Assessing Survey Design for Long-Term Population Trend Detection in Piping Plovers

Abstract

Determining appropriate spatio-temporal scales for monitoring migratory shorebirds is challenging. Effective surveys must detect population trends without excessive or insufficient sampling, yet many programs lack formal evaluations of survey effectiveness. Using data from 2012 to 2019 on Louisiana’s barrier islands (Whiskey, west Raccoon, east Raccoon, and Trinity), we assessed how spatial and temporal scales influence population trend inference for piping plovers (Charadrius melodus). Point count data were aggregated to grid sizes from 50 to 200 m and analyzed using Bayesian dynamic occupancy models. We found occupancy and colonization estimates varied by spatial resolution, with space–time autocorrelation common across scales. Smaller islands (east and west Raccoon) yielded higher trend detection power due to better detectability, while larger islands (Trinity and Whiskey) showed lower power. Detectability, more than sampling frequency, drove trend inference. Models incorporating spatial autocorrelation outperformed traditional Frequentist approaches but showed poorer fit at coarser scales. These findings underscore how matching analytical scale to ecological processes and selecting appropriate models can influence predictions. Power analysis revealed that increasing survey frequency may improve inference, especially in low-detectability areas. Overall, our study highlights how careful scale selection, model diagnostics, and survey design can enhance monitoring efficiency and support long-term conservation of migratory shorebirds.

1. Introduction

Sustained population monitoring of threatened and endangered species provides critical insights to guide conservation planning and management strategies [1,2,3]. To achieve effective conservation monitoring, survey designs can address uncertainties related to sampling design and scale, ensuring sufficient power to detect changes in population trends or address underlying scientific questions [4,5]. Statistical power analyses, often employed alongside initial survey baseline data and estimates, can help to optimize monitoring efforts. This adaptive approach allows for the identification of alternative designs to update existing programs [3,6,7].

The development of field sampling protocols includes careful consideration of several factors: the size and number of sampling units, plot placement, sampling duration, spacing of samples, and the study’s time horizon [8,9]. Additional considerations include (a) the suitability of presence–absence versus count data as a sampling scheme [10], (b) the necessity of tracking abundance versus occupancy trends for conservation prioritization [11], and (c) budgetary constraints [12]. The efficacy of a sampling scheme depends on these factors and influences the effort required to detect population trends over time.

Common sampling designs involve repeated surveys at sampled sites and distinct locations, which can generate presence–absence data [13]. Occupancy models accommodate presence–absence data while addressing errors from imperfect detection [14] and spatial autocorrelation [15]. The spatial scale and number of sites for a species are typically determined by the organism’s home range or a human-defined scale. Research on occupancy scale indicates that the spatial grain, extent, and number of temporal replicates can influence occupancy definitions and estimates [16]. During field data collection, presence/absence or count data are collected at one scale and analyzed across multiple scales to determine the optimal scale for analysis [17].

Recent advancements in occupancy modeling frameworks provide tools for allocating survey effort effectively. Asymptotic variance approximations are used to determine appropriate replications and sample sites when sample sizes are large [18]. Statistical power analyses help optimize the frequency of temporal surveys to approximate occupancy estimators [6] and assess projected population declines, considering spatial scale, site number, and survey duration [19]. Power analyses simulate spatial and temporal variations to determine the minimum survey frequency and spatial scale necessary to detect changes in occupancy over time.

Dynamic occupancy models, when sufficient data are available, offer effective simulations for determining spatial scale and survey frequency [20]. Basic single-season occupancy models assume population closure within a survey period, which may lead to limitations in assessing endangered or threatened species if the period is too short [21]. Multi-season or multi-year datasets can be analyzed using dynamic occupancy models, which incorporate state–space formulations to address trends and drivers over time [22,23]. These models offer insights into species turnover and the dynamics of site occupancy probabilities resulting from colonization and extinction over extended periods.

Spatial autocorrelation presents additional challenges in modeling species distributions and abundance [24,25,26]. Autocorrelation arises in time–space models where spatial dependencies or site connectivity through dispersal processes exist [27,28]. Statistical models must address the assumption that residuals are independent and identically distributed [29]. Hierarchical spatial modeling approaches are increasingly used to account for spatial autocorrelation [20,30]. Incorporating spatial terms to distinguish neighborhood effects, such as autologistic models that extend logistic presence–absence models with spatial components and neighborhood weights, enhances model accuracy [31,32,33,34,35]. These models introduce a spatial term that includes neighborhood size, with weights assigned to each element to capture the dependencies among neighboring observations [36,37].

Populations of the piping plover (Charadrius melodus), a migratory shorebird, are highly sensitive to even minor declines in its vital rates, such as adult and juvenile survival. This sensitivity underscores how preserving and protecting both migratory and wintering habitats can support populations [38]. Conservation efforts are complicated by the fact that breeding and wintering sites are geographically disparate [39]. Piping plovers spend approximately ten months annually (July–May) on migration and wintering grounds, demonstrating site fidelity during winter [39]. Key wintering areas include the shorelines of North Carolina, South Carolina, Georgia, Florida, Alabama, Mississippi, Louisiana, and Texas, encompassing 1793 miles and 165,211 acres designated as federal critical habitat [38]. Monitoring piping plovers across their range can be both time-consuming and costly yet provides information for detecting population declines.

To enhance monitoring efficiency, we analyzed seven years of baseline data collected on the barrier islands of Louisiana. Our study examines the impact of spatial grain at various grid sizes to determine the optimal scale for dynamic occupancy models. We utilize space–time Moran’s I to assess residual autocorrelation and apply autologistic dynamic occupancy models to understand both spatial and temporal autocorrelation [40]. By evaluating model fit using goodness-of-fit measures, we aim to identify the most effective analytical scale for dynamic occupancy models, including those incorporating autologistic spatial terms. This research addresses challenges related to occupancy studies, particularly discrepancies and issues arising from sampling scale.

Optimizing survey efforts often involves simulating monitoring scenarios through power analyses to determine the minimum effort required to detect population trends. Our use of dynamic occupancy models, based on seven years of baseline surveys, provides estimates of occupancy, colonization, and extinction rates, facilitating power analyses. Although current survey efforts are extensive, this study aims to examine the frequency and intensity of surveys for the most suitable temporal and spatial scales for understanding occupancy trends over time.

2. Materials and Methods

2.1. Study Area

This study focuses on several barrier islands within the Isles Dernieres chain off the Louisiana coast, including Whiskey Island (29.1945° N, −90.7771° W), east Raccoon Island (29.2221° N, −90.7796° W), west Raccoon Island (29.2342° N, −90.8121° W), and Trinity Island (29.2617° N, −90.8587° W) (Figure 1). These islands serve as barriers, protecting inland marshes and mangrove forests from saltwater intrusion and pollution from the Deepwater Horizon oil spill in 2010 [41]. These islands are part of a dynamic coastal environment that provides essential habitat for a variety of wildlife, including migratory shorebirds, which rely on these environments during migration and non-breeding periods [42,43]. A mix of sandy beaches, salt marshes, and mangrove forests characterizes the islands’ habitats [42,44]. The climate is classified as subtropical, with hot, humid summers and mild winters. Precipitation is frequent, with the region experiencing seasonal variations in rainfall and occasional extreme weather events, such as hurricanes, which can significantly alter island topography and vegetation [42,45].

2.2. Study Species: Piping Plovers

Piping plovers are divided into two subspecies: C. m. melodus, breeding along the Atlantic Coast of the USA and Canada, and C. m. circumcinctus, breeding in the Northern Great Plains of the USA and Canada as well as the Great Lakes [38]. Both subspecies are listed as threatened or endangered in various regions [46]. Conservation efforts, including International Piping Plover Winter Censuses conducted every five years since 1991, indicate regional population fluctuations. For example, wintering populations in Louisiana declined from 750 individuals in 1991 to 86 individuals in 2011 [47]. Factors influencing population trends include localized weather, habitat quality, and anthropogenic impacts [47], such as coastal development and recreational use of beach habitats [48]. Conservation interventions have focused on key regions such as the Great Lakes and critical wintering habitats [49]. Previous research has shown that tidal stages influence piping plovers that prefer sand flat islands [50]. Understanding the species’ sensitivity to environmental changes and various ecological scenarios can inform effective management efforts. Degradation of coastal shorebird habitats has led to declines in species like the piping plover, as changes in beach environments reduce prey availability and disrupt foraging and roosting areas [51]. Anthropogenic disturbances have been linked to lower body mass and survival rates in piping plovers [51].

2.3. Data Collection

Data collection followed standardized protocols set by the U.S. Geological Survey (USGS). Surveys were conducted throughout the year (2012–2019) during beach patrol surveys [52]. Surveyors (two per survey, working independently) employed an area search protocol and covered all suitable shorebird habitat by foot on each survey, ensuring consistent coverage of the island throughout the survey period [53]. This protocol allowed observers to maximize detections by limiting the need to search more than 100 m on either side of a survey track. Surveyors collected fine-scale data for all focal shorebird species including piping plover and four additional shorebird species (Wilson’s plover (Charadrius wilsonia), snowy plover (Charadrius nivosus), American oystercatcher (Haematopus palliatus), and red knot (Calidris canutus)). The data collection included latitude–longitude coordinates (using global positioning system technology) for the locations of all individual birds detected. Surveys were conducted during all seasons year-round (2012–2019) (

Table 1. Number of surveys conducted each year from 2012 to 2019 during peak migratory season across different islands—Trinity, west Raccoon, Whiskey, and east Raccoon. Cells marked “NA” indicate years when no surveys were recorded for that island.

Year	Trinity	West Raccoon	Whiskey	East Raccoon
2012	11	12	12	NA
2013	10	10	21	2
2014	15	13	21	NA
2015	8	15	32	2
2016	2	4	34	3
2017	4	1	30	4
2018	NA	NA	28	NA
2019	NA	NA	2	NA

), though only Whiskey Island was surveyed every year. Data are available in [45] (https://doi.org/10.5066/P93MVS0S).

The surveys resulted in 1789 observations of piping plovers after filtering the data to the dates of the peak migratory season (September to March) across years and islands (

Table 2. Annual Piping Plover population observations by location during peak migratory season (September to March) from 2012 to 2019. The “-” indicates there was no survey conducted.

Island	2012	2013	2014	2015	2016	2017	2018	2019	Total
East Raccoon	-	13	-	13	42	78	-	-	146
Trinity	31	101	87	42	5	19	-	-	285
West Raccoon	169	130	44	75	-	-	-	-	418
Whiskey	70	59	103	179	163	187	170	9	940

). Observers recorded species, behavior (breeding, foraging, or leisure), and tide stage. The number of surveys during the peak migration season was subset (Table 1). Models were run separately for each island based on these refined temporal subsets. The data were then collated into grid cells and transformed into presence/absence data for analysis in an occupancy framework, separately for each survey year.

2.4. Grid Scales

The presence/absence data were collated into grids for occupancy analysis. We applied various grid sizes (15 m, 25 m, 50 m, and 100 m) within the island boundaries (Figure 2). We filtered the grids for a “Plover-Only Subset” to include only cells with at least one plover detection over the duration of the study.

2.5. Modeling Frameworks

Occupancy models utilize repeated detection/non-detection data to simulate species presence–absence, acknowledging that some species might be present but not detected [14,54]. These models are hierarchical and typically extend from Bernoulli generalized linear models (GLMs), zero-inflated binomial models, or logistic regressions [55]. The core structure of an occupancy model includes two linked Bernoulli regressions: one for spatial variation in occurrence and another for the spatio-temporal variation in detection/non-detection data at specific sites [56]. This framework allows for integration of models for species occurrence (Equations (1) and (5)) with models for imperfect detection (Equations (4) and (6)). Covariates can be included to account for variability in presence and detection across sites (Equation (8)) [14]. To extend this framework to dynamic occupancy models, we incorporate probabilistic random processes to explain transitions between occupied and unoccupied states. This extension models the probability of sites becoming unoccupied (1 − ϕ) and experiencing “extinction” (Equations (3) and (7)), as well as the probability of sites transitioning from unoccupied to occupied, also modeled with a Bernoulli distribution, with the probability of remaining unoccupied (1 − γ) (Equations (2) and (5)).

Occupancy Model Structure:

$$\mathrm{Occupancy}: z_{i,1}~Bernoulli\left({\Psi }_i\right)$$

(1)

$$\mathrm{Colonization}: z_{i,t+1}=1|z_{i,t}=1~Bernoulli(\varphi )$$

(2)

$$\mathrm{Extinction}: z_{i,t+1}=1|z_{i,t}=0~Bernoulli(\gamma )$$

(3)

$$\mathrm{Observation}: y_{i,j,t}|z_{i,t}~Bernoulli(z_t{p}_{i,j,t})$$

(4)

$${logit(\mathsf{\Psi }}_i)=\alpha$$

(5)

$${logit(\varphi }_{i,t})=\alpha$$

(6)

$${logit(\gamma }_i,\mathrm{t})=\alpha$$

(7)

Covariate information is added to the detection model on the logit scale.

$${logit(p}_{i,j,t})=\alpha +{\beta }_1 \ast Julian Da{y}_{i,j,t}+{\beta }_2 \ast Julian Da{y}_{i,j,t}^2+{\beta }_3 \ast Tide Stag{e}_{i,j,t}$$

(8)

Here, i denotes sites, j represents temporal repetitions within the season, and t indicates the year. Models were initially fitted using the unmarked package in R to obtain maximum likelihood estimates and perform goodness-of-fit tests [57]. Bayesian models were subsequently fitted using the jagsUI package in R [58]. For Bayesian analyses, non-informative priors were employed with three chains, 10,000 iterations, a burn-in of 1000, and thinning of 10. Model convergence was assessed with R-hat values less than 1.1.

2.6. Autologistic Terms

Autologistic terms, previously applied to logistic regression [35] and more recently to dynamic occupancy models [20,59,60,61,62], include spatial terms to account for local neighborhood grid cells or first-order neighbors (i.e., the eight adjacent cells surrounding any given grid cell) [30]. If neighboring cells are occupied, the likelihood of occupancy in the focal cell increases.

Autocovariate terms are defined as the spatially weighted mean of presence/absence data in neighborhood locations (Equation (9)) [30,32,34,63]:

$$aut{o}_{i,t}={\displaystyle \frac{{\sum }_{j=1}^{k_i}{w}_i{y}_{i,t}}{{\sum }_{j=1}^{k_i}{w}_i}}$$

(9)

where y_it represents the presence/absences, w_i denotes the weights, and k_i is the neighborhood size around the sample i at time t [30].

The inclusion of this autocovariate term in the dynamic occupancy model modifies the colonization and extinction components as follows (Equations (10) and (11)):

$${logit(\varphi }_{i,t})={\alpha }_{phi}+{\beta }_{phi} \ast aut{o}_{i,t}$$

(10)

$${logit(\gamma }_{i,t})={\alpha }_{gamma}+{\beta }_{gamma} \ast aut{o}_{i,t}$$

(11)

This neighborhood spatial term estimates the number of occupied cells in the previous year using a Queen’s neighborhood matrix with eight surrounding cells [40]. The presence of occupied neighboring cells in the prior year increases the likelihood of continued plover presence in the focal cell.

We employed both Frequentist and Bayesian approaches to dynamic occupancy modeling to compare model performance across frameworks. The Frequentist models were implemented using the unmarked package [57] in program R 3.6.3, which estimates parameters via maximum likelihood and relies on asymptotic properties for inference, such as confidence intervals and p-values. In contrast, Bayesian models were implemented using custom JAGS code [64] in program R 3.6.3, which incorporates prior distributions and uses posterior distributions derived from Markov Chain Monte Carlo (MCMC) sampling for inference. Unlike Frequentist models, Bayesian methods provide full probability distributions for parameters and allow more flexible modeling structures, such as incorporating autocovariate effects (e.g., spatial or temporal dependence) [56]. This dual approach allowed us to evaluate the robustness of occupancy dynamics under differing statistical assumptions.

2.7. Space–Time Moran’s I

Spatial-temporal Moran’s I was employed to examine Pearson Chi-squared residuals from the unmarked models for spatial and temporal autocorrelation. Moran’s I was adjusted for spatial-temporal distances using an anisotropic covariance function, providing an overall measure of autocorrelation across space and time. Moran’s I was also calculated for each survey day across all grid cells, with significance determined by p-values. Temporal autocorrelation of residuals was assessed using the Durbin–Watson test [40].

2.8. Goodness-of-Fit

For the unmarked models, goodness-of-fit (GoF) was evaluated using the Pearson’s chi-squared test [65,66]. The overdispersion parameter (c-hat) was calculated as the ratio of the observed to expected chi-squared statistic to assess model fit and potential overdispersion.

For the Bayesian models fitted in JAGS, GoF was assessed through posterior predictive checks, which compare discrepancy measures—specifically Chi-squared and Freeman–Tukey statistics—between the observed dataset and simulated replicates drawn from the posterior predictive distribution this approach provides Bayesian analogs to c-hat by estimating overdispersion as the ratio of observed to expected discrepancy values across the posterior samples. These GoF techniques enable separate evaluation of the open (occupancy, colonization, extinction) and closed (detection) components of the dynamic occupancy models [56,67].

2.9. Power Analysis

Power analyses were conducted via simulations to determine the necessary number of sites and surveys to achieve optimal power for detecting trends over a 10-year period [20]. Dynamic occupancy estimates for occupancy, colonization, extinction, and detection were used to simulate data. The simulations varied site and survey parameters using the AHMbook package in R [20]. This classical approach to power analysis involved simulating datasets with a predefined effect—in this case, a 20% decline in occupancy probability (proportion of occupied sites) over 10 years. For each simulated dataset, models were fitted and the p-value of the trend test recorded, with power calculated as the proportion of simulations yielding a statistically significant result. The simulations varied the number of sites and survey replicates to identify the optimal allocation of sampling effort given a fixed total number of visits. Detection probability (p) was also varied across datasets. Specifically, a factorial design compared four sampling allocations totaling 500 visits (e.g., 250 sites × 2 surveys, 100 sites × 5 surveys, 50 sites × 10 surveys). The results demonstrated that power to detect the 20% decline ranged from approximately 17% to 80%, increasing with both the number of sites and surveys, but more rapidly with increasing site numbers. Notably, power more than doubled when sampling shifted from 20 sites with 25 surveys to 250 sites with 2 surveys, highlighting how maximizing spatial replication can help to improve trend detection.

3. Results

3.1. Space–Time Moran’s I

The results of the unmarked models applied to both the Full Grid and the Plover Subset Grid across various islands indicate distinct spatial and temporal autocorrelation patterns (Appendix A 

Table A1. Results from unmarked models for (A) Full Grid or (B) Plover-Only Subset Grid over each island. Space–time Moran’s I for each scale and each island are reported separately, along with grid scale, # grid cells, and final space–time autocorrelation p-values.

Island	Scale	Percent Temporal Autocorrelation	# Grid Cells	Percent Spatial Autocorrelation	Space–Time Autocorrelation (p-Value)
(A) Full Grid
East Raccoon	50	0	435	37.5	0
East Raccoon	100	0	110	25	0.004
East Raccoon	150	0	51	12.5	0.014
East Raccoon	200	0	28	12.5	0.042
Trinity	50	0	1549	29	0.00
Trinity	100	0	394	17	0.00
Trinity	150	0	177	13	0.00
Trinity	200	2	103	25	0.00
West Raccoon	50	0	178	0	0.00
West Raccoon	100	0	44	0	0.062
West Raccoon	150	0	20	0	0.356
West Raccoon	200	0	11	0	0.479
Whiskey	50	107.088	1690	5.714	0.00
Whiskey	100	72.066	426	9.091	0.00
Whiskey	150	59.474	190	9.091	0.00
Whiskey	200	44.762	105	9.091	0.00
(B) Plover Subset
East Raccoon	50	0	60	0	0.872
East Raccoon	100	0	40	0	0.461
East Raccoon	150	0	30	0	0.404
East Raccoon	200	0	21	0	0.437
Trinity	50	0.61	163	0.00	0.01
Trinity	100	0.00	104	4.17	0.00
Trinity	150	0.00	81	4.17	0.00
Trinity	200	3.51	57	4.17	0.00
West Raccoon	50	1.538	65	0	0.00
West Raccoon	100	3.226	31	6.667	0.00
West Raccoon	150	12.5	16	0	0.00
West Raccoon	200	0	11	0	0.00
Whiskey	50	40.82	343	7.69	0.00
Whiskey	100	33.89	180	6.15	0.00
Whiskey	150	36.89	122	18.46	0.00
Whiskey	200	25.97	77	16.92	0.00

). For the Full Grid, east Raccoon, Trinity, west Raccoon, and Whiskey Islands were evaluated at grid scales ranging from 50 m to 200 m. Temporal autocorrelation was consistently low or absent across most islands and scales, while spatial autocorrelation showed moderate values, particularly on east Raccoon (37.5% at the 50 m scale) and Trinity (25% at the 200 m scale). Space–time autocorrelation was significant across most grid scales (p < 0.05), except for higher scales on west Raccoon, where p-values exceeded 0.05. For the Plover Subset Grid, the analysis similarly revealed limited temporal autocorrelation across most islands, with slight increases at higher grid scales on Trinity (3.51% at 200 m) and west Raccoon (12.5% at 150 m). Spatial autocorrelation was relatively low but was highest on Whiskey Island (18.46% at the 150 m scale). Space–time autocorrelation was significant (p < 0.05) across all grid scales and islands, except for east Raccoon, where p-values were non-significant at all scales.

In summary, space–time autocorrelation was largely significant across grid scales, with notable spatial variation between islands and low temporal autocorrelation in the Plover Subset Grid, indicating the necessity of the autologistic terms.

3.2. Model Estimates

The results of the unmarked dynamic occupancy models, Bayesian dynamic occupancy models, and dynamic autologistic models for both the Full Grid and the Plover Subset reveal differences in colonization (Col), extinction (Ext), detection probability (p), and occupancy (Psi) estimates across different spatial scales and islands (Appendix A 

Table A2. Model estimates from three dynamic occupancy modeling approaches: unmarked (MLEs), Bayesian, and dynamic autologistic models. Results are shown for (A) the Full Grid and (B) Plover-Only Subset. Mean parameter estimates are shown with 95% credible intervals in parentheses for Bayesian and autologistic models, as well as 95% confidence intervals for MLEs.

			Unmarked Estimates			Dynamic Occupancy			Dynamic Autologistic
Scale	Island		MLEs	(2.50–97.50%)		Mean	(2.50–97.50%)		Mean	(2.50–97.50%)
	(A) Full Grid
50	Whiskey	Psi	0.053	0.038	0.073	0.072	0.04	0.118	0.068	0.042	0.107
		Col	0.459	0.369	0.551	0.412	0.134	0.617	0.657	0.347	0.875
		Ext	0.041	0.034	0.050	0.031	0.004	0.058	0.842	0.561	0.969
		P	0.046	0.036	0.059	0.04	0.021	0.066	0.036	0.009	0.163
100	Whiskey	Psi	0.123	0.088	0.169	0.152	0.093	0.218	0.150	0.101	0.226
		Col	0.312	0.229	0.409	0.346	0.131	0.558	0.663	0.188	0.942
		Ext	0.077	0.061	0.097	0.055	0.008	0.105	0.884	0.554	0.986
		P	0.075	0.060	0.094	0.073	0.045	0.113	0.045	0.012	0.123
150	Whiskey	Psi	0.188	0.133	0.259	0.229	0.155	0.321	0.237	0.149	0.338
		Col	0.273	0.192	0.372	0.269	0.114	0.434	0.565	0.231	0.879
		Ext	0.104	0.079	0.136	0.069	0.006	0.141	0.840	0.550	0.978
		P	0.112	0.091	0.138	0.106	0.072	0.152	0.044	0.004	0.107
200	Whiskey	Psi	0.300	0.212	0.405	0.345	0.239	0.468	0.410	0.276	0.544
		Col	0.248	0.164	0.355	0.202	0.054	0.376	0.696	0.236	0.971
		Ext	0.137	0.097	0.191	0.139	0.025	0.275	0.892	0.645	0.985
		P	0.136	0.111	0.167	0.126	0.079	0.176	0.075	0.003	0.215
50	Trinity	Psi	0.109	0.066	0.175	0.131	0.058	0.293	0.175	0.079	0.385
		Col	0.423	0.238	0.634	0.698	0.448	0.875	0.296	0.007	0.967
		Ext	0.050	0.032	0.078	0.085	0.015	0.162	0.682	0.205	0.991
		P	0.045	0.028	0.071	0.059	0.018	0.118	0.019	0.001	0.093
100	Trinity	Psi	0.215	0.147	0.302	0.258	0.161	0.385	0.310	0.204	0.408
		Col	0.260	0.133	0.445	0.265	0.024	0.526	0.557	0.014	0.979
		Ext	0.050	0.026	0.096	0.048	0.002	0.128	0.463	0.014	0.950
		P	0.092	0.064	0.133	0.103	0.06	0.159	0.042	0.000	0.137
150	Trinity	Psi	0.338	0.230	0.465	0.405	0.223	0.589	0.519	0.391	0.645
		Col	0.313	0.181	0.484	0.459	0.215	0.672	0.629	0.048	0.988
		Ext	0.113	0.066	0.186	0.125	0.008	0.29	0.553	0.033	0.971
		P	0.127	0.089	0.178	0.143	0.085	0.238	0.030	0.000	0.116
200	Trinity	Psi	0.446	0.313	0.588	0.405	0.223	0.589	0.610	0.474	0.767
		Col	0.237	0.127	0.399	0.459	0.215	0.672	0.693	0.148	0.993
		Ext	0.098	0.043	0.207	0.125	0.008	0.29	0.499	0.037	0.957
		P	0.168	0.121	0.230	0.143	0.085	0.238	0.038	0.001	0.134
50	West Raccoon	Psi	0.683	0	1	0.539	0.04	0.992	0.452	0.029	0.954
		Col	0.011	0	1	0.557	0.035	0.97	0.548	0.000	1.000
		Ext	0.000	0	1	0.474	0.03	0.964	0.453	0.000	1.000
		P	0.000	0	1	0	0	0.001	0.569	0.000	1.000
100	West Raccoon	Psi	0.989	0	1	0.465	0.018	0.953	0.488	0.021	0.990
		Col	0.000	0	1	0.529	0.038	0.981	0.520	0.000	1.000
		Ext	0.006	0	1	0.437	0.016	0.957	0.447	0.000	1.000
		P	0.002	0	0.092	0	0	0.004	0.469	0.000	1.000
150	West Raccoon	Psi	0.006	0	1	0.508	0.021	0.973	0.543	0.027	0.983
		Col	0.007	0	1	0.539	0.029	0.986	0.666	0.000	1.000
		Ext	0.149	0	1	0.459	0.036	0.963	0.575	0.000	1.000
		P	0.007	0	1	0.001	0	0.005	0.571	0.000	1.000
200	West Raccoon	Psi	0.001	0	1	0.5	0.014	0.974	0.537	0.049	0.983
		Col	0.001	0	1	0.552	0.024	0.978	0.634	0.000	1.000
		Ext	0.227	0.006	0.931	0.433	0.023	0.947	0.484	0.000	1.000
		P	0.025	0.001	0.780	0.004	0	0.019	0.469	0.000	1.000
50	East Raccoon	Psi	0.446	0.293	0.073	0.547	0.107	0.978	0.355	0.070	0.968
		Col	0.011	0.211	0.000	0.475	0.018	0.901	0.257	0.000	0.874
		Ext	0.071	0.200	0.000	0.48	0.024	0.965	0.276	0.000	0.951
		P	0.031	0.018	0.009	0.031	0.008	0.097	0.232	0.000	1.000
100	East Raccoon	Psi	0.999	0.100	0.000	0.641	0.224	0.981	0.598	0.228	0.940
		Col	0.308	0.150	0.530	0.337	0.019	0.799	0.199	0.000	0.750
		Ext	0.000	0.000	1.000	0.522	0.044	0.971	0.214	0.000	0.767
		P	0.100	0.046	0.204	0.084	0.033	0.218	0.083	0.000	0.791
150	East Raccoon	Psi	0.995	0.145	0.000	0.542	0.163	0.972	0.640	0.217	0.984
		Col	0.174	0.116	0.041	0.349	0.022	0.827	0.140	0.000	0.800
		Ext	0.002	0.090	0.000	0.657	0.085	0.983	0.103	0.000	0.650
		P	0.148	0.054	0.070	0.203	0.06	0.463	0.532	0.000	1.000
200	East Raccoon	Psi	0.393	0.133	0.731	0.501	0.185	0.958	0.510	0.167	0.966
		Col	0.574	0.196	0.881	0.537	0.077	0.937	0.437	0.000	0.967
		Ext	0.922	0.000	1.000	0.736	0.188	0.987	0.250	0.000	0.760
		P	0.283	0.113	0.552	0.31	0.105	0.637	0.802	0.000	1.000
	(B) Plover Subset
50	Whiskey	Psi	0.246	0.176	0.332	0.364	0.200	0.642	0.329	0.182	0.651
		Col	0.508	0.402	0.614	0.460	0.157	0.683	0.244	0.002	0.725
		Ext	0.292	0.235	0.357	0.213	0.040	0.388	0.411	0.040	0.931
		P	0.051	0.040	0.065	0.041	0.019	0.071	0.380	0.016	0.853
100	Whiskey	Psi	0.278	0.200	0.373	0.357	0.237	0.505	0.382	0.243	0.571
		Col	0.375	0.282	0.477	0.353	0.126	0.570	0.443	0.107	0.788
		Ext	0.252	0.202	0.309	0.169	0.015	0.307	0.359	0.120	0.646
		P	0.083	0.067	0.104	0.077	0.047	0.120	0.181	0.017	0.348
150	Whiskey	Psi	0.291	0.207	0.391	0.359	0.247	0.494	0.364	0.252	0.498
		Col	0.300	0.215	0.403	0.267	0.127	0.439	0.205	0.045	0.465
		Ext	0.193	0.148	0.248	0.130	0.018	0.255	0.197	0.036	0.446
		P	0.121	0.098	0.149	0.109	0.072	0.159	0.127	0.016	0.262
200	Whiskey	Psi	0.405	0.289	0.532	0.473	0.326	0.610	0.512	0.353	0.682
		Col	0.285	0.195	0.396	0.213	0.074	0.378	0.091	0.014	0.255
		Ext	0.230	0.166	0.310	0.224	0.035	0.402	0.148	0.033	0.338
		P	0.148	0.120	0.182	0.128	0.087	0.189	0.175	0.004	0.445
50	Trinity	Psi	0.769	0.413	0.940	0.609	0.283	0.985	0.808	0.501	0.994
		Col	0.309	0.030	0.867	0.439	0.020	0.820	0.202	0.000	0.801
		Ext	1.000	0.000	1.000	0.795	0.109	0.999	0.250	0.000	0.868
		P	0.060	0.036	0.097	0.114	0.049	0.224	0.917	0.091	1.000
100	Trinity	Psi	0.780	0.407	0.948	0.829	0.598	0.989	0.826	0.569	0.990
		Col	0.357	0.180	0.582	0.147	0.005	0.453	0.154	0.001	0.660
		Ext	0.668	0.320	0.896	0.422	0.035	0.947	0.130	0.002	0.523
		P	0.100	0.068	0.146	0.117	0.076	0.171	0.756	0.124	1.000
150	Trinity	Psi	0.733	0.429	0.909	0.788	0.522	0.979	0.832	0.557	0.991
		Col	0.335	0.181	0.535	0.317	0.041	0.579	0.231	0.003	0.583
		Ext	0.562	0.317	0.779	0.628	0.079	0.982	0.367	0.004	0.841
		P	0.128	0.089	0.182	0.155	0.094	0.236	0.664	0.027	1.000
200	Trinity	Psi	0.806	0.453	0.954	0.835	0.615	0.993	0.863	0.658	0.992
		Col	0.277	0.151	0.452	0.397	0.162	0.613	0.473	0.082	0.938
		Ext	0.421	0.211	0.663	0.684	0.090	0.986	0.191	0.006	0.630
		P	0.172	0.123	0.238	0.183	0.117	0.257	0.471	0.020	0.985
50	West Raccoon	Psi	0.711	0.352	0.917	0.686	0.463	0.965	0.741	0.480	0.968
		Col	0.521	0.263	0.769	0.392	0.043	0.720	0.244	0.000	0.854
		Ext	0.466	0.214	0.737	0.538	0.082	0.950	0.230	0.000	0.813
		P	0.154	0.090	0.255	0.157	0.078	0.259	0.773	0.009	1.000
100	West Raccoon	Psi	0.639	0.409	0.819	0.665	0.441	0.866	0.692	0.468	0.922
		Col	0.525	0.339	0.705	0.340	0.030	0.672	0.277	0.011	0.666
		Ext	0.386	0.217	0.589	0.481	0.059	0.907	0.556	0.080	0.899
		P	0.319	0.209	0.462	0.289	0.152	0.440	0.715	0.088	1.000
150	West Raccoon	Psi	0.675	0.386	0.873	0.656	0.407	0.905	0.652	0.414	0.901
		Col	0.377	0.202	0.590	0.289	0.023	0.585	0.230	0.006	0.600
		Ext	0.356	0.154	0.627	0.591	0.140	0.949	0.602	0.072	0.971
		P	0.410	0.268	0.583	0.352	0.178	0.523	0.490	0.006	0.979
200	West Raccoon	Psi	0.658	0.341	0.878	0.630	0.348	0.866	0.635	0.370	0.905
		Col	0.426	0.214	0.669	0.249	0.013	0.607	0.169	0.000	0.560
		Ext	0.387	0.151	0.690	0.611	0.080	0.966	0.567	0.000	0.946
		P	0.448	0.278	0.653	0.534	0.323	0.754	0.632	0.012	1.000
50	East Raccoon	Psi	0.364	0.189	0.584	0.711	0.332	0.994	0.796	0.383	0.995
		Col	0.697	0.332	0.914	0.275	0.015	0.743	0.090	0.000	0.649
		Ext	1.000	0.000	1.000	0.702	0.094	0.994	0.056	0.000	0.485
		P	0.197	0.114	0.319	0.197	0.083	0.416	0.810	0.000	1.000
100	East Raccoon	Psi	0.999	0.000	1.000	0.602	0.243	0.973	0.637	0.272	0.986
		Col	0.000	0.000	1.000	0.315	0.012	0.776	0.141	0.000	0.743
		Ext	0.968	0.000	1.000	0.764	0.223	0.995	0.087	0.000	0.664
		P	0.150	0.088	0.245	0.287	0.102	0.587	0.864	0.000	1.000
150	East Raccoon	Psi	0.514	0.179	0.837	0.523	0.218	0.975	0.536	0.209	0.952
		Col	0.351	0.065	0.808	0.527	0.040	0.933	0.398	0.000	0.932
		Ext	1.000	0.000	1.000	0.787	0.290	0.993	0.189	0.000	0.770
		P	0.262	0.132	0.453	0.374	0.136	0.686	0.908	0.165	1.000
200	East Raccoon	Psi	0.424	0.182	0.709	0.644	0.241	0.982	0.736	0.360	0.990
		Col	0.557	0.258	0.819	0.400	0.014	0.868	0.242	0.000	1.000
		Ext	0.999	0.000	1.000	0.659	0.063	0.992	0.243	0.000	0.969
		P	0.358	0.192	0.568	0.151	0.063	0.343	0.789	0.000	1.000

Abbreviations: Psi = occupancy probability; Col = colonization probability; Ext = extinction probability; P = detection probability; MLEs = maximum likelihood estimates.

). The Bayesian Dynamic Occupancy model generally produced estimates with narrower confidence intervals compared to models incorporating autologistic terms. The inclusion of spatial terms in the models led to wider variances in estimates overall, although these models provided presumably more accurate fine-scale occupancy estimates.

For the Full Grid models, Whiskey Island shows higher occupancy (Psi) estimates at larger spatial scales, with Psi increasing from 0.053 at the 50 m scale to 0.300 at the 200 m scale. Bayesian models generally estimate higher Psi values compared to unmarked models. For example, the 200 m scale on Whiskey shows a Psi of 0.345 in the Bayesian model compared to 0.300 in the unmarked model. Trinity Island shows a similar pattern, with higher occupancy estimates at larger spatial scales, reaching 0.446 at the 200 m scale. In contrast, west Raccoon has lower and more variable occupancy estimates across scales, with a Psi of 0.001 at the 200 m scale in the unmarked model but 0.537 in the dynamic autologistic model. Detection probability (p) is generally lower across all islands but tends to increase with scale.

In the Plover-Only Subset, the dynamic autologistic models yield higher Psi estimates compared to the unmarked models, particularly at larger spatial scales. For example, on Whiskey Island, Psi ranges from 0.246 at the 50 m scale to 0.405 at the 200 m scale in the unmarked models, while the dynamic autologistic model estimates range from 0.329 to 0.512 at the same scales. Trinity Island consistently shows high occupancy across all models, with Psi estimates peaking at 0.806 in the unmarked models and 0.863 in the dynamic autologistic models at the 200 m scale.

Overall, the best-fit models according to GoF tests indicate that the Bayesian dynamic occupancy models and the dynamic autologistic models generally provide better estimates of occupancy and colonization/extinction dynamics, particularly at larger spatial scales, across the Full Grid and Plover Subset. The GoF evaluation employed the MacKenzie and Bailey test [65], extended for use with Bayesian dynamic occupancy models through posterior predictive checks and chi-squared ratio tests, as described by Kéry and Royle [56]. Our approach uses these statistics to identify models that do not exhibit lack of fit rather than to select a single best model. This reflects a focus on model adequacy rather than traditional model selection. The results highlight spatial heterogeneity in species occupancy across islands and emphasize how scale influences interpretation of dynamic occupancy patterns.

3.3. Goodness-of-Fit

The GoF tests for the dynamic models, applied to both the Full Grid and Plover-Only Subset, revealing varying levels of model fit across islands and spatial scales (Appendix A 

Table A3. Goodness-of-fit (GoF) results for dynamic occupancy models across the Full Grid (A) and Plover-Only Subset (B). MacKenzie and Bailey GoF test results from the unmarked models (columns: p-value, c-hat, Chisq, fT) are shown, alongside Bayesian model results. For Bayesian dynamic occupancy models—with and without autologistic (autocovariance) terms—GoF was assessed separately for the open (occupancy, colonization, extinction) and closed (detection) parts of the model using posterior predictive checks and Chi-squared ratio tests. Bolded values in the table indicate model fits closest to expected values.

		Unmarked Dynamic				Bayesian Dynamic		Bayesian Dynamic Autologistic
Scale	Island	p-Value	ĉ	Chisq	fT	Open	Closed	Open	Closed
	(A) Full Grid
50	Whiskey	0.105	1.232	118,215	730	1.043	1.464	0.999	1.493
100	Whiskey	0.000	530	29,313	641	1.036	1.681	1.205	1.684
150	Whiskey	0.000	1500	12,818	575	0.816	2.067	1.319	2.069
200	Whiskey	0.000	235	7001	512	0.918	1.032	0.79	1.039
50	West Raccoon	0.273	1.367	178	2	1.502	905	1.129	2456
100	West Raccoon	0.073	3.586	303	4	1.093	193,805	19.736	104,556
150	West Raccoon	0.613	1.393	19	2	1.372	141	5.856	340
200	West Raccoon	0.137	1.897	51	3	0.998	8143	1.12	48,129
50	Trinity	0.093	1.560	37,346	332	0.911	1.008	0.95	1.053
100	Trinity	0.072	1.861	9328	293	0.813	1.134	0.997	1.23
150	Trinity	0.022	2.385	4094	260	0.746	1.253	1.01	1.294
200	Trinity	0.013	2.600	2303	235	1.038	1.098	1.127	1.107
50	East Raccoon	0.045	2.197	6931	97	56.523	1.103	232.057	1.085
100	East Raccoon	0.062	1.944	3428	93	0.391	1.048	0.458	1.042
150	East Raccoon	0.029	2.171	885	74	0.504	1.038	0.509	1.173
200	East Raccoon	0.417	1.055	373	59	0.536	1.124	0.719	1.224
	(B) Plover-Only Subset
50	Whiskey	0.072	2.19	21,818	655	0.905	1.16	0.878	1.101
100	Whiskey	0.000	282	11,230	578	1.062	1.448	1.098	1.504
150	Whiskey	0.000	1750	7512	529	1.088	1.706	1.167	1.695
200	Whiskey	0.000	273	4677	470	0.902	2.019	0.94	2.072
50	West Raccoon	0.093	1.425	915	119	0.773	1.136	0.843	1.19
100	West Raccoon	0.700	0.833	404	89	0.878	1.273	0.839	1.312
150	West Raccoon	0.588	0.892	184	56	0.8	1.333	0.796	1.335
200	West Raccoon	0.334	1.045	121	39	0.653	1.265	0.657	1.426
50	Trinity	0.237	1.004	3754	279	0.888	0.902	0.892	0.994
100	Trinity	0.093	1.651	2336	248	0.907	0.934	0.939	0.967
150	Trinity	0.043	2.252	1786	228	0.913	1.132	0.952	1.171
200	Trinity	0.025	2.392	1216	206	0.873	1.202	0.874	1.228
50	East Raccoon	0.03	2.09	421	69.31	1294	0.912	170	0.997
100	East Raccoon	0.04	1.98	272	58.41	0.653	0.897	0.751	1.048
150	East Raccoon	0.04	2.01	196	49.83	0.508	0.985	0.641	1.058
200	East Raccoon	0.52	0.92	130	38.11	0.697	1.029	0.518	1.159

Abbreviations: p-value = significance level from the GoF test; c-hat = overdispersion estimate; Chisq = Chi-squared test statistic; fT = Freeman–Tukey statistic; “Open” = goodness-of-fit for the open model components (occupancy, colonization, extinction); “Closed” = goodness-of-fit for the closed component (detection).

B). GoF tests for the dynamic models, summarized in Appendix A (Table A3), were conducted using the MacKenzie and Bailey GoF test within the unmarked framework, reporting p-values, overdispersion parameters (c-hat, ĉ), and Chi-squared and Freeman–Tukey (fT) statistics [20]. For the Bayesian dynamic occupancy models—with and without autocovariance terms—GoF was evaluated separately for the open components (occupancy, colonization, and extinction) and the closed component (detection) using Chi-squared ratio tests [20]. These analyses were applied to both the Full Grid (Appendix A Table A3A) and Plover-Only Subset (Appendix A Table A3B), enabling assessment of model fit across islands and spatial scales.

For the Full Grid, several islands showed poor fit in unmarked models, particularly at larger spatial scales. For example, Whiskey Island at the 100 m, 150 m, and 200 m scales had p-values of 0.000 and high ĉ values, indicating overdispersion. In contrast, smaller scales (e.g., 50 m scale for Whiskey Island) exhibited better model fit with a p-value of 0.105 and lower ĉ values. Bayesian dynamic and autologistic models generally improved fit, but the closed detection part of the models sometimes showed elevated values (e.g., ĉ = 1.681 for the 100 m scale on Whiskey Island).

West Raccoon Island had better model fit at smaller scales (e.g., p = 0.273 at 50 m scale) but worse at higher scales (p = 0.137 at 200 m scale). The Bayesian models improved fit across both open and closed parts of the models, although some large differences persisted, particularly in the closed detection component (e.g., ĉ = 19.736 at the 100 m scale for the Bayesian model on west Raccoon).

For the Plover-Only Subset, the results followed a similar pattern. Larger scales on Whiskey Island (100 m, 150 m, and 200 m) had poor fit in the unmarked models (p = 0.000), but smaller scales showed better fit (p = 0.072 at the 50 m scale). West Raccoon Island also exhibited better fit at smaller scales (p = 0.093 at 50 m scale) and poorer fit at higher scales. The Bayesian models, particularly those with autocovariance terms, generally improved model fit, though some large discrepancies remained in closed detection components.

Overall, the GoF tests suggest that dynamic occupancy models perform better at smaller spatial scales, while Bayesian models with autocovariance terms improve model fit across both grids and subsets. However, challenges remain in fitting the closed detection part of the models at larger scales.

3.4. Power Analysis

Power analysis simulations, utilizing estimates for occupancy, colonization, extinction, and detectability, were conducted to assess the statistical power to detect trends in occupancy across various spatial scales and islands. These simulations were stratified by island and grid size, spanning scales of 50 m to 200 m (

Table 3. Power analysis results by island and data subset. The number of simulated sites and surveys corresponds to baseline grid sizes (50 m, 100 m, 150 m, and 200 m), yielding different total site counts. Table values indicate the statistical power to detect a trend over 5-, 10-, 15-, and 20-year periods.

East Raccoon—All Grids					Whiskey—All Grid
Number of sites	2	5	10	15	Number of sites	10	15	20	30
30	0.168	0.244	0.289	0.303	100	0.011	0.091	0.013	0.009
50	0.213	0.295	0.366	0.395	190	0.002	0.003	0.01	0.013
110	0.317	0.477	0.573	0.582	420	0.055	0.077	0.124	0.169
430	0.59	0.684	0.746	0.756	1600	0.005	0.025	0.064	0.204
East Raccoon—Plover Only					Whiskey—Plover Only
Number of sites	2	5	10	15	Number of sites	10	15	20	30
20	0.095	0.118	0.164	0.325	77	0.052	0.093	0.011	0.032
30	0.126	0.164	0.208	0.211	120	0.06	0.127	0.107	0.118
40	0.147	0.188	0.271	0.293	180	0.004	0.007	0.013	0.013
60	0.169	0.261	0.347	0.393	340	0.053	0.076	0.104	0.196
West Raccoon—All Grids					Trinity—All Grids
Note					Number of sites	5	10	15	20
Models did not fit the data enough to run a power analysis					100	0.395	0.139	0.267	0.129
					180	0.116	0.128	0.112	0.103
					390	0.256	0.123	0.093	0.093
					1550	0.556	0.061	0.076	0.039
West Raccoon—Plover Only					Trinity—Plover Only
Number of sites	5	10	15	20	Number of sites	5	10	15	20
10	0.121	0.109	0.127	0.148	50	0.161	0.055	0.107	0.058
15	0.127	0.132	0.182	0.206	80	0.15	0.22	0.125	0.09
30	0.139	0.213	0.272	0.323	100	0.365	0.09	0.097	0.089
60	0.195	0.309	0.432	0.455	160	0.091	0.088	0.063	0.043

). The results indicate significant variability in the ability to detect occupancy trends across islands, primarily influenced by the size of the islands and the frequency of surveys.

Whiskey and Trinity Islands showed considerably low power to detect occupancy trends. For instance, at Whiskey Island, power remained below 0.1 across most survey configurations; even with the highest number of sites surveyed (1600 sites), power only reached 0.204. Similarly, Trinity Island showed a maximum power of 0.556 at its largest survey scale of 1550 sites, but this dropped significantly as the number of surveys decreased. The larger geographic size of these islands may contribute to the lower power, indicating that even extensive survey efforts might be insufficient to detect subtle trends.

Conversely, east and west Raccoon Islands demonstrated higher power to detect these trends, attributed to their smaller sizes and possibly more effective survey strategies or higher detectability. East Raccoon Island showed a peak power of 0.756, with 430 sites surveyed 15 times, and west Raccoon showed progressive increases in power with more surveys, reaching up to 0.455 with 60 sites surveyed 20 times.

These findings highlight how detection probabilities can influence the power to detect occupancy trends. Detection probabilities for west Raccoon were notably higher (0.234, 0.448) compared to those for Trinity (0.067, 0.2) and Whiskey (0.085, 0.2), which correlated with higher power values. East Raccoon, with intermediate detection probabilities (0.089, 0.34), showed correspondingly moderate power levels.

The number of sites and the frequency of surveys are pivotal factors, particularly on larger islands, where increasing these parameters may enhance the power to detect ecological changes. The results underscore how tailored survey designs that consider both island size and inherent detectability can be used to optimize monitoring efforts for conservation and management objectives.

4. Discussion

This study utilized spatio-temporal modeling to evaluate the occupancy of piping plovers within different islands in the Louisiana barrier islands, aiming to inform future survey strategies. The power analysis conducted across four islands—Whiskey, Trinity, east Raccoon, and west Raccoon—reveals substantial insights into the efficacy of occupancy surveys in detecting ecological trends. The analysis underscores how survey scale, frequency, and the underlying detectability rates can influence the statistical power of ecological studies.

Our study employed a dynamic occupancy modeling framework to estimate colonization and extinction probabilities across spatial and temporal gradients. This approach was well suited to our data structure, which consisted of detection/non-detection observations with repeated visits across multiple seasons and sites. While alternative methods such as dynamic N-mixture models for counts can also estimate dynamic processes [68], they generally require more intensive data to produce robust estimates, and have shown to incur issues with inflated estimates [52]. Other models investigating shorebird trends have also attempted a modeling framework that adds abundance information in N-mixture models [69]. Studies have used state–space models like a simple Gompertz model [3,70] to determine trends in abundance instead of using a dynamic occupancy model like in this study. Alternative modeling frameworks may reveal different results unexplored in this study, such as examining nested multi-scale estimates. Population trends for the piping plover species could provide additional information as there is an overall lack of knowledge on species trends or drivers of potential declines. Given the sparsity of detections and the prevalence of zero observations, as well as spatial autocorrelation, across gridded sites in our dataset, dynamic occupancy models provided a robust and interpretable means of quantifying colonization and extinction parameters, which were then used in the downstream power analysis.

4.1. Variation in Power Across Island Sizes and Survey Frequencies

The analysis highlighted a stark contrast in detection power between larger islands (Whiskey and Trinity) and smaller ones (east and west Raccoon). Whiskey Island and Trinity Island showed lower power to discern trends in occupancy, despite more surveys having been conducted. This is attributed to their large area, possibly diluting the results due to lower detectability rates across the island. It is also plausible that these islands support fewer total animals in a more clustered distribution, contributing to lower overall occupancy. We recognize that detection probability and abundance are often positively correlated—higher abundance generally increases the likelihood of detection [65]. This finding suggests that the current survey strategies might not be sufficiently robust or frequent enough to capture subtle ecological changes within these larger islands. Current survey efforts on Trinity Island and Whiskey Island between October and March—or even more surveys—are unlikely to satisfy trend detection due to the inherently low occupancy and detectability on these larger islands. The study highlights how assessing monitoring scales and frequencies through power analyses can help to enhance trend detection, yet with sparse data this can be difficult. Our results underscore that detection probabilities and the appropriate scale of analysis influence power analyses. Conversely, east and west Raccoon Islands demonstrated higher power to detect occupancy trends, attributed to higher detectability rates and smaller island sizes. East Raccoon, in particular, shows a marked improvement in power with an increase in the number of surveys, highlighting how enhanced survey frequency can impact trend detection efficacy. These disparities in power among the islands are influenced predominantly by differences in detectability probabilities, which can inform planning effective monitoring strategies. High detectability not only improves the power to detect real changes in occupancy but also can help to support conservation efforts based on reliable and accurate data.

4.2. Effects of Spatial Resolution on Occupancy and Detection Estimates

Our analysis emphasized how sampling and analytical scales can shape model estimates. We observed that adjusting the grid to include only plover-specific data increased occupancy probability but did not significantly improve detection of a trend through power analysis. The models demonstrated variable performance across different islands, highlighting how spatial scale influences ecological studies. For instance, larger scales tended to yield higher occupancy estimates, as seen with Whiskey Island where occupancy (Psi) increased substantially with scale in both Bayesian and unmarked models. Across different scales, the detection probability (P) for various sites consistently fluctuates, with some locations exhibiting much lower detection probabilities at certain grid sizes (e.g., Whiskey Island at 50 m). This variability suggests that sampling frequency and spatial scale can impact estimates of detectability. For example, at the 50 m scale, some sites like west Raccoon have very low mean P, indicating the model is unable to resolve the estimate at such a fine resolution. At smaller scales (e.g., 50 m), detection probability is often lower for most sites, suggesting that finer-scale grids may deter the estimation of detectability due to spatial resolution limitations or sparse occurrences within small areas. Detection probability increases as the scale broadens (e.g., at 100 m, 150 m, and 200 m). This indicates that larger spatial grids are more likely to capture species detectability, which could be a result of a more comprehensive sampling area that increases the chances of estimating detectability for the species, which became the most impactful estimate for the power analysis. In particular, west Raccoon and Whiskey Island show an increase in detection as the scale moves from 50 m to 200 m, suggesting that detection is very sensitive to spatial resolution. Occupancy (Psi) consistently increases with larger spatial scales, particularly at 100 m and 200 m. This is a clear trend, especially for the Whiskey Island data, where occupancy rates increase notably as the grid size grows. For smaller scales (like 50 m), occupancy rates are generally lower, implying that finer scales may underrepresent the species’ presence, or the grid size is too small to capture their true habitat range. Colonization rates also show a positive relationship with scale, with larger scales (100 m, 150 m, and 200 m) yielding higher colonization probabilities. This suggests that at larger scales, the habitat patches are more likely to be colonized by the species, likely due to the greater area available for movement and settlement. At smaller scales, the colonization probabilities appear more variable, with lower values in many cases, particularly in the Plover-Only Subset, where the results for east Raccoon and west Raccoon fluctuate significantly at the 50 m scale. This trend suggests that larger spatial extents may capture more comprehensive patterns of habitat use, potentially increasing detectability and the accuracy of occupancy estimates. However, this also introduces challenges, such as overdispersion, which was evident from the high ĉ values at larger scales on Whiskey Island.

4.3. Influence of Spatial Autocorrelation on Model Fit

Across both the Full Grid and the Plover-Only Subset, the Bayesian dynamic occupancy models demonstrated improved model performance when an autologistic (spatial autocovariance) term was included. This was most apparent in the open (state) component of the model, where inclusion of spatial dependence frequently brought fit metrics closer to unity, particularly at intermediate and larger scales. The closed (detection) component showed less variability across scales, suggesting that detectability may be less sensitive to changes in spatial grain than occupancy dynamics. Additionally, the Plover-Only Subset generally exhibited better model fit (lower ĉ and higher p-values) than the Full Grid, indicating that restricting the analysis to a species-relevant spatial domain can reduce unexplained heterogeneity. Together, these results emphasize that both spatial resolution and species-specific data selection can help to achieve reliable model performance in dynamic occupancy frameworks.

Bayesian dynamic occupancy models generally produced more precise estimates, indicated by narrower confidence intervals. This precision can inform management decisions, especially in conservation areas reliant on species occupancy data. The dynamic autologistic models, which included spatial autocorrelation terms, offered detailed insights at finer scales but also introduced greater variance in the estimates. This variance could reflect a more realistic uncertainty in the models or be an artifact of the complexity introduced by spatial terms. While autologistic terms offered detailed spatial estimates, they did not enhance trend detection compared to models without these terms. Although sophisticated spatially explicit simulation methods exist, parameterizing spatial dynamic occupancy models appropriately is complex. The most impactful parameter for the power analysis was having an accurate estimate for detectability.

4.4. Model Precision and the Role of Bayesian Frameworks

Our assessment of model performance across spatial scales provides empirical support for the conclusion that optimal resolution varies by process and site, and that scale aggregation can degrade model fit if ecological processes are not scale-invariant. Patterns in Appendix A Table A3 illustrate that model GoF in unmarked dynamic occupancy models often deteriorated with increasing grid size, especially on Whiskey Island. For example, at the 50 m resolution, p-values for Whiskey were acceptable (e.g., 0.105) but dropped to 0.000 at 100 m and coarser scales, with substantial inflation of the overdispersion parameter (ĉ > 500 at 100 m and 1500 at 150 m in the Full Grid). These patterns suggest that coarsening the resolution can obscure spatial signals, leading to misfit. However, this was not universally true across all islands. On west Raccoon, model fit remained relatively stable or even improved at coarser scales, particularly in the Plover-Only Subset, where p-values remained > 0.3 and ĉ values were near or below 1 at 100–200 m resolutions. This variation indicates that scale effects are context-dependent, being, in our case, dependent on what seems to be scarcity of the data on larger islands, and they could be empirically evaluated for each landscape or monitoring objective.

Further evidence comes from the Bayesian dynamic models, which showed that including spatial autocovariance terms improved model fit in many cases, especially for the occupancy (open) component. Fit metrics for the open process often approached 1.0 with the autologistic term, even at coarser scales (e.g., east Raccoon, 200 m: open ChiSq = 0.719 with autocovariance vs. 0.536 without). This suggests that incorporating spatial structure may partly offset the loss of resolution and help stabilize model inference when using aggregated data. Additionally, restricting the analysis to a Plover-Only Subset consistently improved GoF metrics, indicating that focusing on species-relevant subsets can reduce noise and improve detectability of scale effects.

4.5. Comparison Between Frequentist and Bayesian Model Performance

We used both Frequentist and Bayesian models, motivated by the desire to explore how each framework handles the data and provides estimates of occupancy and colonization/extinction dynamics, particularly at different spatial scales. The GoF tests underscored significant discrepancies in model performance, particularly between different types of models and scales. The results demonstrate that both the Bayesian dynamic occupancy models and the dynamic autologistic models (which also use a Bayesian framework) generally provide more reliable estimates compared to the Frequentist unmarked models, especially at larger spatial scales. Poor fits at larger scales in the unmarked models suggest that these models may not adequately account for spatial heterogeneity or autocorrelation, which are better handled by Bayesian models and those incorporating autocovariance terms. The improved fit of Bayesian models on smaller scales, as observed with west Raccoon Island, indicates their robustness in environments where detectability might otherwise be compromised. The use of both Frequentist and Bayesian models was intended to assess the reliability and robustness of the estimates, with the Bayesian models offering greater flexibility in handling uncertainty and spatial heterogeneity.

4.6. Broader Context and Relevance to Conservation Monitoring

Prior studies have employed power analyses and state–space modeling to explore variability in survey frequency and predict declining trends in species populations [70,71]. Ecological monitoring programs differ in their effectiveness at detecting population trends [3]. Accurate local estimates at key migratory sites can advance understanding population trends and inform design of effective conservation interventions. Given the observed declines in piping plover populations, this study provides new insights into the challenges of designing robust monitoring programs over extended periods, as well as the downstream analytical framework for fine scale count data, particularly in sandy beach environments where demarcated sampling locations are limited.

4.7. Recommendations for Future Research and Monitoring Design

Future research could extend this study by standardizing the data collection workflows, as well as modeling all islands simultaneously with block effects to determine if larger more coordinated sampling units reveal more pronounced trends island-wide. It is possible that standardized surveys with finer-scale grid units over larger areas likely yield more reliable population surveys to detect trends over time than surveying the individual islands separately.

We focused our analysis on the non-breeding season, a period when shorebirds are not bound to nest sites and may range more widely in response to foraging opportunities, disturbance, or environmental conditions. This seasonal context does present challenges for the closure assumption traditionally required in occupancy models. While data on individual movement during the non-breeding season are limited, previous studies have shown relatively high site fidelity across years, with birds often returning to the same wintering grounds—particularly when foraging resources are abundant and human disturbance is minimal [39]. It is not certain whether the birds in our study regularly return to the same islands or redistribute among nearby islands. At this fine spatial scale of data collection, uncertainty about movement patterns raises questions about both geographic closure and individual site fidelity. Additionally, incorporating habitat covariates—distance to shore, Julian date, elevation, habitat type (mud or sand), vegetation cover (<25%, 25–50, 50–75, 75–100) could assist in designing surveys. Other occupancy based surveys have included these factors [52]. Data from UAVs could also be incorporated due to the shifting shoreline. Finally, studies could help to distinguish between broader-scale habitat selection for stopover sites and fine-scale selection within each island.

5. Conclusions

This study presents findings from applying dynamic occupancy models and conducting a comprehensive power analysis to piping plover detection and occupancy data across multiple Louisiana barrier islands and spatial scales. These methodologies have elucidated the complexity of species distribution dynamics and have underscored how adaptive survey designs can be tailored to the specific ecological contexts of each study area. The results have demonstrated that the sensitivity of occupancy estimates varies considerably across spatial scales and model types. Larger scales generally yield higher occupancy estimates, as observed on Whiskey and Trinity Islands, but are also prone to issues such as overdispersion, which affects the robustness of the results. These scales are considerations when designing surveys and interpreting occupancy data. The Bayesian dynamic occupancy models and dynamic autologistic models showed generally better performance, providing narrower confidence intervals and accounting for spatial autocorrelation more effectively. These models can be especially useful in fine-scale habitat studies for understanding the spatial distribution of species. However, the simplicity of unmarked models may still be useful in broader-scale studies or initial surveys less focused on detailed spatial dynamics. The goodness-of-fit analysis highlighted how model fit can help to ensure the reliability of ecological assessments. The identified discrepancies across different scales and model types indicate how evaluation of model performance can support conservation strategies based on the most reliable data.

Effective accurate power analysis projections include a thorough understanding of baseline colonization and extinction rates. In this study, we provided baseline estimates from dynamic occupancy models across various spatial scales and identified the most appropriate scale through goodness-of-fit tests. Given the prevalent spatial autocorrelation observed in both temporal and spatial dimensions, we incorporated an autologistic term to evaluate the utility of fine-scale estimates that account for autocorrelation. Our power analyses indicated that detection probability and other parameters, such as colonization and extinction rates, significantly influence the outcomes of dynamic occupancy models, affected by the determination of optimal scales and temporal frequencies. These findings represent an initial step toward optimizing monitoring efforts and addressing broader scaling issues for the Louisiana barrier islands. Current monitoring efforts, which vary significantly among islands, have proven inadequate for detecting long-term trends and occupancy declines by these methods. To enhance the efficacy of monitoring programs, future efforts may aim to establish a more consistent monitoring framework that encompasses all studied islands together in one cohesive monitoring system to leverage the data together for an estimate. This approach could help to standardize data collection methodologies across different environments and improve the comparability of results, especially given unknowns about bird site fidelity across islands. Continuing to monitor these islands over longer periods and incorporating additional ecological and environmental variables could enable more robust and accurate model results. Such longitudinal studies could advance understanding long-term trends and the impacts of environmental changes on species dynamics. Future research could explore landscape-scale monitoring or adopt a multi-scale analytical approach to enhance trend detection and conservation effectiveness. In conclusion, the adaptive management of ecological monitoring strategies, guided by rigorous model selection and scale-appropriate methodologies, supports accurate detection and responses to changes in species occupancy and overall ecosystem health. These efforts can help to optimize resource allocation and provide robust and precise scientific data to inform conservation actions. This study may be informative for future research aimed at refining these strategies and enhancing the conservation of sensitive species across diverse environmental landscapes.