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

• Published in: Journal of Animal Ecology
• Main Authors: Creel, Scott, Creel, Michael
• Format: Article in Journal/Newspaper
• Language: English
• Published: Wiley 2009
• Subjects: Davidson; Canis lupus
• Online Access: http://dx.doi.org/10.1111/j.1365-2656.2009.01581.x; https://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1111%2Fj.1365-2656.2009.01581.x; https://besjournals.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2656.2009.01581.x

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 ...