Abundance varies by several of orders of magntiude across the range of a single species, and it varies in a systematic fashion that has been described as a peak-and-tail pattern. This pattern has important implications for conservation (reserves in high abundance areas are presumably superior to reserves in low abundance areas). Range boundaries are also in a sense a special case of this pattern, since boundaries are where abundances become zero. Yet, our understanding of the causes of these patterns remains at a very low level. New evidence is contradicting what little theory had been developed. I review this evidence. I then present a conceptual four step model and describe what is and is not known about each of these steps. I conclude by presenting a mathematical model that matches what is known about these four conceptual steps.