Contents lists available at ScienceDirect Biological Conservation journal homepage: www.elsevier.com/locate/biocon Letter to the editor Reply to comments by Treves et al. on Liberg et al. (2020) Olof Liberg a, ⁎ , Johanna Suutarinen a , Mikael Åkesson a , Henrik Andrén a , Petter Wabakken b , Camilla Wikenros a , Håkan Sand a a Grimsö Wildlife Research Station, Department of Ecology, Swedish University of Agricultural Sciences, Riddarhyttan SE-73091, Sweden. b Faculty of Applied Ecology and Agricultural Sciences, Inland Norway University of Applied Sciences, NO-2480 Koppang, Norway. This is a response to a number of comments by “Treves et al. to our paper “Poaching-related disappearance rate of wolves in Sweden was positively related to population size and negatively to legal culling” (Liberg et al., 2020). First, Treves et al. raises a number of problems with our logistic regression at the population level, claiming that we have used a con- tinuous response variable (“disappearance rate”) instead of a binary. This is not correct. In our logistic regression in the population models, wolves that disappeared during a season were coded as 1 and wolves that not disappeared were coded as 0. This can be summarized for each season and analysed using logistic regression. Thus, we have used the binary outcome for each individual; disappeared or not disappeared, and summarized the data per monitoring season which we consider as the independent sample size in this analysis. We have not analysed the number of wolves that disappeared divided by the number of terri- tories, as Treves et al. claims. Further, Treves et al. worries that we regress y/x against x, where y = the absolute number of disappearances divided by x = number of territories to make disappearance rate. Treves et al. correctly points out that regressions of y/x on x always will produce negative slope parameters when simulated with random numbers, not a null hypothesis of a zero slope. However, in our case disappearance rate was positively related to both population size and legal culling rate (not negatively), suggesting that these relationships are not statistical artefacts. The negative effect of harvest rate on dis- appearance rate was revealed only when the effect of population size was controlled for. Using absolute numbers, as Treves et al. suggests, does not solve the problem to understand how disappearance, legal culling and population size are related to one another, but rather will miss the point. A positive correlation between absolute number of disappeared wolves and po- pulation size or legally culled wolves can occur in three very different scenarios. A strict proportion will give a positive correlation with ab- solute numbers but no correlation at all if rates are used, an increased proportion will give positive correlation in both cases and a decreased proportion will still give a positive correlation using absolute numbers but negative using rates. So, using absolute numbers will give positive correlations in all three scenarios, but using rates will give three dif- ferent outcomes with very different ecological consequences. In our situation legal culling rate increased with population size, which is a common wildlife management decision to reduce the growth rate as one approaches a management goal. In that situation it is indeed relevant to estimate the effect of both population size and legal culling rate on disappearance rate. There are several ways to analyse the kind of data we have. We decided to use maximum likelihood methods (logistic regression and Cox proportional hazard) to test different alternative models with dif- ferent variables and combination of variables and model selection using Akaike information criterion (AIC). Chapron and Treves (2016) decided to use one Bayesian hierarchical model to test the effect of only one variable, “policy signal” (=number of days that culling was allowed) on wolf growth rate, without testing alternative models with other variables and therefore without any model selection at all. We used Cox proportional hazard models where a wolf individual enters a season at time 1 and exits the season at time 2 (“we pooled the data among years resulting in enter = 1 and exit = 2 for all wolves”; page 3 right column). Thus, all wolves have an exposure time of 1 for each monitoring season, or in other words, there is only one time-step for each season. Treves et al. suggests that we should report the dis- appearance rate at endpoint of interest. However, we report one dis- appearance rate for the whole of each monitoring season, which is the shortest possible time span, as well as the endpoint of interest. Further, Treves et al. claims that Fig. 2-B presents impossible out- come as the disappearance rate is > 0 even when the legal culling rate is 1. However, this criticism is based on a misunderstanding, in turn based on misreading our paper. It seems that Treves et al. believes that the whole population is culled when culling rate is 1 (and thus no room for any disappearances). However, we clearly explained that the legal culling rate we present was “calculated by dividing the number of all legally killed wolves (both damage control and quota) during the whole monitoring year by the number of territorial pairs the same monitoring year” (page 3, left column, our emphasis), and not by the whole po- pulation. We thus used number of territorial pairs as a proxy for po- pulation size and can be multiplied with approximately 5.5 to get the https://doi.org/10.1016/j.biocon.2020.108644 ⁎ Corresponding author. E-mail address: olof.liberg@slu.se (O. Liberg). Biological Conservation xxx (xxxx) xxxx 0006-3207/ © 2020 Published by Elsevier Ltd. Please cite this article as: Olof Liberg, et al., Biological Conservation, https://doi.org/10.1016/j.biocon.2020.108644