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

Inferring predator–prey interactions from camera traps: A Bayesian co‐abundance modeling approach

“…We assessed how this model performed using camera trapping data of two Asian apex predators and two of their key prey species that exhibit contrasting detection probabilities and natural densities. We found that explicitly classifying both the source of true zeros with the iZIP distribution in the abundance formula and false zeros with our detection formula containing the ODRE were necessary to infer ecologically meaningful predator–prey interactions while ensuring parameter convergence across all species pairs (Blasco‐Moreno et al, 2019; Martin et al, 2005). Failing to classify true zeros, such as at landscapes where a species has been extirpated, leaves the model to estimate nonzero abundance due to imperfect detection (i.e., false zeros) that leads to overconfidence in the posterior estimates and increases the risk of a type I error (Martin et al, 2005).…”

“…However, we expanded upon Brodie et al's approach by including informed zero‐inflated Poisson (hereafter “iZIP”) distributions for both dominant and subordinate species to account for true zeros in count history matrices when either species was known to be absent. Traditional uniformed ZIP N‐mixture models define the occupancy status of species i at sampling unit j , Z i,j as a random Bernoulli trial and multiply the expected count of species i at sampling unit j , λ i,j , by Z i,j (Blasco‐Moreno et al, 2019; Kéry & Royle, 2016; Martin et al, 2005). We informed the occupancy status of species i at sampling unit j , Z i,j based on our observational camera trapping data where Z ij was 1 if the sampling unit was in a landscape where the species was detected, and Z ij was 0 in the event the species was never detected and existing literature corroborated their extirpation (Amir et al, 2022; Blasco‐Moreno et al, 2019; Martin et al, 2005).…”

“…Traditional uniformed ZIP N‐mixture models define the occupancy status of species i at sampling unit j , Z i,j as a random Bernoulli trial and multiply the expected count of species i at sampling unit j , λ i,j , by Z i,j (Blasco‐Moreno et al, 2019; Kéry & Royle, 2016; Martin et al, 2005). We informed the occupancy status of species i at sampling unit j , Z i,j based on our observational camera trapping data where Z ij was 1 if the sampling unit was in a landscape where the species was detected, and Z ij was 0 in the event the species was never detected and existing literature corroborated their extirpation (Amir et al, 2022; Blasco‐Moreno et al, 2019; Martin et al, 2005). Therefore, our iZIP N‐mixture model assumes that:$$$$ {N}_{i,j}\sim \mathrm{Poisson}\ \left({\lambda_{i,j}}^{\ast }\ {Z}_{ij}\right) $$$$Fixing local abundance to zero rather than estimating nonzero abundance where the species was extirpated minimizes the chances of making a type I error (Martin et al, 2005).…”

“…However, modern sampling methods that rely on passively observed occurrence data (e.g., from camera traps, acoustic monitors, or eDNA) face numerous analytical barriers to inferring interactions (Blanchet et al, 2020; Ford & Goheen, 2015). Observational studies rarely account for processes influencing both predator and prey, such as environmental and anthropogenic covariates, the complete absence of either species from specific landscapes (i.e., true zeros), and imperfect detection of each species (i.e., false zeros), all of which can bias estimates of interactions (Blanchet et al, 2020; Blasco‐Moreno et al, 2019). For example, generalized joint attribute models can accommodate zero‐inflated and over‐dispersed data to infer species interactions (Clark et al, 2017), but such approaches fail to account for imperfect detection.…”

Effectiveness of acoustic lures for increasing tropical forest understory bat captures

“…The response variable was number of bats caught per hour as treatment and control nets were changed hourly. The model included total trapping effort, including time periods with no captures, as these are true random zeros (Blasco‐Moreno et al, 2019) within the sampling variability ( n = 88; 11 field nights × 2 trapping sites × 4 h per night). We then analyzed the number of bats caught only when a lure was broadcasting to assess any effect of the device used or call type broadcast using Chi‐squared tests ( n = 24).…”