What does a zero mean? Understanding false, random and structural zeros in ecology

Zeros (i.e. events that do not happen) are the source of two common phenomena in count data: overdispersion and zero-inflation. Zeros have multiple origins in a dataset: false zeros occur due to errors in the experimental design or the observer; structural zeros are related to the ecological or evolutionary restrictions of the system under study; and random zeros are the result of the sampling variability. Identifying the type of zeros and their relation with overdispersion and/or zero inflation is key to select the most appropriate statistical model. Here we review the different modelling options in relation to the presence of overdispersion and zero inflation, tested through the dispersion and zero inflation indices. We then examine the theory of the zero-inflated (ZI) models and the use of the score tests to assess overdispersion and zero inflation over a model. In order to choose an adequate model when analysing count data we suggest the following protocol: Step 1) classify the zeros and minimize the presence of false zeros; Step 2) identify suitable covariates; Step 3) test the data for overdispersion and zero-inflation and Step 4) choose the most adequate model based on the results of step 3 and use score tests to determine whether more complex models should be implemented. We applied the recommended protocol on a real dataset on plant-herbivore interactions to evaluate the suitability of six different models (Poisson, NB and their zero-inflated versions-ZIP, ZINB). Our data were overdispersed and zero-inflated, and the ZINB was the model with the best fit, as predicted. Ignoring overdispersion and/or zero inflation during data analyses caused biased estimates of the statistical parameters and serious errors in the interpretation of the results. Our results are a clear example on how the conclusions of an ecological hypothesis can change depending on the model applied. Understanding how zeros arise in count data, for example identifying the potential sources of structural zeros, is essential to select the best statistical design. A good model not only fits the data correctly but also takes into account the idiosyncrasies of the biological system.