An integrated population model to uncover informative discrepancies in population growth

Background/Question/Methods

Information on unobservable population processes (discrepancies) can contribute to fuller understanding of observed patterns and processes whereas  implications of failing to include unobservable population processes lead to a misunderstanding of population dynamics and, potentially, to ineffective management.  However, few flexible, rigorous models are available to accurately estimate discrepancies in population growth.  A promising method for estimating unobserved population processes is through integrated population models (IPMs) where multiple data sources with shared parameters are used in a common model.  Our goal was to improve on the IPM framework to help conservationists, managers, and researchers make more informed decisions about conservation and management of populations through estimation of discrepancies in the growth process.  In this paper, we 1) introduce a flexible, general IPM and method to estimate unknown population processes with commonly collected population data, 2) provide an example of  our IPM to uncover informative discrepancies in growth of Wisconsin’s gray wolf (Canis lupus) population, and 3) study the implications of hidden population processes. 

Results/Conclusions

We demonstrate a flexible IPM that integrates annual population counts and recruitment and survival data.  A realistic treatment of population growth is accommodated by fitting threshold density dependent responses for each demographic process.  Because different data sources have common parameters, we find the discrepancy between the demographic processes and the annual population trajectory.  The discrepancies most likely represent unobserved additions or removals from the population.  Our model also allows for testing differences in discrepancies because of external factors, like management or policy changes.  We applied our IPM to Wisconsin’s wolf population in a period of recovery and growth (1980-2011).  Keying in on policy differences, we estimated 2% additional mortality in 1980-1995, 6% additional mortality in 1996-2002, and 13% additional mortality in 2003-2011 was needed to explain growth.  This additional mortality informs potentially the density dependent changes, changes in illegal killing with shifts in wolf management, and a level of informative censoring in the survival data.  By using multiple sources of data with shared parameters, we may uncover informative discrepancies in the growth process that may include cryptic poaching rates, informative censoring, density dependent changes in growth, or human actions on the population resulting from management changes.