Compound Poisson‐gamma vs. delta‐gamma to handle zero‐inflated continuous data under a variable sampling volume

Ecological data such as biomasses often present a high proportion of zeros with possible skewed positive values. The Delta-Gamma (DG) approach, which models separately the presence-absence and the positive biomass, is commonly used in ecology. A less commonly known alternative is the compound Poisson-gamma (CPG) approach, which essentially mimics the process of capturing clusters of biomass during a sampling event. Regardless of the approach, the effort involved in obtaining a sample (henceforth called the sampling volume, but could also include swept areas, sampling durations, etc.), which can potentially be quite variable between samples, needs to be taken into account when modelling the resulting sample biomass. This is achieved empirically for the DG approach (using a generalized linear model with sampling volume as a covariate), and theoretically for the CPG approach (by scaling a parameter of the model). In this study, the consequences of this disparity between approaches were explored first using theoretical arguments, then using simulations and finally by applying the approaches to catch data from a commercial groundfish trawl fishery. The simulation study results point out that the DG approach can lead to poor estimates when far from standard idealized sampling assumptions. On the contrary, the CPG approach is much more robust to variable sampling conditions, confirming theoretical predictions. These results were confirmed by the case study for which model performances were weaker for the DG. Given the results, care must be taken when choosing an approach for dealing with zero-inflated continuous data. The DG approach, which is easily implemented using standard statistical softwares, works well when the sampling volume variability is small. However, better results were obtained with the CPG model when dealing with variable sampling volumes.