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.

Blood does not buy goodwill: allowing culling increases poaching of a large carnivore

“…Instead, we used additional data in a Bayesian model that were biologically meaningful to detect density dependence (average pack size, probability a pack reproduces, and area occupied by wolf packs, see electronic supplementary material, table S2 and figures S1–S4). As with prior studies on Wisconsin's wolf population [ 28 ], we did not detect any negative density dependence. A second plausible alternative explanation for the observed decrease in population growth rates would be super-additive mortality, i.e.…”

Reply to comment by Pepin et al . 2017

“…Therefore, we believe that only three factors could have caused the slow-down in population growth we observed in both US states: (i) decline in births (for which we found the opposite evidence in reproductive performance of wolf packs); (ii) emigration (but there is no known or hypothesized mechanism by which emigration out of state would respond to a policy signal independent of the number of wolves culled); and (iii) a new source of mortality that is influenced by the policy signal. Our finding is consistent with [16], which reported no density-dependent effect on survival and hinted at a new factor needed to explain the Wisconsin wolf population slow-down we observed. Pepin et al [1] wrote there were no data on poaching rates for testing the poaching hypothesis, but we disagree.…”

Demographic and Component Allee Effects in Southern Lake Superior Gray Wolves

“…Once a demographic Allee effect is detected, hypothesized mechanisms leading to the Allee effect should be evaluated, and individual-based models provide a useful framework for testing these hypotheses. A well-parameterized individual-based model can be used to study specific mechanisms as well as the emergent population properties to which they contribute [ 44 ] and can inform important conservation concerns such as long-term population viability, or how novel mortalities that vary in space and time (e.g., hunting, illegal killing, infectious disease) will affect the population [ 37 , 61 , 62 ].…”