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As we have seen, network data are necessarily imperfect. Missing and spurious nodes and edges can create uncertainty in what the observed data tell us about the original network. In this chapter, we dive deeper into tools that allow us to quantify such effects and probe more deeply into the nature of an unseen network from our observations. The fundamental challenge of measurement error in network data is capturing the error-producing mechanism accurately and then inferring the unseen network from the (imperfectly) observed data. Computational approaches can give us clues and insights, as can mathematical models. Mathematical models can also build up methods of statistical inference, whether in estimating parameters describing a model of the network or estimating the networks structure itself. But such methods quickly become intractable without taking on some possibly severe assumptions, such as edge independence. Yet, even without addressing the full problem of network inference, in this chapter, we show valuable ways to explore features of the unseen network, such as its size, using the available data.
We used capture-recapture analyses to estimate the density of a tiger Panthera tigris population in the tropical forests of Huai Kha Khaeng Wildlife Sanctuary, Thailand, from photographic capture histories of 15 distinct individuals. The closure test results (z = 0.39, P = 0.65) provided some evidence in support of the demographic closure assumption. Fit of eight plausible closed models to the data indicated more support for model Mh, which incorporates individual heterogeneity in capture probabilities. This model generated an average capture probability = 0.42 and an abundance estimate of = 19 (9.65) tigers. The sampled area of = 477.2 (58.24) km2 yielded a density estimate of = 3.98 (0.51) tigers per 100 km2. Huai Kha Khaeng Wildlife Sanctuary could therefore hold 113 tigers and the entire Western Forest Complex c. 720 tigers. Although based on field protocols that constrained us to use sub-optimal analyses, this estimated tiger density is comparable to tiger densities in Indian reserves that support moderate prey abundances. However, tiger densities in well-protected Indian reserves with high prey abundances are three times higher. If given adequate protection we believe that the Western Forest Complex of Thailand could potentially harbour >2,000 wild tigers, highlighting its importance for global tiger conservation. The monitoring approaches we recommend here would be useful for managing this tiger population.
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