title: Are the numbers adding up? Exploiting discrepancies among complementary population models.
abstract: Large carnivores are difficult to monitor because they tend to be sparsely distributed, sensitive to human activity, and associated with complex life histories. Consequently, understanding population trend and viability requires conservationists to cope with uncertainty and bias in population data. Joint analysis of combined data sets using multiple models (i.e., integrated population model) can improve inference about mechanisms (e.g., habitat heterogeneity and food distribution) affecting population dynamics. However, unobserved or unobservable processes can also introduce bias and can be difficult to quantify. We developed a Bayesian hierarchical modeling approach for inference on an integrated population model that reconciles annual population counts with recruitment and survival data (i.e., demographic processes). Our modeling framework is flexible and enables a realistic form of population dynamics by fitting separate density-dependent responses for each demographic process. Discrepancies estimated from shared parameters among different model components represent unobserved additions (i.e., recruitment or immigration) or removals (i.e., death or emigration) when annual population counts are reliable. In a case study of gray wolves in Wisconsin (1980-2011), concordant with policy changes, we estimated that a discrepancy of 0% (1980-1995), -2% (1996-2002), and 4% (2003-2011) in the annual mortality rate was needed to explain annual growth rate. Additional mortality in 2003-2011 may reflect density-dependent mechanisms, changes in illegal killing with shifts in wolf management, and nonindependent censoring in survival data. Integrated population models provide insights into unobserved or unobservable processes by quantifying discrepancies among data sets. Our modeling approach is generalizable to many population analysis needs and allows for identifying dynamic differences due to external drivers, such as management or policy changes.
authors.affiliation: Department of Forest and Wildlife Ecology, University of Wisconsin - Madison 1630 Linden Drive, Madison, Wisconsin, 53706.
authors.forename: Jennifer L
authors.initials: JL
authors.lastname: Stenglein
authors.affiliation: Department of Statistics, University of Wisconsin - Madison 1300 University Avenue, Madison, Wisconsin, 53706 ; Department of Entomology, University of Wisconsin - Madison 1605 Linden Drive, Madison, Wisconsin, 53706.
authors.forename: Jun
authors.initials: J
authors.lastname: Zhu
authors.affiliation: Department of Statistics, University of Wisconsin - Madison 1300 University Avenue, Madison, Wisconsin, 53706 ; Department of Plant Pathology, University of Wisconsin - Madison 1605 Linden Drive, Madison, Wisconsin, 53706.
authors.forename: Murray K
authors.initials: MK
authors.lastname: Clayton
authors.affiliation: Department of Forest and Wildlife Ecology, University of Wisconsin - Madison 1630 Linden Drive, Madison, Wisconsin, 53706.
authors.forename: Timothy R
authors.initials: TR
authors.lastname: Van Deelen
keywords: Bayesian inference; correction factor; gray wolves; hierarchical model; integrated population model; latent variable; population counts; radiotelemetry data; state-space model; survival analysis