Estimation of Successful Breeding Pairs for Wolves in the Northern Rocky Mountains, USA

Abstract

Under the Endangered Species Act, documenting recovery and federally mandated population levels of wolves (Canis lupus) in the Northern Rocky Mountains (NRM) requires monitoring wolf packs that successfully recruit young. United States Fish and Wildlife Service regulations define successful breeding pairs as packs estimated to contain an adult male and female, accompanied by ≥2 pups on 31 December of a given year. Monitoring successful breeding pairs will become more difficult following proposed delisting of NRM wolves; alternatives to historically intensive methods, appropriate to the different ecological and regulatory context following delisting, are required. Because pack size is easier to monitor than pack composition, we estimated probability a pack would contain a successful breeding pair based on its size for wolf populations inhabiting 6 areas in the NRM. We also evaluated the extent to which differences in demography of wolves and levels of human‐caused mortality among the areas influenced the probability of packs of different sizes would contain successful breeding pairs. Probability curves differed among analysis areas, depending primarily on levels of human‐caused mortality, secondarily on annual population growth rate, and little on annual population density. Probabilities that packs contained successful breeding pairs were more uniformly distributed across pack sizes in areas with low levels of human mortality and stable populations. Large packs in areas with high levels of human‐caused mortality and high annual growth rates had relatively high probabilities of containing breeding pairs whereas those for small packs were relatively low. Our approach can be used by managers to estimate number of successful breeding pairs in a population where number of packs and their sizes are known. Following delisting of NRM wolves, human‐caused mortality is likely to increase, resulting in more small packs with low probabilities of containing breeding pairs. Differing contributions of packs to wolf population growth based on their size suggests monitoring successful breeding pairs will provide more accurate insights into population dynamics of wolves than will monitoring number of packs or individuals only.

Temporal validation of an estimator for successful breeding pairs of wolves Canis lupus in the U.S. northern Rocky Mountains

“…Mitchell et al (2008) presented models for estimating the number of successful breeding pairs of wolves, b, based on observed pack sizes for six analysis areas within the NRM. Their results suggested that pack size explained much of the variation in the probability that a pack contained a successful breeding pair within the NRM, with models varying across the analysis areas due to differences in growth rate of wolf populations and human-caused mortality.…”

“…We used a model-based b estimator specific to the six analysis areas developed by Mitchell et al (2008) using data that were collected during and prior to 2005. Pre- Our use of mean pack size to impute missing data for 18 packs among the three states assumed mean pack size was an accurate estimate of expected pack size for those packs.…”

“…Wolf populations within each recovery area experienced different levels of isolation, protection, management and exposure to humans, based largely on geography and administrative boundaries (Mitchell et al 2008, USFWS 2009). …”

“…where the summation is over pack sizes i ¼ 4 to k of the number of known packs of size i, n i ,P i is the predicted probability a pack of size i containing a successful breeding pair from the logistic models developed in Mitchell et al (2008) independently for each of six analysis areas, andP iL andP iU are the back-transformed lower and upper confidence bounds onP I (Neter et al 1996:603-604 (Table 1). Mean range for 95% prediction intervals of b across all states in both years was 12.62 (SD¼5.19).b slightly exceeded b MIN for all states in both years, except for Montana and Wyoming in 2007 when they were approximately equal (see Table 1).…”

Internal Validation of Predictive Logistic Regression Models for Decision‐Making in Wildlife Management

“…The confidence interval (CI) estimators for probabilities that wolf packs are BPs presented in Mitchell et al (2008) used the standard normal method as an approximation for binomial data on the logit scale, then back-transformed CI endpoints to the probability (0-1) scale. This method is known to have coverage rates that do not match the 100*(1 -a) nominal coverage rate, where a is defined as the type I error rate, particularly for estimated probabilities closer to 0 and 1 than to 0.5 (Jennings 1987).…”