Mismeasured mortality: correcting estimates of wolf poaching in the United States

Poaching has been underestimated systematically by biologists and policy makers.

Journal of Mammalogy cover for research published on mismeasured risks of poaching due to bias.

This scientific paper, published in 2017 by the Oxford University Press on behalf of American Society of Mammalogists, was conducted by researchers at Raincoast, Simon Fraser University, University of Victoria, University of Wisconsin-Madison, Hakai Institute, and Project Coyote. The lead author was Adrian Treves of the University of Wisconsin-Madison.

This research tests and rejects the long-held idea that data lost when known animals disappear were unbiased, under conditions common to most, if not all, studies using marked animals. Published government estimates are affected by the biases discovered. And so government estimates are systemically underestimating risks of poaching.

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“An accurate understanding of causes of death in animal populations is important for effective management and legitimate policy. Contemporary study of wild animal populations has benefited enormously from mark–recapture methods to estimate life history variables, such as mortality. However, marked animals in such studies sometimes elude recapture, which leads to loss of data (i.e., unknown fates). When the proportion of unknown fates among marked animals is low, the potentially biasing effects of data loss might be correspondingly low.”

“Mismeasured mortality: correcting estimates of wolf poaching in the United States” (PDF)


Measuring rates and causes of mortalities is important in animal ecology and management. Observing the fates of known individuals is a common method of estimating life history variables, including mortality patterns. It has long been assumed that data lost when known animals disappear were unbiased. We test and reject this assumption under conditions common to most, if not all, studies using marked animals. We illustrate the bias for 4 endangered wolf populations in the United States by reanalyzing data and assumptions about the known and unknown fates of marked wolves to calculate the degree to which risks of different causes of death were mismeasured. We find that, when using traditional methods, the relative risk of mortality from legal killing measured as a proportion of all known fates was overestimated by 0.05–0.16 and the relative risk of poaching was underestimated by 0.17–0.44. We show that published government estimates are affected by these biases and, importantly, are underestimating the risk of poaching. The underestimates have obscured the magnitude of poaching as the major threat to endangered wolf populations. We offer methods to correct estimates of mortality risk for marked animals of any taxon and describe the conditions under which traditional methods produce more or less bias. We also show how correcting past and future estimates of mortality parameters can address uncertainty about wildlife populations and increase the predictability and sustainability of wildlife management interventions.


Adrian Treves, Kyle A Artelle, Chris T Darimont, David R Parsons; Mismeasured mortality: correcting estimates of wolf poaching in the United States, Journal of Mammalogy, Volume 98, Issue 5, 3 October 2017, Pages 1256–1264, https://doi.org/10.1093/jmammal/gyx052

Figure 1

Systematic bias in calculating the risk of mortality from legal killing when some marked animals have unknown fates (unobservable with question marks ?) and causes of death vary in the accuracy of documentation. The green squares represent legal kills (perfectly documented) and the blue squares denote other causes of death (inaccurately documented). Observed (silhouette with binoculars) known fates (check marks ✓, and calculation in red text) alone would overestimate the real risk of legal killing. A) Positive bias in estimating risk of legal killing is 0.16. B) Positive bias increases by 0.17 as the proportion of legal kills increases.

Figure 1 from Journal of Mammalogy paper, on systemic bias.

Figure 3

Endangered wolves (gray: Canis lupus, Mexican gray: C. l. baileyi, and red: C. rufus) and risk of mortality from poaching as a proportion of all deaths. Approximate geographic locations are shown for 4 populations in the United States. The relative risks of mortality from poaching by government estimates (dark gray bars, no uncertainty estimates available) are paired with the same estimates from this study (light gray bars; error bars: lower bound derived from the equal apportionment approach and upper bound derived from the Scandinavian estimate of cryptic poaching C = 2). See Supplementary Data SD2 for poaching values separated from other human causes: Wisconsin (Natural Resources Board 2012); Northern Rocky Mountain (NRM): (Murray et al. 2010; Smith et al. 2010); Mexican: (USFWS 2015: table 4); red (USFWS 2007: figure 7).

Endangered wolves (gray: Canis lupus, Mexican gray: C. l. baileyi, and red: C. rufus) and risk of mortality from poaching as a proportion of all deaths.


Earth to Ocean Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, British Columbia, Canada.
Kyle A. Artelle

Raincoast Conservation Foundation, Sidney, British Columbia, Canada.
Kyle A. Artelle & Chris T. Darimont

Hakai Institute, British Columbia, Canada.
Kyle A. Artelle & Chris T. Darimont

Nelson Institute for Environmental Studies, University of Wisconsin–Madison, Madison, WI, USA.
Adrian Treves

Department of Geography, University of Victoria, Victoria, British Columbia, Canada.
Chris T. Darimont

Project Coyote, Albuquerque, NM
David R. Parsons


We thank field agents and pathologists who documented causes of death for wolves and the private citizens who reported dead wolves. We thank R. C. Crabtree, P. Paquet, and B. J. Bergstrom for advice.


The relative risks of different causes of death for marked animals have often been miscalculated under 1 or both of the following common conditions: 1 or more causes of death were perfectly reported but others were not, or marked animals had unknown fates (i.e., disappeared without a trace or were recovered but the cause of death was undetermined). The resulting bias overestimates the perfectly reported causes of death, such as legal killing, and underestimates the others, such as poaching. With evidence from 4 endangered wolf populations in the United States, we showed the miscalculation biased estimates substantially upwards for legal killing and biased them substantially downwards for other human causes (mainly poaching and vehicle collisions; Fig. 3 and Supplementary Data SD3). The error is non-random (systematic bias) and will increase under several common conditions: high rates of legal killing (Fig. 1B), high proportions of unknown fates (Fig. 2A), and high rates of cryptic poaching (i.e., unreported killing associated with destruction of evidence; Fig. 2B).

The corrections we applied, under even the most conservative equal apportionment approach, yielded estimates indicating that unregulated human-caused mortality was the major cause of death in endangered wolf populations in the United States (Supplementary Data SD3). Observed poaching in all the populations we studied outnumbered the primary other human cause of death, vehicle collisions, by a factor of 2 or more. That means most of the underestimation of other human causes was due to underestimating poaching. When we corrected the bias, we found substantial underestimates of poaching (Fig. 3). Indeed, for every wolf population we examined, we found poaching was the greatest threat. In the NRM wolf populations from 1982 to 2004, poaching replaced legal killing as the major threat to wolves after correcting for the mathematical miscalculation of legal killing. For the other wolf populations, the official reports had correctly identified poaching as the major threat, although they underestimated it.

There are several reasons our estimates of poaching are higher than previous ones. First, we demonstrated that prior estimates would have underestimated causes of death that are not perfectly documented. Second, we took 2 approaches to reconstruct the unknown fates of radiocollared wolves. The first approach, equal apportionment, assumes unmonitored wolves die of the same fates at the same rates as monitored wolves. This is unlikely to hold in any population of marked animals, let alone controversial ones such as wolves that are subject to high relative risks of legal and illegal killing. As such, the equal apportionment approach should be seen as a minimum bound on estimates of the risk of mortality from poaching. By contrast, we provided maximum bounds on the estimated risk of mortality from poaching, when we used the cryptic poaching approach, which apportions unknown fates to cryptic poaching first, informed by prior estimates of cryptic poaching from the literature. We used 2 published values for cryptic poaching from the literature (50% and 66%) and found the higher one probably too high (Table 3 footnote d). Accordingly, we recommend the 50% cryptic poaching estimate be used as the median for the likely range of values to estimate the risk of wolf mortality from poaching. These values and approaches may need adjustment for other sites and other species.

The traditional assumption that the causes of death in individuals of known fate are representative of those of unknown fate is inaccurate whenever known fates include both perfectly documented and inaccurately documented causes of death. The bias increases in proportion to the number of legal kills and the number of unknown fates because each one adds additional bias (overrepresenting perfectly documented causes of death and underrepresenting inaccurately documented causes of death, respectively). By accounting fully for all marked animals and by estimating the unknown fates, we can extract more information from the sample of marked animals than has been done traditionally. Extracting more information is desirable from the standpoint of management efficiency (less effort to mark animals is wasted when data are lost) and also for accuracy.

Some authorities will dismiss relative risk estimates as irrelevant for populations perceived to be large, growing, and resilient. Such a dismissal might be biologically inappropriate. Three studies of gray wolves, 1 in Wisconsin and 2 separate populations in Alaska (Schmidt et al. 2015; Borg et al. 2016; Treves et al. 2017b), demonstrate that mortality rates (per capita hazard) for marked wolves were as different as 15–28% from the per capita hazard rate for unmarked wolves. A mechanistic link between mismeasured risk and unrepresentative hazard rates for marked animals might exist. For example, it might relate to the methods used in recent years to mark wolves, such as livetrapping in areas where few people spend time or livetrapping in core areas of established wolf pack territories, both of which may capture individuals with lower exposure to human-caused mortality (Treves et al. 2017b). Alternatively, hunters and poachers may be able to target (or avoid) marked wolves with high accuracy, a possibility that has not been studied from the perspective of hunters and trappers, to our knowledge. If marked and unmarked animals experience differential per capita hazard rates, then marked animals will become less representative of the population as the relative risk of human-caused mortality increases. Such a relationship could account for the empirical observations of accelerating declines in wolf population growth as human-caused mortality increases (Adams et al. 2008; Creel and Rotella 2010; Vucetich 2012).

Pending further study, we advise against extrapolation from data on haphazardly marked animals of any species. Moreover, one should not discard the lost data from marked animals of unknown fate as is common in wildlife mortality analyses (Liberg et al. 2012). We recommend governments and researchers report data on marked and unmarked animals transparently, including “time on the air” for telemetry data. Additionally, spatial variation in human density and activity across the range of marked animals might be useful when poaching is a major cause of death for study subjects. Together, such steps would improve estimates of mortality parameters for marked animals and, consequently, help to avert policy errors.

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