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1. The study of plantpollinator interactions in a network context is receiving increasing attention. This approach has helped to identify several emerging network patterns such as nestedness and modularity. However, most studies are based only on qualitative information, and some ecosystems, such as deserts and tropical forests, are underrepresented in these data sets.

2. We present an exhaustive analysis of the structure of a 4-year plant-pollinator network from the Monte desert in Argentina using qualitative and quantitative tools. We describe the structure of this network and evaluate sampling completeness using asymptotic species richness estimators. Our goal is to assess the extent to which the realized sampling effort allows for an accurate description of species interactions and to estimate the minimum number of additional censuses required to detect 90% of the interactions. We evaluated completeness of detection of the community-wide pollinator fauna, of the pollinator fauna associated with each plant species and of the plant-pollinator interactions. We also evaluated whether sampling completeness was influenced by plant characteristics, such as flower abundance, flower life span, number of interspecific links (degree) and selectiveness in the identity of their flower visitors, as well as sampling effort.

3. We found that this desert plant-pollinator network has a nested structure and that it exhibits modularity and high network-level generalization.

4. In spite of our high sampling effort, and although we sampled 80% of the pollinator fauna, we recorded only 55% of the interactions. Furthermore, although a 64% increase in sampling effort would suffice to detect 90% of the pollinator species, a fivefold increase in sampling effort would be necessary to detect 90% of the interactions.

5. Detection of interactions was incomplete for most plant species, particularly specialists with a long flowering season and high flower abundance, or generalists with short flowering span and scant flowers. Our results suggest that sampling of a network with the same effort for all plant species is inadequate to sample interactions.

6. Sampling the diversity of interactions is labour intensive, and most plant-pollinator networks published to date are likely to be undersampled. Our analysis allowed estimating the completeness of our sampling, the additional effort needed to detect most interactions and the plant traits that influence the detection of their interactions.