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

Abstract

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.

Freshwater snails of biomedical importance in the Niger River Valley: evidence of temporal and spatial patterns in abundance, distribution and infection with Schistosoma spp.

“…In all count models, a negative binomial distribution showed an improved fit over the Poisson distribution, and was therefore chosen as the family. Zero inflation, which assumes a mix of structural and sampling zero data, was initially considered as initial data exploration revealed a high proportion of zeros in the data, which can indicate zero inflation, or overdispersion relative to the Poisson distribution [55]. However, we did not find sufficient reason to consider zeros as structural, and zero inflation tests in DHARMa (function: ‘testZeroInflation()’) did not show statistical support that data were zero-inflated.…”

“…Variation in snail counts was analysed using generalized linear mixed effect models (GLMM) in the package glmmTMB [54]. This package efficiently fits negative binomial models that can account for overdispersed count data, while also allowing for arguments to account for zero inflation, if needed [55]. The fit of all constructed models was investigated visually and statistically using a simulation-based approach in the package DHARMa [56].…”

Spatial patterns of tree recruitment in a montane Hawaiian wet forest after cattle removal and pig population control

“…A high proportion of plots exhibited no recruits for a given species (e.g., 70% for Leptecophylla tameiameiae and 80% for Coprosma ochracea ), resulting in zero inflation (i.e., an excess of zeros in comparison to those expected from a classical count probability distribution). This can entail biased parameter estimates, overestimation of standard errors, and result in the selection of excessively complex models and poor ecological inference (see Blasco‐Moreno, Pérez‐Casany, Puig, Morante, & Castells, ). To avoid zero inflation, we grouped recruits according to their dispersal syndrome.…”

Scientometric correlates of high-quality reference lists in ecological papers

“…We also observed that over 40% of the articles in our dataset were never cited ( Fig. 1a), but since these represent "true zeros" 36 we didn't apply zero-inflated models to infer citation patterns over time 37 . No collinearity was detected among the seven explanatory variables-all |r|< 0.7.…”