Imperfect observations in ecological studies

Every ecological data set is the result of sampling the biota at sampling locations. Such samples are rarely a census of the biota at the sampling
locations and so will inherently contain biases. It is crucial to account for the bias induced by sampling if valid inference on biodiversity quantities is
to be drawn from the observed data. The literature on accounting for sampling effects is large, but most are dedicated to the specific type of inference
required, the type of analysis performed and the type of survey undertaken. There is no general and systematic approach to sampling. Here, we explore
the unification of modelling approaches to account for sampling. We focus on individuals in ecological communities as the fundamental sampling element,
and show that methods for accounting for sampling at the species level can be equated to individual sampling effects. Particular emphasis is given to the case
where the probability of observing an individual, when it is present at the site sampled, is less than one. We call these situations ‘imperfect observations’.
The proposed framework is easily implemented in standard software packages. We highlight some practical benefits of this formal framework: the ability of
predicting the true number of individuals using an expectation that conditions on the observed data, and designing appropriate survey plans accounting for