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Edited by: Phil J. Bouchet, University of St Andrews, United Kingdom

Reviewed by: Elizabeth Henderson, SPAWAR Systems Center Pacific (SSC Pacific), United States; Chandra Paulina Salgado Kent, Edith Cowan University, Australia

This article was submitted to Marine Megafauna, a section of the journal Frontiers in Marine Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Technological innovation in underwater acoustics has progressed research in marine mammal behavior by providing the ability to collect data on various marine mammal biological and behavioral attributes across time and space. But with this comes the need for an approach to distill the large amounts of data collected. Though disparate general statistical and modeling approaches exist, here, a holistic quantitative approach specifically motivated by the need to analyze different aspects of marine mammal behavior within a Before-After Control-Impact framework using spatial observations is introduced: the Global-Local-Comparison (GLC) approach. This approach capitalizes on the use of data sets from large-scale, hydrophone arrays and combines established spatial autocorrelation statistics of (Global) Moran’s I and (Local) Getis-Ord Gi^{∗} (Gi^{∗}) with (Comparison) statistical hypothesis testing to provide a detailed understanding of array-wide, local, and order-of-magnitude changes in spatial observations. This approach was demonstrated using beaked whale foraging behavior (using foraging-specific clicks as a proxy) during acoustic exposure events as an exemplar. The demonstration revealed that the Moran’s I analysis was effective at showing whether an array-wide change in behavior had occurred, i.e., clustered to random distribution, or vice-versa. The Gi^{∗} analysis identified where hot or cold spots of foraging activity occurred and how those spots varied spatially from one analysis period to the next. Since neither spatial statistic could be used to directly compare the magnitude of change between analysis periods, a statistical hypothesis test, using the Kruskal-Wallis test, was used to directly compare the number of foraging events among analysis periods. When all three components of the GLC approach were used together, a comprehensive assessment of group level spatial foraging activity was obtained. This spatial approach is demonstrated on marine mammal behavior, but it can be applied to a broad range of spatial observations over a wide variety of species.

Studies investigating marine mammals in the wild have historically relied on human observers (

Over the past few decades, technological advancements have led to the ability to track animals further at or near the water’s surface, at a wider range of depths and distances, in remote locations, and over longer periods of time than previously possible (

With the ability to ask new and more complex questions related to marine mammal acoustic behavior comes the need to be able to analyze data collected to answer previously intractable questions. The goal of this work was to demonstrate a quantitative and comprehensive approach for examining and comparing group level marine mammal spatial behavior, the Global-Local-Comparison (GLC) approach. This approach was specifically developed for utilizing the spatial information derived from large-scale hydrophone receiver arrays and passive acoustic monitoring systems that receive, detect, and classify sounds emitted by marine mammals (e.g., ^{∗}) and hypothesis testing (Kruskal-Wallis).

The GLC approach was applied to 10 simulated pattern data sets to provide examples of the utility, limitations, and benefits of the approach. Datasets from large spatial arrays, like those from navy ranges, set within a Before-After Control-Impact (BACI) framework, provided ideal empirical examples upon which to demonstrate this multi-faceted approach for assessing spatial change across analysis periods. Thus two BACI studies,

While the aforementioned BACI studies incorporated coarse spatial modeling (i.e., edge vs. inner hydrophone comparison), the focus of the original studies was on the temporal analysis of beaked whale foraging behavior. The GLC approach fills a need for a more comprehensive and quantitative approach for assessing the spatial aspects of group level marine mammal behavior. Other quantitative spatial methods have been used to examine specific study population attributes—e.g., local decrease/increase of populations (

This spatial analysis approach to assessing changes in marine mammal behavior capitalizes on the spatial detections representing a specific behavioral state of the study population –referred to here as group level behavior—across distinct time periods. Group, here, refers to a number of animals (typically 10 s of animals as opposed to a few individuals) of one species that occupy a local area. Group is used rather than population (

To demonstrate the GLC approach, spatial detections of acoustic signals consistent with foraging, or Group Vocal Periods (GVPs), were used as a proxy to assess beaked whale foraging behavior. A GVP is a vocal event of at least one, up to several, animals foraging together in close proximity to one another. During a GVP, beaked whales echolocate to find prey, producing several hundred species-specific echolocation clicks. If the animals are foraging within a sufficiently spaced hydrophone array, such as the U.S. Navy hydrophone arrays, there is a high probability that at least some of the thousands of highly directional echolocation clicks will be received on at least one hydrophone. Using detection and classification algorithms (e.g.,

Two types of data were examined: (1) simulated GVP data representing specific spatial patterns, and (2) extracted GVP data from two previously published exemplar marine mammal behavior studies (

GVPs were analyzed here, but the approach is not limited to the study of marine mammal foraging behavior. Any spatial feature could be studied assuming both a feature value and its spatial location information are available. In addition, the spatial layout of the observation array must be conducive to an examination of that feature. For example, a specific array with fixed and coarsely spaced acoustic recorders may be appropriate for studying certain features over others, i.e., high frequency acoustic signals vs. lower, or vice-versa.

The GLC approach entails calculating two spatial statistics, Moran’s I and Getis-Ord Gi^{∗} for each analysis period, along with a data appropriate hypothesis test for comparing all analysis periods. The Moran’s I statistic provides a global view of the spatial behavior over the entire region under study, i.e., the hydrophone receiver array, while the Getis-Ord Gi^{∗} statistic provides a more localized view of spatial behavior and spatial use, i.e., hot spots and cold spots of activity, within the array that would not otherwise be captured through the global statistic. Due to inherent differences in distributions and variances of observations across analysis periods, the spatial statistics cannot be directly compared across analysis periods. Thus, the statistical hypothesis test is required to provide insight about order-of-magnitude differences across analysis periods in the feature of interest.

The Moran’s I statistic is used to assess the global spatial pattern of the feature of interest, i.e., number of GVPs, over the entire array. The Moran’s I statistic (Equation 1) characterizes spatial patterns by measuring the overall spatial autocorrelation of a data set, producing a single value. The spatial correlation coefficient is normalized by the sum of the variance of the data so that the values of I range between (–1, 1) (

Spatial depiction of ideal Moran’s I values:

The Moran’s I statistic is given by the formula (

where _{i,j} is the weighting between the

The weighting matrix (_{i,j}) determines the contribution that each set of hydrophones (the _{i,j}= 0) to the Moran’s I statistic. The “Bishop’s case” (

Three examples of contiguity weighting schemes for generating weighting matrices. “Queen’s case” (

To determine if the observed spatial pattern deviates significantly from random (i.e., I = 0) the Moran’s I statistic is converted to a z-statistic (_{I})(

where

A

In the demonstration of the GLC approach, a change in significance of the Moran’s I z-statistic from one analysis period to another is interpreted as a change in mammal behavior globally—e.g., from spatially random to spatially clustered. However, no change would be detected if, for example, all mammals were on the east side of the array as in _{1} and moved to the west side at time _{2}. Hence, a coupled analysis of behavior at a local scale is necessary.

The Getis-Ord Gi^{∗} statistic (^{∗}. The Gi^{∗} z-statistic is computed for each spatial unit, or hydrophone, using the following formula (

where ^{∗} statistic assumes that the data examined are asymptotically normal (i.e., as the number of observations increases the distribution approaches normality) (

Using a two-tailed test, a

Examining locational changes of areas of clustering from one analysis period to the next, provides insight into spatial behavior not captured by the global Moran’s I result. In the exemplars, if all mammals move from the east to the west from one period to the next, as described earlier, a clear change in the location of hot and cold spots would be observed which would not have been detected by using only the global Moran’s I statistic.

Each spatial statistic takes into account the distribution and variance of only a single set of observations from one unit of time, or analysis period. Since the distribution and variance of a feature (e.g., number of GVPs) can change across analysis periods, it is not appropriate to compare the spatial statistic (i.e., Moran’s I or Gi^{∗}) values across analysis periods (i.e., a comparison of a Moran’s I value of 0.2 for one period to a Moran’s I value of 1.2 in another period is meaningless if the distribution and variance of each period is different). In addition, the Gi^{∗} z-statistic is scale-invariant (^{∗} will detect that there has been a substantial change if there are two analysis periods where the hot spot cluster remains in the western corner of the array. But if one cluster has 30 GVPs, while in the next analysis period the cluster only has one GVP, a substantial change has occurred. This would be detected by comparing the order-of-magnitude across analysis periods. A comparison test is necessary for determining if the number of observations across analysis periods has changed (i.e., do the two samples come from a similar population or not). It is recommended that statistical test-specific assumptions be evaluated to decide the most appropriate statistical hypothesis comparison test to use for a specific data set.

Here, the non-parametric Kruskal-Wallis test (

The Kruskal-Wallis test works by ranking the observations in each analysis period and comparing the mean ranks of each (

Finally, difference plots are generated to show the relative change (e.g., increase, decrease, or no change) in the number of observations on a per hydrophone basis between consecutive analysis periods. It is worth noting that the difference plots are based on binary rather than continuous values; a hydrophone that has a change of positive 1 between two periods will be represented the same as a hydrophone that has a change of positive 0.1 from one period to the next. Thus, these plots, as well as visualizing the original data, are only used to aid in the interpretation of the spatial statistics.

Note that the choice of statistical hypothesis test and

Several patterned GVP data sets were created and tested to reveal how this approach would perform on known types of spatial distributions. The types of spatial distributions tested were chosen because they represent simple but realistic patterns of what might be expected of marine mammal foraging. This was conducted on a mock 50 “hydrophone” (10 row by 5 column) equi-spaced array. The simulated GVP data sets included seven patterned data sets (Alternate, Diagonal, Striped, Steep Grade, Graded, Cluster, and Graded Cluster) and three randomly generated data sets (Random 1–3). The ten simulated data sets tested are shown in

Visualization of the Gi* results for the Alternate, Diagonal, Striped, Steep Grade, and Graded Patterns (top to bottom). From left to right: first column: average GVP per hour with color bar ranging from 0 (dark blue) to 10 (red); second column: Gi* z-statistic with color bar ranging from –3.5 (dark blue) to 3.5 (dark red); third column: 95% confidence level, where red indicates a significant hot spot and blue indicates a significant cold spot, while green is not significant. For ease in displaying, individual hydrophone values were rounded to the closest number on the color bar for columns one and two. The numbers provided on

Visualization of the Gi* results for the Cluster, Graded Cluster, Random 1, Random 2, and Random 3 patterns (top to bottom). From left to right: first column: average GVPs per hour with color bar ranging from 0 (dark blue) to 10 (red); second column: Gi* z-statistic with color bar ranging from –3 (dark blue) to 7 (red) for the Cluster and Graded Cluster patterns and from –3 (dark blue) to 3 (red) for the random arrangements; third column: 95% confidence level, where red indicates a significant hot spot and blue indicates a significant cold spot, while green is not significant. For ease in displaying, individual hydrophone values were rounded to the closest number on the color bar for columns one and two. Letters associated with each plot are used for ease in referencing individual plots in the text.

Specific to the Moran’s I statistic, the Alternate design was hypothesized to represent a scenario of dispersed foraging (i.e., I < 0), while the remaining simulated patterns were hypothesized to represent different configurations of clustered foraging (i.e., I > 0). The random data sets were hypothesized to show spatial patterning no different from random (i.e., I = 0). The Gi^{∗} results were hypothesized to statistically identify the areas of high and low GVP activity (hot and cold spots, respectively) intentionally designed into each of the simulated spatial patterns. For example, it was expected that the Diagonal pattern, consisting of low values in a diagonal pattern across the array would lead to a diagonal pattern of cold spot hydrophones in the same location as the low GVP values. It was expected that the cluster of high values in the center of the Cluster and Graded Cluster patterns would be identified as a cluster of hot spots in the Gi^{∗} analysis. It was also hypothesized that there would be a noticeable difference in the resulting Gi^{∗} values and significance, for the Steep Grade vs. the Graded patterns, as well as the Cluster vs. Graded Cluster patterns due to differences in grading, despite the similar overall pattern within these two sets of patterns. The random patterns were expected to show no significant hot or cold spots.

The data from two previously published marine mammal behavior studies were extracted and tested to demonstrate how the GLC approach performed on empirical spatial behavior data. One study assessed Blainville’s beaked whale foraging behavior during mid-frequency active sonar (MFAS) Naval exercises in 2007 on the Atlantic Undersea Test and Evaluation Center (AUTEC) in the Bahamas (

Since the original data from the ^{∗} analysis would reveal a cluster of hot spot hydrophones in the southwest corner of the array Before, a cluster of cold spot hydrophones in the middle of the array During, and a hot spot cluster again in the southwest corner of the array After Navy MFAS activity. For the PMRF exemplar, it was hypothesized that the Moran’s I analysis would show spatial clustering for all four analysis periods (Before, Phase A, Phase B, After), but that the Gi^{∗} analysis would reveal a change in where the clustering took place on the array. In particular, During Phase B and After the hot spot of activity would shift southward on the array, and a cold spot of activity would be located in the center of the array During Phase B.

Schematic of how the data were extracted from the heat maps in the original studies (left figures) –AUTEC

The Moran’s I analysis results including the Moran’s I value, z-statistic, and

Moran’s I analysis results by exposure period for the patterns and random data sets, including Moran’s I value (I), the z-statistic (z_{I}), and the associated

Exposure period | Moran’s I (I) | Z-statistic (z_{I}) |
Spatial distribution | |

Alternate | 0.053 | 0.9818 | 0.1635 | Random |

Diagonal | 0.583 | 8.0393 | <0.001 | Clustered |

Striped | –0.222 | –2.687 | 0.9803 | Random |

Steep grade | 0.638 | 8.7665 | <0.001 | Clustered |

Graded | 0.705 | 9.6615 | <0.001 | Clustered |

Cluster | 0.494 | 6.8501 | <0.001 | Clustered |

Graded Cluster | 0.773 | 10.5593 | <0.001 | Clustered |

Random 1 | 0.0459 | 0.8823 | 0.189 | Random |

Random 2 | 0.241 | 3.4836 | <0.001 | Clustered |

Random 3 | 0.039 | 0.7852 | 0.218 | Random |

Despite some of the unexpected Moran’s I results, with all ten simulated data sets the Gi^{∗} analysis corroborated the findings of the Moran’s I analysis (^{∗} z-statistics and significance results (^{∗} analysis identified a column of hot spots in the western-most column and cold spot hydrophones in the eastern-most two columns.

The results of the Gi^{∗} analysis of the Alternate and Striped patterns provided further insight into the unexpected result of the Moran’s I analysis that showed these patterns had a random distribution. These patterns had low z-statistic variability with values that deviated little from the mean (^{∗} analysis suggest that the observable patterns in these examples were not sufficiently pronounced to be detected statistically with this analysis.

The spatial distribution of the hot/cold spot hydrophones in the simulated patterns that were identified by the spatial analysis as clustered (i.e., Diagonal, Cluster, Graded Cluster, Steep Grade, and Graded) generally overlapped the designed observable pattern (e.g., a diagonal pattern of cold spot hydrophones was indeed present on the hydrophone array in the Diagonal example). However, with each pattern there were a few exceptions. For example in the Diagonal pattern, there was a cold spot cluster of hydrophones almost entirely overlapping the area of the zero-valued diagonal pattern (^{∗} z-statistic calculation. Edge hydrophones generally have fewer neighbors, meaning the value of those neighbors has a greater weight in comparison to the neighbors of hydrophones in the center of the range and therefore a different contribution to the z-statistic calculation.

The matching Gi^{∗} spatial distribution of hot and cold spots for the Steep Grade and Graded patterns (^{∗} analysis. There were no obvious differences between the two patterns upon which the magnitude difference between the two patterns could be differentiated, supporting the need for the comparison analysis when comparing two data sets or analysis periods.

For the three random patterns the spatial distribution of the Gi^{∗} z-statistic values appeared random, except for Random 2 which had a more graded pattern with high Gi^{∗} z-statistic values toward the south and southeast corner and a row of low values along the northern perimeter of the hydrophone array (

To further explore the likelihood of the Random 2 results, an

Visual interpretation of the GVP data (

Visualization of the Gi* results for the AUTEC exemplar: Before, During, and After, from top row to bottom row, respectively. From left column to right: 1) the average GVP/hour with colorbar ranging from 0 (dark blue) to 0.5 (red) GVP/hour, 2) the Gi*

The Moran’s I, z-statistic, and

Moran’s I analysis results by analysis period for the AUTEC exemplar, including Moran’s I value (I), the z-statistic (z_{I}), and the associated

Exposure period | Moran’s I (I) | Z-statistic (z_{I}) |
Spatial distribution | |

Before | 0.77 | 12.37 | <0.001 | Clustered |

During | 0.7 | 11.24 | <0.001 | |

After | 0.83 | 13.28 | <0.001 |

The Gi^{∗} portion of the GLC analysis corroborated the results of the Moran’s I test since both hot and cold spot hydrophone clusters were found in all analysis periods. In particular, a cluster of hot spot hydrophones were identified by the Gi^{∗} analysis in the southwest of the array for each analysis period (^{∗} analysis also revealed a cluster of cold spots in each of the analysis periods, which clearly changed location on the array from one analysis period to the next. Before, there were only a few cold spot hydrophones along the northern perimeter of the array; During, there was a large cluster of cold spot hydrophones in the center of the array; After there was a large cold spot cluster in the northeastern corner of the array (^{∗} portion of the GLC approach suggest there was a change in where GVP activity was absent on the array During MFAS activity. It also shows that there was an increase in the number of hydrophones upon which no GVP activity took place.

As discussed, the Moran’s I and Gi^{∗} statistics alone do not confirm the change in overall activity. Hence the ability to detect changes in the global level of activity through the comparison test is an integral part of the GLC. The Kruskal-Wallis test showed that there was a difference across the mean ranks of the analysis periods [^{–11}]. The ^{∗} statistic and the global nature of the Moran’s I analysis, this overall understanding about the spatial behavior and magnitude of change was not completely realizable through the spatial statistics alone. This emphasizes the importance of considering each of the three parts to the GLC approach in interpreting and understanding spatial behavior change.

Spatial layout of mock AUTEC hydrophone array, where the circles represent the hydrophones of the array, and the color represents the change in the number of GVP on each hydrophone from one analysis period to the next: blue = decrease, red = increase, black = no change.

A visual analysis of the PMRF exemplar revealed that the most GVP activity appeared in the top part of the southern half of the array. During Phase B and After, there was a shift southward in where the most activity occurred in comparison to the earlier periods (i.e., there was also high GVP activity along the bottom southwest edge of the array). The least amount of GVP activity appeared to be along the southern edge of the array Before, but then shifted to the northern edge of the array during Phase A, and then to the center of the array during Phase B and After (

Visualization of the Gi* results for the PMRF exemplar: Before, Phase A, Phase B, and After, from top row to bottom row, respectively. From left column to right: (1) the average GVP/hour standardized to total time where the colorbar ranges from 0 (dark blue) to 3.5 (red) GVP/hour the Gi*

The Moran’s I values, associated z-statistics, and

Moran’s I analysis results by analysis period for the PMRF exemplar, including Moran’s I value (I), the z-statistic (z_{I}), and the associated

Exposure period | Moran’s I (I) | Z-statistic (z_{I}) |
Spatial distribution | |

Before | 0.60 | 8.3 | <0.001 | Clustered |

Phase A | 0.65 | 8.9 | <0.001 | |

Phase B | 0.66 | 9.09 | <0.001 | |

After | 0.73 | 10.03 | <0.001 |

The Gi^{∗} analysis provided further insight about the clustering result of the Moran’s I portion of the GLC approach analysis. There were clusters of hot and cold spot hydrophones identified in each of the analysis periods. In all four periods there was a large cluster of hot spot hydrophones that spanned across nearly all columns in the southern half of the array (

Overall the Gi^{∗} z-statistic plot for each period had a similar appearance: lower values dominated the northern half of the array (

Using the spatial statistics of the GLC approach alone, it was difficult to tell whether the small changes in location of hot spots were an actual change in spatial behavior over the array or within the natural variation to be expected in marine mammal behavior. It is also possible that the resolution of the hydrophone spacing was not fine enough to fully capture the potential spatial behavior change—a danger present in all spatial studies. However, the comparison analysis provided further insight. The Kruskal-Wallis test revealed that there was a difference in the mean ranks of the four analysis periods [

Spatial layout of PMRF hydrophone array, where the circles represent the hydrophones of the array, and the color represents the change in the number of GVP on each hydrophone from one analysis period to the next: blue = decrease, red = increase, black = no change.

The results of the spatial analysis for the simulated data sets offered unique insight into how the GLC approach performed and provided guidance on how to interpret the more complex results of the empirical exemplars of group level marine mammal spatial detections representing foraging behavior. The results of the exemplar data sets conveyed the importance and necessity of using all components of the GLC approach together to achieve a comprehensive understanding of spatial behavior patterns. Moreover, the weakness of examining individual statistics in isolation of the others was demonstrated. When the underlying mechanism of the spatial pattern is not known, the insight gained in this three-pronged approach, along with knowledge of the context, can help support or refute potential hypotheses explaining the observations.

Several instances arose within the simulated data sets where edge hydrophones were either non-intuitively identified or not identified as being significant by the Gi^{∗} analysis of the GLC approach in comparison to the visual assessment of the original data. For example, the Gi^{∗} analysis of the Diagonal pattern did not identify some perimeter hydrophones that made up the diagonal pattern as significant, while in the Cluster pattern some hydrophones outside of the cluster pattern were significant. This is because edge hydrophones have fewer neighbors than center hydrophones, so the contribution of each neighbor in the edge hydrophone case, has a larger weight in the Gi^{∗} statistic calculation than in the case of a center hydrophone (^{∗} significance test using an adjacent neighbor weighting scheme. When using a similar weighting scheme it is recommended that the general area of hot/cold spot hydrophone clusters be compared rather than scrutinizing differences between individual hydrophones. Alternatively, a distance weighting scheme can be used, where every pair of hydrophones within some distance of the hydrophone of interest is represented in the Gi^{∗} calculation for that hydrophone. As the distance from the hydrophone of interest increases, the contribution of other hydrophones (i.e., the weighting coefficient) toward the Gi^{∗} value decreases. It is therefore possible to minimize the edge effect (i.e., ensure all hydrophones have the same number of neighbors) using this scheme, since the number of weights is no longer a function of edge vs. non-edge hydrophone, but rather a function of distance. Whether this is realized would depend on the exact parameter (i.e., distance threshold) and array layout used. A distance weighting scheme is especially appropriate for observations that change on a gradient. This was not assumed to be the case for beaked whale foraging behavior, which is strongly linked to–often patchy and heterogeneous–prey distributions (

The type of neighbor-weighting rule can also have significant implications on the overall outcome of the Moran’s I statistic. The Moran’s I analysis of the simulated pattern data sets revealed that it was difficult to attain a perfectly dispersed pattern (i.e., I = –1). The only pattern for which a negative Moran’s I value was achieved was the Striped pattern, though it was not statistically different from random. This is understandable given the “Queen’s case” neighbor-weighting rule, which takes into account all adjacent hydrophone values. The more hydrophones that are considered a neighbor to a particular hydrophone, the more dependence the result for that particular hydrophone will have on surrounding values. To achieve a truly dispersed pattern a particular hydrophone either has to have less dependence on neighboring values, which can be achieved with a more constrained neighbor-weighting rule (i.e. “Rook’s” or “Bishop’s”), or the array needs to be larger so that similar values are more separated. The array sizes used in the exemplars were already quite large, rare in reality, and resource intensive. Given these challenges, the ability to detect perfect dispersion (I = –1) may not be possible without modifying certain parameters of the GLC approach, such as the neighbor-weighting rule. However, the neighbor –weighting rule should be chosen based on the specific assumptions of the research question. In the exemplars, the “Queen’s case” most accurately described hydrophone adjacency with respect to beaked whale foraging. If, for example, the more restrictive “Rook’s case” neighbor-weighting rule was used for the Alternate pattern it would have likely elicited a dispersed Moran’s I result. The hydrophones in only the perpendicular directions would have been considered adjacent neighbors to a particular hydrophone. This would have resulted in adjacent neighbors with a value that was always opposite to the center hydrophone, characteristic of a dispersed pattern.

In the case of beaked whale foraging, these animals have been shown to consistently forage in the same areas where aggregations of their prey exist (

Many marine mammals forage on organisms, such as fish and plankton, that tend to aggregate either based on favorable environmental conditions (

For hydrophone arrays that are regularly spaced, the binary neighbor-weighting rules (e.g., Queen’s, Bishop’s and Rook’s), which do not require a distance measure, is appropriate. However, a neighbor-weighting rule that takes distance into account may be more fitting for other applications, such as irregularly spaced data where the spatial distribution between hydrophones is not uniform. Different neighbor-weighting rules and irregular hydrophone spatial arrangements were not addressed in this study.

The observed significance of a few of the hydrophones in the Gi^{∗} analysis of the Random 2 data recalls the need to understand the assumptions made in the hypothesis test. One way to interpret the use of a 95% confidence level is that if the study were repeated over and over again, the results may match the underlying model 95% of the time (

Synthesizing these findings from the simulated patterned and random data sets, the exemplars of marine mammal spatial behavior were more easily understood. For example, the issue of scale-invariance with the Gi^{∗} analysis (

Though this approach provides a way to view group level behavior over a large spatial scale, the ability of the test to identify spatial patterns is constrained to the resolution and layout in which the data are sampled. If a hypothesis test leads to the conclusion that no spatial autocorrelation exists, this only means that a spatial pattern does not exist at the resolution the data were sampled, but it does not mean spatial patterns at a smaller scale do not exist. The PMRF exemplar serves as a good case to this point. Though a spatial change was detected, it might have been more obvious with a finer spatial sampling resolution. Tagging efforts and other approaches (

Observations of marine mammals can be limited, which raises the question of whether a statistical test applied to such data has enough power to detect an effect (^{∗}Power and MRSeaPower) for determining effect size and statistical power (

It is worth reiterating that the purpose of this paper was strictly to introduce and demonstrate the GLC approach on empirical data, and not to reassess the spatial effect of the MFAS activities on beaked whale foraging behavior in the

Inherent in any analysis is the need to interpret the results. The spatial analyses of previous studies assessing marine mammal spatial behavior using hydrophone arrays during noise-generating activities heavily relied on heat maps to visually assess differences in the spatial distribution of animals across analysis periods (

The significance of establishing the GLC approach is that it combines many of the strengths of existing methods (visual and statistical, global and local) in an organized manner, providing a comprehensive assessment of empirical spatial observations of marine mammals and objective descriptions of different group level animal behaviors. It builds off approaches that use visual representations of quantitative data by statistically quantifying patterns that can be illustrated through visual representations. The Gi^{∗} analysis essentially performs the same job as our eyes when looking at a heat map: it identifies spatial patterns and changes to those patterns, but without subjectivity. In evaluating the effects of anthropogenic noise on marine mammal behavior, visuals can be extremely intuitive, providing a powerful tool for communicating the statistics to policy makers and other stakeholders. Thus the GLC approach incorporates visualizations of the local results. Other efforts largely focus on the local scale. But the global analysis provides a quick way to assess whether a broad-scale change has occurred, which is one way of assessing whether animal behavior in the system under study was disturbed. Finally, the comparison analysis brings another dimension to the spatial question providing insight about the degree of change identified, or standalone knowledge when spatial change is not identified. Together, the three-prongs of the GLC approach provide a reliable, objective, and standardized approach to assessing spatial change in marine mammal behavior. It ensures a robust statistically backed analysis without compromising on the ability to effectively communicate the findings.

Not only is this approach applicable to a BACI data set—for which it was originally designed and demonstrated here—but a final strength of the GLC approach is that it is not limited to the study of marine mammal behavior, or the assessment of anthropogenic noise impact. For example, the value of spatial autocorrelation analyses has been demonstrated in other applications, such as marine spatial planning (

The GLC approach serves as a tool to quantitatively measure spatial patterns, or lack thereof, allowing for the identification of changes in group level spatial behavior on large observational arrays. Within the approach are two scales of spatial assessment: global and local. The global statistic, Moran’s I, provides a coarse overview of the type of spatial distribution of a set of features which can be used to quickly evaluate whether an array-wide change in behavior has occurred when comparing two or more analysis periods. The local statistic, Getis-Ord Gi^{∗}, provides the visual and spatial detail about change within an array by identifying local hot and cold spots of activity. An additional statistical hypothesis test (e.g., Kruskal-Wallis test) and difference plots, are used to detect potential differences in the overall level of activity on the array not identified by the spatial statistics alone.

The GLC approach was demonstrated using simulated patterned data sets that revealed the global analysis, utilizing a Queen’s case neighbor-weighting, would be most effective at detecting a shift from clustered to random distributions, or vice-versa. The exemplar data sets provided two empirical examples of how to use this spatial analysis approach to evaluate spatial change in group level marine mammal behavior before, during, and after anthropogenic noise events. Overall the GLC approach provides a quantitative and intuitive way to assess group level spatial behavior change, but with careful consideration of the assumptions discussed herein, its use can be much broader than just this application.

The original contributions presented in the study are included in the article/

HK through the guidance of KL conceived of the presented idea and performed the reported analyses. JM-O provided guidance on the interpretation and communication of the findings of this work. All authors discussed the results and contributed to the final manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

This material was based upon work supported by the NOAA Grant NA15NOS4000200 provided to the Center for Coastal and Ocean Mapping at the University of New Hampshire.

We thank E. McCarthy, D. Moretti, L. Thomas, N. DiMarzio, R. Morrissey, S. Jarvis, J. Ward, A. Izzi, and A. Dilley, the authors of “Changes in spatial and temporal distribution and vocal behavior of Blainville’s beaked whales (

The Supplementary Material for this article can be found online at:

^{∗}Power3: a flexible statistical power analysis program for the social, behavioral, and biomedical sciences.