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K. Nasman is employed by Western Ecosystems Technology, Inc., as were T.N. Johnson (now employed by University of Idaho) and R.M. Nielson (now employed by Eagle Environmental, Inc.) at the time of this study. This affiliation does not alter our adherence to PLOS ONE policies on sharing data and materials.

Current address: Eagle Environmental, Inc., Santa Fe, New Mexico, United States of America

Given the uncertain population status of low-density, widely-occurring raptors, monitoring changes in abundance and distribution is critical to conserving populations. Nest-based monitoring is a common, useful approach, but the difficulty and expense of monitoring raptor nests and importance of reliable trend data to conservation requires that limited resources are allocated efficiently. Power analyses offer a helpful tool to ensure that monitoring programs have the ability to detect trends and to optimize financial resources devoted to monitoring. We evaluated alternative monitoring designs for raptors to identify appropriate survey effort to detect population trends. We used data collected from a territory-occupancy study of ferruginous hawks throughout Wyoming to guide simulations and evaluate the ability to detect trends in occupancy rates. Results suggest that greater gains in precision of trend estimation may be achieved through the addition of more sites and not more visits; statistical power was ≥80% when monitoring lasted 20 years and population declines were 20%; and probability of detection affected statistical power less than rates of population decline. Monitoring at least 150 sites for 20 years would provide reasonable estimates of trend in occupancy given certain rates of detection and occupancy, but only for population declines of 20%. Removal sampling did not result in substantial changes of any metrics used to evaluate simulations, providing little justification for employing the standard design if territory occupancy is the variable of interest. Initial rates of territory occupancy may be biased high, a problem inherent to many studies that monitor territory occupancy. We explored the effects of lower rates of initial occupancy on the ability to detect trends. Although we present data from a study of ferruginous hawks, our simulations can be applied to other raptor species with similar life history and population dynamics to provide guidance for future trend estimation of territory occupancy.

Anthropogenic transformation of natural systems is currently a primary driver of species abundance and distribution patterns, leading to population declines for many species [

Human alteration of landscapes is a primary threat to many raptor species. Direct mortality results from collisions with human infrastructure and electrocution [

Given the uncertain population status of low-density, widely occurring species, monitoring changes in both the abundance and distribution of raptors will be critical to conserving their populations. Bald eagles (

The low density of many raptor populations, combined with their high fidelity to territories and nest sites, and the conspicuousness of their large stick nests, has resulted in monitoring focused on known (historic) nests or territories e.g., [

Methods for estimating site occupancy rates, for example proportion of nests or territories occupied for breeding, are employed when there is interest in occurrence-based indices of species but imperfect detection of individuals [

Here, our objective is to provide practical guidance on effort and sample designs based on simulations of population parameters and multiple aspects of a territory-occupancy based monitoring program. We use ferruginous hawks as a case study because this species is dependent on sagebrush-dominated ecosystems that are increasingly impacted by anthropogenic change. Furthermore, we lack standardized monitoring protocols for this species given the difficulty in assessing its population status, and we have available a dataset of territory occupancy for ferruginous hawks across Wyoming, U.S.A. that provided an ideal framework to evaluate power analyses as they relate to guiding the development of raptor monitoring programs. We use simulations to evaluate alternative designs for monitoring given a range of values for survey effort and population-level parameters that may influence the power to detect population trends. We consider multiple aspects of survey effort in order to achieve specific monitoring objectives, including: the number of sites to be monitored, how many surveys per site to conduct within a season, and total duration of the monitoring program. We examine two approaches to multi-season occupancy estimation: a standard site-occupancy design which includes an equal number of visits among all sampling units (e.g., nesting territories) throughout the breeding season, and a removal design in which surveys are discontinued (within the respective breeding season only) after detection of the target species. A removal design may improve efficiency and reduce cost through fewer visits to some sites within a season. The analysis presented here was facilitated by a need for guidance on the development of a territory-occupancy monitoring program for ferruginous hawks throughout the state of Wyoming, but the simulations and other considerations we present can provide guidance for monitoring other raptors for which estimation of territory-occupancy is of interest at broad scales. Based on these simulations, we offer recommendations on sample design and effort while considering logistical constraints.

Briefly, we used data presented in [

The study area at which data were collected that formed the basis for simulations included 1,230 townships comprising the range of ferruginous hawks in Wyoming [

To evaluate the ability to detect trends in occupancy of ferruginous hawks under different scenarios we developed simulations that varied: 1) survey effort, including number of monitored territories, number of visits to a territory within a breeding season, and total duration of monitoring (i.e., number of years), 2) the observation process (probability of detection; _{1}], and annual rates of decline in regional ferruginous hawk occupancy. We conducted simulations using a standard sampling design in which all sampling units are visited an equal number of times, and a removal sampling design in which visits to sampling units cease (within the current breeding season) once presence is confirmed. We arrived at the values used for simulations (

Parameter | Simulated values |
---|---|

Number of sites | 100–200 |

Number of visits | 2–6 per season^{a} |

Total duration | 10 yrs; 20 yrs |

Probability of detection | 0.44; 0.67; 0.79 |

Probability of extinction | 0.33 (fixed) |

Initial probability of occupancy | 0.42; 0.57; 0.72 |

Annual population decline | 1.12%; 0.55%^{b} |

^{a} For the standard sampling design, this value represents the total number of visits to a given site per season. For the removal sampling design, this value represents the maximum number of visits to a given site per season.

^{b} Annual decreases represent a 20% and 10% decline over 20 years, respectively.

The range of values for survey effort was based on exploratory simulations and logistical and financial constraints identified during previous survey efforts [

The range of values we used for probability of detection (

Managers tasked with monitoring ferruginous hawks may want the ability to detect relatively small declines in occupancy to prepare management or mitigation responses should the trend continue. Thus, we explored the ability to detect relatively small annual decreases in the ferruginous hawk population (π) of 0.55% and 1.12% (π = 0.0055 and 0.0112, respectively) representing a 10% or a 20% decline over 20 years, respectively.

To explore the effect that the initial probability of occupancy (_{1}) would have on the power to detect trends in occupancy over time, we chose three values of _{1}. Because we were interested in the effect of lower values of _{1} than were observed by Wallace et al. [_{1}. The lowest value for _{1} we selected was 0.42, which represented the same distance from the lower limit of the 95% CI of

We estimated the average probability of colonization for season _{i}) as:

The probability that a site was occupied in the first season (_{1}) was a parameter defined for a simulation. The probability that a site was occupied in subsequent seasons was given as:

For season _{i}. If the site was determined to be occupied based on the Bernoulli draw, we determined if occupancy was detected using random additional draws from a binomial distribution with probability

Reliable trend estimation may require monitoring to extend for a relatively long time period. Long-lived species that have high site fidelity, like ferruginous hawks, might require longer time periods for changes in occupancy to manifest in obvious trends. Furthermore, a long-term data set might be required to separate true population trends from inter-annual variation inherent to populations [

We used four metrics to evaluate how sampling effort and occupancy parameters affected the ability to detect trends in site occupancy: relative bias (RBIAS), coefficient of variation (CV), confidence interval (CI) coverage, and statistical power. Using multiple metrics is preferable because evaluating a single metric can be misleading; when selecting an appropriate monitoring design, understanding the precision and bias associated with the monitoring effort are as important as understanding statistical power.

We measured RBIAS as the difference between the estimated trend and the true trend standardized by the true trend:

Strict guidelines on acceptable benchmarks for these metrics are not available, but a goal for this analysis was to evaluate the performance of particular monitoring scenarios to provide guidance on a monitoring program for ferruginous hawks. Thus, we selected conservative benchmark values for each metric to help identify monitoring effort appropriate for this species (

Metric to evaluate simulation | Benchmark value^{a} |
---|---|

Relative bias | ≤ 5% |

Coefficient of variation | ≤ 20% |

Confidence interval coverage | 90% |

Statistical power | 80% |

^{a} See text for justification of benchmark values.

The plausibility of a removal design was of primary interest given the logistical and financial difficulties of monitoring raptors at broad spatial scales. Thus, we present results from the removal design first, followed by results from a standard sampling design for comparison. Furthermore, we concentrate on results from 20 years of monitoring, assuming the long-term data would provide the most robust estimates of occupancy trend, followed by results from 10 years of monitoring to address whether trends could be detected in a shorter time frame.

Using the removal sampling design, our simulations suggested that increasing the number of sites from 100 to 200 resulted in largest improvements of metrics related to precision and statistical power, but the magnitude of improvement was dependent on rates of occupancy and size of population decline. Relative bias remained < 20% as the number of sites increased regardless of initial occupancy rate and rate of population decline. When occupancy was high (0.72), improvements in RBIAS were larger as number of sites increased but was outside our acceptable benchmark of 5% even at the greatest number of sites (200;

Mean relative bias (A: 10% decline; B: 20% decline) and coefficient of variation (C) for 100–200 sites, three initial occupancy rates, and two rates of population decline following a 20-yr period, assuming a maximum of three visits and a probability of detection = 0.67. These results reflect removal sampling in which territories are not visited after they are confirmed to be occupied within a given breeding season. Gray lines indicate benchmark values for respective metrics (

Monitoring design; total duration | Metric | Number of sites | Probability of occupancy = 0.42 | Probability of occupancy = 0.57 | Probability of occupancy = 0.72 | |||
---|---|---|---|---|---|---|---|---|

10% decline | 20% decline | 10% decline | 20% decline | 10% decline | 20% decline | |||

Removal; 20 yrs | Confidence interval coverage (%) | 100 | 87.9 | 88.1 | 88.3 | 87.7 | 79.7 | 77.7 |

125 | 87.6 | 89.0 | 88.9 | 88.8 | 76.6 | 80.8 | ||

150 | 89.4 | 88.7 | 87.4 | 89.1 | 70.5 | 83.9 | ||

175 | 88.6 | 88.6 | 88.4 | 87.1 | 73.6 | 87.2 | ||

200 | 87.4 | 89.2 | 87.9 | 87.5 | 87.3 | 86.7 | ||

Statistical power (%) | 100 | 44.3 | 59.9 | 69.2 | ||||

125 | 50.1 | 63.7 | 78.5 | |||||

150 | 57.4 | 72.0 | 78.0 | |||||

175 | 58.1 | 72.2 | ||||||

200 | 61.8 | 79.2 | ||||||

Standard; 20 yrs | Confidence interval coverage (%) | 100 | 86.3 | 88.6 | 88.8 | 86.9 | 88.1 | |

125 | 89.4 | 89.1 | 88.2 | 87.2 | 89.0 | 87.3 | ||

150 | 89.3 | 89.8 | 87.1 | 87.0 | 87.1 | 85.9 | ||

175 | 89.2 | 88.2 | 88.7 | 88.2 | 87.7 | |||

200 | 88.6 | 87.3 | 88.5 | 86.2 | 86.5 | |||

Statistical power (%) | 100 | 43.8 | 58.6 | 73.0 | ||||

125 | 51.1 | 65.8 | ||||||

150 | 53.9 | 71.0 | ||||||

175 | 57.9 | 74.9 | ||||||

200 | 63.3 | |||||||

Standard; 10 yrs | Confidence interval coverage (%) | 100 | 88.3 | 87.3 | 89.1 | 85.5 | 84.6 | 86.7 |

125 | 86.3 | 88.4 | 87.3 | 86.5 | 86.7 | 86.3 | ||

150 | 87.7 | 86.9 | 87.3 | 88.7 | 85.3 | 85.8 | ||

175 | 86.1 | 87.0 | 85.9 | 87.3 | 87.3 | 86.3 | ||

200 | 88.1 | 87.2 | 88.4 | 87.7 | 87.3 | 88.1 | ||

Statistical power (%) | 100 | 19.1 | 34.4 | 23.4 | 43.7 | 34.4 | 61.1 | |

125 | 24.0 | 41.3 | 28.3 | 51.2 | 35.5 | 63.9 | ||

150 | 27.3 | 40.7 | 25.9 | 55.8 | 38.9 | 71.5 | ||

175 | 26.3 | 43.0 | 29.8 | 58.5 | 37.5 | 78.3 | ||

200 | 25.0 | 46.2 | 33.6 | 60.7 | 41.2 |

Confidence interval coverage (%) and statistical power (%) for 100–200 sites, three initial occupancy rates, and two rates of population decline following 20-yr and 10-yr monitoring periods, and assuming a maximum of three visits/breeding season and probability of detection = 0.67. Results from the removal design reflect monitoring for which territories are not visited after they are confirmed to be occupied within a given breeding season; results from the standard design reflect monitoring for which all territories are visited an equal number of times within a season. Bold font indicates values that met or exceeded benchmarks used to evaluate simulations (i.e., ≥90% confidence interval coverage and ≥80% statistical power;

Using the removal sampling design, our simulations suggested that increasing the number of visits resulted primarily in improvements of bias and precision. As the maximum number of visits increased from two to six, RBIAS decreased (

Mean relative bias (A: 10% decline; B: 20% decline) and coefficient of variation (C) for a maximum of two to six visits, two detection rates, and two rates of population decline following a 20-yr monitoring period assuming 150 sites, and initial probability of occupancy = 0.57. These results reflect removal sampling in which territories are not visited after they are confirmed to be occupied within a given breeding season. Gray lines indicate benchmark values for respective metrics (

Monitoring design; total duration | Metric | Number of visits per season | Probability of detection = 0.44 | Probability of detection = 0.79 | ||
---|---|---|---|---|---|---|

10% decline | 20% decline | 10% Decline | 20% Decline | |||

Removal; 20 yrs | Confidence interval coverage (%) | 2 | 69.5 | 63.7 | 82.1 | 89.0 |

3 | 79.6 | 79.1 | 88.4 | 91.5 | ||

4 | 85.0 | 83.8 | ||||

5 | 88.6 | 88.3 | 89.5 | 89.3 | ||

6 | 88.8 | 88.6 | 89.3 | |||

Statistical power (%) | 2 | 70.4 | 65.5 | |||

3 | 68.2 | 71.2 | ||||

4 | 70.4 | 73.7 | ||||

5 | 73.2 | 72.6 | ||||

6 | 70.6 | 71.3 | ||||

Standard; 20 yrs | Confidence interval coverage (%) | 2 | 66.7 | 66.3 | 87.7 | 87.3 |

3 | 80.5 | 78.3 | 89.8 | 89.0 | ||

4 | 82.8 | 85.1 | 89.9 | 86.9 | ||

5 | 88.7 | 85.9 | ||||

6 | 86.9 | 88.6 | 88.9 | 89.2 | ||

Statistical power (%) | 2 | 65.1 | 72.8 | |||

3 | 72.8 | 73.7 | ||||

4 | 70.8 | 72.2 | ||||

5 | 68.8 | 69.5 | ||||

6 | 73.0 | 74.5 | ||||

Standard; 10 yrs | Confidence interval coverage (%) | 2 | 68.5 | 67.7 | 87.6 | 86.8 |

3 | 80.3 | 81.4 | 87.5 | 87.8 | ||

4 | 85.5 | 84.2 | 89.6 | 86.2 | ||

5 | 86.6 | 87.5 | 89.9 | 88.7 | ||

6 | 87.8 | 87.2 | 87.0 | 88.5 | ||

Statistical power (%) | 2 | 39.2 | 54.2 | 30.7 | 54.2 | |

3 | 33.4 | 53.9 | 26.5 | 54.2 | ||

4 | 32.6 | 53.0 | 28.1 | 55.3 | ||

5 | 27.6 | 52.7 | 28.7 | 53.2 | ||

6 | 31.0 | 53.0 | 28.4 | 54.7 |

Confidence interval coverage (%) and statistical power (%) for a two to six visits per site, two detection rates, and two rates of population decline following 20-yr and 10-yr monitoring periods, assuming 150 sites and initial probability of occupancy = 0.57. Results from the removal design reflect monitoring for which territories are not visited after they are confirmed to be occupied within a given breeding season; results from the standard design reflect monitoring for which all territories are visited an equal number of times within a season. Bold font indicates values that met or exceeded benchmarks used to evaluate simulations (i.e., ≥90% confidence interval coverage and ≥80% statistical power;

For the standard sampling design, increasing number of sites resulted in greatest improvement of precision and statistical power. Relative bias was < 10% and often < 5%; increasing the number of sites from 100 to 200 did not improve RBIAS under scenarios we evaluated (

Mean relative bias (A: 10% decline; B: 20% decline) and coefficient of variation (C) for 100–200 sites, three initial occupancy rates, and two rates of population decline following a 20-yr monitoring period, assuming three visits and a probability of detection = 0.67. These results reflect a standard sampling design in which all territories are visited an equal number of times within a season. Gray lines indicate benchmark values for respective metrics (

For the standard sampling design, increasing number of visits resulted in greatest improvement of bias and precision. Increasing from two to six visits reduced RBIAS most when the rate of detection was lower (0.44;

Mean relative bias (A: 10% decline; B: 20% decline) and coefficient of variation (C) for two to six visits to each site, two detection rates, and two rates of population decline following a 20-yr monitoring period, assuming 150 sites and initial probability of occupancy = 0.57. These results reflect a standard sampling design in which all territories are visited an equal number of times within a season. Gray lines indicate benchmark values for respective metrics (

For the standard sampling design, the number of years of monitoring (10 vs. 20) had the largest effect on precision and statistical power. There was no clear difference in patterns of RBIAS (Figs

Mean relative bias (A: 10% decline; B: 20% decline) and coefficient of variation (C) for 100–200 sites, three occupancy rates, and two rates of population decline following a 10-yr monitoring period, assuming three visits and a probability of detection = 0.67. These results reflect a standard sampling design in which all territories are visited an equal number of times within a season. Gray lines indicate benchmark values for respective metrics (

Mean relative bias (A: 10% decline; B: 20% decline) and coefficient of variation (C) for two to six visits to each site, two detection rates, and two rates of population decline following a 10-yr monitoring period, assuming 150 sites and initial probability of occupancy = 0.57. These results reflect a standard sampling design in which all territories are visited an equal number of times within a season. Gray lines indicate benchmark values for respective metrics (

For the removal design, lower probability of detection (0.44) generally resulted in higher values of RBIAS (

For the standard sampling design, detection probability had similar effects as the removal design on all four evaluation metrics. Lower detection probability (0.44) resulted in higher RBIAS, but RBIAS approached our acceptable level of 5% at 4–5 visits (Figs

For the removal sampling scheme, initial occupancy primarily affected measures of precision and statistical power. Initial occupancy influenced RBIAS but only when occupancy was high (

For the standard sampling scheme, initial probability of occupancy primarily affected precision and statistical power. Initial probability of occupancy had almost no effect on RBIAS for 20 years of monitoring, which remained acceptable at all three occupancy probabilities (

Under the removal sampling design, rate of population decline had the greatest effect on precision and statistical power. Population decline had less influence on RBIAS than the probability of occupancy (

For the standard sampling design, rate of population decline had little effect on changes in RBIAS when increasing the number of sites (Figs

We demonstrated through simulation that a site-occupancy framework for monitoring ferruginous hawks or other territorial, low-density raptors has the power to detect population declines as small as 10% after a 20-year period under certain conditions of site occupancy and detection rates, many of which have empirical justification. Our results further the science of species monitoring by demonstrating the impact of decisions regarding trade-offs between number of sites and number of visits, and how these trade-offs are influenced by demographic parameters. Similar to Barata et al. [

Any site-based monitoring program will be affected by three general types of influence: survey effort, such as the number of sites to be monitored, number of visits to a site, and total duration of the monitoring program; the observation process, which is affected by the probability of detection, and demographic parameters related to occupancy such as change in regional population size and associated population dynamics, and initial occupancy rates. We have shown that demographic rates influence the ability of a particular suite of sampling parameters to detect changes in occupancy. Thus, over the course of a 20-yr monitoring period, a monitoring program with fixed sampling parameters will vary in its ability to detect population trends.

The trade-off between number of sites and number of visits should be evaluated when deciding on the structure of a monitoring program for raptors. In our study, increasing the number of sites improved nearly every metric we used to evaluate trend estimation, whereas increasing the number of visits primarily improved CI coverage and RBIAS (but not after 3–4 visits within a season). This was not surprising: increasing replication of sites has previously been reported to improve the ability to detect population trends [

The total duration of monitoring influenced the power to detect trends in occupancy more strongly than any other variable related to survey effort, with a 20-yr monitoring program resulting in much more reliable trend estimates. The effect of temporal scale that we observed on the ability to detect a trend is not unusual; 10–20 years has been identified in other studies as the minimum duration of monitoring required to detect population trends for many species with any reasonable statistical power and depending on the amount of variation in the sample [

Probability of detection is an important consideration when designing monitoring programs because of its influence on accuracy of estimates of population parameters [

Higher initial occupancy improved precision and power, a pattern observed in previous power analyses [

Estimating site occupancy status over multiple breeding seasons allows estimation of local extinction and colonization, vital demographic rates by which species respond to changes in environmental conditions. Extinction and colonization rates may reflect changes in population size or may reflect changes in the spatial distribution of raptors (i.e., local immigration or emigration). Altered geographic distribution may be particularly important to consider in light of effects that changing landscapes and climate may impose upon raptor populations. As habitat continues to be converted and prey populations respond to changing environmental conditions, it is possible that raptors could colonize previously unused portions of their geographic ranges and shift their local and regional distributions. Some nest-based studies have addressed this issue by adding new nest sites or territories to samples as they are discovered [

Although we present data from a study of ferruginous hawks, our simulations can be applied to other raptor species that may have similar life history and population dynamics to provide guidance for future surveys of territory occupancy rates and trend estimation. However, simulations are rarely complete (i.e., every possible combination of scenarios cannot reasonably be simulated), and multiple assumptions regarding initial probability of occupancy, detection, extinction, and annual rates of population change must be made. Thus, these simulations are meant to be a guide for developing monitoring programs and may need to be refined following additional data collection.

We are grateful to B. Oakleaf and Z. Walker, Wyoming Game and Fish Department, for providing logistical and technical support throughout the study, and L. A. Starcevich at Western Ecosystems, Inc. for assistance with analysis.