Reciprocity—the mutual provisioning of support/goods—is a pervasive feature of social life. Directed networks provide a way to examine the structure of reciprocity in a community. However, measuring social networks involves assumptions about what relationships matter and how to elicit them, which may impact observed reciprocity. In particular, the practice of aggregating multiple sources of data on the same relationship (e.g., “double-sampled” data, where both the “giver” and “receiver” are asked to report on their relationship) may have pronounced impacts on network structure. To investigate these issues, we examine concordance (ties reported by both parties) and reciprocity in a set of directed, double-sampled social support networks. We find low concordance in people’s responses. Taking either the union (including any reported ties) or the intersection (including only concordant ties) of double-sampled relationships results in dramatically higher levels of reciprocity. Using multilevel exponential random graph models of social support networks from 75 villages in India, we show that these changes cannot be fully explained by the increase in the number of ties produced by layer aggregation. Respondents’ tendency to name the same people as both givers and receivers of support plays an important role, but this tendency varies across contexts and relationships type. We argue that no single method should necessarily be seen as the “correct” choice for aggregation of multiple sources of data on a single relationship type. Methods of aggregation should depend on the research question, the context, and the relationship in question.

Estimates of plant biomass are helpful for many applications in invasive plant science and management, but measuring biomass can be time-consuming, costly, or impractical if destructive sampling is inappropriate. The objective of this study was to assess feasibility of developing regression equations using a fast, nondestructive measure (cover) to estimate aboveground biomass for red brome (Bromus rubens L.), a widespread nonnative annual grass in the Mojave Desert, USA. At three study sites, including one measured for three consecutive years, B. rubens cover spanned 0.1% to 85% and aboveground biomass 1 to 321 g m−2. In log10-transformed linear regressions, B. rubens cover accounted for 68% to 96% of the variance in B. rubens biomass among sites, with all coefficients of determination significant at P < 0.05. For every doubling of percent cover, biomass was predicted to increase by 78%, 83%, and 144% among the three sites. At the site measured for three consecutive years, which ranged in rainfall from 65% to 159% of the long-term average, regression slopes each year differed from other years. Regression results among sites were insensitive to using cover classes (10 classes encompassing 0% to 100% cover) compared with simulated random distribution of integer cover within classes. Biomass of B. rubens was amenable to estimation in the field using cover, and such estimates may have applications for modeling invasive annual plant fuel loads and ecosystem carbon storage.

We propose an estimator for the number of sources, N, which transmit signals according to a Poisson process with a common rate μ. This estimation problem was originated by Starr and pursued by Vardi. Our procedure is a ‘double sampling’ one and has the advantage that it can be used when μ is unknown.