Scaling Occupancy Estimates up to Abundance for Wolves

Uncertainty and precaution in hunting wolves twice in a year: Reanalysis of Treves and Louchouarn

Management of wolves is controversial in many jurisdictions where wolves live, which underscores the importance of rigor, transparency, and reproducibility when evaluating outcomes of management actions. Treves and Louchouarn 2022 (hereafter TL) predicted outcomes for various fall 2021 hunting scenarios following Wisconsin's judicially mandated hunting and trapping season in spring 2021, and concluded that even a zero harvest scenario could result in the wolf population declining below the population goal of 350 wolves specified in the 1999 Wisconsin wolf management plan. TL further concluded that with a fall harvest of > 16 wolves there was a "better than average possibility" that the wolf population size would decline below that 350-wolf threshold. We show that these conclusions are incorrect and that they resulted from mathematical errors and selected parameterizations that were consistently biased in the direction that maximized mortality and minimized reproduction (i.e., positively biased adult mortality, negatively biased pup survival, further halving pup survival to November, negatively biased number of breeding packs, and counting harvested wolves twice among the dead). These errors systematically exaggerated declines in predicted population size and resulted in erroneous conclusions that were not based on the best available or unbiased science. Corrected mathematical calculations and more rigorous parameterization resulted in predicted outcomes for the zero harvest scenario that more closely coincided with the empirical population estimates in 2022 following a judicially prevented fall hunt in 2021. Only in scenarios with simulated harvest of 300 or more wolves did probability of crossing the 350-wolf population threshold exceed zero. TL suggested that proponents of some policy positions bear a greater burden of proof than proponents of other positions to show that "their estimates are accurate, precise, and reproducible". In their analysis, TL failed to meet this standard that they demanded of others.

Effects of lethal management on gray wolf pack persistence and reproduction in Wisconsin, USA

Direct human-caused mortality accounts for about half of all large mammal mortality in North America. For social species like gray wolves (Canis lupus), the death of pack members can disrupt pack structure and cause pack dissolution, and mortality of breeding adults or wolves during reproduction and pup-rearing can decrease pup recruitment. We estimated minimum and maximum probability of wolf pack persistence in Wisconsin, USA, during biological years (15 April-14 April) 2011-2019 and evaluated the influence of pack size and legal harvest mortality on pack persistence during 2012-2014. Harvests comprised 75-161 mortalities within 194 monitored packs during 2012-2014, with 56-74% of packs having no wolves harvested each year. As an index of reproduction during 2013-2019, we also estimated the proportion of packs where pups responded to howl surveys. We evaluated the influence of pack size, legal harvest, and agency removal on reproduction during 2013-2015. Annual maximum pack persistence probability was uniformly high (0.95-1.00), and annual minimum pack persistence probability ranged from 0.86-0.98 with a possible decline during years of harvest. Reproduction was similar in years following harvest and agency removal (2013-2015, pup response = 0.27-0.40), and years without harvest or agency removal the year prior (2016-2019, pup response = 0.28-0.66). Pack size had a positive effect on pack persistence and reproduction. Total number of wolf mortalities and number of adult male and females removed did not influence pack persistence or reproduction. We suggest that low per-pack mortality, timing of harvest and agency removal, and harvest characteristics during 2012-2014 supported stable pack persistence and reproduction.

Estimating Wolf Population Size and Dynamics by Field Monitoring and Demographic Models: Implications for Management and Conservation

We estimated the current size and dynamics of the wolf population in Tuscany and investigated the trends and demographic drivers of population changes. Estimates were obtained by two different approaches: (i) mixed-technique field monitoring (from 2014 to 2016) that found the minimum observed pack number and estimated population size, and (ii) an individual-based model (run by Vortex software v. 10.3.8.0) with demographic inputs derived from a local intensive study area and historic data on population size. Field monitoring showed a minimum population size of 558 wolves (SE = 12.005) in 2016, with a density of 2.74 individuals/100 km2. The population model described an increasing trend with an average annual rate of increase λ = 1.075 (SE = 0.014), an estimated population size of about 882 individuals (SE = 9.397) in 2016, and a density of 4.29 wolves/100 km2. Previously published estimates of wolf population were as low as 56.2% compared to our field monitoring estimation and 34.6% in comparison to our model estimation. We conducted sensitivity tests to analyze the key parameters driving population changes based on juvenile and adult mortality rates, female breeding success, and litter size. Mortality rates played a major role in determining intrinsic growth rate changes, with adult mortality accounting for 62.5% of the total variance explained by the four parameters. Juvenile mortality was responsible for 35.8% of the variance, while female breeding success and litter size had weak or negligible effects. We concluded that reliable estimates of population abundance and a deeper understanding of the role of different demographic parameters in determining population dynamics are crucial to define and carry out appropriate conservation and management strategies to address human-wildlife conflicts.

Integrating basic and applied research to estimate carnivore abundance

A clear connection between basic research and applied management is often missing or difficult to discern. We present a case study of integration of basic research with applied management for estimating abundance of gray wolves (Canis lupus) in Montana, USA. Estimating wolf abundance is a key component of wolf management but is costly and time intensive as wolf populations continue to grow. We developed a multimodel approach using an occupancy model, mechanistic territory model, and empirical group size model to improve abundance estimates while reducing monitoring effort. Whereas field-based wolf counts generally rely on costly, difficult-to-collect monitoring data, especially for larger areas or population sizes, our approach efficiently uses readily available wolf observation data and introduces models focused on biological mechanisms underlying territorial and social behavior. In a three-part process, the occupancy model first estimates the extent of wolf distribution in Montana, based on environmental covariates and wolf observations. The spatially explicit mechanistic territory model predicts territory sizes using simple behavioral rules and data on prey resources, terrain ruggedness, and human density. Together, these models predict the number of packs. An empirical pack size model based on 14 years of data demonstrates that pack sizes are positively related to local densities of packs, and negatively related to terrain ruggedness, local mortalities, and intensity of harvest management. Total abundance estimates for given areas are derived by combining estimated numbers of packs and pack sizes. We estimated the Montana wolf population to be smallest in the first year of our study, with 91 packs and 654 wolves in 2007, followed by a population peak in 2011 with 1252 wolves. The population declined ~6% thereafter, coincident with implementation of legal harvest in Montana. Recent numbers have largely stabilized at an average of 191 packs and 1141 wolves from 2016 to 2020. This new approach accounts for biologically based, spatially explicit predictions of behavior to provide more accurate estimates of carnivore abundance at finer spatial scales. By integrating basic and applied research, our approach can therefore better inform decision-making and meet management needs.

Assessment of the residential Finnish wolf population combines DNA captures, citizen observations and mortality data using a Bayesian state-space model

Assessment of the Finnish wolf population relies on multiple sources of information. This paper describes how Bayesian inference is used to pool the information contained in different data sets (point observations, non-invasive genetics, known mortalities) for the estimation of the number of territories occupied by family packs and pairs. The output of the assessment model is a joint probability distribution, which describes current knowledge about the number of wolves within each territory. The joint distribution can be used to derive probability distributions for the total number of wolves in all territories and for the pack status within each territory. Most of the data set comprises of both voluntary-provided point observations and DNA samples provided by volunteers and research personnel. The new method reduces the role of expert judgement in the assessment process, providing increased transparency and repeatability.

AbundanceR: A Novel Method for Estimating Wildlife Abundance Based on Distance Sampling and Species Distribution Models

Appropriate field survey methods and robust modeling approaches play an important role in wildlife protection and habitat management because reliable information on wildlife distribution and abundance is important for conservation planning and actions. However, accurately estimating animal abundance is challenging in most species, as usually only a small proportion of the population can be detected during surveys. Species distribution models can predict the habitat suitability index, which differs from species abundance. We designed a method to adjust the results from species distribution models to achieve better accuracy for abundance estimation. This method comprises four steps: (1) conducting distance sampling, recording species occurrences, and surveying routes; (2) performing species distribution modeling using occurrence records and predicting animal abundance in each quadrat in the study area; (3) comparing the difference between field survey results and predicted abundance in quadrats along survey routes, adjusting model prediction, and summing up to obtain total abundance in the study area; (4) calculating uncertainty from three sources, i.e., distance sampling (using detection rate), species distribution models (using R squared), and differences between the field survey and model prediction [using the standard deviation of the ratio (observation/prediction) at different zones]. We developed an R package called abundanceR to estimate wildlife abundance and provided data for the Tibetan wild ass (Equus kiang) based on field surveys at the Three-River-Source National Park, as well as 29 layers of environmental variables covering the terrestrial areas of the planet. Our method can provide accurate estimation of abundance for animals inhabiting open areas that can be easily observed during distance sampling, and whose spatial heterogeneity of animal density within the study area can be accurately predicted using species distribution models.

Space-for-time is not necessarily a substitution when monitoring the distribution of pelagic fishes in the San Francisco Bay-Delta

Occupancy models are often used to analyze long-term monitoring data to better understand how and why species redistribute across dynamic landscapes while accounting for incomplete capture. However, this approach requires replicate detection/non-detection data at a sample unit and many long-term monitoring programs lack temporal replicate surveys. In such cases, it has been suggested that surveying subunits within a larger sample unit may be an efficient substitution (i.e., space-for-time substitution). Still, the efficacy of fitting occupancy models using a space-for-time substitution has not been fully explored and is likely context dependent. Herein, we fit occupancy models to Delta Smelt (Hypomesus transpacificus) and Longfin Smelt (Spirinchus thaleichthys) catch data collected by two different monitoring programs that use the same sampling gear in the San Francisco Bay-Delta, USA. We demonstrate how our inferences concerning the distribution of these species changes when using a space-for-time substitution. Specifically, we found the probability that a sample unit was occupied was much greater when using a space-for-time substitution, presumably due to the change in the spatial scale of our inferences. Furthermore, we observed that as the spatial scale of our inferences increased, our ability to detect environmental effects on system dynamics was obscured, which we suspect is related to the tradeoffs associated with spatial grain and extent. Overall, our findings highlight the importance of considering how the unique characteristics of monitoring programs influences inferences, which has broad implications for how to appropriately leverage existing long-term monitoring data to understand the distribution of species.