Treves, A.
Louchouarn, N.X.


In the associated publication [1], we explained and modeled how uncertainty about Wisconsin gray wolf vital statistics would interact with a wolf-hunting quota in relation to three precautionary thresholds set by law and society. We estimated probable distributions of births and deaths, then imposed ten possible quotas to estimate the wolf population size (N2022) by April 2022.
We concluded the quota for wolf-hunting set by the Natural Resource Board (300) posed a small but detectable risk of extirpating wolves from the state outside tribal reservations and a substantial risk of lowering the wolf population to the statutory level for listing under the state threatened and endangered species list. We also showed how the more moderate quota recommended by the state wildlife agency (130) posed a small but detectable risk of passing the latter threshold and a substantial risk of lowering the wolf population below the 1999 wolf management plan’s population goal of 350 wolves outside of tribal reservations in late. winter. Finally, we showed that a court-ordered quota of zero kills had a small but detectable risk of lowering the population below the latter threshold of 350. Here we recalculate these probabilities based on new information.
Colleagues pointed out a discrepancy in our parametrization of the proportion of packs breeding in summer 2021. We correct this 4% discrepancy below. However, we reiterate a mitigating issue mentioned in our original paper [1]. Namely, the methods for estimating the proportion of packs that breed each year in Wisconsin derive from [2], Table 6.3, which has serious shortcomings. First the methods have not been independently replicated and validated; they deserve cautious scrutiny because they are not based on direct observation of breeding except in a small, non-random subset of wolf packs. Indeed, we long ago pointed out the statistical dependence of estimates of reproductive output in a given pack with estimates of the size of that same pack [3]. Second, the data in [2] only extend to 2007 and therefore may over-estimate the proportion of packs breeding because they are dominated by years without legal, lethal management of wolves (winter 1979-March 31, 2003; [4]). The proportion of packs breeding each summer might presumably have been lower after lethal management began in April 2003-summer 2021, which we modeled.
Here we recalculated our models in [1]. We did not recreate figures in the original but instead provide readers with another estimate of the Wisconsin wolf population in April 2022 (N2022) based on the realized quota of zero set by court order in November 2021. We estimated the April 2022 wolf population using the traditional census estimate.

In the original paper [1], our estimate of N2022 was “361 SD 44 with a 13% chance of falling below the state population goal…” (Figure 4), where that goal was 350 wolves outside of tribal reservations in late winter. Re-calculating without the possible 4% over-estimate in proportion of packs breeding, we get 405 SD 44, n=3600 with 12.4% falling below the state population goal. This slight decrease in risk does not change our conclusions quantitatively.
Moreover, even if we combine this correction with the unsubstantiated typographical error in the comment above regarding pup survival [5], which we doubt for the reasons explained above in the first comment, the average only changes to 411 with 9% of values falling below the threshold. The two re-calculations above and their associated estimates should not be considered better than the original estimate for two reasons.
First, as we discussed in detail above, the claim that [5] made a typographical error has neither been substantiated nor has it been corrected by any formal scientific publication by the original authors or editors of that edited book. Therefore, deferring to the authority of [2] that did not use mark-recapture methods of pup research seems dubious and difficult to justify. Second, as we stated in the original [1], our estimates of vital rates may over-estimate successful reproduction and under-estimate mortality in 2021 because that summer included an unprecedented spate of USDA-WS wolf-killing. Neither the number of breeders killed nor the attendant loss of pups during this period have been reported.. We emphasize the need for more transparent data-sharing by all agencies working with wolves in Wisconsin.
Our conclusions remain qualitatively unchanged, and we reiterate the most cautious approach was to set a quota of zero for the second wolf-hunt of the calendar year in Fall 2021 and the county court was justified in granting a temporary injunction on wolf-hunting that season, especially when faced with the quotas of 130 and 300 preferred by the WDNR and the NRB respectively.
References
1. Treves, A. and N.X. Louchouarn, Uncertainty and precaution in hunting wolves twice in a year. PLoS One, 2022. 17(3): p. e0259604. 10.25.465697. https://journals.plos.org...
2. Wydeven AP, Wiedenhoeft J, Schultz RN, Thiel RP, Jurewicz RR, Kohn B, Van Deelen TR. History, population growth and management of wolves in wisconsin. In: Wydeven AP, Van Deelen TR, Heske EJ, editors. Recovery of gray wolves in the great lakes region of the united states: An endangered species success story. New York: Springer; 2009. p. 87-106.
3. Wydeven AP, Treves A, Brost B, Wiedenhoeft JE. Characteristics of wolf packs in Wisconsin: Identification of traits influencing depredation. In: Fascione N, Delach A, Smith ME, editors. People and predators: From conflict to coexistence. Washington, D. C.: Island Press; 2004. p. 28-50.
4. Chapron G, Treves A. Blood does not buy goodwill: Allowing culling increases poaching of a large carnivore. Proceedings of the Royal Society B. 2016; 283(1830):20152939.
5. Thiel RP, Hall W, Heilhecker E, Wydeven AP. A disjunct gray wolf population in central wisconsin. In: Wydeven AP, Van Deelen TR, Heske EJ, editors. Recovery of gray wolves in the great lakes region of the united states: An endangered species success story. New York: Springer; 2009. p. 107-18.