Large bodied, highly mobile predators can exertpowerful effects on ecosystems (Ripple & Beschta2007, Ferretti et al. 2010). In marine communities,direct predation and behavioral changes driven bytop-down forces have been shown to fundamentallyshape ecosystems over large spatial and temporal
Critical threshold identified in the functional relationship between beaked whales and their prey
Kelly J. Benoit-Bird1,*, Brandon L. Southall2,3, Mark A. Moline4, Diane E. Claridge5,6, Charlotte A. Dunn5,6, Karin A. Dolan7, David J. Moretti8
1Monterey Bay Aquarium Research Institute, Moss Landing, CA 95039, USA2Southall Environmental Associates, Inc., Aptos, CA 95003, USA
3University of California, Santa Cruz, Long Marine Laboratory, Santa Cruz, CA 95060, USA4School of Marine Science and Policy, University of Delaware, Lewes, DE 19958, USA
5Bahamas Marine Mammal Research Organisation, Marsh Harbour, Abaco, The Bahamas6University of St Andrews, Scottish Oceans Institute, St Andrews, Fife, KY16 8LB, UK
7Naval Undersea Warfare Center, Newport, RI 02841, USA8Naval Undersea Warfare Center, Newport, RI 02841, USA (Retired)
ABSTRACT: Anthropogenic noise is increasingly rec-ognized as a potentially significant stressor for marineanimals. Beaked whales, deep-diving cephalopod pre -dators, have been disproportionally present in atypicalmass stranding events coincident with military sonarexercises, while frequently disturbed populations thatdo not strand may have reductions in fitness. We pres-ent in situ measures of prey availability, a key factor af-fecting fitness, for 2 distinct populations of Mesoplodondensirostris: one on a US Navy range in The Bahamasand one nearby in an area less exposed to sonar. Thevariables most strongly correlated with beaked whalehabitat use were related to the distribution of deep-seasquid (mode spacing, peak depth, and 100 m scale vari-ability). All squid metrics were more favorable forbeaked whales at the less exposed site than those onthe range. To develop a generalized functional rela-tionship between prey resources and beaked whalehabitat use, data from The Bahamas were combinedwith comparable data from another Navy range andthe larger beaked whale, Ziphius cavirostris. A power-law relationship was observed between a normalizedmetric of prey quality and whale habitat use. A criticalthreshold in prey characteristics, below which beakedwhales appear unlikely to be successful, but abovewhich small changes in resource availability enablelarge gains for predators, was observed. This impliesthat modest changes in the behavior of individualwhales associated with disturbance can have conse-quential population effects. Our results elucidate theecological realities of these elusive and sensitivebeaked whales, and the importance of environmentalcontext in effective spatial planning for the deep sea.
OPENPEN ACCESSCCESS
Mesoplodon densirostris, an elusive, deep-diving beakedwhale, relies on newly described aggregations of squid inthe deep sea to be successful.
scales (Springer et al. 2003, Worm & Myers 2003,Heithaus et al. 2008) and even to modify the globalcarbon cycle (Huntley et al. 1991). High trophic levelpredators including sharks, large teleost fishes, mar-ine mammals, and seabirds have been declining at arapid pace in pelagic marine ecosystems, leading tosignificant ecosystem-level changes (Heithaus et al.2008). These widespread marine predator declineshave intensified attention on the many anthropo -genic stressors these animals face, including directhunting (Myers & Worm 2003), bycatch in fisheries(Žydelis et al. 2009), competition with humans forresources (Cury et al. 2000, Smith et al. 2011), pollu-tion (Maxwell et al. 2013), plastics (Choy & Drazen2013), and consequences of climate change (Veit etal. 1997, Hazen et al. 2013).
Over the last few decades, noise pollution hasincreasingly been recognized as a significant stressorfor animals in the marine environment (e.g. Richard-son et al. 2013, Simmonds et al. 2014, Southall 2017).The biological impacts of underwater anthropogenicnoise from sources like shipping, fishing, oil and gasexploration, offshore construction, and military activ-ities are complex, and our understanding is still de -veloping (Simmonds et al. 2014). While intense noiseexposure may cause injury or even death over shortranges, less intense but more broadly prevalent (inspace and time) exposures can mask biologicallyimportant signals and cause behavioral disturbanceswith potential impacts on physiology and foragingsuccess (Williams et al. 2015, Southall 2017). Odonto-cete cetaceans, or toothed whales, may be particu-larly susceptible to the effects of noise because oftheir reliance on active acoustic sensing (biosonar)coupled with their wide hearing bandwidth (Tyack &Miller 2002).
Odontocete species of specific concern with regardto ocean noise include beaked whales, comprising 21species of deep-diving cephalopod predators. Thereis considerable evidence of atypical mass strandingevents of these species associated with military sonarexercises (Cox et al. 2006, Filadelfo et al. 2009).Recent evidence suggests that in addition to rela-tively rare mortality events, beaked whales that in -habit naval training ranges experience frequentbehavioral disturbances including reduced dive ratesand spatial displacement from preferred habitats(McCarthy et al. 2011, Moretti et al. 2014, Joyce et al.2019). These behavioral changes likely have ener-getic and reproductive consequences which maylead to changes in population demographics (King etal. 2015, Hin et al. 2019). Bioenergetics models, forexample, suggest that beaked whales require rela-
tively high-quality habitat to meet their energyrequirements, and that regular displacement frompreferred feeding habitats could potentially impactsurvival and reproduction through compromisedbody condition (New et al. 2013). Understandinghow these sublethal ‘harassments’ affect the popula-tion is mandated for activities likely to cause distur-bance to species listed under protective statutes,including the US Marine Mammal Protection Act of1972 (Roman et al. 2013). The energetic and demo-graphic effects of disturbance on individuals and thepopulations of which they are part, however, canonly be understood in the context of the local envi-ronment and the ecology of the species (Friedlaenderet al. 2016). In fact, in models that integrate behaviorand demographic data to predict population conse-quences of disturbance, environmental quality isamong the most sensitive parameters (Southall et al.2019). In pelagic marine ecosystems, however, con-trolled manipulations of environmental context arerarely possible, and data on the deep-sea habitats ofbeaked whales are scarce.
In addition to being regions of intense interactionbetween humans and numerous protected marinemammals, including beaked whales, US Navy under-sea testing and training ranges provide a unique op-portunity to study these elusive animals. Numerouscabled hydrophones within each Navy testing rangehave allowed for long-term monitoring of populationdynamics, habitat use, foraging behavior, and re-sponse to human activities (Moretti et al. 2010, Mc-Carthy et al. 2011, Tyack et al. 2011). One well-studied population includes Blainville’s beakedwhales Mesoplodon densirostris (hereafter Meso-plodon) residing on the US Navy’s Atlantic UnderseaTest and Evaluation Center (AUTEC). Inhabiting asubmarine canyon in The Bahamas known as theTongue of the Ocean (TOTO), this population is re-peatedly exposed to high levels of military activities,including sonar. Although there have been no recordedatypical stranding events at AUTEC (such as thosedescribed by Fernández et al. 2005, Cox et al. 2006),frequent disruptions and displacements off of therange (Joyce et al. 2019) may reduce the fitness of thepopulation relative to a nearby population off AbacoIsland that is less exposed to military sonar (Claridge2013, Moretti 2019).
We present in situ measures of the availability of akey factor affecting animal fitness — food resources —from the deep ocean on and near the AUTEC range.To inform ongoing efforts to incorporate environ-mental variability into population models for man-agement of beaked whale species (New et al. 2013,
Benoit-Bird et al.: Beaked whale predator−prey relationships 3
Moretti 2019), we assessed whether underlying dif-ferences occurred in prey availability associated withconcomitant and historical differences in habitatusage and published measures of population param-eters. We compared these newly collected data withsimilar data collected on and around a test rangelocated off Southern California that is home toCuvier’s beaked whales Ziphius cavirostris (here-after Ziphius). The objective was to develop a gener-alized empirical relationship between a key environ-mental metric, prey availability, and habitat use bybeaked whales in order to elucidate ecological rela-tionships within this elusive family of whales and toinform deep-sea spatial planning.
2. MATERIALS AND METHODS
2.1. Approach
Data on deep-water biological resources in thewaters around The Bahamas were collected usingechosounders on 2 platforms: a purpose-built, deep-diving, autonomous underwater vehicle (AUV) and aresearch vessel. Together, these platforms providedmeasurements of acoustic scattering over nearly thefull diving range of foraging Mesoplodon (Johnson etal. 2004, Baird et al. 2006, Johnson et al. 2008). Thesedata were analyzed following Benoit-Bird et al.(2016) to provide estimates of integrated prey bio-mass, the number of separable individual prey, indi-vidual prey size, and relative composition of the preyfield as well as descriptions of the distributional char-acteristics of these resources. To examine the effectsof the multiple prey characteristics on beaked whalepotential energetic gains, we followed the Southall etal. (2019) approach to integrate these metrics, tunedto the subject predator species in The Bahamas withavailable behavioral and energetic data to provide asimple, relativistic assessment of foraging habitat qual-ity. We used this foraging habitat quality metric tocompare the suitability of resources for Mesoplodonacross sampling areas in and near the AUTEC range.
We also used the foraging habitat quality metric tosynthesize measurements from The Bahamas withthose collected similarly over deep waters in theSouthern California Bight (Benoit-Bird et al. 2016,Southall et al. 2019). The area to the west of SanClemente Island off the coast of Southern Californiahosts the Southern California Anti-Submarine War-fare Range (SOAR) and is important habitat forZiphius (Falcone et al. 2009). Z. cavirostris is largerthan M. densirostris (5−7 m long, ~1600 kg, and
4.4−4.6 m long, ~850 kg, respectively). The foraginghabitat metric from Southall et al. (2019) was normal-ized to the body size of both predator and observedpotential prey, facilitating comparison across con-texts. In addition to differences in beaked whale spe-cies across study sites, the habitats of the 2 regionsare quite different. Low nutrient, low productivity,sub-tropical waters surround The Bahamas, whilethe temperate waters of the California current arestrongly influenced by coastal upwelling and arehighly productive. The diversity of these data allowedus to use the data sets together to develop a general-ized empirical relationship between a key environ-mental metric, prey availability, and habitat use bydeep-diving beaked whales. The functional form ofthis relationship can reveal much about the pro-cesses controlling beaked whale populations and isimportant for informing ongoing management ofthese species.
2.2. Field site
The Tongue of the Ocean (TOTO) in The Bahamasis a submarine canyon approximately 30 km wide by200 km long that forms the southern branch of theGreat Bahamas Canyon (Fig. 1). TOTO exceeds2000 m depth in some locations but, with the excep-tion of its northern end, is separated from the openocean by numerous islands, reefs, and shallow(<10 m) carbonate banks. The US Navy’s AUTEC, adeep-water test and training facility that includes anextensive array of cabled hydrophones, is located inthe TOTO. Animals in this area are repeatedlyexposed to high levels of military activities, includingsonar, which has been shown elsewhere to result inunusual mass strandings (e.g. Fernández et al. 2005,Cox et al. 2006), and more frequent disruptions thatmay reduce the fitness of the population (Claridge2013, Moretti 2019). Long-term hydrophone record-ings (McCarthy et al. 2011, Tyack et al. 2011 NavalUndersea Warfare Center unpubl. data) at AUTEChave revealed spatial variability in foraging effort,with more foraging animals on the western side ofthe range than the eastern. Based on these observa-tions, echosounder and other mobile sampling wasblocked by these zones within the instrumented por-tion of the range (Fig. 1, darker gray regions). Previ-ous efforts in these areas suggested that there werealso biological differences in fish and invertebratesin the upper water column between these 2 zones(Hazen et al. 2011). Two additional, similarly sizedzones were sampled in areas adjacent to the north
Mar Ecol Prog Ser 654: 1–16, 20204
and south of the active range, as these areas arelikely used by animals as a refuge during navy sonarexercises (McCarthy et al. 2011, Tyack et al. 2011,Joyce et al. 2019). Data from these 4 zones were com-pared with a region approximately 170 km north ofthe range, on the southwest of Great Abaco Island.That area is unlikely to be disturbed by sonar and hasa higher proportion of juvenile Mesoplodon thanAUTEC (Claridge 2013). Abaco has been used togenerate demographic rates for the Mesoplodon inthe region (Claridge 2013) (Fleishman et al. 2016,Moretti 2019) and as a comparative site to assess theeffects of sonar disturbance on the AUTEC popula-tion (Fleishman et al. 2016, Moretti 2019), the metricof management mandated by the Marine MammalProtection Act (1972).
To investigate whether historical Mesoplodon spa-tial distributions used to design the sampling weresimilar to the survey period, AUTEC hydrophoneswere monitored for echolocation signals during themonth in which prey sampling was conducted
(Moretti et al. 2010, McCarthy et al. 2011, Jarvis et al.2014). The 1500 km2 monitored portion of the range(shaded in dark grey in Fig. 1) consists of 79 hy-drophones separated by ~4 km and two 7 hydrophonehexagonal arrays with a baseline of 1.5 km (knownas Whisky arrays; Whisky 1 is indicated by a star inFig. 1). Based on the hydrophone characteristics andMesoplodon signals, any echolocating individual willmost likely be detected on at least one hydrophone(DiMarzio et al. 2008, Moretti et al. 2014).
2.3. Field sampling
During 2−14 July 2015, 8 transects (20 km long)were sampled during the daytime in each of these 5zones using a surface vessel and an AUV (Sato &Benoit-Bird 2017). Two regions known for relativelyhigh habitat use by beaked whales were sampled ata finer spatial scale, using an expanding box with amaximum dimension of 1.5 km on a side (Moline &
77.5°78.0° 77.0°W 76.5° 76.0°78.5°
26°
25°N
24°
AUTEC
2000 300010000Mesoplodon click duration (min)
Abaco
Abaco slope
IslandAndros
Whiskey 1
Fig. 1. Sampling locations in The Bahamas, blocked into 5 similarly sized (~500 km2) zones: 2 on the instrumented portion ofthe US Navy’s Atlantic Undersea Test and Evaluation Center (AUTEC) range off Andros Island (W: West; E: East, shown indark gray), 2 areas adjacent to the range to its North (N) and South (S), and one at the nearby deep-water habitat adjacent toAbaco Island. Prey data were collected using ship-based echosounders and a deep-diving autonomous underwater vehiclealong eight 20 km long transects within each of the zones. In color is the total duration of Mesoplodon densirostris clicksdetected by hydrophones on the range in July of 2015. As shown in previous sampling, the species’ foraging effort was higher
on the western part of the range than the eastern part
Benoit-Bird et al.: Beaked whale predator−prey relationships 5
Benoit-Bird 2016): an area surrounding Whiskey 1and the Abaco slope (Claridge 2013). At each ofthese locations, measurements of the distribution anddensity of animals in the upper 600 m of the watercolumn were made using multifrequency (38, 70,120, 200 kHz Simrad EK60s) hydro-acoustics fromthe R/V ‘Sharp’, which also conducted net samplingfor zooplankton and mesopelagic fishes and verticalCTD plus fluorometer profiles to 600 m. Discussed indetail in Sato & Benoit-Bird (2017), these measure-ments provide environmental context for compar-isons between the study regions. An autonomousechosounder system (38 and 120 kHz Simrad EK60s)integrated into a 600 m depth-capable AUV (Molineet al. 2015) was used to measure the distribution anddensity of squid and other resources from 600− 1200 m,covering much of the depth range over whichbeaked whales forage (Johnson et al. 2008). Between2 and 4 pseudo-randomly chosen transects weresampled with both platforms in concert each day tominimize the effects of time within the survey periodwhile optimizing the use of sampling time.
2.4. Data analysis
We utilized methods and selected squid metricsfrom Benoit-Bird et al. (2016) to summarize theacoustic data from both platforms. Acoustic dataanalysis was conducted using a combination ofEchoview 10.0 and custom LabView routines whilestatistical analyses were conducted in SPSS Statistics24 (IBM). Metrics included an integrated biomassproxy (integrated 38 kHz scattering); the numberof separable individuals; the proportion of these in -dividuals consistent with squid; the ratio of fishesto crustaceans; estimates of individual size (targetstrength) by taxonomic class; total energy contentper individual squid; the depth of highest squid den-sity (peak depth); and distributional heterogeneity ofsquid targets measured as relative variance, the den-sity of squid aggregations, and the modal density ofindividuals within these patches. It is important torecognize that conversion of acoustic proxies to bio-logical parameters always involves simplificationsand assumptions. Estimation of target length, forexample, assumes that all of the animals with asimilar frequency response have the same targetstrength-to-length relationship, an assumption that islargely correct for animals with similar morphologi-cal characteristics but is affected by material prop -erties of animals that can vary between species(McClatchie et al. 2003), introducing potential errors
if relative species composition varies across units ofcomparison. However, within fluid-like scatterers,such as squid, those that have a stronger acousticcontrast with seawater and, as a result, higher targetstrength values, also generally have higher energydensities. Thus the conversion of target strength tocaloric content is fairly robust across squid species(Benoit-Bird & Au 2002). See a further discussion andsensitivity analysis in Southall et al. (2019). Thesevariables and proxies were calculated for a numberof fixed depth ranges (10−1200, 10−600, 600−1200,10−300, 300−600, 600−900, 900−1200 m) includingsome driven by knowledge of beaked whale foraging(650−1050, 850−1050, 900−1000 m; Johnson et al.2004, 2008, Baird et al. 2006) at a range of horizontalscales (10 km, 1000 m, 100 m, 10 m). We also calcu-lated the variability in these parameters with depthin 50 m depth bins.
MANOVA was used to examine the effect of sam-pling zone on the metrics of prey resources. Levene’stest for equality of variances and Shapiro-Wilk’s (SW)test of normality to determine if the data conformedto the assumptions of ANOVA. Tukey’s HSD post hoctests were used to examine which zones accountedfor significant effects. Discriminant function analysiswas used to further explore the relationships be -tween prey variables and sampling zone. To examinethe differences in mean estimated squid length amongmajor habitats (TOTO and Abaco), an ANOVA wasused after Levene’s and SW tests.
AUTEC hydrophones were monitored for echolo-cation signals during the month prey sampling wasconducted to investigate the spatial distributions ofMesoplodon. Following Southall et al. (2019), clicksrecorded on the AUTEC range hydrophones weredetected using a custom classifier for each dive. Thehydrophone with the largest number of clicks wasdesignated the central hydrophone for that detectionto provide a geolocation of the beaked whale group,and the group vocal period (time from the first clickfor that group to the last) was determined. Groupvocal period is a proxy for foraging rather than sim-ple searching (Moretti et al. 2010).
Our study was not designed to explicitly test theeffects of our surveys on beaked whale behavior. Itdid not include a controlled exposure nor high reso-lution measurements of individual behavior. How-ever, we did evaluate potential responses to our sur-vey operations in a general sense. We comparedMesoplodon group vocal period on the range during,prior to, and after the survey by breaking the rangeinto 4 quadrants and testing the effect of time periodrelative to the study on the vocal period using an
Mar Ecol Prog Ser 654: 1–16, 20206
ANOVA blocked by these quadrants, following Lev-ene’s and SW tests to validate conformation to theassumptions of ANOVA. To further examine the pos-sibility of effects on animal distributions of our pres-ence on the range, we evaluated the spatial distribu-tion of the acoustic detections of Mesoplodon relativeto the location of the survey. As the ship and AUVwere closer to one another throughout the study thanthe 4 km spacing between hydrophones, we used theship’s position in estimating the distance from thecentral hydrophone for each Mesoplodon detectionto our sampling. If the ship’s position and the ani-mals’ position were random, the convolution of the 2would result in a Rayleigh distribution, also de -scribed as a Weibull distribution with a shape para -meter of 2 (Grinstead & Snell 1997). A Kolmogorov-Smirnov test was used to compare the distribution ofdistance between the ship and each beaked whalesignal against the predicted Rayleigh distribution forall time periods and for just the periods the AUV wasdeployed. A quartile−quartile plot of the observedversus expected distribution was examined to iden-tify any specific scales of effects.
To examine the effects of the multiple prey charac-teristics on beaked whale potential energetic gains,we followed Southall et al. (2019), integrating thesemetrics with available behavioral and energetic datato develop a simple, relativistic comparative assess-ment of foraging habitat quality. This foraging habitatquality metric provides a simple yet quantitativemeans of evaluating the fitness implications of spatialprey heterogeneity and the potential for associatedconsequences of disturbance to beaked whales acrossvariable ecological contexts. Foraging habitat qualitywas compared across sampling zones as well as at thefiner scale areas known for consistently high beakedwhale activity. Importantly, the metric is also scaled toaverage whale body size so it also allows comparisonwith data collected and analyzed similarly for themuch larger Ziphius off Southern California (Benoit-Bird et al. 2016, Southall et al. 2019). To facilitate com-parisons, a qualitative relative habitat use score wasdeveloped for each sampling zone using a combina-tion of available data including passive acoustic esti-mates of foraging activity during and prior to ourstudy and previously published visual survey data. Avalue of 1.0 was assigned to the highest use zone oneach naval range, with other zones given a habitatuse value scaled as a fraction of that value. For exam-ple, at AUTEC where acoustically detected animalforaging rates were 2.5 times higher on the highest-use, western part of the range than the eastern part ofthe range, the eastern site had a habitat use score of
0.4 while the western had a score of 1.0. We used re-gression analysis to determine the best functional re-lationship between the metrics of prey quality andhabitat use from among linear, logarithmic, inverse,cubic, power, quadratic, logistic, exponential, andgrowth. The regression model with the best adjustedvalue of fit was retained.
3. RESULTS
3.1. The Bahamas
3.1.1. Beaked whales
Hydrophones on the AUTEC range were moni-tored for beaked whale foraging sounds in themonth-long period around our surveys. As the resultof a confluence of unusual events, no testing or train-ing exercises were conducted at AUTEC during thistime period, limiting the animals’ exposure to anthro-pogenic noise sources including mid-frequencyactive sonar. The spatial pattern of habitat used byforaging Mesoplodon during July 2015 was similar toearlier observations of habitat use (Hazen et al.2011). An average of 2.5 times higher foraging effort(quantified as total duration of echolocation clicks)occurred in western versus eastern AUTEC rangeareas (Fig. 1). These differences were not as stark asthose observed in foraging Ziphius at the SOARrange off southern California, where a 10 fold differ-ence was observed between regions of the range atsimilar spatial scales (Southall et al. 2019).
In evaluating potential behavioral responses toactive sonar during the survey, it is noteworthy thatthe general distribution of vocalizing whales was notdifferent from historical observations nor did it differbetween survey and non-survey periods. ANOVAshowed a significant effect of the block of samplingzone (F = 181.4, df = 3, p < 0.01) but no significanteffect of time period relative to the survey (F = 1.06,df = 2, p > 0.05). Data did not violate the normalityand homogeneity of variance assumptions of ANOVA(SW = 0.91, p = 0.79; Levene’s F = 0.8, p = 0.61)This suggests that beaked whales generally re -mained in similar areas and continued to forage insimilar ways prior to, during, and after the surveyperiod. At a smaller scale, we examined the distancebetween the center hydrophone and the ship fordetections of Mesoplodon on the range. Using Kol-mogorov-Smirnov tests, we found that the observeddistribution of distances was not different from theexpected Weibull distribution for the entire survey
Benoit-Bird et al.: Beaked whale predator−prey relationships 7
(D = 0.84, p > 0.20, n = 509 detections)nor for just the time periods when theAUV was deployed (D = 0.73, p > 0.20,n = 289). Based on the quartile−quar-tile plot of the ob served versus ex -pected distances, the data fell quiteclose to the 1:1 line for both data sets,and there were no obvious drop downsin the line at any scale as we mightexpect if animals were actively avoid-ing the ship at some ranges. There wasa small de gree of mismatch at the tailends of the distribution where therewere very few data points. Theseresults are consistent with observa-tions of Ziphius re sponse off SouthernCalifornia to the same systems andsimilar survey design (Southall et al. 2019) and a sim-ilar survey using a multibeam echosounder (KatesVarghese et al. 2020), though in other locationsbeaked whales have been observed to respond toechosounders at finer scales than were possible toobserve here (Cholewiak et al. 2017). Here, habitatused by the whales matched the historical observa-tions that guided the sampling design and did nothave a spatially variable response to the sampling.The strong fit of the distances between beakedwhales and the ship to the expected distribution pro-vides support for the interpretation of spatial patternsin whales and resources during the time of sampling.
3.1.2. Potential beaked whale prey
Acoustic samples of potential beaked whale preyin The Bahamas were collected in 5 zones: a rela-tively higher use habitat on the western part of therange, a lower use area on the eastern part of therange, south of the range, north of the range, and aless-disturbed comparison site off the range nearGreat Abaco Island. Results from the MANOVAshowed a significant effect of sampling zone on preymetrics (Table 1; F = 15.36, df = 24,36.1, p < 0.001,where data did not violate the ANOVA assumptionsof homogeneity [Levene’s F = 0.69, p = 0.61] or nor-mality [SW = 0.71, p = 0.75]). Tests of the between-subjects’ effects of sampling zone were significant forall dependent variables (df = 4, p < 0.05 for all com-parisons) with the exception of the ratio of fish tocrustacean targets (F = 0.32, df = 4, p > 0.1). Tukey’sHSD post hoc tests showed that all zones were signif-icantly different from each other for these dependentvariables (p < 0.05 for all comparisons)
To determine which dependent variables and com-binations of variables were important in separatingzones, we used discriminant function analysis. Sam-pling zones were generally well separated (Fig. 2) by2 discriminant functions which accounted for 95.3%of the variance observed at the transect level. The
Squid variable South AUTEC AUTEC AbacoEast West
Proportion 9 18 31 37(% of all targets)
Density 0.03 0.54 0.63 0.66(no. per 1000 m3)
Peak depth (m) 900 1000 1000 1100Distribution Near Near 100 m patches, 100 m patches,
random random 400−800 m apart 600−1200 m apartMode spacing (m) 2600 280 26 16Mean mantle 11 12 15 16
length (cm)
Table 1. Prey variables measured between 600 and 1200 m depth in each zonein The Bahamas. The Zone to the North of the Atlantic Undersea Test andEvaluation Center (AUTEC) was not included because it was not a coherent,
statistically distinct region
WestAbaco
North
East
South
5.0
2.5
0.0
–2.5
Func
tion
2
–5.0
Function 1–5.0 –2.5 0.0 5.02.5
AbacoNorth (West)North (East)SouthEastWest
Fig. 2. Discriminant analysis plot of the first 2 discriminantfunctions representing 95.3% of the variance in prey meas-ures observed between the 5 zones in Fig. 1. Dots: functionvalues for individual transects with each zone in a differentcolor; squares: centroid for each zone. Patterns in both dis-criminant functions were consistent with our understandingof the relative use of the habitat by Mesoplodon, with highervalues of each function for zones with greater habitat use.Only the North habitat was not well separated from othersampling zones; transects on the east side of the North zone(orange dots outlined in red) were in the same reduced vari-able space as those from the eastern range while thoseon the west side of the North zone (orange dots outlined inyellow) were close to the western transects in variable space
Mar Ecol Prog Ser 654: 1–16, 20208
North Zone was not well separated from the zones onthe instrumented part of the AUTEC range; transectson the east side of the North Zone were in the samereduced variable space as those from AUTEC East,while those on the west side of the North Zone wereclose to AUTEC West transects in variable space.Because of this spatial variation, foraging habitatquality was not estimated for the North Zone.
Patterns in both discriminant functions (Fig. 2)were consistent with our understanding of the rela-tive use of the habitat by Mesoplodon, with highervalues of each function for zones with greater habitatuse. Based on foraging click activity, the least usedhabitat on the instrumented range, AUTEC East, isnear the lower left while the most used zone on theinstrumented range, AUTEC West, is near the upperright. Abaco, which has more favorable populationdemographic characteristics compared to AUTEC, ison the upper right of the plot. Function 1, explaining78.5% of the variance, consisted of the variables (indescending order of influence) mode squid spacing
(900−1000 m), peak squid depth, 100 m scale patchi-ness of squid targets (850−1050 m), and focal preyproportion (900−1200 m). Function 2, explaining16.8% of the variance, included maximum density ofsquid targets (850−1050 m), mean squid targetstrength (600−1200 m), and 100 m scale variabilityover depth (600−1200 m).
There were differences across zones in coherencebetween the upper water column and the depths atwhich beaked whales forage (Fig. 3). For example, inthe upper 600 m of the water column, we foundhigher total acoustic scattering at 38 kHz on the east-ern side of the AUTEC range than the west, while theopposite pattern was observed at depths between900 and 1200 m. This is in contrast to previous workthat found higher scattering in the upper water col-umn on the west side of the range (Hazen et al. 2011)but is similar to the incoherence between the surfaceocean and the deep observed off Southern California(Benoit-Bird et al. 2016). In contrast, we observedcoherence between acoustic scattering in the upper
Integrated acoustic scattering 100 m-scale variability0–600 m 900–1200 m 0–600 m
Sampling900–1200 m
m
m2 nmi–2 100 m–1(38 kHz) 100 m variance/10 km variance
2 nmi‐2 100m‐1(38kHz) 100m variance/10kmvariancem2 nmi‐2 100m‐1 100m variance/10kmvariance(38kHz)● transect center
Fig. 3. Distribution of potential prey in the upper water column compared to the depths over which Mesoplodon are mostlikely to forage. Black dots: center of each sampling transect. Map surfaces were generated using minimum curvature inter-
polations. Note the differences in scale bars between panels
Benoit-Bird et al.: Beaked whale predator−prey relationships 9
and lower water column in some locations, like theSouth Zone, where acoustic scattering was relativelylow throughout the water column, and Abaco wherethe highest integrated scattering measures of anyzone were observed from the surface to 1200 m, par-ticularly in the northern transects. Measures of spa-tial variability at 100 m scales showed similar inco-herence between surface waters and the depthswhere beaked whales forage (Fig. 3).
Throughout the food chain, biotic features weredeeper at Abaco than in the TOTO sites, beginningwith the subsurface chlorophyll max, includingmesopelagic scattering layers as well as the peakdepth of larger animals consistent with squid(Fig. 4). Across these biotic features, there were nosubstantial differences in the levels or integratedproxies of biomass between the 2 sites. However,deep-water acoustic targets identified as squids(ANOVA: F = 3.49, df = 1,19, p < 0.05) and thoseidentified as fishes (ANOVA: F = 2.81, df = 1,19,p < 0.05) were significantly larger (ANOVA: F =3.49, df = 1,19, p < 0.05) at Abaco than the TOTOsites and between AUTEC West and Abaco (Tukey’sHSD: Squid: mean difference = 1.02 cm, 95% CI =0.74−1.78 cm, p < 0.05; Fishes: mean difference =1.22 cm, 95% CI = 0.51−2.08 cm, p < 0.05). All
data met the homogeneity and normality assump-tions of ANOVA (SW, p > 0.25; Levene’s, p > 0.18for all comparisons)
3.2. Comparative results
To examine the collective effects of prey variableson potential Mesoplodon foraging gains, we utilizedan integrated foraging habitat quality metric. Thismetric is in units of dives per day that an individualbeaked whale would need to meet its basic energyneeds if it could consume every squid it encountered.While simplistic, this relativistic measure incorporatesmultiple prey variables with the biology and behaviorof the predator, allowing us to compare across zonesand habitats. Importantly, the metric is scaled to aver-age body size so it also allows comparisons betweenspecies. The relative Mesoplodon foraging habitatquality metrics for The Bahamas sites are shown inFig. 5. Data presented in Southall et al. (2019) forZiphius in Southern California are also shown. Therelative ordering of the zones in The Bahamas corre-sponds with the pattern of zones identified by dis-criminant function analysis in Fig. 2. The ordering atboth The Bahamas and California sites generally cor-
responds with obser vations of relativehabitat use by beaked whales acrossthese zones, with areas of highest userequiring the fewest dives for an indi-vidual beaked whale to access re -sources, while areas of low use wouldrequire many more dives per day thanthese animals can undertake based ontheir physiological constraints. Finerscale sampling regions at AUTEC andAbaco in areas known to have consis-tently high beaked whale foragingshowed these areas would have re-quired the fewest dives per day forbeaked whale prey acquisition duringour sampling period.
Differences in habitat use in passiveacoustic and visual survey data werequantified using a scoring systemwhere relative habitat use is referencedto the highest use zone on each navalrange. These scores are plotted as afunction of the prey quality metric indives per day in Fig. 6 (F1,6 = 1724.47,p < 0.001, adjusted R2 = 0.99). Therewas a consistent power function rela-tionship between these variables across
0 0.4 1000 0 10
0
300
600
900
Dept
h (m
)
1200
AUTEC
Fluorescence
mg l–1
Integrated scattering
0
38 kHz m2 nmi–2 50 m–1
‘Squid’ targets
No. 1000 m–3
Abaco
Fig. 4. Throughout the food chain, biotic features were deeper at Abaco thanthe AUTEC sites, beginning with the subsurface chlorophyll max (left), in -cluding mesopelagic scattering layers (center) as well as the peak depth of
larger animals consistent with squid (right)
Mar Ecol Prog Ser 654: 1–16, 202010
sites and zones, with habitat use best predicted by oneover the square root of the foraging habitat qualitymetric. A power distribution is scale-free, meaning thatas we change the units by which we measure environ-mental quality, the shape of the distribution is un-changed except for an overall multiplicative constant,making our precise means of quantifying environmen-tal quality and habitat use less important than theirrelative scaling. However, because of the small num-ber of data points, the specific details of the numericalrelationship must be extrapolated with care.
4. DISCUSSION
The distribution of potential prey plays a criticalrole in driving the observed distribution of beakedwhales and explaining the persistent use of USNavy ranges by beaked whales despite repeateddisturbance from many human noise sources,including powerful active sonar systems associatedwith whale strandings. Understanding the distribu-tion of prey and how it relates to patterns of whaledistribution and disturbance plays a vital role indetermining the energetic and potential populationcosts of these range activities for population man-agement. The list of important potential prey vari-ables separating these zones does not include theestimated biomass of resources. Instead, these vari-ables separating sampling zones describe the spatialorganization of squid, similar to findings from otherbeaked whales off Southern California (Southall etal. 2019) as well as in other predator−prey systems(Benoit-Bird et al. 2013). As off Southern California,beaked whales in The Bahamas also preferentiallyused habitats with larger individual squid thatlikely have greater energy content and those wheresquid made up a greater proportion of potentialprey targets. Both of these factors potentially reducesearch and handling costs (Warburton & Thomson2006) by increasing the signal-to-noise ratio inbiosonar echoes while reducing the need to processacoustic information from non-target prey and makedecisions about whether and when to pursue preyas well as reducing the chance of prey targetingerrors.
Our prey analyses focused on the characteristics oftargets consistent with squid because of the primarilyteuthivorous diet described for beaked whales. How-ever, species in the genus Mesoplodon consume fishin some locations (Clarke 1996, MacLeod et al. 2003).A variety of recent evidence, including stable isotopeanalysis, fecal samples, and gut contents, suggeststhat Mesoplodon in The Bahamas include fishes intheir diet as well (D. E. Claridge et al. unpubl. data),though the relative importance of fishes in their over-all energy budget is not clear. The relative propor-tion of squid between 600− 1200 m varied signifi-cantly between zones. However, at beaked whaleforaging depths, the ratio of targets consistent withcrustaceans to those consistent with fishes did notvary significantly across zones, averaging 2.1 crus-taceans:1 fish. Thus, the South Zone, with only 9%squid targets had a greater proportion of fishes thanAbaco, which had 37% squid. Differences in thedensity of targets between these sites meant the total
Fig. 5. Prey data were combined into a relativistic measureof Mesoplodon foraging habitat quality that incorporatesmultiple prey variables with the biology, behavior, and sizeof the predator to allow comparison across zones, habitats,and species (Southall et al. 2019). Each sampling zone isshown in black, for Southern California and The Bahamas.The North zone in The Bahamas is split into east and westparts, shown in dashed lines. Finer scale sampling at knownbeaked whale hotspots in The Bahamas is shown in grey.The high-use habitats in each location have prey qualitymetrics of approximately 1 dive d−1 or around 10% of the ob-served daily dive rate for beaked whales. SOAR: SouthernCalifornia Anti-Submarine Warfare Range; W1: Whiskey 1.
See Fig. 1 for locations in the Bahamas
Benoit-Bird et al.: Beaked whale predator−prey relationships 11
number of fish targets was similar across all locationsduring the study. The target strength of each taxo-nomic class was signi ficantly higher at Abaco than atthe TOTO sites.
All of the prey variables statistically separatingzones defined a priori by Mesoplodon activity in -clude depth ranges overlapping with the peakdepths of foraging buzzes between 650 and 1050 mobserved in this area (L. S. Hickmott et al. unpubl.data) and in this species in other areas (Johnson et al.2004, 2008). The differences between zones weobserved at these depths were, however, not alwaysevident in the upper water column, as we observeddifferences in coherence between the upper anddeep column across the study area with low scatter-ing in the portion of the range most used by beakedwhales. This is in contrast to previous work thatfound higher scattering in the upper water columnon the western, high-use side of the range (Hazen etal. 2011) but is similar to the incoherence betweenthe surface ocean and the deep observed off South-ern California (Benoit-Bird et al. 2016). In contrast,we observed coherence between acoustic scatteringin the upper and lower water column in some loca-tions, such as the South Zone where acoustic scatter-ing was relatively low throughout the water column,
and Abaco where the highest inte-grated scattering measures of anyzone were observed from the surfaceto 1200 m. Measures of spatial vari-ability at 100 m scales showed similarincoherence between surface watersand the depths where beaked whalesforage (Fig. 3). These observationsconfirm the conclusion that for deep-diving predators, surface-based sam-pling to predict prey resources canlead to inappropriate conclusionswhen the mechanisms and time scalesof connection between surface andthe deep are not well known. In theecosystems that are critical habitat forbeaked whales, such as most pelagicsystems, large-scale, long-term, con-trolled manipulations are difficult.Instead, pseudo-experimental analy-ses that treat independent beakedwhale populations as ‘replicates’ andspatial contrasts in disturbance as‘treatments’ are used to disentanglethe effects of disturbance like sonarfrom natural variation and statisticalnoise on pop ulations. One such com-
parison has been the AUTEC range, where humandisturbance is a regular feature of the environment,and the area around Great Abaco Island, where dis-turbance by military sonars is comparatively infre-quent (Moretti 2019). Despite their close proximity(170 km separates the 2 sites), the home ranges ofanimals in these 2 areas do not appear to overlap(Claridge 2013). The average annual abundance ofanimals at AUTEC West and calf-to-female ratios aresignificantly lower than at Abaco, leading to the sug-gestion that military activities at AUTEC have led tonegative population consequences to Mesoplodon onthe range (Claridge 2013, Moretti 2019). Compar-isons between locations can provide a powerful toolfor revealing the processes driving populations. Weobserved that the zones most used by beaked whalesat both sites share a number of prey features at thedepths over which beaked whales forage, includingrelatively high proportions of larger squid distributedin aggregations. These same features were observedto correlate with beaked whale habitat use off South-ern California (Southall et al. 2019), revealing muchabout what prey features are important for beakedwhale success. In terms of the distribution of deep-water squid, AUTEC West was more similar to Abacothan it was to the contiguous area, AUTEC East. The
S. California zonesThe Bahamas zonesThe Bahamas fine-scale sites
Fig. 6. Habitat use by beaked whales for each sampling unit scored relative tothe highest use site on each Navy range using a combination of available pas-sive acoustic and visual survey data. These scores (N = 8) are shown as a func-tion of the foraging habitat quality metric developed by Southall et al. (2019)using prey data collected in the same areas. Not included are the North andSouth zones adjacent to AUTEC as not enough data on beaked whale distri-butions exists to establish a habitat use score. The best-fit regression, a powerre lationship, is shown as a solid line. Data for Southern California from Benoit-
Bird et al. (2016)
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differences within AUTEC have been proposed to bedriven by localized upwelling, the location of steeptopography, and the strength of the thermocline(Hazen et al. 2011).
Despite the general similarities in prey characteris-tics in Mesoplodon foraging habitat, our results high-light substantial differences in resources during ourstudy between even the parts of the AUTEC rangemost used by Mesoplodon and the Abaco site. Squidmeasurements at Abaco were more favorable forbeaked whales than those at AUTEC on all measuresconsidered, with higher overall densities of squidthat are larger, more closely spaced, and make up alarger proportion of potential acoustic targets. Thesedifferences are less pronounced but still statisticallysignificant when comparing only AUTEC West andAbaco. Overall, during the 2 wk timeframe of thisstudy, Abaco appeared to be a more energy efficientecosystem, with more extensively migrating meso-pelagic animals, larger animals from zooplankton tonekton, and a greater degree of vertical overlapamongst trophic steps than TOTO (Sato & Benoit-Bird 2017). This resulted in an approximately 20%difference in foraging habitat quality metrics be -tween similarly sized zones on the parts of theAUTEC range most used by Mesoplodon and Abacoand up to a 20 fold difference from Abaco if the entireTOTO region sampled is considered, though thescale differences in this comparison must be consid-ered. These differences in foraging habitat charac-teristics should not be surprising given the dramaticdifferences in oceanography between the 2 sites,with Abaco experiencing conditions consistent withan open-ocean ecosystem, while TOTO is isolatedfrom these oceanic influences, acting as a closed eco-system from a physical and likely biological perspec-tive. Much more subtle variations in topography andoceanography have been shown to influence thehabitat preferences of Mesoplodon in The Bahamas(MacLeod & Zuur 2005). Our observations of preyresources, while limited in time, combined with theseoverall differences in habitat characteristics providean alternative hypothesis to disturbance to accountfor the differences in beaked whale populationsobserved between TOTO and Abaco slope. Theresults presented here highlight the care that mustbe taken in interpreting pseudo-experimental popu-lation contrasts where natural environmental varia-tion cannot be accounted for. Vital rates establishedfor one population should not be considered a base-line for the other without careful consideration ofcontext provided by the habitat, including prey. Thisstudy has advanced our ability to interpret demo-
graphic differences between AUTEC West and Abacoand will better inform models predicting populationconsequences of disturbance.
4.1. Comparative results
Using a comparative metric of foraging habitatquality that integrates prey variables and normalizesthem using knowledge of whale biology lets us com-bine the results from The Bahamas sites with simi-larly collected data off Southern California, provid-ing information on the relationship between beakedwhales and their deep-water prey more generally.Despite the differences in the size of the species ofbeaked whale found in the 2 locations and the con-trasts in the ecosystems themselves, those zones his-torically observed to have the greatest rates of forag-ing by beaked whales had prey quality metrics at orbelow a value of 1 dive d−1, about 10% of observeddaily dive rates (Southall et al. 2019). This proportionof observed daily dives may perhaps be an evenmore robust indicator of the potential foraging gains.However, the value of the metric, which is affectedby the specifics of the parameterization, is less impor-tant than the consistency observed and the shape ofthe relationship between the metric and habitat useby beaked whales. Determining the form of predator−prey relationships is critical for understanding eco-system dynamics and managing predator popula-tions relative to the host of threats that they face. Forbeaked whales, the functional relationship devel-oped with their prey in and near US Navy test rangesshows that small changes in prey can have large con-sequences for how beaked whales use their habitat.Using this understanding, it is possible to comparelocations to determine where whales are likely tospend the most time. For example, based on the datapresented here, we hypothesize that Mesoplodonshould spend relatively little time foraging in theSouth zone. Animals that avoid activities on therange by moving to the north should be able toaccess similar levels of food on the western side ofthat zone, though concentration of animals or overlapwith animals that generally inhabit the northern areacould increase competition for these resources.These predictions could be extrapolated to includechanges over time as resources change naturally oras a result of climate change. Prey information, inte-grated with predator information as is done here,could also inform site selection for activities withinranges, the selection of sites for new activities withthe goal of minimizing impacts on beaked whale
Benoit-Bird et al.: Beaked whale predator−prey relationships 13
populations, or the selection of protected areas(Hooker et al. 2002).
Far from the linear relationship between resourcesand gains assumed in existing models, our resultsindicate a critical threshold in prey characteristics forbeaked whale foraging success measured as habitatuse, below which predators are unlikely to be suc-cessful but above which small changes in resourcesallow large gains to the predator. The power-lawfunctional relationship observed indicates that only asmall range of measured habitat quality values ispreferred by beaked whales. Responses to thresholdlevels of prey are commonly observed in oceanicpredators (Cury et al. 2011), though the shape typi-cally involves an asymptote above which gains areno longer realized (Holling 1959), a point notobserved here.
Our empirical observations are most consistentwith the form of a Type III functional responsedescribed by Holling (1959). Type III responses occurin predators that increase their search activity withincreasing prey density or exhibit dietary switchingto the most abundant prey species, which can resultin regulation of prey density by a stable population ofpredators. This observation provides insight into the-oretical and mathematical avenues for future exami-nation of beaked whale populations. For example,the shape of the relationship between beaked whalesand their resources informs the ongoing develop-ment of energetic models aimed at connecting obser-vations of short-term behavioral responses of beakedwhales facing disturbance with population-level con-sequences (New et al. 2013, Hin et al. 2019, Moretti2019). The appearance of an apparently sharp thresh -old in the functional relationship between beakedwhale habitat preferences and their prey has signifi-cant ecological as well as management implications;relatively small behavioral changes resulting fromdisturbance could have unpredicted yet consequen-tial population effects, including decreased individ-ual growth, reproductive, and other vital rates. Anadditional consequence is that models of beakedwhale populations seeking to incorporate prey willbe very sensitive to the parameters chosen, empha-sizing the importance of these difficult to obtain andcurrently rare data.
4.2. Conclusions
We observed extensive spatial heterogeneity inforaging habitat at submesoscales (<100 km; thescale of oceanic eddies and similar interactions
between currents and other bodies of water) in botha temperate upwelling and low-productivity sub-tropical ecosystem. Strong variation in resourcesover horizontal distances smaller than the potentialhabitat range of an individual beaked whale sug-gests that careful direct evaluation of the habitat isneeded for siting of human activities within thesehabitats. Further evaluation of potential differencesin prey species composition that cannot currently beaddressed with acoustic tools should also be exam-ined at these scales by employing large deep-watertrawls, video imaging on robotic platforms, or othertechniques.
In The Bahamas, Mesoplodon appear to have muchto gain in the western sector of the AUTEC range.While it may be practically infeasible to suggestestablishing a sonar-free area in this region given thepresence of the expensive, extensive range facility,one potential mitigation action consistent with ourresults would be to concentrate mid-frequency activesonar (MFAS) operations on the eastern side of theAUTEC range rather than the western, higher-useside when possible. This spatially explicit actioncould reduce the potential consequences of distur-bance in this important habitat for Mesoplodon, atleast for those occurring at higher sonar intensitiesand at the shorter ranges where the greatest behav-ioral changes have been shown to occur (Falcone etal. 2017). In addition, care should be taken to avoidactivities that shepherd animals southward, whereprey resources immediately adjacent to the rangewere observed to be unfavorable for beaked whaleforaging. Activities that limit movement of southerlyanimals to regions to the northwest of the range,where our habitat measures suggest prey were simi-lar to the most used parts of the range, should also beavoided. Incorporation of our results into modelsevaluating the population consequences of distur-bance from Navy MFAS will allow explicit compar-isons of the relative energetic consequences of vari-ous disturbance scenarios, further enabling decisionmaking about the spatio-temporal dynamics of sonaractivities.
Our historical view of the deep sea as unchangingand disconnected from surface-driven processes(Menzies 1965) is being challenged by recent re -search showing how susceptible these extensive anddiverse habitats, particularly the top predators inthem, are to threats from fishing, mining, dumping,climate change, and other anthropogenic stressors,including sound (Davies et al. 2007). The unprece-dented deep-sea data provided by our combinedwork within 2 ecologically disparate regions of naval
Mar Ecol Prog Ser 654: 1–16, 202014
importance tells us about these areas, about beakedwhale ecology, and the biological and managementrelevance of spatial heterogeneity of resources. Thiswork also contributes to our changing perspective onthe ocean and how we manage it. We are in a race todescribe and understand this ‘last great wilderness’(Roberts 2002) where there may be ‘a million unde-scribed species, with biological adaptations and eco-logical mechanisms that we cannot yet imagine’(Robison 2004, p. 253). The empirically derived, func-tional relationship between beaked whale predatorsand their deep-dwelling squid prey provides newand surprising insights into the processes affectingocean predators, the ecological structure and dynam-ics of the deep-sea ecosystems they inhabit, and thepotential effects of human activities on the ecologi-cally and economically valuable habitat that makesup the largest living space on our planet.
Acknowledgements. We thank the crew of the R/V ‘Sharp’and staff at the Atlantic Undersea Test and Evaluation Cen-ter for field support. Thomas Leo, Nancy DiMarzio, andStephanie Watwood provided logistical support for therange. Chad Waluk provided technical expertise, assistedwith equipment setup and data collection, and conductedpre-processing of the CTD and acoustic data. Marnie Jo Zir-bel provided taxonomic expertise. Mei Sato, Ian Robbins,Megan Cimino, and Matthew Breece participated in thefield operations. This work was funded by the Office ofNaval Research Marine Mammal Biology Program (GrantNo.: N00014-15-1-2204). We thank program managerMichael Weise for his assistance coordinating with the Navyand supporting other logistics that made this work possible.This work was conducted under a research permit (No. 12A)issued by The Bahamas Department of Marine Resources asauthorized under The Bahamas Marine Mammal ProtectionAct (2005).
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Editorial responsibility: Peter Corkeron,Woods Hole, MA, USA
Reviewed by: M. Vecchione and 1 anonymous referee
Submitted: August 15, 2020Accepted: October 1, 2020Proofs received from author(s): November 6, 2020
