Chase, J.B., Huslander, B., Strum, M., Lea, C., Gutierrez, B.T., and Sterne, T.K., 2023, Assateague Island seabeach amaranth survey data—2001 to 2018: U.S. Geological Survey data release,
Gutierrez, B.T., Heslin, J.L., Henderson, R.E., Sterne, T.K., and Sturdivant, E.J., 2023, Seabeach amaranth presence-absence and barrier island geomorphology metrics as relates to shorebird habitat for Assateague Island National Seashore—2008, 2010, and 2014: U.S. Geological Survey data release,
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This work was funded by a U.S. National Park Service Northeast Region Regional Block grant. We thank Bill Hulslander and Jonathan Chase of the Natural Resources Division of Assateague Island National Seashore for providing the impetus for this work. We would also like to thank Tami Pearl, also of the Natural Resources Division of Assateague Island National Seashore. This work grew out of a long-term collaboration to study
Multiply | By | To obtain |
Length | ||
---|---|---|
inch (in.) | 2.54 | centimeter (cm) |
inch (in.) | 25.4 | millimeter (mm) |
foot (ft) | 0.3048 | meter (m) |
mile (mi) | 1.609 | kilometer (km) |
mile, nautical (nmi) | 1.852 | kilometer (km) |
yard (yd) | 0.9144 | meter (m) |
Multiply | By | To obtain |
Length | ||
---|---|---|
centimeter (cm) | 0.3937 | inch (in.) |
millimeter (mm) | 0.03937 | inch (in.) |
meter (m) | 3.281 | foot (ft) |
kilometer (km) | 0.6214 | mile (mi) |
kilometer (km) | 0.5400 | mile, nautical (nmi) |
meter (m) | 1.094 | yard (yd) |
Vertical coordinate information is referenced to the local mean high water (MHW).
Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).
Altitude, as used in this report, refers to distance above the vertical datum.
Assateague Island National Seashore
Bayesian network
Maryland Department of Natural Resources
global positioning system
Intergovernmental Panel on Climate Change
kilometer marker
Kolmogorov-Smirnov test
light detection and ranging
Maryland Department of Agriculture
National Park Service
over-sand vehicle [zone]
probability
point model
seabeach amaranth
standardized precipitation index
transect model
tree-augmented naïve Bayes
U.S. Fish and Wildlife Service
U.S. Geological Survey
In April 1993,
Map showing Assateague Island located along the mid-Atlantic coast of the United States.
Figure 1. Map showing Assateague Island located along the mid-Atlantic coast of the United States
Assateague Island is the only historically known Maryland site for SBA (
A large-scale restoration effort was undertaken at ASIS between 2000 and 2002 to re-establish the species (
Maps of Assateague Island showing
Figure 2. Maps of Assateague Island showing locations of seabeach amaranth planting sites and years planted, kilometer markers used as reference locations, and the spatial distribution of wild seabeach amaranth plants from 2001 to 2018
Despite the recognition of SBA as an important beach species, there have been few studies of its habitat preferences. Much of what has been written about SBA comes from the U.S. Fish and Wildlife Service recovery plan (
Despite the long history of monitoring at ASIS, the SBA population and the physical characteristics of where it occurs have not been studied in depth on the island. Although individual management actions have improved the probability of plant establishment and (or) growth, the relative efficacy of these efforts has yet to be evaluated. Also, the impact of individual management actions may depend upon location and the specific conditions of the year in which these actions were implemented. Because of this, NPS natural-resources staff at ASIS identified a need to conduct an in-depth evaluation of the SBA population data that have been collected since 2001 and develop a habitat model to evaluate SBA habitat suitability along ASIS. It is important to better understand SBA population variations over the last 20 years and how they may relate to barrier island morphological characteristics to better inform management efforts. Higher sea-level and more frequent and intense coastal storms due to future climate change will likely drive an increase in overwash events and create more open beach habitats along ASIS suitable to SBA. The potential effects to seashore infrastructure will require that both habitat and infrastructure needs be factored into long-term management practices. Consequently, developing a deeper understanding of the barrier island characteristics that constitute quality SBA habitat on Assateague Island can also inform future management efforts.
This report focuses on evaluating demographic and environmental monitoring data alongside physical observations of the coastal landscape to determine if there are unique physical characteristics that can describe SBA habitat and understand what may have contributed to SBA population decline. Our investigation first examines SBA population trends over a 20-year period during which SBA has been monitored at ASIS in comparison to meteorological factors. In addition, we examine the spatial distribution over this time period to determine if there are preferred settings where SBA tends to occur. While we focused on evaluating remote-sensing data sampling physical habitat characteristics, we also examined SBA population trends through comparison climatic factors such as precipitation and yearly observations of grazing to see if factors other than habitat descriptors influenced the plant population over time. Next, we evaluated physical habitat metrics using three datasets, for three different years—2008, 2010, and 2014—that capture a period when the population was relatively high (2008) and periods of decline (2010, 2014). We sampled remote sensing data via two sampling schemes to determine if there are unique characteristics where SBA tends to occur. In the last part of our analysis, we use these datasets to build probabilistic modeling frameworks, relying on Bayesian networks (BNs), to capture the essential physical barrier-island characteristics that describe suitable SBA habitat. The model framework is used to evaluate physical and environmental characteristics that occur in locations where SBA has been observed. We assess the sensitivity of predictions to different parameters in the model, which can in turn provide information to evaluate the relative importance of a variety of management actions for protecting SBA. Finally, we use prediction uncertainty to highlight knowledge gaps in our understanding of habitat preference, which can be used to guide future monitoring and management efforts.
A better physical understanding, based on the modeling parameters, of the landscape characteristics that the species prefers can help streamline monitoring efforts by allowing the most likely sites to be prioritized. This understanding can also improve management practices and increase the chance of establishing a viable SBA population on ASIS. Ultimately, the work described here is intended to provide information to support a better use of limited resources to protect the species. It also can be used to inform development of an adaptive management plan that is responsive to changing future conditions (
Assateague Island is a 60-kilometer (km)-long barrier island located along the mid-Atlantic coast of the United States. The island is oriented south-southwest, spanning the southern, ocean coast of Maryland and Virginia from Ocean City Inlet to Chincoteague Inlet (
A sustained management effort was undertaken in the early 2000s to address decades of sediment starvation resulting from the stabilization of the Ocean City Inlet (reviewed in
Aerial photograph showing the northern part of Assateague Island and southern part of Fenwick Island overlain by contours of shoreline position in 1850 and 1942, and the Ocean City Inlet that was created during a storm in August 1933 (data source:
Figure 3. Aerial photograph showing the northern part of Assateague Island and southern part of Fenwick Island overlain by contours of shoreline position in 1850 and 1942, and the Ocean City Inlet that was created during a storm in August 1933
Since the initiation of the north-end restoration project in 2002, the SBA population along ASIS has been carefully monitored and actively managed on an annual basis to support population growth and demography. The result is over a decade of detailed census data on individual plant locations and size for reintroduced and wild plants, the latter being those that germinated from seeds in the environment. In addition, seed-bank dynamics, fecundity, seed dispersal, measures of habitat quality, and ungulate grazing impacts on survival and growth have all been studied in situ.
Analyses of SBA population trends and habitat metrics were conducted in three phases. The first phase focused on examining SBA population trends and their relation to meteorological trends and grazing as well as the spatial distribution of SBA on Assateague Island. The second phase focused on sampling presence-absence data and barrier island transect characteristics to determine if there were specific physical characteristics of SBA habitat. This in turn informed the development of BNs to model SBA habitat. The BN was used to evaluate the relative importance of each parameter in contributing to suitable habitat and refined to include those environmental characteristics found to be most important to the spatial distribution of SBA over time. These phases are described in the following sections.
Existing SBA census data for ASIS (collected by ASIS staff annually since 2001) were compiled to assist in developing the environmental variables for screening (
Because we relied on an existing monitoring dataset, we did not have the ability to design and execute a data-collection protocol; therefore, our initial phase required identifying datasets and conducting exploratory data analysis of metrics describing the physical environment during the 2001–20 time period. Although there have been a number of lidar surveys of Assateague Island, relatively few cover the entire island, and a number of these surveys followed severe coastal storms when island morphology differed from that present during the SBA growing season. Consequently, we selected three lidar datasets, two of which cover the entire subaerial extent of Assateague Island (2008, 2014) and one that covers mainly the ocean side of the island but was collected near a time when the island was surveyed for SBA (August 2010). Initially, our analysis focused on 2008 data (
Table 1. Metrics recorded at each plant or random point location on Assateague Island
[Data source:
Metric | Description |
Distance from the MHW shoreline (m) | The Euclidian distance between the center of the 5 x 5 m cell surrounding each point from the MHW shoreline on the ocean side of Assateague Island. The MHW shoreline was obtained from datasets compiled by |
Elevation (m) | The mean elevation of each 5 x 5 m cell surrounding each point relative to local MHW defined by |
Slope (%) | The mean slope of each 5 x 5 m cell surrounding each point |
Aspect (degrees from north) | The compass orientation of the mean slope of each 5 x 5 m cell surrounding each point |
Distance from nearest dune (m) | The Euclidean distance to the nearest foredune crest, as compiled by |
Distance from nearest inlet (m) | The along-shoreline distance from Ocean City Inlet |
Vegetation type | The density and type of vegetation present in a 5 x 5 m cell surrounding each point. Vegetation-type shapefiles were created by the NPS staff at ASIS ( |
Distance to nearest plant from the previous year (m) | The Euclidean distance of each point from the nearest plant observed in the previous year |
Number of plants within 30 m from previous year | The number of plants encountered in a 30-m radius of each point |
Occurs with 2014 dataset only.
Our second sampling strategy used measurements derived from lidar collected in 2008 and 2014 to sample metrics on barrier-island cross sections spaced every 50 meters (m) along the length of Assateague Island from Ocean City Inlet to Chincoteague Inlet (
Schematic cross section illustrating the Assateague barrier-island metrics determined from existing light detection and ranging (lidar) and lidar-derived datasets. Metrics determined at plant and random-point locations are specified in italics. Metrics not in italics specify transect-based variables.
Figure 4. Schematic cross section illustrating the Assateague barrier-island metrics determined from existing light detection and ranging (lidar) and lidar-derived datasets
Table 2. Barrier-island cross-section metrics sampled along 50-meter transects on Assateague Island
[Data source:
Metric | Description |
Distance to the nearest tidal inlet (m) | The alongshore distance of each sampling transect intersects with the corresponding MHW shoreline for the sampling year (from |
Long-term shoreline change rate (m/yr) | The long-term shoreline change rate determined by linear regression of 6–10 shoreline positions spanning a time period from 1845 to 2000 ( |
Barrier width (m) | The horizontal distance between the transect intersections with the MHW position for a particular year, on the seaward facing shore, and the mean tide-level position on the landward facing shore ( |
Mean transect elevation (m) | The average elevation sampled within 5-m bins sampled along each barrier-island transect. Mean barrier elevations were not calculated for transects having less than 20% missing values. In these cases, fill values were inserted. |
Foredune crest height (m) | The elevation of the foredune crest relative to MHW as defined in |
Beach width (m) | The horizontal distance between the dune toe location ( |
Beach height (m) | The difference in elevation between the MHW shoreline (MHW=0) and the dune toe elevation |
Human modificationsa | The presence of human modifications to Assateague Island. Six classifications were applied: |
Plant presence | Indicates that at least one plant was observed within 30 meters of a transect |
Number of plants within 30 m from the previous year (ND30) | The average number of plants within 30 meters of a transect from the previous year |
Distance to the nearest plant from the previous year (D_trans) (m) | The absolute value of the distance of the transect to the nearest plant from the previous year |
Field is the result of combining two definitions for human modification: “human_mod” and “human_modV2” in
Prior to development of the Bayesian networks (BNs), we conducted basic statistical analyses of the extracted metrics describing physical characteristics. First, bivariate Pearson correlation coefficients among sampled variables were calculated to identify variables that had high correlations. Those with high correlation were eliminated from the habitat models to minimize redundancies. Second, summary statistics for sampled variables (mean, standard deviation, and maxima and minima values) were used to determine if (a) there were distinct differences between locations/transects with observed plants and randomly selected locations, (b) transects where no plants were observed could help to identify preferred habitat characteristics spatially, and (c) whether changes in barrier-island morphology with time might correspond to changes in plant distribution. As part of this, we conducted t-tests to compare sample means between locations where SBA was and was not observed as well as Kolmogorov-Smirnov tests (
U.S. Geological Survey (USGS) and NPS collaborators worked together to develop Bayesian networks to serve as SBA habitat models. The BN is a predictive tool informed by observational data on both ecosystem response and external parameters that uses the relationships between them to make probabilistic predictions of a particular outcome—in this case, the probability of SBA presence. USGS collaborators have used this approach in coastal environments to predict the likelihood of change under various sea level rise (SLR) scenarios to evaluate piping plover habitat suitability (
In
Bayesian networks combine Bayes’ theorem with graphical models of a system, such as physical or biological systems (
We developed 24 versions of the point model BNs and 18 versions of the transect model BNs (
Schematic diagrams showing examples of the three main Bayesian network (BN) structures (simple, structured, and tree-augmented naïve Bayes [TAN]-structured) developed for the Assateague Island
Figure 5. Schematic diagrams showing examples of the three main Bayesian network structures developed for the Assateague Island point and transect models
Table 3. Variables included in the point model Bayesian networks used as models of seabeach amaranth habitat on Assateague Island
[no., number; Dist. MHW, distance to the ocean-side mean high water shoreline; VT, vegetation type; ND30, number of plants within 30 meters of the location during the previous year; Dnp, distance to the nearest plant from the previous year; PM, point model; X (with shading), variable included in the BN; - (without shading), variable was not included]
Model no. | Variable | ||||||
Elevation | Aspect | Slope | Dist. MHW | VT | ND30 | Dnp | |
PM1 | X | X | X | X | X | X | - |
PM2 | X | X | X | X | - | X | - |
PM3 | X | X | X | X | X | - | X |
PM4 | X | X | X | X | - | - | X |
PM5 | X | X | X | X | X | - | - |
PM6 | X | X | X | X | - | - | - |
Table 4. Variables included in the transect model Bayesian networks used as models of seabeach amaranth habitat on Assateague Island
[no., number; Nour, nourishment; Const., construction; Devel., development; Dist., distance; ND30, number of plants within 30 meters of the location during the previous year; D-trans, distance to the nearest plant from the previous year; T, transect model; X (with shading), variable included in the BN; - (without shading), variable was not included]
Model no. | Variable | |||||||||
Shoreline change rate | Nour, Const., Devel. | Dist. to inlet | Barrier width | Mean elevation | Dune crest height | Beach width | Beach height | ND30 | D-trans | |
T3 | X | X | X | X | X | X | X | X | - | X |
T5 | X | X | X | X | X | X | X | X | X | - |
T3b | X | X | - | X | X | X | X | X | - | X |
T3c | X | - | - | X | X | X | X | X | - | X |
T3d | - | - | - | X | X | X | X | X | - | X |
T3e | - | - | - | X | X | X | X | X | - | - |
For each of the three BN structures, several BNs were constructed using different combinations of input metrics. We used the correlation coefficients determined from the sampled data analysis to eliminate variables that were correlated from the BN. We also varied the number of variables in each model structure. This resulted in removing the vegetation-type variable and developing BNs with and without the seed-bank variables in the point models. Developing and evaluating BNs with differing structures and variables allowed us to develop reference comparisons for different BNs and understand the range of possible results. Our overall goal was to identify the best performing model and identify models that performed well with limited input variables.
We selected six BNs for fivefold calibration-validation testing (
The models were used to hindcast the probability of plant presence, and the hindcast outcomes were compared to the outcomes observed in the training data. The comparisons were used to calculate scoring metrics, two of which—error rate and false negatives and positives—we focus on in this report. The error rate is the percentage of outcomes in which the predicted outcome did not equal the observed outcome in the testing dataset. For the predicted outcomes, we defined probabilities as proportions where the probability of plant presence is
We also calculated spherical payoff and quadratic loss (Brier score), which are recommended metrics for models like BNs where the nuances of probabilities are an important consideration (
Table 5. Example confusion matrix referred to in equations 6 and 7
[Symbols + and − represent example classifications of positive or negative. In this matrix,
Predicted outcome | Actual outcome | |
+ | − | |
We used a variance reduction scheme included with the Netica software (
Our results are organized into three parts. First, we examine the SBA population trends and the spatial distribution of plants on Assateague Island and relate them to observations of plant grazing and precipitation. Second, we analyze the morphological characteristics of SBA habitat from the remotely sampled data. Finally, we highlight the most successful BNs in modeling SBA habitat suitability.
Between 2001 and 2009, the SBA population consisted of 500 or more plants with numbers reaching almost a thousand individuals in 2001 and 2002 and exceeding 1,000 plants in 2006–9 (
Numbers of observed seabeach amaranth plants from 2001 to 2020, Assateague Island. The timing of some of the large storms that affected Assateague Island is also shown.
Figure 6. Numbers of observed seabeach amaranth plants from 2001 to 2020, Assateague Island
SBA plants were spread predominantly along the northern ~40 km of Assateague Island. The northernmost plants occurred adjacent to Ocean City Inlet in 2002 and 2005. The southernmost plants were observed south of Toms Cove in 2004 nearly 25 km south of the southern-most planting area (see
We examined the spatial and temporal distribution of SBA plants using the kilometer markers (KMs) provided by ASIS as spatial references (
Table 6. Number of seabeach amaranth plants observed for each year in each kilometer zone, 2001–18, Assateague Island
[Data source:
KM number | Plants observed, by year | Total plants /km | % Tot. pop. | |||||||||||||||||
2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | |||
1 | npo | 1 | 1 | npo | 1 | 2 | 1 | 1 | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | 7 | 0.07 |
2 | npo | npoa | 2 | npo | 2 | 13 | 9 | 15 | 5 | 1 | 1 | npo | npo | npo | npo | npo | npo | npo | 48 | 0.46 |
3 | npo | npoa | 14 | 7 | 66 | 20 | 9 | 12 | 6 | npo | 1 | 2 | npo | npo | npo | npo | npo | npo | 137 | 1.31 |
4 | npo | npoa | 10 | 28 | 29 | 64 | 42 | 1 | 3 | npo | npo | npo | npo | npo | npo | npo | npo | npo | 177 | 1.69 |
5 | npo | npoa | 1 | 8 | 11 | 18 | 7 | 6 | 11 | npo | 8 | 1 | npo | npo | npo | npo | npo | npo | 71 | 0.68 |
6 | npo | npo | 1 | 4 | 1 | 1 | 1 | 2 | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | 10 | 0.1 |
7 | npo | 1 | npo | 3 | 1 | 1 | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | 6 | 0.06 |
8 | 1 | 10 | 1 | 2 | 1 | 3 | 12 | npo | npo | npo | 1 | npo | npo | npo | npo | npo | npo | npo | 31 | 0.3 |
9a | 282a | 57 | 10 | 19 | 12 | 24 | 12 | 14 | 16 | 2 | 12 | 30 | npo | npo | 75 | npo | 3 | 2 | 570 | 5.45 |
10 | 30a | 227 | 47 | 53 | 29 | 176 | 86 | 80 | 190 | 120 | 15 | 8 | npo | 2 | npo | npo | npo | npo | 1,063 | 10.16 |
11 | npo | npo | 4 | 1 | 3 | 1 | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | 9 | 0.09 |
12 | 1 | npo | 3 | 5 | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | 9 | 0.09 |
13 | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | 0 | 0 |
14 | 4 | 2 | 1 | npo | 3 | 11 | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | 21 | 0.2 |
15 | npo | npo | 2 | 1 | 1 | 3 | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | npo | 7 | 0.07 |
16 | 1 | 10 | 2 | npo | 1 | npo | npo | npo | npo | 1 | npo | npo | npo | npo | npo | npo | npo | npo | 15 | 0.14 |
17 | npo | npo | 2 | 7 | 6 | 4 | 8 | 5 | 4 | 1 | 15 | npo | npo | npo | npo | npo | npo | npo | 52 | 0.5 |
18 | npo | npo | 111 | 78 | 33 | 3 | 5 | 5 | 13 | 13 | npo | npo | npo | npo | npo | npo | npo | npo | 261 | 2.5 |
19 | npo | npoa | npo | 4 | 3 | npo | 3 | npo | npo | npo | 1 | npo | npo | npo | npo | npo | npo | npo | 11 | 0.11 |
20 | 19 | 6 | 10 | 7 | 4 | npo | 8 | 2 | 2 | 1 | npo | npo | npo | npo | npo | npo | npo | npo | 59 | 0.56 |
21a | 165 | 47 | 30 | 58 | 81 | 2 | 6 | npo | 2 | 1 | npo | npo | npo | npo | npo | npo | npo | npo | 392 | 3.75 |
22 | 1 | 33 | 11 | 15 | 6 | npo | 8 | 8 | 1 | 7 | 5 | 5 | 6 | 7 | npo | 3 | npo | npo | 116 | 1.11 |
23 | 3a | 233 | 63 | 101 | 58 | 18 | 92 | 24 | 5 | 4 | 48 | 25 | npo | npo | npo | 1 | 6 | npo | 681 | 6.51 |
24 | 2 | 10a | 1 | 15 | 15 | 46 | 81 | 17 | 65 | 20 | 107 | 95 | npo | 2 | 3 | npo | npo | npo | 479 | 4.58 |
25 | 3 | npo | 12 | 60 | 105 | 560 | 261 | 385 | 616 | 21 | 6 | 83 | 1 | 27 | 44 | 31 | 15 | 2 | 2,232 | 21.34 |
26 | 1 | npo | 12 | 2 | 6 | 32 | 14 | 70 | 74 | 5 | 7 | npo | npo | npo | npo | 2 | npo | npo | 225 | 2.15 |
27a | 92 | 33 | 7 | 9 | 4 | 11 | 18 | 60 | 79 | npo | 2 | npo | npo | npo | npo | npo | npo | npo | 315 | 3.01 |
28 | 4 | 22 | 14 | 9 | 10 | 60 | 557 | 115 | 70 | 2 | 1 | 2 | npo | 1 | npo | 3 | npo | npo | 870 | 8.32 |
29 | 3 | 11 | 13 | 6 | 12 | 215 | 248 | 131 | 50 | 1 | 1 | npo | 1 | npo | npo | 3 | npo | npo | 695 | 6.65 |
30 | 1a | 62 | 29 | 14 | 9 | 93 | 321 | 32 | 14 | 1 | 5 | npo | npo | npo | npo | 1 | 2 | npo | 584 | 5.58 |
31 | npo | 9a | 12 | 1 | 9 | 27 | 40 | 12 | 1 | npo | npo | npo | npo | npo | npo | 3 | npo | npo | 114 | 1.09 |
32 | 2 | 2a | 2 | npo | 2 | 2 | 5 | 11 | 6 | npo | npo | npo | npo | npo | npo | npo | npo | npo | 32 | 0.31 |
33 | 2 | 2 | 1 | 1 | 1 | 1 | npo | 3 | 3 | 2 | npo | npo | npo | npo | npo | npo | npo | npo | 16 | 0.15 |
34a | 217 | 2 | 1 | 5 | 6 | 9 | 24 | 5 | 2 | npo | npo | npo | npo | npo | npo | npo | npo | npo | 271 | 2.59 |
35 | 35a | 87 | 46 | 9 | 28 | 67 | 80 | 9 | 4 | npo | npo | npo | npo | npo | npo | npo | npo | npo | 365 | 3.5 |
35.5b | 7 | 6 | 3 | 1 | 1 | 12 | 8 | 9 | 8 | npo | 1 | npo | npo | npo | npo | npo | npo | npo | 56 | 0.54 |
60c | 14 | 58 | 23 | 2 | 41 | 51 | 234 | 14 | 10 | npo | 4 | npo | npo | npo | npo | npo | npo | npo | 451 | 4.31 |
Shaded cells specify the kilometer zone and year when plantings occurred (see
Denotes the 0.5-km span between the 35-km marker and the Maryland-Virginia State line that defines the northern extent of Chincoteague National Wildlife Refuge.
Denotes entire area south of the southernmost marked kilometer zone (35.5) at Assateague Island National Seashore. This spans the southern 24.5 km of the island, which contains the Chincoteague National Wildlife Refuge.
There were a few regions in the Maryland portion of Assateague Island where plants were relatively sparse for the entire 20-year observation period. In the northern 20 kilometers, a rapid decline was observed from 2009 to 2012, and plants were only observed in KM 9 and KM 10 after 2012. In KMs 6–8, where a berm was put in place in 1999 to build up the barrier elevation and prevent an unnatural breach until the long-term sediment restoration program could be implemented (see
Plant population declines were slower to the south. Here, low abundance coincided with Assateague State Park (KMs 11–15) and the beginning of over-sand vehicle (OSV) access (KMs 16–26). Assateague State Park is operated by the State of Maryland, and KMs 14–16 contain popular recreational beaches, campgrounds, and supporting infrastructure, such as parking lots and bathhouses. The infrastructure is protected by periodic dune maintenance to remediate erosion and to reduce the likelihood of overwash. During the 20-year observation period, 61 plants were observed between KMs 11–17 (0.6 percent of population) with none occurring at KM 13.
The spatial distribution of SBA varied during the period when we evaluated the models and their input data: 2008, 2010, and 2014. During 2008, observed SBA plants were widely distributed, extending from KM 1 just south of Ocean City Inlet to several km south of the Maryland-Virginia border, where 14 plants were identified (
Grazing by ungulates and insects was observed on many SBA plants.
Table 7. Summary of the number of observed seabeach amaranth plants that were grazed from 2005 to 2018, Assateague Island
[Data source:
Year | Plants |
Number of plants observed to have been grazed and percent of plants grazed | ||||
Insect (%) | Ungulate (%) | Both (%) | Unknown (%) | Total (%) | ||
2005 | 601 | 370 (62) | 16 (3) | 8 (1) | 2 (0.3) | 396 (66.3) |
2006 | 1,550 | 597 (39) | 85 (5) | 27 (2) | 303 (20) | 1,012 (66) |
2007 | 2,200 | 663 (30) | 68 (3) | 50 (2) | 42 (2) | 823 (37) |
2008 | 1,048 | 497 (47) | 12 (1) | 35 (3) | 6 (1) | 550 (52) |
2009 | 1,260 | 261 (21) | 37 (3) | 20 (2) | 0 (0) | 318 (26) |
2010 | 203 | 71 (35) | 6 (3) | 2 (1) | 0 (0) | 79 (39) |
2011 | 241 | 163 (68) | 13 (5) | 13 (5) | 0 (0) | 189 (78) |
2012 | 251 | 123 (49) | 2 (1) | 16 (6) | 0 (0) | 141 (56) |
2013 | 8 | 4 (50) | 0 (0) | 0 (0) | 0 (0) | 4 (50) |
2014 | 39 | 11 (28) | 0 (0) | 0 (0) | 0 (0) | 11 (28) |
2015 | 122 | 59 (48) | 1 (1) | 1 (1) | 0 (0) | 61 (50) |
2016 | 47 | 11 (23) | 1 (2) | 1 (2) | 0 (0) | 13 (27) |
2017 | 26 | 5 (19) | 0 (0) | 0 (0) | 0 (0) | 5 (19) |
2018 | 4 | 4 (100) | 0 (0) | 0 (0) | 0 (0) | 4 (100) |
It has also been observed that early season conditions, such as drought, can have impacts on SBA.
Graphs showing number of plants and precipitation data for Assateague Island from 2001 to 2020.
Figure 7. Graphs showing number of plants and precipitation data for Assateague Island from 2001 to 2020
We evaluated the characteristics of both observed plant point locations and transects affiliated with plant observations. Our data analysis focused on three questions:
Do the characteristics of locations and transects where plants were observed differ from characteristics of randomly selected locations (or transects) where plants were absent?
Do the characteristics of plant locations vary in time?
Are the physical characteristics of ASIS regions where plants were abundant (KMs 8–10 and KMs 24–25) different from those where plants were less abundant?
We found that the characteristics of observed SBA locations were distinct from random points in the 2008, 2010, and 2014 datasets (
Boxplots summarizing 2008, 2010, and 2014 seabeach amaranth data, Assateague Island.
Figure 8. Boxplots summarizing 2008, 2010, and 2014 seabeach amaranth data, Assateague Island
Histograms showing the distribution of vegetation zones on Assateague Island for random point locations (panels
Figure 9. Histograms showing the distribution of vegetation zones on Assateague Island for random point locations and for locations where plants were observed in 2008, 2010, and 2014
Table 8. Statistics comparing observed seabeach amaranth locations with random point locations, 2008, 2010, and 2014, Assateague Island
[See footnotes for key to KS statistic column. Std. dev., standard deviation; Max, maximum; Min, minimum; KS, Kolmogorov-Smirnov statistic comparing values for observed seabeach amaranth locations (O) and values for random point locations (R); n/a, not applicable; Dist2 Shore, distance to shore; Dist DH, distance to the nearest dune crest; Dist DL, distance to the nearest dune toe; Dist 2 Inlet, distance to inlet; ND30, number of plants within 30 meters (m) of the location during the previous year; Dist 2, distance to;
Variable | Year | Statistic | ||||
Mean | Std. dev. | Max | Min | KS-statistic | ||
Elevation R | 2008 | 0.51 | 0.85 | 7.69 | −0.88 | 0.6288 |
O | 2008 | 1.32 | 0.64 | 4.97 | 0.32 | n/a |
Elevation R | 2010 | 0.62 | 0.91 | 4.97 | −0.52 | 0.7685 |
O | 2010 | 1.53 | 0.31 | 2.83 | 0.85 | n/a |
Elevation R | 2014 | 0.38 | 0.86 | 4.64 | −0.83 | 0.828 |
O | 2014 | 1.19 | 0.41 | 2.53 | 0.47 | n/a |
Slope R | 2008 | 2.6 | 3.1 | 30.4 | 0.04 | 0.2271 |
O | 2008 | 3.9 | 3.8 | 30.8 | 0.07 | n/a |
Slope R | 2010 | 2.41 | 3.07 | 25.31 | 0.02 | 0.3153a |
O | 2010 | 2.23 | 1.67 | 12.45 | 0.12 | n/a |
Slope R | 2014 | 3.1 | 5 | 41.1 | 0.02 | 0.4528 |
O | 2014 | 1.4 | 2.1 | 11.8 | 0.21 | n/a |
Dist2 Shore R | 2008 | 809.4 | 722.8 | 4,226.2 | 0 | 0.7824 |
O | 2008 | 123.5 | 51.8 | 240.8 | 35.4 | n/a |
Dist2 Shore R | 2010 | 918 | 644.3 | 3,906.3 | 0 | 0.803 |
O | 2010 | 178 | 35.4 | 336.2 | 51.5 | n/a |
Dist2 Shore R | 2014 | 525.1 | 429.2 | 1,904 | 5 | 0.812 |
O | 2014 | 120.1 | 29.6 | 190.4 | 44.7 | n/a |
Aspect R | 2008 | 186.1 | 105.9 | 359.9 | 0.3 | 0.1775 |
O | 2008 | 157 | 102.9 | 359.8 | 0.2 | n/a |
Aspect R | 2010 | 182 | 111.9 | 359.2 | 0.4 | 0.8963a |
O | 2010 | 180.8 | 68.2 | 359.8 | 4.4 | n/a |
Aspect R | 2014 | 191.9 | 101.6 | 350.6 | 4.9 | 0.5425 |
O | 2014 | 260.3 | 291.4 | 359.9 | 1.9 | n/a |
Dist DH R | 2008 | 77 | 54.9 | 199.6 | 0 | 0.1634 |
O | 2008 | 62.1 | 43.7 | 194.2 | 0 | n/a |
Dist DH R | 2010 | 94.1 | 54.7 | 188.5 | 5 | 0.494a |
O | 2010 | 54.3 | 39.4 | 170 | 11.2 | n/a |
Dist DH R | 2014 | 92.3 | 62.5 | 197.2 | 5 | 0.5172b |
O | 2014 | 64.9 | 21.7 | 96.2 | 10 | n/a |
Dist DL R | 2008 | 93.7 | 59.5 | 197 | 5 | 0.2831 |
O | 2008 | 62.6 | 54 | 198 | 0 | n/a |
Dist DL R | 2010 | 104.8 | 56.5 | 191.4 | 5 | 0.2441c |
O | 2010 | 100.9 | 43.4 | 199.1 | 11.2 | n/a |
Dist DL R | 2014 | 89.8 | 61.2 | 190.1 | 10 | 0.4226a |
O | 2014 | 81 | 29.7 | 134.6 | 7.1 | n/a |
Dist 2 Inlet R | 2008 | 34,642 | 15,072 | 58,165 | 621.7 | 0.5687 |
O | 2008 | 23,884 | 6,862 | 38,874 | 1,002 | n/a |
Dist 2 Inlet R | 2010 | 35,326.3 | 15,177.9 | 58,552.4 | 719.5 | 0.6749 |
O | 2010 | 150.72.5 | 6,850.9 | 34,435.6 | 1,838.7 | n/a |
Dist 2 Inlet R | 2014 | 14,187.9 | 8,500.9 | 29,444.1 | 489.3 | 0.7179 |
O | 2014 | 23,403.1 | 3,475.5 | 28,248.8 | 9,642.2 | n/a |
ND30 R | 2008 | 0.08 | 1.5 | 47 | 0 | 0.7156 |
O | 2008 | 17.9 | 30.3 | 127 | 0 | n/a |
ND30 R | 2010 | 1 | 1 | 1 | 1 | 0.9193b,c |
O | 2010 | 77.2 | 37.3 | 127 | 1 | n/a |
ND30 R | 2014 | 0 | 0 | 0 | 0 | n/a |
O | 2014 | 0 | 0 | 0 | 0 | n/a |
Dist 2 nearest Plant R | 2008 | 5,556.3 | 6,336.4 | 21,042 | 0 | 0.874 |
O | 2008 | 35.6 | 86.8 | 1561 | 0 | n/a |
Dist 2 nearest Plant R | 2010 | 6,462.4 | 6,775.4 | 22,205.2 | 25 | 0.9261 |
O | 2010 | 35.1 | 114.9 | 1,097.9 | 0 | n/a |
Dist 2 nearest Plant R | 2014 | 14,634.8 | 9,377.7 | 30,304.9 | 229.8 | 0.8547 |
O | 2014 | 1,109.8 | 2,483.7 | 11,737.2 | 68 | n/a |
Indicates t-test not significant at
Specify t-test significant at
Indicates t-test not significant at
Although correlation coefficients indicated weak to no correlation between most variables, several variable combinations did produce coefficients with magnitudes greater than or equal to 0.6 (
Table 9. Correlation coefficients computed for observed seabeach amaranth locations with random point locations for Assateague Island 2008, 2010, and 2014 data
[Dist-Inlet, distance to inlet; DistMHW, distance to the ocean-side mean high water shoreline; distDH, distance to the nearest dune crest; distDL, distance to the nearest dune toe; VT, vegetation type; ND30, number of plants within 30 meters of the location during the previous year; Dnp, distance to the nearest plant from the previous year; ≥, greater than or equal to;
Variable | Elevation | Dist-Inlet | Aspect | Slope | DistMHW | distDH | distDL | VT | ND30 | Dnp |
Elevation | 1 | 0.14b | −0.10b | 0.52b | −0.46b | −0.53b | −0.55b | −0.46b | 0.26b | −0.23b |
Dist-Inlet | 1 | −0.02 | 0.04 | −0.44b | −0.07 | −0.11b | 0.07 | −0.31b | 0.53b | |
Aspect | 1 | −0.11b | 0.04c | 0.07b | 0.31b | −0.01 | −0.04 | 0.06b | ||
Slope | 1 | −0.15b | −0.17b | −0.3b | 0.16b | 0.0 c | −0.06b | |||
DistMHW | 1 | 0.6a,b | 0.67a,b | 0.3b | −0.23b | 0.44b | ||||
distDH | 1 | 0.61a,b | 0.27b | −0.04 | 0.09b | |||||
distDL | 1 | −0.27b | −0.04 | 0.10b | ||||||
VT | 1 | −0.81a,b | 0.18b | |||||||
ND30 | 1 | −0.23b | ||||||||
Dnp | 1 |
Correlation with magnitude ≥0.6.
Statistically significant at
Statistically significant at
Comparison of metrics between transects where plants were present within 30 m and those where they were absent show that there were distinct characteristics at locations where SBA occurred in 2008 but not as consistently in 2014 (
Boxplots summarizing 2008 and 2014 seabeach amaranth data, Assateague Island.
Figure 10. Boxplots summarizing 2008 and 2014 seabeach amaranth data, Assateague Island
Table 10. Statistics for transects with seabeach amaranth, without seabeach amaranth, randomly sampled without seabeach amaranth, and transects from kilometer markers 9 and 25 where plants were abundant, 2008 and 2014, Assateague Island
[Randomly sampled transects without plants consisted of three-times the number of transects where plants were observed. Std. dev., standard deviation; Max, maximum; Min, minimum, KS, Kolmogorov-Smirnov; m/year, meter per year; w, transects with seabeach amaranth: number of observations (
Variable | Year | Statistic | |||||
Sampled transects | Mean | Std. dev. | Max | Min | KS-statistic | ||
Shoreline change rate (m/yr) | 2008 | w | −0.92 | 1.6 | 2 | −6.2 | n/a |
w/o | 0.06 | 3.83 | 21.5 | −6.24 | 0.3429 | ||
r-w/o | 0.55 | 3.42 | 21.5 | −5.3 | 0.5 | ||
KM 9 | −0.85 | 0.09 | −0.74 | −1.01 | n/a | ||
KM 25 | −0.5 | 0.08 | −0.41 | −0.67 | n/a | ||
2014 | w | −0.31 | 0.3 | 0.03 | −0.9 | n/a | |
w/o | −0.11 | 3.6 | 21.5 | −6.2 | 0.3167a | ||
r-w/o | −0.31 | 4.9 | 18.7 | −5.7 | 0.875 | ||
KM 9 | −0.85 | 0.1 | −0.7 | −1 | n/a | ||
KM 25 | −0.5 | 0.1 | −0.4 | −0.7 | n/a | ||
Barrier width (m) | 2008 | w | 996.5 | 412.6 | 2,134.2 | 311.8 | n/a |
w/o | 1,143.6 | 655.3 | 3,440.6 | 109.6 | 0.1923 | ||
r-w/o | 1,272.1 | 612.5 | 3,440.6 | 109.6 | 0.3554a | ||
KM 9 | 555.61 | 191.03 | 976.1 | 326.9 | n/a | ||
KM 25 | 838.4 | 88.86 | 1,010.7 | 695.9 | n/a | ||
2014 | w | 915.3 | 303.5 | 1,301.1 | 376.9 | n/a | |
w/o | 1,133.1 | 705.3 | 3,889.4 | 125.8 | 0.2915a,b | ||
r-w/o | 1,162.6 | 960.9 | 3,475 | 125.8 | 1 | ||
KM 9 | 525 | 180 | 894.7 | 305.4 | n/a | ||
KM 25 | 800.5 | 68.8 | 937.9 | 691.7 | n/a | ||
Mean elevation (m) | 2008 | w | 0.48 | 0.26 | 1.69 | 0.04 | n/a |
w/o | 0.56 | 0.31 | 1.99 | 0.02 | 0.135 | ||
r-w/o | 0.51 | 0.3 | 1.85 | 0.03 | 0.6548 | ||
KM 9 | 0.61 | 0.14 | 0.88 | 0.39 | n/a | ||
KM 25 | 0.29 | 0.08 | 0.46 | 0.15 | n/a | ||
2014 | w | 0.6 | 0.2 | 1.1 | 0.3 | n/a | |
w/o | 0.7 | 0.4 | 2.2 | −0.01 | 0.2276a | ||
r-w/o | 0.8 | 0.7 | 1.9 | 0.2 | 0.6944 | ||
KM 9 | 0.9 | 0.1 | 1.3 | 0.5 | n/a | ||
KM 25 | 0.5 | 0.1 | 0.8 | 0.4 | n/a | ||
Foredune crest height (m) | 2008 | w | 2.41 | 1 | 6.16 | 1.06 | n/a |
w/o | 3.38 | 1.32 | 6.76 | 0.96 | 0.3239 | ||
r-w/o | 3.44 | 1.32 | 6.76 | 0.96 | 0.2983 | ||
KM 9 | 2.46 | 1.23 | 4.36 | 1.36 | n/a | ||
KM 25 | 1.68 | 0.46 | 2.66 | 1.26 | n/a | ||
2014 | w | 2.8 | 0.8 | 4.3 | 2 | n/a | |
w/o | 3.4 | 1.3 | 7.6 | 0.7 | 0.3013a | ||
r-w/o | 2.9 | 1.2 | 7.2 | 1 | 0.2411a | ||
KM 9 | 3 | 1.3 | 5.5 | 1.9 | n/a | ||
KM 25 | 2.3 | 0.4 | 3.1 | 1.9 | n/a | ||
Beach width (m) | 2008 | w | 82.1 | 40.1 | 195.5 | 24.4 | n/a |
w/o | 67.9 | 59.1 | 546.5 | 14 | 0.3138 | ||
r-w/o | 67.3 | 56 | 512.1 | 14.9 | 0.403a | ||
KM 9 | 59.62 | 41.62 | 184.13 | 27.25 | n/a | ||
KM 25 | 60.39 | 37.31 | 170.13 | 24.44 | n/a | ||
2014 | w | 54.5 | 47.4 | 161.9 | 11.3 | n/a | |
w/o | 58.2 | 46.4 | 380.4 | 2.4 | 0.2411a | ||
r-w/o | 63.6 | 58.3 | 240.3 | 12.3 | 0.3529a | ||
KM 9 | 86.2 | 55.3 | 178.1 | 26.5 | n/a | ||
KM 25 | 64.3 | 51.3 | 156.7 | 16.4 | n/a | ||
Beach height (m) | 2008 | w | 1.75 | 0.4 | 3.92 | 1.05 | n/a |
w/o | 2.01 | 0.56 | 4.69 | 0.64 | 0.259 | ||
r-w/o | 2.04 | 0.57 | 4.69 | 0.67 | 0.2732 | ||
KM 9 | 1.6 | 0.3 | 2.39 | 1.28 | n/a | ||
KM 25 | 1.55 | 0.28 | 2.11 | 1.27 | n/a | ||
2014 | w | 1.5 | 0.3 | 2.3 | 1 | n/a | |
w/o | 1.9 | 0.6 | 4 | 0.7 | 0.5244a | ||
r-w/o | 1.6 | 0.5 | 2.5 | 0.9 | 0.4363a | ||
KM 9 | 1.7 | 0.3 | 2.7 | 1.3 | n/a | ||
KM 25 | 1.5 | 0.3 | 2.2 | 0.9 | n/a | ||
Number of plants from 2007 within 30 m | 2008 | w | 9.7 | 32.8 | 288 | 0 | n/a |
w/o | 0.5 | 6 | 184 | 0 | 0.4627 | ||
r-w/o | 1.9 | 13.4 | 217 | 0 | 0.2449 | ||
KM 9 | 4.09 | 10.51 | 49 | 0 | n/a | ||
KM 25 | 14.52 | 23.29 | 90 | 0 | n/a | ||
Number of plants from 2013 within 30 m | 2014 | w | 0.2 | 0.6 | 2 | 0 | n/a |
w/o | 0.01 | 0.1 | 4 | 0 | 0.6734a | ||
r-w/o | 0 | 0 | 0 | 0 | 1.0a | ||
KM 9 | 0 | 0 | 0 | 0 | n/a | ||
KM 25 | 0.1 | 0.3 | 1 | 0 | n/a | ||
Distance to nearest 2007 plant (m) | 2008 | w | 67.2 | 152.4 | 15,42.4 | 0.4 | n/a |
w/o | 4,909.3 | 6,390.6 | 19,707 | 0.6 | 0.6496 | ||
r-w/o | 5,005 | 6,391 | 19,707 | 0.6 | 1.0 | ||
KM 9 | 43.91 | 57.28 | 220.86 | 1.3 | n/a | ||
KM 25 | 17.78 | 19.84 | 67.25 | 0.69 | n/a | ||
Distance to nearest 2013 plant (m) | 2014 | w | 2,400.6 | 4,318.2 | 11,723.8 | 10.2 | n/a |
w/o | 12,149.6 | 8,760.4 | 28,897.3 | 17 | 0.0825a | ||
r-w/o | 13,507.6 | 8,932.5 | 28,281 | 546.1 | 0 | ||
KM 9 | 11,499 | 325 | 12,023 | 10,974 | n/a | ||
KM 25 | 461 | 298 | 952 | 21 | n/a |
KS-tests and t-tests are not significant at
The distributions for KS-tests and t-tests are not significant at
We also compared the transect characteristics in regions KMs 9 and 25 (where SBA tended to be most abundant) with other transects to determine whether there were distinctions among the sites that might help to explain plant abundance (
To explore whether temporal changes in morphology may have been a factor in population declines, we compared morphological characteristics of Assateague Island and SBA habitat in 2008 and 2014, which were years of relatively high and low populations, respectively (where data measuring Assateague Island were available). Metrics for mean elevation, foredune crest height, beach width, and beach height were compared for three groups of transects (
Table 11. Comparison of 2008 and 2014 morphological metrics for the entire Assateague barrier island and for locations where seabeach amaranth was present in 2008
[Note: there were no exact transects in common between 2008 and 2014. Shaded regions indicate specific results that are discussed in the text: beach width and beach height in table parts
Year | Variable | Statistic | ||||
Mean | Std. dev. | Max. | Min. | KS-Statistic | ||
A. 2008 versus 2014 morphology | ||||||
---|---|---|---|---|---|---|
2008 | Mean elevation (m) | 0.55 | 0.31 | 1.99 | 0 | 0.1453a |
2014 | 0.66 | 0.35 | 2.18 | −0.01 | ||
2008 | Foredune crest height (m) | 3.2 | 1.3 | 6.8 | 0 | 0.1327b |
2014 | 3.3 | 1.3 | 7.6 | 0.7 | ||
2008 | Beach width |
70.3 | 56.5 | 546.5 | 0 | 0.1525a |
2014 | 58.2 | 46.4 | 380.4 | 2.4 | ||
2008 | Beach height (m) | 2.0 | 0.6 | 4.7 | 0 | 0.1396a |
2014 | 1.9 | 0.6 | 4.0 | 0.7 | ||
2008 | Mean elevation (m) | 0.5 | 0.3 | 1.7 | 0.4 | 0.4252c |
2014 | 0.6 | 0.2 | 1.1 | 0.3 | ||
2008 | Foredune crest height (m) | 2.4 | 1.0 | 6.2 | 1.1 | 0.4433d |
2014 | 2.8 | 0.8 | 4.3 | 2.0 | ||
2008 | Beach width (m) | 82.1 | 40.1 | 195.5 | 24.4 | 0.589c |
2014 | 54.5 | 47.4 | 161.9 | 11.3 | ||
2008 | Beach height (m) | 1.8 | 0.4 | 3.9 | 1.1 | 0.4367c |
2014 | 1.5 | 0.3 | 2.3 | 1.0 | ||
2008 | Mean elevation (m) | 0.5 | 0.3 | 1.7 | 0.04 | 0.1185 |
2014 | 0.5 | 0.3 | 1.5 | −0.01 | ||
2008 | Foredune crest height (m) | 2.4 | 1.0 | 6.2 | 1.1 | 0.3969a |
2014 | 3.5 | 1.2 | 6.7 | 1.3 | ||
2008 | Beach width (m) | 82.1 | 40.1 | 195.5 | 24.4 | 0.2472a |
2014 | 62 | 40.0 | 244.5 | 6.9 | ||
2008 | Beach height (m) | 1.8 | 0.4 | 3.9 | 1.1 | 0.3328a |
2014 | 2.1 | 0.6 | 3.9 | 0.9 |
Significant at
t-test not significant at
Significant at
Not significant at
Examination of correlation coefficients revealed that only three sets of metrics showed moderate correlation, while the rest showed weak or no correlation (
Table 12. Correlation coefficients for Assateague barrier-island transect metrics from 2008 and 2014
[SLC, shoreline change; WL, barrier width; MeanZ, mean transect elevation; MaxZ, maximum transect elevation; DHZ, foredune crest elevation; BW, beach width; BH, beach height; DIN, distance to nearest inlet; Nd30, number of plants within 30 meters (m) from the previous year; D_trans, distance to nearest plant from the previous year]
Variable | SLC | WL | MeanZ | MaxZ | DHZ | BW | BH | DIN | Nd30 | D_trans |
SLC | 1 | 0.51a | −0.17a | 0.07b | 0.08a | 0.27a | 0.04 | 0.08a | −0.02 | 0.39a |
WL | 1 | −0.38a | 0.35a | 0.22a | −0.03 | 0.21a | 0.37a | −0.02 | 0.17a | |
MeanZ | 1 | 0.21a | −0.06b | 0.01 | −0.04 | −0.6a | −0.04 | 0.35a | ||
MaxZ | 1 | 0.65a | −0.27a | 0.43a | 0.19a | −0.06 | 0.14a | |||
DHZ | 1 | −0.23a | 0.59a | 0.21a | −0.07b | 0.15a | ||||
BW | 1 | −0.12a | −0.01 | 0.05 | −0.02 | |||||
BH | 1 | 0.18a | −0.04 | 0.07b | ||||||
DIN | 1 | 0.14a | −0.43a | |||||||
Nd30 | 1 | −0.09b | ||||||||
D_trans | 1 |
Statistically significant at
Statistically significant at
We constructed 24 BNs using point metrics. In this section, we focus on six of these BNs listed in
Table 13. Performance metrics for fivefold cross-validation using Bayesian network point model data for Assateague Island
[See
BN no. | Metric | ||||
Error rate | Quadratic loss | Spherical payoff | aKappa | Kappa-standard error | |
PM1 Cal. | 5.1 | 0.06 | 0.97 | 0.89–0.9 | 0.01 |
PM1 Val. | 16.3 | 0.21 | 0.88 | 0.66–0.69 | 0.04 |
PM2 Cal. | 5.6 | 0.07 | 0.96 | 0.89 | 0.01 |
PM2 Val. | 16.2 | 0.22 | 0.88 | 0.65–0.69 | 0.04 |
PM3 Cal. | 2.1 | 0.03 | 0.98 | 0.95–0.96 | 0.007 |
PM3 Val. | 12.7 | 0.22 | 0.88 | 0.72–0.78 | 0.03 |
PM4 Cal. | 2.3 | 0.03 | 0.98 | 0.95–0.96 | 0.007 |
PM4 Val. | 12.8 | 0.22 | 0.88 | 0.73–0.77 | 0.03 |
PM5 Cal. | 7.0 | 0.1 | 0.95 | 0.85–0.87 | 0.01 |
PM5 Val. | 13.4 | 0.23 | 0.88 | 0.72–0.74 | 0.03 |
PM6 Cal. | 7.7 | 0.11 | 0.94 | 0.84–0.85 | 0.01 |
PM6 Val. | 13.7 | 0.23 | 0.87 | 0.71–0.74 | 0.03 |
Indicates that a range is given where applicable.
Graphs showing the percent variance reduction for each variable included in four different Bayesian networks (BNs) used as models of seabeach amaranth habitat on Assateague Island:
Figure 11. Graphs showing the percent variance reduction for each variable included in four different Bayesian networks used as models of seabeach amaranth habitat on Assateague Island
To further evaluate hindcast capability, we also compared the percentage of suitable habitat hindcast for KM zones where SBA was abundant with those where SBA was not observed during the 20-year time period with the six variations of the simple BN (
Table 14. Percent habitat hindcast for two sections of Assateague Island: kilometer marker (KM) 12 using the point model, where seabeach amaranth has not been observed, and KMs 24–25 where it has been abundant
[Numbers are percentages where
BN number | KM 12 | KM 24–25 |
PM1 | 6/4 | 7/5 |
PM2 | 6/4 | 7/5 |
PM3 | 0/0 | 10/8 |
PM4 | 0/0 | 10/9 |
PM5 | 12/7 | 11/5 |
PM6 | 14/7 | 12/5 |
Aerial photographs from 2008 showing locations of the example model hindcasts and forecasts presented in the “Point Model Hindcasts” section of this report.
Figure 12. Aerial photographs from 2008 showing locations of the example model hindcasts and forecasts presented in the “Point Model Hindcasts” section of this report
Hindcast point model results showing the habitat suitability probabilities for seabeach amaranth along
Figure 13. Hindcast point model results showing the habitat suitability probabilities for seabeach amaranth along kilometer markers (KMs) 6 to 8 and KM 10 on Assateague Island
Hindcast point model results showing the habitat suitability probabilities for seabeach amaranth along
Figure 14. Hindcast point model results showing the habitat suitability probabilities for seabeach amaranth along kilometer marker (KM) 12 and KMs 24–25 on Assateague Island
Overall, point models that included seed-bank proxy variables (PMs 1–4, number of plants within 30 m from the previous season, and distance to nearest plant from the previous season) were the best performing BNs with the lowest error rates and highest Kappa scores, spherical payoff, and quadratic loss scores (
Performance scores for BNs were slightly better when vegetation type was included (
Differences from the BN hindcast models were most apparent for KMs 11–13 (
We tested a new application of the PM4 BN using hypothetical input data. Because PM4 was the best performing model that did not include vegetation type as an input, we were interested in its response to hypothetical seed-bank proxies in regions that were otherwise deemed as having a low probability of being habitat (
Example application of point model 4 to simulate the result of placing a planting site in a location where there have not recently been plants, Assateague Island.
Figure 15. Example application of point model 4 to simulate the result of placing a planting site in a location where there have not recently been plants, Assateague Island
Eighteen BNs were constructed using transect metrics. In this section we focus on six of these BNs listed in
Based on the results of the initial performance evaluation, we elected to use models T3 and T5 for more in-depth performance evaluation with the intent to use them for hindcasting. In addition, we included four more variations of T3 to evaluate the impact of different variables on model results. With these BNs, we conducted a performance evaluation using k-fold cross validation with five folds, and we developed five variations of the simple BN to evaluate the impact of different variables on hindcasts.
Table 15. Performance metrics for fivefold cross-validation using Bayesian networks used as models of seabeach amaranth habitat on Assateague Island: T3, T5, and several variations of T3
[BN, Bayesian network; no., number; T, transect; Cal., calibration; Val., validation]
BN no. | Metric | ||||
Error rate | Quadratic loss | Spherical payoff | Kappaa | Kappa-Standard Errora | |
T3b – Cal. | 3.4 | 0.042 | 0.98 | 0.85–0.88 | 0.02 |
T3b – Val. | 15.6 | 0.34 | 0.81 | 0.25–0.47 | 0.09–0.10 |
T5c – Cal. | 3.8 | 0.05 | 0.97 | 0.85–0.87 | 0.02 |
T5c – Val. | 17.3 | 0.35 | 0.81 | 0.16–0.37 | 0.10–0.12 |
T3bd – Cal. | 4.8 | 0.06 | 0.97 | 0.8–0.84 | 0.02–0.02 |
T3bd – Val. | 17.1 | 0.35 | 0.81 | 0.27–0.41 | 0.09–0.10 |
T3ce – Cal. | 4.4 | 0.05 | 0.97 | 0.82–0.85 | 0.02–0.03 |
T3ce – Val. | 16.9 | 0.35 | 0.81 | 0.28–0.38 | 0.010 |
T3df – Cal. | 6.04 | 0.08 | 0.96 | 0.75–0.79 | 0.03 |
T3df – Val. | 17.8 | 0.33 | 0.82 | 0.26–0.41 | 0.09–0.10 |
T3eg – Cal. | 10.4 | 0.14 | 0.92 | 0.55–0.62 | 0.04 |
T3eg – Val. | 20.5 | 0.34 | 0.82 | 0.12–0.29 | 0.10 |
Indicates that a range is given where applicable.
T3 includes variables: shoreline change rate, distance to inlet, human modification, barrier width, mean elevation, foredune crest height, beach width and beach height, and distance to 2007 plants.
T5 includes variables: shoreline change rate, distance to inlet, human modification, barrier width, mean elevation, foredune crest height, beach width and beach height, and number of plants within 30 m from previous year.
T3b includes variables: shoreline change rate, human modification, barrier width, mean elevation, foredune crest height, beach width and beach height, and distance to 2007 plants.
T3c includes variables: shoreline change rate, barrier width, mean elevation, foredune crest height, beach width, beach height, and distance to 2007 plants.
T3d includes variables: barrier width, mean elevation, foredune crest height, beach width, beach height, and distance to 2007 plants.
T3e includes variables: barrier width, mean elevation, foredune crest height, beach width, and beach height.
Graphs showing the percentage of variance reduction for each variable included in six different Bayesian networks (BNs) used as models of seabeach amaranth habitat on Assateague Island.
Figure 16. Graphs showing the percentage of variance reduction for each variable included in six different Bayesian networks used as models of seabeach amaranth habitat on Assateague Island
We used the five variations of the T3 BN and the T5 BN to hindcast the probability of plant presence for Assateague Island in 2008 (
Table 16. Percent habitat hindcast calculated using the transect model for two sections of Assateague Island: kilometer marker (KM) 12, where seabeach amaranth has not been observed, and KMs 24–25, where plants have been abundant
[See
BN number | KM 12 | KM 24–25 |
T3 | 0/0 | 56/56 |
T5 | 0/0 | 56/56 |
T3b | 0/0 | 54/54 |
T3c | 0/0 | 54/54 |
T3d | 0/0 | 56/56 |
T3e | 0/0 | 39/39 |
Maps of Assateague Island showing the probability of seabeach amaranth habitat using five transect (T) Bayesian networks (BNs) with different numbers of input variables.
Figure 17. Maps of Assateague Island showing the probability of seabeach amaranth habitat using five transect Bayesian networks with different numbers of input variables
Table 17. Statistics for transects comparing morphological metrics for all transects where seabeach amaranth were observed and for those transects where Bayesian network T3e, which contained only morphological variables, hindcast habitat on Assateague Island
[Std. Dev., standard deviation; Max., maximum value; Min.; minimum value; WL, barrier width; MnZ, mean elevation; DHz, foredune crest height; BW, beach width; BH, beach height; w, transects where seabeach amaranth was observed; T3e, transect model including morphology variables only; T3, transect model including all variables]
Variable | Source | Statistic | |||
Mean | Std. Dev. | Max. | Min. | ||
WL | w | 996.5 | 412.6 | 2,134.2 | 311.8 |
T3e | 987.3 | 363.7 | 2,134.1 | 311.8 | |
T3 | 1,016.9 | 417.5 | 2,134.2 | 311.8 | |
MnZ | w | 0.48 | 0.26 | 1.69 | 0.04 |
T3e | 0.47 | 0.3 | 1.7 | 0.14 | |
T3 | 0.48 | 0.3 | 1.7 | 0.04 | |
DHz | w | 2.41 | 1 | 6.16 | 1.06 |
T3e | 2.4 | 1.1 | 5.4 | 1.0 | |
T3 | 2.49 | 1.1 | 5.4 | 1.05 | |
BW | w | 82.1 | 40.1 | 195.5 | 24.4 |
T3e | 81.0 | 40.1 | 195.5 | 24.4 | |
T3 | 82.2 | 39.3 | 195.5 | 26.1 | |
BH | w | 1.75 | 0.4 | 3.92 | 1.05 |
T3e | 1.7 | 0.37 | 2.8 | 1.05 | |
T3 | 1.74 | 0.4 | 2.8 | 1.05 |
We also conducted hindcasts using the T3 BN trained on 2008 or 2014 data only and then combined 2008 and 2014 datasets to train the BN to evaluate whether morphological differences between the two datasets contributed to differences in the probabilities of habitat.
Plots showing the probability of habitat along Assateague Island for four different Bayesian networks trained (TR) with either 2008 or 2008 and 2014 data and hindcast for either 2008 or 2014.
Figure 18. Plots showing the probability of habitat along Assateague Island for four different Bayesian networks trained with either 2008 or 2008 and 2014 data and hindcast for either 2008 or 2014
To evaluate the influence of changes in morphology and seed-bank proxies between 2008 and 2014 in more detail, we also conducted hindcasts using the T3 and T6 BNs with three different combinations of training data. For this evaluation, each BN was trained on 2008 data only, 2014 data only, and then 2008 and 2014 data together. Performance scores and the percentage of transects with habitat were calculated for Assateague Island and six of the KM zones where (a) there were no SBA observed (KMs 7 and 13), (b) no SBA was observed after 2010 (KMs 10 and 18), and (c) large numbers of SBA were observed (KMs 9 and 25) over the 20-year observation period (see
Results show that the highest performance scores occur when both 2008 and 2014 datasets are used for training. Comparison of results between BNs and years indicated that both the seed-bank proxy and morphological differences between the two time periods had an influence on the percentages of habitat. For the T3 hindcasts, when training was conducted with 2008 or 2014 data and tested with the corresponding years of data, hindcasts were relatively consistent with observations for the respective years and showed a slight tendency for underprediction for 2008 hindcasts (
Table 18. Error rates, spherical payoff scores, and percent of transects classified as habitat for Assateague Island and six kilometer marker zones for two Bayesian networks trained and tested with combinations of 2008 and 2014 datasets
[Habitat percentages indicate percent of habitat where
BN training | Testing | Error rate (%) | Spherical payoff | Percent of transects classified as habitat | ||||||
%a Habitat | %b Hab. KM 7 | %b Hab. KM 9 | %b Hab. KM 10 | %b Hab. KM 13 | %b Hab. KM 18 | %b Hab. KM 25 | ||||
BN T3 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Both | 2008 | 3.9 | 0.97 | 14/11 | 0/0 | 40/40 | 36/36 | 0/0 | 9.5/9.5 | 76/76 |
2014 | 0.33 | 0.99 | 0.5/0.5 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 9.5/9.5 | |
2008 | 2008 | 3.8 | 0.97 | 14/11 | 0/0 | 40/40 | 36/36 | 0/0 | 9.5/9.5 | 76/76 |
2014 | 1.7 | 0.76 | 0.5/0.5 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | |
2014 | 2008 | 16.9 | 0.74 | 0.0007 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 |
2014 | 0.1 | 0.99 | 0.9/0.9 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 9.5/9.5 | |
BN T6 | ||||||||||
Both | 2008 | 10.3 | 0.92 | 7/4 | 0/0 | 10/10 | 32/32 | 0/0 | 5/5 | 67/67 |
2014 | 1.5 | 0.99 | 0.7/0.3 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | |
2008 | 2008 | 8.6 | 0.94 | 10/6 | 0/0 | 10/10 | 36/36 | 0/0 | 5/5 | 81/81 |
2014 | 15.3 | 0.85 | 10/7 | 16/16c | 0/0 | 5/5c | 0/0 | 9.5/9.5c | 38/38c | |
2014 | 2008 | 16.9 | 0.81 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 |
2014 | 0.1 | 0.99 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | 0/0 | |
Observed | 2008 | - | - | 16.7 | 0 | 40 | 50 | 0 | 19 | 86 |
2014 | - | - | 1 | 0 | 0 | 0 | 0 | 0 | 9.5 |
Specifies percent suitable habitat for all of Assateague Island.
Specifies percent suitable habitat within each KM zone.
Shading used to emphasize four cases that are compared in detail in the text.
Comparison of the T3 and T6 hindcasts demonstrated differing outcomes. First, for KM 9, the percentage of habitat predicted using T6 trained with 2008 data is lower than what was observed by 30 percent (
Evaluation of SBA point data and barrier island transect data results indicate that there are distinct morphological conditions in which SBA occurred on Assateague Island. Elevations and distances to the ocean shoreline sampled from 2008, 2010, and 2014 for SBA plants differed from those sampled from randomly selected points on Assateague Island. Evaluation of these datasets showed SBA tended to occupy locations where (a) elevation ranged from 0.3 to 4.9 m MHW; (b) distance from the ocean shoreline was <250 m (the mean distance was 120 m); and (c) where data were available, vegetation was sparse to unvegetated. Of the three plant and random point location datasets, data from 2010 produced the fewest statistically significant differences between variables. This is likely due to the incomplete 2010 lidar dataset, in which measurements did not include the landward portions of Assateague Island.
Barrier-island transect metrics, which were examined for the 2008 and 2014 datasets, differed for those where SBA was observed versus where they were not. SBA transects had lower mean elevations and lower foredune crests compared to those where the plants were not present. In addition, the results indicate that variables serving to represent the seed bank are important components of SBA habitat. Together, results from the point and transect data support the long-held observation that the plants are prone to occur in regions subject to disturbance (for example, overwash,
The regions of Assateague Island with the most persistent presence of SBA were KMs 10, 24, and 25. Interestingly, these regions are on the upper (KM 9) and lower (KMs 24, 25) end of the elevation range for transects where plants were observed (
Light detection and ranging (lidar) elevation maps of northern Assateague Island between kilometer markers (KMs) 7 and 11.
Figure 19. Light detection and ranging elevation maps of northern Assateague Island between kilometer markers 7 and 11
The development of several BNs using metrics from either point data or transect data allowed us to evaluate the two different data sampling approaches. In general, model performance for both point BNs and the transect BNs were comparable (
For both model types, the highest performing BNs included the variables that serve as seed-bank proxies. In the absence of the seed-bank proxy variables, the models did not perform as well and produced lower certainty hindcasts. In particular, seed-bank proxy variables were important to include with the point BNs to effectively hindcast SBA presence and distinguish between high and low probability habitat (
When the seed-bank proxies (minimum distance to a plant from the previous year or number of plants within 30 m) were not included, habitat was hindcast in regions of ASIS where plants were absent (
Our analysis relied mainly on variables that could be sampled from datasets that were obtained in the years when SBA plants were observed. The metrics we sampled and analyzed were defined a posteriori, counter to recommended practices for habitat modeling (
The variables included in the transect BNs provided broad measures of barrier island morphology, including beach width, island cross-section elevation and foredune height. While the transect variables were sampled at a relatively coarse resolution compared to the point data, transect BN results provided clear differences in regions of high and low habitat density (
Our data analysis and models of SBA habitat characteristics suggest that seed bank is an important factor contributing to habitat suitability. Both statistical comparison of point data/transect data and the evaluation of Bayesian networks using the two different data sampling schemes show that distance and number of plants near a site in the previous year are important factors contributing to higher probability habitat. Even so, from the analysis of transect metrics, we cannot rule out that changes in morphology also contributed to SBA decline. From our comparison of 2008 to 2014 transects, we found that where plants were present, transect metrics were similar from 2008 to 2014 (
Comparison of model results from BNs T3 and T6 and the different training and testing dataset combinations provided additional evidence that both seed bank and morphology have large influences on habitat presence such that it is difficult to isolate the influence of one over the other in our analysis (
Both the population trends and model results suggest that a sustained effort to plant SBA was effective in establishing a viable population on Assateague Island. While the single-year population never exceeded the ~5,000 plantings between 2000 and 2002, the SBA population exceeded at least 500 plants for 9 years after the last planting effort in 2002. In addition, from 2003 to 2009, SBA was observed in at least 25 of the 36 KM zones along the Maryland portion of ASIS (
Our analysis suggests that it will be important to conduct planting efforts to sustain the population over the long term. In a natural state, seeds from adjacent barrier islands (Fenwick Island to the north and Wallops Island to the south) could be sources for Assateague Island, but it is unknown if SBA is present at these sites, both of which are highly developed and have undergone significant shoreline and (or) erosion management efforts. Ideally, to sustain the Assateague Island population, planting would occur after seasons of substantial population decreases. More study is needed to determine if there is a critical population size that is required to sustain a long-term population. From our examination of the 20-year record at Assateague Island, planting cultivated SBA plants may be optimal following large population declines, such as in 2008 when the population decreased by half or after 2010 when the population declined by 84 percent (1,260 to 203 plants).
A deeper understanding of seed-bank dynamics and dispersal pathways could help improve understanding of SBA population trends. During the initial few years, plants dispersed up to 6–7 km from the previous year’s planting sites. In 2001 and 2002, the regions with the largest numbers of plants were regions planted the previous year. By 2003, plants were widely dispersed, suggesting robust natural dispersal. From the four regions planted in 2000, there were 22 regions where wild plants were observed in 2001, increasing to 27 regions in 2002 and 33 regions in 2003, despite a population decrease of nearly 400. Such spread suggests conditions were suitable for natural dispersion during these years. Following the substantial decline in 2010, the SBA population ranged from 203 to 251 plants for three seasons before dropping to 8 individuals in 2013. By 2015, the population reached 122 plants, almost all of which were located at KMs 9 and 25; two regions where plants were observed most often. Despite plants tending to be most common in these regions, even when population was small, it is unknown if the seeds that sustained this population were from the previous year’s plants or had germinated from older seed stock buried on the barrier island.
Examination of the SBA population distribution clearly shows that plants are generally absent from two areas on the Maryland portion of Assateague Island (
Hindcasts for 2014 using the T6 BN trained with 2008 data indicated that the morphology of the KM 7 region was suitable for habitat. This is notable since this region occurred where passageways for overwash were bulldozed to allow periodic overwash to improve piping plover habitat (
If there is an opportunity to collect additional data on SBA habitat, there are a few parameters that should be included: (a) soil moisture, (b) direct observations of high-water impacts to plants, (c) on-the-ground photographs of SBA sites, and (d) plant fate. Soil-moisture measurements would provide a direct means of evaluating the impact of drought on SBA seed germination success. Monitoring of high-water events would provide information on the timing and spatial distribution of plant disturbance and habitat creation and assist in evaluating the effect of high-water events on plant fate. While washover deposits appear to be important for SBA habitat, the plants have low tolerance to direct saltwater exposure (
The two modeling approaches using Bayesian networks (BNs) we developed performed well. Both BN approaches produced comparable performance scores, with the point model exhibiting slightly higher scores than the transect model. Despite this, the transect model produced hindcasts that consistently distinguished SBA habitat from nonhabitat areas irrespective of the variables included in the BN. Analysis of point data and barrier island transect data in addition to the BN model results indicate that variables serving as proxies for seed bank are important to include in models to accurately distinguish SBA habitat from nonhabitat regions. The two variables that we considered, distance to the nearest plant from the previous year and number of plants within 30 meters, produced well-performing BNs, with the former resulting in slightly better model performance. We were unable to determine conclusively that morphological changes in island characteristics contributed directly to SBA population decline. We speculate that population decline occurred due to a combination of factors, wherein the largest declines co-occurred with successive years of drought and significant storm impacts to Assateague Island. It is possible that the combination and timing of these factors contributed to a decrease in viable seeds on the barrier island to a point where the population was unable to sustain itself. Our analysis of SBA habitat data and model results suggest that it is important to allow overwash to create suitable substrate for SBA and to maintain planting efforts to sustain the population.
We developed 24 different Bayesian network (BN) models for the presence-absence data and 18 different BNs for the transect data. The BNs for each were configured using three different model structures (simple, structured, TAN) (
For each BN structure, several BNs were constructed consisting of different combinations of variables (
[no., number; DisMHW, the distance to mean high water variable; VT, vegetation type; No_30, number of plants within 30 meters from the previous year; Dnp, the distance to the nearest plant from the previous year; PM, point model; “-o” designates that edges point away from the posterior node; TAN, tree-augmented naïve Bayes algorithm; X (with shading), variable included in the Bayesian network; - (without shading), variable was not included]
Model no. | Configuration | Variable | ||||||
Elevation | Aspect | Slope | DisMHW | VT | No_30 | Dnp | ||
PM1 | Simple | X | X | X | X | X | X | - |
PM2 | Simple | X | X | X | X | - | X | - |
PM3 | Simple | X | X | X | X | X | - | X |
PM4 | Simple | X | X | X | X | - | - | X |
PM5 | Simple | X | X | X | X | X | - | - |
PM6 | Simple | X | X | X | X | - | - | - |
PM7 | Structured | X | X | X | X | X | X | - |
PM8 | Structured | X | X | X | X | - | X | - |
PM9 | Structured | X | X | X | X | X | - | X |
PM10 | Structured | X | X | X | X | - | - | X |
PM11 | Structured | X | X | X | X | X | - | - |
PM12 | Structured | X | X | X | X | - | - | - |
PM13 | TAN-o | X | X | X | X | X | X | - |
PM14 | TAN | X | X | X | X | X | X | - |
PM15 | TAN-o | X | X | X | X | - | X | - |
PM16 | TAN | X | X | X | X | - | X | - |
PM17 | TAN-o | X | X | X | X | X | - | X |
PM18 | TAN | X | X | X | X | X | - | X |
PM19 | TAN-o | X | X | X | X | - | - | X |
PM20 | TAN | X | X | X | X | - | - | X |
PM21 | TAN-o | X | X | X | X | X | - | - |
PM22 | TAN | X | X | X | X | X | - | - |
PM23 | TAN-o | X | X | X | X | - | - | - |
PM24 | TAN | X | X | X | X | - | - | - |
[no., number; Nour, nourishment; Const., constructed features; Devel., development; Dist. to Inlet, distance to Ocean City Inlet; No_30, number of plants within 30 meters from the previous year; D_trans, distance to the nearest plant from the previous year; T, transect model; TAN, tree-augmented naïve Bayes algorithm; X (with shading), variable included in the BN; - (without shading), variable was not included]
Model no. | Configuration | Variable | |||||||||
Shoreline change rate | Nour, Const., Devel | Dist. to Inlet | Barrier width | Mean elevation | Dune crest height | Beach width | Beach height | No_30 | D_trans | ||
T1 | Simple | X | X | X | X | X | X | X | X | - | - |
T2 | Simple | X | - | - | X | X | X | X | X | - | - |
T3 | Simple | X | X | X | X | X | X | X | X | - | X |
T4 | Simple | X | - | - | X | X | X | X | X | - | X |
T5 | Simple | X | X | X | X | X | X | X | X | X | X |
T6 | Simple | X | - | - | X | X | X | X | X | X | - |
T7 | Structured | X | X | X | X | X | X | X | X | - | - |
T8 | Structured | X | - | - | X | X | X | X | X | - | - |
T9 | Structured | X | X | X | X | X | X | X | X | - | X |
T10 | Structured | X | - | - | X | X | X | X | X | - | X |
T11 | Structured | X | X | X | X | X | X | X | X | X | - |
T12 | Structured | X | - | - | X | X | X | X | X | X | - |
T13 | TAN | X | X | X | X | X | X | X | X | - | - |
T14 | TAN | X | - | - | X | X | X | X | X | - | - |
T15 | TAN | X | X | X | X | X | X | X | X | - | X |
T16 | TAN | X | - | - | X | X | X | X | X | - | X |
T17 | TAN | X | X | X | X | X | X | X | X | X | - |
T18 | TAN | X | - | - | X | X | X | X | X | X | - |
The following figures show examples of selected BNs from
Bayesian network (BN) for point model (PM) 3: BN trained using data from 2008. Dashed vertical lines indicate 25, 50, and 75 percent. MHW, mean high water.
Bayesian network (BN) for point model (PM) 1: BN trained using data from 2008. Dashed vertical lines indicate 25, 50, and 75 percent. MHW, mean high water.
Bayesian network (BN) for point model (PM) 9: BN trained using data from 2008. Dashed vertical lines indicate 25, 50, and 75 percent. MHW, mean high water.
Bayesian network (BN) for point model (PM) 17: BN trained using data from 2008. Dashed vertical lines indicate 25, 50, and 75 percent. MHW, mean high water.
Bayesian network (BN) for point model (PM) 18: BN trained using data from 2008. Dashed vertical lines indicate 25, 50, and 75 percent. MHW, mean high water.
Bayesian network (BN) for transect model (T) 3: BN trained using data from 2008 and 2014. Dashed vertical lines indicate 25, 50, and 75 percent.
Bayesian network (BN) for transect model (T) 5: BN trained using data from 2008 and 2014. Dashed vertical lines indicate 25, 50, and 75 percent.
Bayesian network (BN) for transect model (T) 9: BN trained using data from 2008 and 2014. Dashed vertical lines indicate 25, 50, and 75 percent.
Bayesian network (BN) for transect model (T) 15: BN trained using data from 2008. Dashed vertical lines indicate 25, 50, and 75 percent.
For initial model selection, we calculated performance scores for each of the BNs and compared the percentage of habitat predicted for regions of low (kilometer marker [KM] 12) and high (KMs 24–25) SBA occurrence at Assateague Island (
[Bold entries specify scoring metrics for PM4, the Bayesian network used for the cross-validation hindcast evaluation. Shaded region specifies “structured” Bayesian networks (PM7–PM12) to distinguish them from the “simple” (PM1–PM6) and “TAN” Bayesian networks (PM13–PM18). TAN, tree-augmented naïve Bayes algorithm; no., number; SE, standard error (
Model no. | Performance score | |||||||
Error rate | False positives | False negative | Kappa (SE) | Spherical payoff | Logarithmic loss | Quadratic loss | Receiver operating curve | |
PM1 | 5.6 | 0.06 | 0.05 | 0.89 (0.01) | 0.96 | 0.1 | 0.07 | 0.99 |
PM2 | 6.2 | 0.05 | 0.07 | 0.88 (0.01) | 0.96 | 0.11 | 0.08 | 0.99 |
PM3 | 2.4 | 0.03 | 0.02 | 0.95 (0.01) | 0.98 | 0.05 | 0.03 | 0.99 |
PM5 | 7.5 | 0.11 | 0.03 | 0.85 (0.01) | 0.94 | 0.17 | 0.11 | 0.98 |
PM6 | 8.2 | 0.12 | 0.04 | 0.84 (0.01) | 0.94 | 0.18 | 0.12 | 0.97 |
PM7 | 5.96 | 0.07 | 0.04 | 0.88 (0.01) | 0.96 | 0.12 | 0.08 | 0.99 |
PM8 | 10.6 | 0.06 | 0.14 | 0.79 (0.01) | 0.92 | 0.22 | 0.14 | 0.97 |
PM9 | 2.3 | 0.03 | 0.01 | 0.95 (0.01) | 0.98 | 0.05 | 0.03 | 0.99 |
PM10 | 4.3 | 0.04 | 0.05 | 0.91 (0.01) | 0.97 | 0.09 | 0.06 | 0.99 |
PM11 | 7.8 | 0.12 | 0.03 | 0.84 (0.01) | 0.94 | 0.18 | 0.11 | 0.98 |
PM12 | 22.3 | 0.2 | 0.24 | 0.55 (0.02) | 0.84 | 0.42 | 0.28 | 0.88 |
PM13 | 9.7 | 0.1 | 0.09 | 0.81 (0.01) | 0.93 | 0.19 | 0.12 | 0.98 |
PM14 | 5.2 | 0.06 | 0.04 | 0.9 (0.01) | 0.96 | 0.1 | 0.07 | 0.99 |
PM15 | 9.4 | 0.1 | 0.1 | 0.81 (0.01) | 0.93 | 0.19 | 0.12 | 0.98 |
PM16 | 6.2 | 0.05 | 0.07 | 0.88 (0.01) | 0.96 | 0.11 | 0.08 | 0.98 |
PM17 | 5.4 | 0.06 | 0.04 | 0.89 (0.01) | 0.96 | 0.13 | 0.08 | 0.99 |
PM18 | 2.2 | 0.03 | 0.01 | 0.96 (0.01) | 0.98 | 0.04 | 0.02 | 0.99 |
PM19 | 5.8 | 0.06 | 0.05 | 0.88 (0.01) | 0.95 | 0.13 | 0.08 | 0.99 |
PM20 | 2.7 | 0.03 | 0.03 | 0.95 (0.01) | 0.98 | 0.05 | 0.03 | 0.99 |
PM21 | 10 | 0.15 | 0.04 | 0.8 (0.01) | 0.92 | 0.24 | 0.15 | 0.95 |
PM22 | 7.1 | 0.11 | 0.03 | 0.86 (0.01) | 0.94 | 0.16 | 0.1 | 0.98 |
PM23 | 9.9 | 0.14 | 0.04 | 0.8 (0.01) | 0.92 | 0.24 | 0.15 | 0.95 |
PM24 | 8.2 | 0.12 | 0.04 | 0.84 (0.01) | 0.94 | 0.18 | 0.12 | 0.97 |
[Numbers reflect percentages where
BN number | Percent habitat hindcast | |
KM 12 (State park) | KM 24–25 | |
PM1 | 0.06/0.04 | 0.07/0.05 |
PM2 | 0.06/0.04 | 0.07/0.05 |
PM3 | 0/0 | 0.1/0.08 |
PM5a | 0.12/0.07 | 0.11/0.05 |
PM6a | 0.14/0.07 | 0.12/0.05 |
PM7 | 0.07/0.04 | 0.08/0.05 |
PM8 | 0.02/0.01 | 0.04/0.03 |
PM9 | 0/0 | 0.12/0.09 |
PM10 | 0/0 | 0.12/0.09 |
PM11a | 0.14/0.07 | 0.13/0.05 |
PM12a | 0.1/0.02 | 0.07/0.02 |
PM13 | 0.04/0 | 0.08/0.05 |
PM14 | 0.06/0.04 | 0.08/0.05 |
PM15 | 0.06/0 | 0.08/0.04 |
PM16 | 0.06/0.04 | 0.07/0.05 |
PM17 | 0/0 | 0.14/0.06 |
PM18 | 0/0 | 0.1/0.09 |
PM19 | 0/0 | 0.13/0.06 |
PM20 | 0/0 | 0.1/0.09 |
PM21a | 0.19/0.02 | 0.16/0.03 |
PM22a | 0.13/0.07 | 0.12/0.06 |
PM23a | 0.15/0.04 | 0.14/0.03 |
PM24a | 0.14/0.07 | 0.12/0.05 |
Specifies BNs that do not include seed-bank variables.
[Shaded region specifies “structured” Bayesian networks (T7–T12) to distinguish them from the “simple” (T1–T6) and “TAN” Bayesian networks (T13–T18). TAN, tree-augmented naïve Bayes algorithm; no., number; SE, standard error (
Model no. | Performance score | |||||||
Error rate | False positives | False negative | Kappa (SE) | Spherical payoff | Logarithmic loss | Quadratic loss | Receiver operating curve | |
T1 | 6.8 | 0.7 | 6.1 | 0.74 (0.03) | 0.95 | 0.12 | 0.08 | 0.98 |
T2 | 8.9 | 1.1 | 7.8 | 0.66 (0.03) | 0.94 | 0.17 | 0.11 | 0.96 |
T3 | 3.8 | 0.8 | 3.1 | 0.86 (0.02) | 0.97 | 0.07 | 0.05 | 0.99 |
T4 | 5.2 | 0.8 | 4.4 | 0.81 (0.02) | 0.96 | 0.1 | 0.06 | 0.98 |
T5 | 4.3 | 0.4 | 3.8 | 0.84 (0.02) | 0.97 | 0.08 | 0.05 | 0.99 |
T6 | 6.1 | 0.05 | 5.6 | 0.77 (0.03) | 0.96 | 0.12 | 0.08 | 0.98 |
T7 | 16.1 | 0 | 16.1 | 0.19 (0.06) | 0.88 | 0.34 | 0.22 | 0.83 |
T8 | 16.1 | 0 | 16.1 | 0.19 (0.06) | 0.87 | 0.35 | 0.22 | 0.81 |
T9 | 13.3 | 0.7 | 12.6 | 0.54 (0.04) | 0.91 | 0.22 | 0.15 | 0.93 |
T10 | 13.2 | 0.8 | 12.4 | 0.52 (0.04) | 0.91 | 0.23 | 0.15 | 0.93 |
T11 | 11.3 | 0.5 | 10.8 | 0.51 (0.04) | 0.91 | 0.25 | 0.16 | 0.91 |
T12 | 11.4 | 0.5 | 10.9 | 0.51 (0.04) | 0.91 | 0.26 | 0.16 | 0.9 |
T13 | 6.8 | 0.6 | 6.2 | 0.74 (0.03) | 0.95 | 0.12 | 0.08 | 0.98 |
T14 | 8.9 | 1.1 | 7.8 | 0.66 (0.03) | 0.94 | 0.17 | 0.11 | 0.96 |
T15 | 3.9 | 0.7 | 3.2 | 0.86 (0.02) | 0.97 | 0.07 | 0.05 | 0.99 |
T16 | 12.3 | 2.8 | 9.5 | 0.54 (0.03) | 0.9 | 0.27 | 0.18 | 0.91 |
T17 | 4.3 | 0 | 3.8 | 0.84 (0.02) | 0.97 | 0.08 | 0.05 | 0.99 |
T18 | 6.1 | 0.5 | 5.6 | 0.77 (0.03) | 0.96 | 0.12 | 0.08 | 0.98 |
[Numbers reflect percentages where
BN number | Percent habitat hindcast | |
State park | KM 24–25 | |
T1a | 0/0 | 0.54/0.54 |
T2a | 0/0 | 0.51/0.51 |
T3 | 0/0 | 0.56/0.56 |
T4 | 0/0 | 0.54/0.54 |
T5 | 0/0 | 0.63/0.63 |
T6 | 0/0 | 0.54/0.54 |
T7a | 0/0 | 0.02/0.02 |
T8a | 0/0 | 0.02/0.02 |
T9 | 0/0 | 0.05/0.05 |
T10 | 0/0 | 0.05/0.05 |
T11 | 0/0 | 0.29/0.29 |
T12 | 0/0 | 0.29/0.29 |
T13a | 0/0 | 0.54/0.54 |
T14a | 0/0 | 0.51/0.51 |
T15 | 0/0 | 0.56/0.56 |
T16 | 0/0 | 0.54/0.54 |
T17 | 0/0 | 0.56/0.56 |
T18 | 0/0 | 0.54/0.54 |
Specifies BNs that do not include seed-bank variables.
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U.S. Geological Survey
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