The wireless sensor networks community, has now an increased understanding of the need for realistic link layer models. Recent experimental studies have shown that real deployments have a "transitional region" with highly unreliable links, and that therefore the idealized perfect-reception-within-range models used in common network simulation tools can be very misleading. In this paper, we use mathematical techniques from communication theory to model and analyze the low power wireless links. The primary contribution of this work is the identification of the causes of the transitional region, and a quantification of their influence. Specifically, we derive expressions for the packet reception rate as a function of distance, and for the width of the transitional region. These expressions incorporate important channel and radio parameters such as the path loss exponent and shadowing variance of the channel; and the modulation and encoding of the radio. A key finding is that for radios using narrow-band modulation, the transitional region is not an artifact of the radio non-ideality, as it would exist even with perfect-threshold receivers because of multi-path fading. However, we hypothesize that radios with mechanisms to combat multi-path effects, such as spread-spectrum and diversity techniques, can reduce the transitional region.