression is linked to spine shrinkage. Indeed, spines are dynamic structures: they form, change their shapes and volumes, or can disappear in the space of hours. Do all such changes result from synaptic activity, or do some changes result from intrinsic processes? How do enlargement and shrinkage of spines relate to elimination and generation of spines, and how do these processes contribute to the stationary distribution of spine volumes? To answer these questions, we recorded the volumes of many individual spines daily for several days using two-photon imaging of CA1 pyramidal neurons in cultured slices of rat hippocampus between postnatal days 17 and 23. With normal synaptic transmission, spines often changed volume or were created or eliminated, thereby showing activity-dependent plasticity. However, we found that spines changed volume even after we blocked synaptic activity, reflecting a native instability of these small structures over the long term. Such "intrinsic fluctuations" showed unique dependence on spine volume. A mathematical model constructed from these data and the theory of random fluctuations explains population behaviors of spines, such as rates of elimination and generation, stationary distribution of volumes, and the long-term persistence of large spines. Our study finds that generation and elimination of spines are more prevalent than previously believed, and spine volume shows significant correlation with its age and life expectancy. The population dynamics of spines also predict key psychological features of memory.