414 S. P. Woodruff et al.
and thus the actual number of samples collected would be c. 33% higher (e.g. for 300 consensus genotypes, you collect 400 samples). We used true population sizes of 100, 150, 200, 250 and 300 with a male : female ratio of 0.66 : 1. This ratio reflects sex ratios in our study area as estimated by managers during aerial counts (J.J. Hervert, pers. comm.). We applied a simulation method for the single session
(capwire) and multi-session (MARK) estimators separately because the sampling designs are substantially different (see Supplementary Material 1 for R code). We sought to simulate collecting the same number of scats for each de- sign. Therefore, the target number of scats was collected in a single session in the capwire simulation but spread over multiple sessions in the MARK simulation. This repre- sents the way sampling would be designed in a field study for each of these methods. For each simulated sampling session we looped through the animal population and assigned scat deposition. Then, we simulated detection of the deposited scats. Finally,we estimated population size using R packages for each method (capwire: Pennell et al., 2013; RMark: Laake, 2013).
Individuals with higher deposition rates were set to have
a higher probability of being sampled. Previous research in- dicated deposition rates averaged one pellet pile per prong- horn per day (Woodruff et al., 2015) and an approximately equal ratio of males and females visiting drinkers (as seen on remote cameras; S. Doerries, University of Arizona, pers. comm.). However, our results (Woodruff et al., 2016b) indi- cated 2.5–3 times more male than female samples at the drinkers and a male : female sex ratio of c. 1.5 : 1. Given this information, we assumed males have higher deposition rates than females. Thus for 1–3 sessions we chose to simu- late mean deposition over a 7-day period, with males having twice the mean deposition rate of females. We simulated sampling every 7 days as, per current agency procedures, each drinker is visited c. every 7 days for restocking of sup- plemental feed. Per session, we randomly selected 50–600 samples with replacement, allowing individuals to be sampled more than once in a sampling session (i.e. 0–x times, where x is the total number of depositions by an in- dividual; Supplementary Table 1). With a range of 50–750 samples collected in each session for any particular popula- tion size, the resulting consensus genotyping rate was 0.33– 3.33 times per individual in a session (i.e. 50–500 samples per session for 150 individuals). Not all ratios (e.g. 0.33, 1.5 or 3.33 times) or number of sampling sessions were employed for every sampling design (Supplementary Table 1). All simula- tionswere conducted in R 3.3.0 (R Development Core Team, 2013).
Abundance estimation and comparison of methods
To compare sampling design and estimators, we estimated abundance using both multi- and single-session modelling
approaches. In multi-session models, populations are sampled during.1 sessions at distinct time points or with- in discrete sampling sessions (Chao, 2001). Although there may be multiple captures of the same individual within a sampling session, only a single capture per individual per sampling session is counted, resulting in binary data (1 = captured, 0 = not captured). In contrast, single session sampling, such as in capwire, uses the total number of cap- tures (count data) for each individual and allows capture of an individual multiple times within sessions (Miller et al., 2005). The individual identification represents the animal’s mark, yet all captures in all sessions are included, creating a capture distribution. For multi-session models we used the top model (de-
scribed above) implemented in RMark, to build the multi- session model. For every true abundance in each sampling design we simulated 100 datasets for estimating abundance and 95% confidence intervals using MARK and capwire. Simulations included one session in capwire, and two and three sessions in MARK. A likelihood-ratio test in capwire chooses between the
two available models: the even capturability model (ECM), which assumes individuals have an equal chance of being captured, and the two innate-rates model (TIRM), which models two mixtures of capturability (a lower and a higher rate) and is comparable to heterogene- ity models. In capwire the likelihood ratio indicated the TIRM model was the appropriate model in all cases, and thus we did not estimate sex and age classes separately, as capwire inherently accounts for variation in capture prob- ability when using the TIRM model (Miller et al., 2005). Abundance estimates and confidence intervals were
averaged over the 100 simulations. We evaluated the per- formance of each sampling design and estimator by com- paring the simulated abundance estimates to the true population size (per cent bias), the coefficient of variation (CV), and the relative mean squared error (RMSE). We calculated the CV as the ratio standard error : estimate ex- pressed as a per cent (Buckland et al., 2001) to evaluate the precision of each sampling design and estimator. The CV is commonly used to describe the precision of an abundance estimate. As a general rule, CV ,10%is ideal but ,20% indicates a precise estimate (White et al., 1982; Pollock et al., 1990). Thus, determining an ac- ceptable level of precision is dependent on the question being asked (e.g. What is the harvest limit? Or how much is this population growing or shrinking?; Mowat, 2005). RMSE incorporates accuracy (bias) and precision (variance), and low values indicate better performance and a good balance between bias and precision. Additionally, we examined the 95% confidence interval (CI) coverage probability, the proportion of times (out of 100 in this case) the true value was contained within the interval.
Oryx, 2020, 54(3), 412–420 © 2018 Fauna & Flora International doi:10.1017/S003060531800011X
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