Wolves and human-caused mortality—a reply to Cassidy et al.

Cassidy et al. (2023) evaluated the effect of mortality on aspects of gray wolf (Canis lupus) demography, concluding that “…human activities can have major negative effects on the biological processes…”. We agree that the effects of human-caused mortalities on wildlife are of broad interest (eg Caudill et al. 2017; Schmidt et al. 2017; Frye et al. 2022). However, we contend Cassidy et al.'s study has shortcomings with regard to its data, design, biological inference, and statistical interpretation.

Although potentially resolvable, Cassidy et al.'s data contain inconsistencies and are sparse across covariate values (as detailed in Data S1, available at https://irma.nps.gov/DataStore/Reference/Profile/2302764), leading to uncertainty in the reliability and generalizability of their results. For example, missing covariate values resulted in the misapplication of model selection procedures and the exclusion of nearly all data from Voyageurs National Park from some models. Furthermore, the random effects were inappropriately structured and unstable, potentially because one site (Yukon-Charley Rivers National Preserve; YUCH) contained all observations of human-caused mortalities of >4 wolves and most observations of ≥2 leaders lost. Cassidy et al.'s results were also disproportionately influenced by YUCH (Data S1). Moreover, wolf harvest legally occurs within portions of Denali National Park and Preserve and YUCH, and about 62% of mortalities observed in YUCH were attributable to lethal control programs in the surrounding area (~25% of mortalities in the entire dataset were attributed to lethal control). Hence, inference on harvest and wolf control in general (eg transboundary management) is ambiguous. Instead, the results of Cassidy et al. may reflect the previously documented negative impact on wolf demography from a specific lethal management action conducted adjacent to YUCH (Schmidt et al. 2017).

The most critical limitation within Cassidy et al. is the study design. To provide reliable inference, a design must adequately exclude alternate hypotheses (ie Platt 1964). A design focused on any subset of mortality types in isolation could represent an a priori false null hypothesis because mortality in general could be negatively related to pack demography. The mixed logistic regression models in Cassidy et al. compared a group of packs in which human-caused mortality was observed (along with an unknown level of natural mortality) to a “contaminated” control group of packs in which human-caused mortality was not observed (but which also experienced unknown levels of natural mortality and human-caused mortality of non-collared pack members). This design cannot exclude the alternate hypothesis that any type of mortality (including natural mortality) could have caused the observed effect that Cassidy et al. attributed specifically to human-causes. Using a subset of these same data with cases where breeding wolves died, Borg et al. (2015) compared cause-specific outcomes by categorizing each loss as natural or human-caused, but found no support for a human-specific effect (JAE 2017). While Cassidy et al.'s design can support the negative association between pack dynamics and mortality in general (ie Borg et al. 2015), it cannot provide the asserted human-specific inference that is the focus of the paper.

Finally, statistically significant results are not necessarily biologically meaningful (Johnson 1999; Wasserstein and Lazar 2016). Cassidy et al. interpreted large, statistically significant odds ratios and conditional probabilities as biologically large impacts. However, logistic regression estimates parameters from statistical populations (Sokal and Rohlf 1981), which can be difficult to interpret (Agresti 2013) and require context to evaluate their biological importance. For example, large odds ratios or conditional probabilities may represent little absolute risk (see Andrade 2015). In Cassidy et al., the contaminated control group contained most of the sample of pack-years, which persisted at high rates. Fewer pack-years were in the group with observed human-caused mortality of a leader and just over half of those persisted (see Appendix S1: Figure S1). Consequently, logistic regression estimated large odds ratios due to the high probability of pack persistence observed in the contaminated control group, but the joint probabilities of pack dissolution were more similar (Data S2, available at https://irma.nps.gov/DataStore/Reference/Profile/2302764). We contend that in addition to conditional metrics, an absolute measure of risk provides improved context for assessing biological importance. For instance, ignoring contamination of the control samples, we calculated the Population Attributable Risk (PAR; Fleiss et al. 2003) to quantify the proportion of dissolutions that would be specifically attributable to observed human-caused mortality. Assuming the amount of observed human-caused mortality in the sample was representative of that in the population, we estimated a PAR of 2.9% (Data S2).

Humans can certainly impact wolves (Hornaday 1913; Schmidt et al. 2017) and human–predator conflicts may require management at scales finer than populations (eg Mech 1995; Caudill et al. 2019). However, biological populations are commonly the scale at which wildlife management occurs (Krausman 2022), in part because populations are the units with the potential to adapt and persist, beyond the life of any individual. Although death is certainly consequential for affected individuals (or packs), wildlife populations often exhibit compensatory mechanisms that can offset biological impacts (Cooch et al. 2014; Caudill et al. 2017). Regardless, management objectives, and thus acceptable biological impacts, are ultimately dictated by value-based goals set by policy makers. To perform their trust responsibilities, particularly for controversial issues (eg along administrative boundaries with divergent management goals), policy makers require rigorous and clearly communicated scientific information. Our intent is to highlight limitations of Cassidy et al., so that readers and policy makers will have improved context to better interpret the findings therein.