Density dependence and climate effects in Rocky Mountain elk: an application of regression with instrumental variables for population time series with sampling error

Abstract

Summary 1. Sampling error in annual estimates of population size creates two widely recognized problems for the analysis of population growth. First, if sampling error is mistakenly treated as process error, one obtains inflated estimates of the variation in true population trajectories (Staples, Taper & Dennis 2004). Second, treating sampling error as process error is thought to overestimate the importance of density dependence in population growth (Viljugrein et al. 2005; Dennis et al. 2006). 2. In ecology, state‐space models are used to account for sampling error when estimating the effects of density and other variables on population growth (Staples et al. 2004; Dennis et al. 2006). In econometrics, regression with instrumental variables is a well‐established method that addresses the problem of correlation between regressors and the error term, but requires fewer assumptions than state‐space models (Davidson & MacKinnon 1993; Cameron & Trivedi 2005). 3. We used instrumental variables to account for sampling error and fit a generalized linear model to 472 annual observations of population size for 35 Elk Management Units in Montana, from 1928 to 2004. We compared this model with state‐space models fit with the likelihood function of Dennis et al. (2006). We discuss the general advantages and disadvantages of each method. Briefly, regression with instrumental variables is valid with fewer distributional assumptions, but state‐space models are more efficient when their distributional assumptions are met. 4. Both methods found that population growth was negatively related to population density and winter snow accumulation. Summer rainfall and wolf (Canis lupus) presence had much weaker effects on elk (Cervus elaphus) dynamics [though limitation by wolves is strong in some elk populations with well‐established wolf populations (Creel et al. 2007; Creel & Christianson 2008)]. 5. Coupled with predictions for Montana from global and regional climate models, our results predict a substantial reduction in the limiting effect of snow accumulation on Montana elk populations in the coming decades. If other limiting factors do not operate with greater force, population growth rates would increase substantially.

Climate change intensification of herbivore impacts on tree recruitment

“…Climate change can affect aspen survival directly through impacting sucker survival, and indirectly by altering the strength of herbivory (figure 3a), but can also affect herbivore abundance. Indeed, though the elk population in northern Yellowstone itself has declined since the late 1990s [33], elk populations in many other localities in the Rocky Mountains are predicted to increase [13,34] owing to reduced winter snowpack across much of the western United States [35]. Thus, across the northern Rocky Mountain region, aspen recruitment could be precluded owing to more intense herbivory combined with changed abiotic conditions.…”

“…It is an ecologically important tree species [14] that is in widespread decline across much of the US northern Rocky Mountains [15] owing to recruitment failure in the face of intense elk herbivory [16], possibly in combination with climatic factors [15]. Indeed, aspen demography is affected directly by both climate [17,18] and elk herbivory [16], while elk themselves may be affected by climate change-altered snowpack conditions [13]. Elk browse on woody shrubs in the winter while during the growing season they are grazers.…”

Mexican wolves, elk, and aspen in Arizona: Is there a trophic cascade?

“…While declining snowpacks may have implications for plant communities and patterns of streamflow, they may also influence elk populations. For example, Creel and Creel (2009) found that the steady growth of Montana elk populations in recent decades was inversely correlated with declining snowpacks. When they coupled their analysis with regional predictions of global climate change over the next 20-50 years, results indicated increased elk population growth rates were likely if snowpack amounts continue to decline as predicted.…”

Climate and management interact to explain the decline of woodland caribou (Rangifer tarandus caribou) in Jasper National Park

“…Elk cope poorly with deep snow and severe winter weather (Creel & Creel, 2009, Hebblewhite et al, 2002, and in Jasper, severe winter weather did cause two elk population crashes. The crash of the late 1940s occurred during an era of intense predator control, and the elk population subsequently recovered.…”

“…In particular, we weighed the evidence to discriminate among three general hypotheses of caribou decline in Jasper National Park: climate change, human disturbance, and wildlife management. The hypothesis of caribou decline due to climate change is that warmer temperatures and shallower snow should favour elk (Creel & Creel, 2009, Hebblewhite et al, 2002 to the detriment of caribou via apparent competition. The hypothesis of caribou decline due to human disturbance is that large numbers of people using wilderness areas can displace caribou from important habitat, thus causing population decline.…”