Petracca LP, B Gardner, BT Maletzke, and SJ Converse. 2023. Merging integrated population models and individual-based models to project population dynamics of recolonizing species. Biological Conservation.
Recolonizing species exhibit unique population dynamics, namely dispersal to and colonization of new areas, that have important implications for management. A resulting challenge is how to simultaneously model demographic and movement processes so that recolonizing species can be accurately projected over time and space. We introduce a framework for spatially explicit projection modeling that harnesses the rigorous parameter estimation made possible by an integrated population model (IPM) and the flexible movement modeling made possible by an individual-based model (IBM). Our framework has two components: [1] a Bayesian IPM-driven age- and state-structured population model that governs the population state process and estimation of demographic rates, and [2] an IBM-driven spatial model that allows for the projection of dispersal and habitat colonization. We applied this model framework to estimate current and project future dynamics of gray wolves (Canis lupus) in Washington State, USA. We used data from 74 telemetered wolves and yearly pup and pack counts to parameterize the model, and then projected statewide dynamics over 50 years. Mean population growth was 1.29 (95% Bayesian Credible Interval = 1.26-1.33) during initial recolonization from 2009-2020 and decreased to 1.02 (95% Prediction Interval = 0.98-1.04) in the projection period (2021-2070). Our results suggest that gray wolves have a ~100% probability of colonizing the last of Washington State’s three specified recovery regions by 2030, regardless of alternative assumptions about how dispersing wolves select new territories. Our spatially explicit projection model can be used to project the dynamics of any species for which spatial spread is an important driver of population dynamics.
- Scripts: The main folder (described here) contains three codes -- one to run the IPM for the data collection period (2009-2020) and two different versions of the projection model for the years 2020-2070. The latter scripts differ based on chosen territory selection method.
The "Bonus_Model_Formulation_with_Many_Ages" folder contains the script for a projection model formulation that is age-structured and removes wolves from the model after reaching 15 years of age. This script uses the categorical RSF territory selection process.
Lastly, this folder has four scripts in the "Preliminary_Analysis_Steps" folder for processing of GPS collar data for the territory size and RSF analyses. However, these data are not available publicly due to their sensitive nature. Interested parties should contact Donny Martorello at WDFW ([email protected]).
- Functions: The main folder (described here) contains all functions related to the individual-based movement model. These functions allow for attraction of lone wolves, lethal removals, and dispersal of wolves depending on chosen territory selection method.
The "Bonus_Model_Formulation_with_Many_Ages" folder contains the same functions for the 15 age class model described above.
Data files used to run the models in this paper are found in the data folder. Please see here for more information.
The scripts as of the above date reflect the Corrigendum to our 2024 paper (https://www.sciencedirect.com/science/article/pii/S0006320724001952). We also fixed an additional index, whereby the impact of this correction (e.g., about one wolf after 50 years) was much smaller than simulation error.
We identified an error in the coding of out-of-state immigration in the baseline projection model. We updated the code, and also improved the estimation of immigration to better capture wolf population dynamics.
We estimated numbers of out-of-state immigrants per active pack during the data period. We previously used the mean number of total number of immigrants every six months from the data period in the projection model. However, this is likely to underestimate immigration because so few packs were available to receive immigrants early in the data period. Conversely, immigration won't increase indefinitely because it is limited by the number of wolves moving into the state. Therefore, we fit a von Bertalanffy growth curve to the posterior estimates of the total number of immigrants per year from the data period. We used the estimated asymptote from the fitted model for the immigrants in the projection.
With this modified approach to estimating out-of-state immigration, estimates of geometric mean of lambda (1.02), median probability of wolf recovery in 2070 (0.91), median probability of the Southern Cascades and NW Coast recovery region having >=1 territory with 2+ adults by 2030 (1.00), median probability of quasi-extinction at any point in the next 50 years (0.00), and median probability of extinction (i.e., zero wolves by 2070) (0.00) did not change. Changes are as follows: (1) a six-year and nine-year delay in estimated wolf pack establishment (>=1 territory with 2+ adults) in the Olympic Peninsula for the RSF and Least Cost Path models, respectively (i.e., from 2036 to 2042 for the RSF and from 2053 to 2062 for the Least Cost Path model); (2) a lower estimate of wolf abundance in 2030 (230 [95% PI 60-431] vs. 257 [76-487]); (3) a slightly higher estimate of wolf abundance in 2070 (474 [95% PI 35-1254] vs 470 [51-1259]) ; and (4) a slightly lower median probability of recovery at any point in the next 50 years (0.62 [95% PI 0.00-0.84] versus the previous 0.64 [0.00-1.00]).