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BackgroundThe analysis of ecological networks can be affected by sampling effort, potentially leading to bias. Ecological network structure is often summarised by descriptive metrics but these metrics can vary according to the proportion of the total interactions that have been observed. Therefore, to know the likely degree of bias, it is valuable to estimate the total number of interactions in a network, and so calculate the proportion of interactions that have been observed (sampling completeness of interactions). Existing approaches to estimate sampling completeness of interactions use the Chao family of asymptotic species richness estimators to predict the total number of interactions, but do not fully utilise information about the relative specialisation of species within the network.ResultsHere, we propose a modification of previously-used methods, that places equal weight on each interaction (whether or not it has been observed), rather than on each species. Our approach is therefore equivalent to weighting the interaction sampling completeness of each species in the network according to its relative specialisation. We demonstrate that, for the subset of species that are observed and when assuming that species richness estimators accurately project the number of unobserved interactions per observed species, our approach is mathematically more accurate. Our approach can be universally applied to any quantitative, bipartite network.We propose two methods to estimation using our approach, using abundance-based and incidence-based species richness estimators respectively, and give recommendations when each should be applied. We discuss the effect of unobserved species and the potential use of a threshold of minimum abundance for species inclusion. Finally, we consider these advances in the context of some of the main issues surrounding estimation of interaction sampling completeness in network ecology.ConclusionsWe recommend that future studies of bipartite networks utilise our approach and methods to estimate the sampling completeness of interactions, to assist with the quantitative and comparative analysis and interpretation of network properties.

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The yield of hay on the Palace Leas meadow hay plots has increased significantly with time on the higher yielding plots but has remained constant on the iower yielding plots. Yield on the higher yielding plots shows a relatively low fluctuation from year to year, and yields of plots treated with farmyard manure show high intercorrelations with each other, but lower correlations with the other plots. Yield is influenced by weather, but even the most successful climatic parametermaximum soil moisture deficit-only accounts for 30% of the year on year variation in yield. There are highly significant autocorrelations between yields within each of the farmyard manure, treated plots indicating cyclic efi"ects with periods of up to 6 years, but these are not related to the cyclic patterns of manure application.

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