Misleading Overestimation Bias in Methods to Estimate Wolf Abundance that use Spatial Models

Population abundance is the main criterion used by agencies to manage and conserve species and it allows adaptive decision-making in response to impacts. Its estimation is particularly important for large mammals, especially carnivores that are notoriously difficult to monitor yet have high ecological and economic importance to humans. Reversal of their historic population decline is also vital to restoring ecosystem health through the ecosystem service of trophic interactions.

Because bias and precision (variance) are the independent yardsticks of the quality and reliability of population estimates, we preliminarily assessed new abundance estimators for wolves that non-traditionally use spatial models to estimate the area that an observation represents. Among many biases and problems identified by recent assessments, we focused one that obviously violated the assumption of closure, critically important in occupancy modeling (OM) used to determine the area occupied (AO) by territorial pack members. We then chose to simulate the effect of spatial resolution (grid size) on the direction and magnitude of that inherent bias in a recent method called iPOM used in Montana. We also examined the potential bias in their estimate of variance and confidence intervals when reporting wolf abundance.

We found that even the use of small grid cells in OM (relative to wolf territory size) inflated the total area occupied (AO) by wolf territories as well as the number of wolf packs. Furthermore, the overestimation bias rapidly increases with increasing grid cell size. WIth the large grid cell size used in iPOM for Montana (600 km2) there was a severe overestimation bias of 150% that proliferated through iPOM’s submodel structure and resulted in estimated wolf abundance 2.5 times larger than true abundance. The problem inherent in the use of occupancy modeling to estimate AO is that any wolf observation anywhere within a large cell adds the entire 600km2 area to the total area occupied by wolf packs that are ‘assumed’ to be spatially and numerically stable during the survey period. iPOM methods further exacerbates this problem by also relying upon surveys of hunters that confirms their observation is that of a territorial pack member (not a lone wolf) during the fall when packs are spatially and numerically unstable due a natural low in territorial behavior, dispersal of young wolves, and hunter
mortality that breaks apart wolf packs into fragments.

This bias alone when combined with a misapplication and underreporting of iPOM’s estimate of variance (biased low) results in a precariously misleading situation for decision-makers that threatens wolf populations. Other identified biases that inflate abundance likely make this situation worse but they should be further examined and tested.

Due to these biases and the high sensitivity of iPOM’s spatial models to estimate area, we suggest that such spatial models should not be used in population estimation methods or such methods, iPOM for example, should be improved and/or restructured with submodels robust to assumption violation thereby reducing bias. Given iPOM’s current design, there is no ability to detect change let alone determine wolf population size.

We provide a comparative framework for testing and improvement and strongly suggest proper model-assisted sampling designs and hierarchical modeling such as is used in capture-recapture models, especially those that use non-invasive procedures that avoid costly capture and marking. We also recommend collaborative activities that lead to using the best available scientific methods to determine carnivore abundance.