Spatially balanced designs that incorporate legacy sites

Foster, Scott D.; Hosack, Geoffrey R.; Lawrence, Emma; Przeslawski, Rachel; Hedge, Paul; Caley, M. Julian; Barrett, Neville S.; Williams, Alan; Li, Jin; Lynch, Tim; Dambacher, Jeffrey M.; Sweatman, Hugh; Hayes, Keith R.

doi:10.1111/2041-210x.12782

Cited by 30 publications

(38 citation statements)

References 33 publications

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“…Following from Foster et al. (), we sample proportional to a Gaussian Kernel,

f false(D false) = 1 - exp false(- D^{2} false/ σ^{2} false),

where σ controls the area of influence around legacy units. It is necessary in this case to re‐scale the inclusion probabilities so that they sum to n .…”

Section: Methodsmentioning

confidence: 99%

“…Spatially balanced designs use a local neighbourhood variance (LNV) estimator (Stevens & Olsen, ), but as the proportion of legacy units is increased the LNV tends to underestimate true variance (Foster et al., ). If the

n_{l}

legacy units and the

n_{b}

augmented units are considered separately, the population mean can be estimated using the convex combination

\overset{false^}{normalμ} = (\frac{n_{l}}{n}) {\overset{μ}{true}}_{l} + (\frac{n_{b}}{n}) {\overset{μ}{true}}_{b},

where

{\overset{false^}{normalμ}}_{l}

and

{\overset{false^}{normalμ}}_{b}

the sample means of the legacy and augmented units, respectively.…”

Section: Methodsmentioning

confidence: 99%

“…Scenarios similar to Foster et al. () using the program R (R Core Team, ) were run. We used an overall sample size of n = 60 and a number of legacy units

(n_{l} \in 3, 4, \dots, 57)

were generated either as SRS or SS.…”

Section: Methodsmentioning

confidence: 99%

“…In practice, model‐based estimation is often used and any analyses should account for the spatial aspect of the design as in Foster et al. ().…”

Section: Methodsmentioning

confidence: 99%

“…Otherwise, use LNV (n l < 3) or the legacy variance estimator (n b < 4) for all points. In practice, model-based estimation is often used and any analyses should account for the spatial aspect of the design as inFoster et al (2017).…”

mentioning

confidence: 99%

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Using balanced acceptance sampling as a master sample for environmental surveys

Dam‐Bates¹,

Gansell²,

Robertson

2018

Methods Ecol Evol

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Well‐designed environmental monitoring programmes for management organisations are important for evidence‐based decision making. However, many environmental problems are not single agency issues that require intervention or monitoring at one spatial scale. A master sample can be used to coordinate and scale monitoring designs to ensure consistency in information gathered and robustness of estimators at the different spatial scales. We propose using balanced acceptance sampling (BAS) to generate a master sample. In this context, practical applications and justification of BAS as a master sample are addressed. These include sample generation, stratification, unequal probability sampling, rotating panel designs, and regional intensification. A method for incorporating legacy sites is also provided. Using BAS as a master sample is conceptually simple, gives good spatial balance over different spatial scales, and is computationally efficient to generate. An example for terrestrial biodiversity monitoring in New Zealand is provided. Environmental monitoring can benefit from increased coordination between agencies. A master sample is an excellent way to incorporate coordination directly into the sample design. BAS improves on methods previously described and provides an effective method to monitor populations at multiple spatial scales.

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“…Following from Foster et al. (), we sample proportional to a Gaussian Kernel,

f false(D false) = 1 - exp false(- D^{2} false/ σ^{2} false),

where σ controls the area of influence around legacy units. It is necessary in this case to re‐scale the inclusion probabilities so that they sum to n .…”

Section: Methodsmentioning

confidence: 99%

n_{l}

legacy units and the

n_{b}

augmented units are considered separately, the population mean can be estimated using the convex combination

\overset{false^}{normalμ} = (\frac{n_{l}}{n}) {\overset{μ}{true}}_{l} + (\frac{n_{b}}{n}) {\overset{μ}{true}}_{b},

where

{\overset{false^}{normalμ}}_{l}

and

{\overset{false^}{normalμ}}_{b}

the sample means of the legacy and augmented units, respectively.…”

Section: Methodsmentioning

confidence: 99%

“…Scenarios similar to Foster et al. () using the program R (R Core Team, ) were run. We used an overall sample size of n = 60 and a number of legacy units

(n_{l} \in 3, 4, \dots, 57)

were generated either as SRS or SS.…”

Section: Methodsmentioning

confidence: 99%

“…In practice, model‐based estimation is often used and any analyses should account for the spatial aspect of the design as in Foster et al. ().…”

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

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Using balanced acceptance sampling as a master sample for environmental surveys

Dam‐Bates¹,

Gansell²,

Robertson

2018

Methods Ecol Evol

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Non‐invasive mark–resight surveys for brown bears: Incorporating spatial information to improve landscape‐scale monitoring of density and distribution

Schmidt,

Deacy,

Hughes

et al. 2023

Ecol Sol and Evidence

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Effective wildlife monitoring and management are reliant on unbiased estimators of population parameters. Most standard survey approaches ignore spatial pattern in the data although spatial relationships can be leveraged to produce more efficient designs for future surveys, thereby reducing project cost. Landscape‐scale surveys for brown bears are notoriously expensive and difficult to complete, leading to the development of a non‐invasive mark–resight aerial survey approach as a practical alternative to more commonly employed approaches for estimating brown bear density across large areas. Here we extend that model to accommodate spatial covariate information and explicitly model residual spatial autocorrelation. Using brown bear survey data from northwestern Alaska, USA from 2015 to 2021, we demonstrate how our extension can be useful in exploring ecological factors related to spatial variation in bear density and detection probability. We found that detection probability was higher in more rugged terrain, and occurrence probability was higher at mid‐elevations where denning habitat was more prevalent and in areas with more salmon streams. The descriptive model of residual autocorrelation confirmed that additional unmeasured factors were associated with bear distribution. While these findings were not unexpected, they are very useful when considering future survey effort. Using this information, we explored a hypothetical redesign of the 2021 brown bear survey that removed 50% of the survey subunits with elevation values below the mean, where bears were least likely to occur. We demonstrated that the resulting estimates were unbiased, suggesting that adopting the spatial approach to analysis could reduce overall project costs by ~20%–30% going forward. Overall, our work indicates that directly accounting for spatial pattern within the non‐invasive mark–resight framework has substantive advantages over the original non‐spatial approach and may be useful in increasing the amount of information available for brown bear populations.

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