Comparing survey and multiple recruitment–mortality models to assess growth rates and population projections

Abstract Estimation of population trends and demographic parameters is important to our understanding of fundamental ecology and species management, yet these data are often difficult to obtain without the use of data from population surveys or marking animals. The northeastern Minnesota moose (Alces alces Linnaeus, 1758) population declined 58% during 2006–2017, yet aerial surveys indicated stability during 2012–2017. In response to the decline, the Minnesota Department of Natural Resources (MNDNR) initiated studies of adult and calf survival to better understand cause‐specific mortality, calf recruitment, and factors influencing the population trajectory. We estimated population growth rate (λ) using adult survival and calf recruitment data from demographic studies and the recruitment–mortality (R‐M) Equation and compared these estimates to those calculated using data from aerial surveys. We then projected population dynamics 50 years using each resulting λ and used a stochastic model to project population dynamics 30 years using data from the MNDNR's studies. Calculations of λ derived from 2012 to 2017 survey data, and the R‐M Equation indicated growth (1.02 ± 0.16 [SE] and 1.01 ± 0.04, respectively). However, the stochastic model indicated a decline in the population over 30 years (λ = 0.91 ± 0.004; 2014–2044). The R‐M Equation has utility for estimating λ, and the supporting information from demographic collaring studies also helps to better address management questions. Furthermore, estimates of λ calculated using collaring data were more certain and reflective of current conditions. Long‐term monitoring using collars would better inform population performance predictions and demographic responses to environmental variability.

when and where surveys are not feasible, such as in densely forested regions or for cryptic species that occur at low densities (DeCesare et al., 2012;Hatter & Bergerud, 1991;Serrouya et al., 2017).
By 2017, Minnesota's northeastern moose (Alces alces Linnaeus, 1758; Figure 1) population (3,710) was 58% lower than at its high point (8,840) in 2006, but it appeared to have stabilized during (DelGiudice, 2017. A study of demographics of the northeastern population in 2002-2008 predicted a slow reduction in numbers (long-term stochastic annual growth rate of 0.85); modeled adult survival rates were 0.74-0.85, and calf survival was 0.24-0.56 (Lenarz, Fieberg, Schrage, & Edwards, 2010). However, the abrupt decline in northeastern Minnesota was not detected by the annual aerial surveys until 2010 (ArchMiller et al., 2018;DelGiudice, 2013;Lenarz et al., 2010), which illustrated that demographic modeling may reveal population trajectories before they are reflected in total population estimates by aerial survey.
Our goal was to compare estimates of population growth rate (λ) derived from demographic information from the adult moose and calf studies versus from the annual aerial surveys, because each source of data has inherent limitations (Hatter & Bergerud, 1991).
Aerial surveys are relatively less costly compared to extensive collaring studies and can cover larger spatial extents. However, there is more precision and a greater detail of information gained from collaring studies. We projected population dynamics for 50 years using each method to gauge how current trends may affect the population's future. We examined the local sensitivity of all parameters to determine which data may be most important to predicting population growth. To model how variability in demographic rates may affect trajectories, we also employed a stochastic model to project the population for 30 years using adult survival rates and litter sizes.

| Study area
The MNDNR's demographic studies and aerial surveys were conducted in northeastern Minnesota along the edge of moose range in North America (Figure 2; Lenarz et al., 2010;Timmermann & Rodgers, 2017). This population of moose inhabits a mosaic of the Superior National Forest and various state, county, and private lands (6,068 km 2 ) between 47°06′N and 47°58′N latitude and 90°04′W and 92°17′W longitude ( Figure 2). Moose harvest was suspended in Minnesota from 2013 until 2016, when a limited tribal harvest was resumed (DelGiudice, 2012;Edwards, 2018;Schrage, 2018). This region is part of the Northern Superior Upland within the Laurentian mixed forest province (MNDNR, 2015). The vegetative cover is a mosaic of wetlands, stands of northern white cedar (Thuja occidentalis), black spruce (Picea mariana), and tamarack (Larix laricina), and upland stands of balsam fir (Abies balsamea), jack pine (Pinus banksiana), eastern white pine (P. strobus), and red pine (P. resinosa), intermixed with quaking aspen (Populus tremuloides) and paper birch (Betula papyrifera). Area of timber harvest and other forest disturbance declined 65% from 2001 to 2009 (Wilson & Ek, 2013).

| Aerial surveys
The MNDNR conducts an aerial survey of the northeastern moose population each winter (DelGiudice, 2019). The current survey design and methods were implemented in 2005. The survey area is ~15,500 km 2 and is divided into 436 total survey plots, each ~36 km 2 .
Each winter, 36-52 of the survey plots are chosen from a stratified random sample based on moose density (low, medium, high). The survey provides estimates of abundance (including 90% confidence intervals [CI]), percent calves, calf:cow and bull:cow ratios, and percent cows observed with twins. A sightability model corrects for visual obstruction and is used to adjust abundance (ArchMiller et al., 2018;Fieberg, 2012;Giudice, Fieberg, & Lenarz, 2012;Steinhorst & Samuel, 1989), but raw data, adjusted for sampling, are used to calculate other metrics using the combined ratio estimator (Cochran, 1977). The sightability model was based on radiocollared moose

| Adult and calf survival rates
Adult moose were captured by aerial darting and handled during winters 2013-2015 (Carstensen et al., 2018). Immobilizations were conducted with carfentanil, thiafentanil, and xylazine, and reversed with naltrexone and tolazoline (Carstensen, Hildebrand, Pauly, Wright, & Dexter, 2014). Moose were fitted with GPS-Iridium collars (Vectronic Aerospace GmbH) variably programmed to collect a location every 4 hr during July-April, but every hour for females during calving (May-June). and 2016, we monitored 50 and 35 calving females for signs of F I G U R E 2 Study area of Minnesota Department of Natural Resources demographic moose studies (6,068 km 2 study area) during May-June 2013-2016, northeastern Minnesota, USA. Annual aerial survey largely overlaps this study area neonatal mortality using changes in adult female velocities and assessed seasonal calf survival by aerial surveys Severud et al., 2019). Adult females were blood sampled to test for pregnancy; a threshold of ≥2 ng/ml of serum progesterone indicated pregnancy (Haigh, Kowal, Runge, & Wobeser, 1982;Murray et al., 2006;Testa & Adams, 1998). We estimated pregnancy rates using these test results and observations of cows that made a calving movement . Annual Kaplan-Meier survival rates were estimated for pooled adult (>1.5 years) males and females and for calves (birth to 1 year) during 2013-2016 (Carstensen et al., 2018;Obermoller, 2017;Severud et al., 2017).

| Population growth rate calculation (λ)
We estimated λ using two different methods. First, to calculate λ survey we used population estimates from the annual aerial survey and the equation: where N was the population estimate, and t is the time interval between surveys. N 0 is the population at time 0.
Second, we used the recruitment-mortality (R-M) Equation (Hatter & Bergerud, 1991) where M is the finite annual adult mortality rate, and R is the finite annual recruitment rate defined as the calf proportion of the population. We used published adult survival estimates from MNDNR's adult collaring study (S adult ) to calculate mortality using 1 -S = M (Carstensen et al., 2018). To obtain estimates of R, we used the population estimate, bull:cow ratio (DelGiudice, 2017), mean twinning rate (M. W. Schrage, Fond du Lac Resource Management Division, unpublished data), pregnancy rates, and annual calf survival from GPS-collared and uncollared calves Severud et al., 2017). We used estimates from the previous year to calculate the current year's R (e.g., 2013 adult population estimate [total population estimate minus calf proportion], bull:cow ratio [from which we derived proportion cows], pregnancy rate, and calf survival to calculate 2014's R), because moose are considered recruited once they reach 1 year of age. First, we calculated calf production as: We then used calf survival to calculate R study as: M can also be calculated by rearranging the R-M Equation to: Using this equation, we estimated adult mortality rates from λ survey and R survey (percent calves as reported in the survey) to compare how closely they tracked mortality rates and percent calves as calculated from the demographic study (i.e., R study vs. R survey and λ R-M vs. λ survey ).

| Population projection
We calculated median and standard deviation of S adult and calf:cow ratios at calving (litter size). We then used the 2014 population estimate for the initial population (4,350 adults; used to coincide with results of collaring study) and projected growth for 30 years and 1,000 Monte Carlo simulations using the R package population (Chapron, 2015). We also projected the population for 50 years using mean λ survey from the recent stable period (2012-2017)  We projected populations 50 years to match climate scenario and long-term forest planning timeframes. We investigated local sensitivity of all parameters used to calculate λ R-M by incrementally increasing a single parameter while holding the others at mean levels until λ increased from 1.00 to 1.10, a level which would reverse the population decline (Hamby, 1994;MNDNR, 2012;Serrouya et al., 2017).

| RE SULTS
The MNDNR collared 173 adult moose from 2013 to 2015 (123 F, 50 M) to assess survival and cause-specific mortality (Carstensen et al., 2018). Survival was pooled for males and females due to a small  Note: N is the population estimate, M is the annual adult mortality rate, S is calf survival, R is recruitment (calf proportion of the population), and preg rate is pregnancy rate as determined by serum progesterone, calving behavior, and calf observations. λ survey was calculated using changes in population estimates; λ R-M was calculated using the R- the MNDNR studies shows the population declining, but with uncertainty (λ = 0.91 ± 0.04; Figure 6).  (Ellner & Fieberg, 2003). Comparing deterministic and stochastic projections can yield opposing results (Nakaoka, 1996). Using stochastic projections may be more appropriate in cases with greater environmental variability (Boyce, 1977;May, 1973).

| D ISCUSS I ON
Climate change, specifically warming temperatures, is expected to influence moose demographics at the southern periphery of their geographic range (Lenarz et al., 2010;Lenarz et al., 2009;McCann, Moen, & Harris, 2013;Murray et al., 2006;Ruprecht et al., 2016; but see Mech & Fieberg, 2014). The northeastern Minnesota moose population has shown some response to warmer than average winter temperatures, including reduced survival (Lenarz et al., 2009; but see Mech & Fieberg, 2014) and Varying adult survival had more of an impact on λ than varying calf survival or any other parameter contributing to R in the R-M Equation (twinning rate, pregnancy rate, bull:cow ratio). Previous research similarly concluded that fertility, calf survival, and adult survival explained 5%, 11%, and 70% of the variation in λ, respectively (Lenarz et al., 2010). The feasibility of applying management strategies and activities that sufficiently alter bull:cow ratios, or increase twinning or pregnancy rates to 100% necessary to markedly affect λ is unlikely. The population is already near its maximum reproductive output.
Our calculations of R study closely tracked R survey , but because there are assumptions (e.g., twinning rate) and uncertainty (calf survival) surrounding parameters used to calculate R study , the close association should be interpreted cautiously. In April 2015, collaring moose was banned and new methods were developed to monitor calf survival Severud et al., 2019). Being newly developed and implemented, the 2015 survival estimate warrants prudent interpretation, yet closely aligns with survival estimates in the years before and after 2015. Furthermore, methods used to estimate recruitment in all years of the calf survival study and from the aerial survey (conducted in January) may have missed late-winter mortality observed elsewhere (Jones, Pekins, Kantar, O'Neil, & Ellingwood, 2017;Musante, Pekins, & Scarpitti, 2010;Serrouya et al., 2017).
To estimate population demographics, a large and geographically dispersed sample of that population is followed to ensure the sample is representative. The MNDNR collared large numbers of adult moose and calves across the study area. The goal of the adult survival study was to maintain an annual starting sample of about 100 animals transmitting throughout the duration of the study; however, the indefinite moratorium on collaring moose plus attrition of existing collars due to mortalities, battery-life expiration, and malfunction greatly reduced sample size to less than half by 2016 . The adult mortality rate has generally been decreasing, but later estimates could be biased due to weakened animals being culled from the population through predation or health-related mortality and stronger animals surviving to later years of the study. A relationship between collared adult survival rates and population-wide assessments of winter nutritional restriction suggests the condition of the collared animals was representative of that of the free-ranging population in the earliest years of the study   Serrouya et al., 2017). Collared animals are also needed to periodically recalibrate sightability models (Serrouya et al., 2017).
Thus, the biologically significant value of resumed collaring cannot be overstated.

| CON CLUS IONS
Aerial survey results indicate that the moose population was sta-

CO N FLI C T O F I NTE R E S T
None declared.

AUTH O R CO NTR I B UTI O N S
WJS and GDD conceived the initial ideas and collected data; WJS primarily conducted data analysis with help from GDD and JKB; WJS, GDD, and JKB contributed critically to writing the manuscript and gave final approval for publication.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data are available at the Data Repository for the University of Minnesota (DRUM), https ://doi.org/10.13020/ bd01-3547.