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Quantifying survey completeness is a key step in designing and interpreting biodiversity assessments. To date this has only been examined either at a local scale through repetitive sampling, or across broader geographic areas through multiple survey sites. In this paper, we determine the completeness of sampling at both local and continental scales, of the phytophagous arthropod assemblage on the Neotropical shrub Parkinsonia aculeata (Leguminosae). We used survey gap analysis (SGA) to determine whether existing surveys adequately sampled the diversity of environments and geographic space covered by the plant. Within defined geographic regions, we determined survey completeness at a local scale with species accumulation curves. SGA identified the highest priority sites for future sampling in the Sonoran Desert and the Pacific Coast of South America. The arthropods sampled on P. aculeata differed significantly between seasons, highlighting the importance of including surveys throughout the year. At the local scale, surveys in most regions were estimated to have sampled < 50 % of all species. Only the Mexican Gulf, following 84 samples including 902 individuals, had a reasonably complete sample of all species (more than 50 %). As in other studies, rare species will continue to be detected even after extensive surveying, and it is likely that close to 100 samples or 1,000 individuals will be needed to attain 50 % survey completeness in a region. However, if the objective is to document close "host-associations" then effort may be better directed at surveying ecologically distinct new areas rather than exhaustive sampling in existing ones. Methods such as SGA can direct such surveys, and in conjunction with species-richness estimates, can be used to assess the adequacy of existing surveys.