Understanding the determinants of population size and performance for desert bighorn sheep (Ovis canadensis mexicana) is critical to develop effective recovery and management strategies. In arid environments, plant communities and consequently herbivore populations are strongly dependent upon precipitation, which is highly variable seasonally and annually. We conducted a retrospective exploratory analysis of desert bighorn sheep population dynamics on San Andres National Wildlife Refuge (SANWR), New Mexico, 1941–1976, by modeling sheep population size as a function of previous population sizes and precipitation. Population size and trend of desert bighorn were best and well described (R² = 0.89) by a model that included only total annual precipitation as a covariate. Models incorporating density-dependence, delayed density-dependence, and combinations of density and precipitation were less informative than the model containing precipitation alone (ΔAICc=8.5–22.5). Lamb:female ratios were positively related to precipitation (current year: F_1,34=7.09, P=0.012; previous year: F_1,33=3.37, P=0.075) but were unrelated to population size (current year: F_1,34=0.04, P=0.843; previous year: F_1,33=0.14, P=0.715). Instantaneous population rate of increase (r) was related to population size (F_1,33=5.55; P=0.025). Precipitation limited populations of desert bighorn sheep on SANWR primarily in a density-independent manner by affecting production or survival of lambs, likely through influences on forage quantity and quality. Habitat evaluations and recovery plans for desert bighorn sheep need to consider fundamental influences on desert bighorn populations such as precipitation and food, rather than focus solely on proximate issues such as security cover, predation, and disease. Moreover, the concept of carrying capacity for desert bighorn sheep may need re-evaluation in respect to highly variable (CV = 35.6%) localized precipitation patterns. On SANWR carrying capacity for desert bighorn sheep was zero when total annual precipitation was <28.2 cm.