How Are Carrying Capacities Estimated For Aquatic Animals

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Inquiry Article

Estimating Cetacean Carrying Capacity Based on Spacing Behaviour

• Janelle E. Braithwaite,
• Jessica J. Meeuwig,
• Thousand. Brusk Due south. Jenner

x

• Published: Dec 7, 2012
• https://doi.org/x.1371/periodical.pone.0051347

Figures

Abstract

Conservation of big ocean wild fauna requires an agreement of how they utilise infinite. In Western Australia, the humpback whale (Megaptera novaeangliae) population is growing at a minimum rate of x% per year. An important consideration for conservation based management in space-limited environments, such every bit coastal resting areas, is the potential expansion in area apply past humpback whales if the carrying capacity of existing areas is exceeded. Here nosotros adamant the theoretical conveying chapters of a known humpback resting area based on the spacing behaviour of pods, where a resting area is defined every bit a sheltered embayment along the coast. 2 separate approaches were taken to estimate this altitude. The outset used the median nearest neighbor altitude between pods in relatively dense areas, giving a spacing distance of ii.xvi km (±0.94). The second estimated the spacing distance as the radius at which fifty% of the population included no other pods, and was calculated as one.93 km (range: 1.62–2.50 km). Using these values, the maximum number of pods able to fit into the resting area was 698 and 872 pods, respectively. Given an average observed pod size of one.7 whales, this equates to a carrying capacity judge of betwixt 1187 and 1482 whales at any given indicate in time. This study demonstrates that whale pods do maintain a distance from each other, which may make up one's mind the number of animals that tin can occupy aggregation areas where infinite is limited. This requirement for infinite has implications when considering boundaries for protected areas or competition for space with the fishing and resource sectors.

Citation: Braithwaite JE, Meeuwig JJ, Jenner KCS (2012) Estimating Cetacean Carrying Capacity Based on Spacing Behaviour. PLoS Ane 7(12): e51347. https://doi.org/10.1371/journal.pone.0051347

Editor: Brock Fenton, University of Western Ontario, Canada

Received: May 29, 2012; Accepted: November 5, 2012; Published: December 7, 2012

Copyright: © 2012 Braithwaite et al. This is an open-admission article distributed under the terms of the Creative Eatables Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original writer and source are credited.

Funding: Funding for data drove was provided for past a Straits Resources grant awarded to the Heart for Whale Inquiry, WA. The funders had no role in study design, data collection and analysis, determination to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

An important consideration for conservation is the population size that a given habitat can support. Estimating this carrying capacity provides a baseline against which changes to habitat can be assessed with respect to the maintenance of conservation values [1]. Here, carrying chapters is defined in terms of density limitation in a particular area at a given time, rather than the overall population carrying capacity (Chiliad) [2]. The limit to animal density in an area is generally related to the total amount of resources available in the habitat and the resource needs of each individual. It is well recognized that density scales inversely with body size across many found and animal communities [three]–[6], as does dwelling house-range size in top predators [6]–[viii]. Private energy need is the main explanation for these trends, with larger animals requiring more food and thus a larger expanse for foraging. Therefore, carrying capacity is often calculated based on nutrient supply [9], [10]: for case, the estimated carrying chapters of sites used by migratory birds is calculated using a 'daily ration model', whereby the total consumable food of the site is divided by the individual energetic requirement [1], [x], [11]. Withal, this conventional arroyo to calculating conveying capacity is limited, and other studies have found that carrying capacity can too be influenced by predation risk [12], freshwater availability [13], shelter [fourteen], and the availability of nesting sites [fifteen]. As the infinite requirement of an brute, for instance its home range, is generally related to the availability of resources, space itself can exist considered equally a resource that will limit density.

According to Tilman [xvi] "all things consumed by a species are potentially limiting resources for information technology", where the term 'consumed' describes those things used, such as an occupied woods hole for a squirrel. Following this definition, we contend that space is a resource, every bit animals swallow space due to the physical requirements to perform behaviours, such every bit individual fish within a school [17], or due to a behavioural preference of the animal, for instance social density in primates [eighteen]. The concept of space as a resource is also reflected in enquiry into the welfare needs of animals in captivity, such equally livestock or zoo animals with welfare positively correlated to size and complexity of enclosures. A classic case is caged hens (Gallus gallus domesticus), where a behavioural study on the confinements of laying hens in the late 1980s found that the existing cage measurements, based on the concrete size of the bird (excluding fly-bridge), did not allow essential behaviour movements for the hens [19], [20]. Increased space availability in livestock has shown to improve welfare, such equally playfulness in juveniles [21], disharmonize avoidance [22], [23], and reduced muscle impairment and fatigue during transportation [24], [25]. In aquaculture, the stocking density of fish tin touch on growth charge per unit [26] and bloodshed [27], however this is non only associated with the behavioural requirement of space for the individual, but with having space to allow for the apportionment of high quality h2o and period rates [27]. A study by Clubb and Bricklayer [28] claims that success for carnivores in captivity is linked to home-range sizes in the wild, whereby infant mortality and stereotypic locomotive behaviour was positively correlated with increasing natural home-range sizes. In captivity food is plentiful, suggesting that the space utilize and natural ranging behaviour of carnivores in the wild can be a factor when considering animal welfare in captivity, regardless of the correlation betwixt home-range size and foraging needs. Many of these examples are of animals in captivity and in that location has been lilliputian research on space as a resource in wild populations. Yet in naturally confined environments, the infinite requirements of an private will make up one's mind the density limitation of animals in that area.

Migrating humpback whales in resting areas nowadays a unique opportunity to investigate spacing behaviour in the wild, and the potential limitation this may take on the carrying capacity of the area. During migration, adult humpback whales are not actively feeding, eliminating energy requirements every bit a gene in density limitation. While calves and juveniles are feeding to varying degrees (Jenner, pers. obs.), their typical presence within a pod containing a fasting developed, where calves are feeding on their mother's milk, means that it is unlikely to be a contributing cistron to density limitation. Resting areas are found in relatively enclosed coastal areas, which provide shelter from open up oceanographic conditions and protection from potential predators such as killer whales (Orcinus orca), and are therefore space express. Along the coast of Western Australia, the apply of coastal areas past the migrating humpback population is an of import conservation upshot; the humpback whale population is increasing at about maximum rates [29], while the coastline is becoming increasingly adult. For case, the large offshore oil and gas developments around the Pilbara region of Western Commonwealth of australia have resulted in the cosmos and expansion of coastal ports, increases in marine vessel traffic and noise, potentially creating competition with migrating whales for infinite in the ocean. This contest for infinite is of particular concern in resting areas, which provide the singled-out conditions for humpback whales to rest, but are also limited in available infinite.

Here, we used innovative techniques to explore the concept of a space-defined carrying capacity in a natural environment by examining the spacing behaviour of humpback whales in Exmouth Gulf, a recognized resting and nursing area [thirty], [31], during the 2004 and 2005 migrations. Temporal use was estimated using aeriform line-transect surveys, and overall space use was investigated through the affluence-occupancy relationship. Two different approaches were then used to determine the average distance maintained between pods. This spacing distance was calculated beyond whale pods in various behavioural states, to obtain a representative distance across the population occupying the Gulf at that point in time. Based on this space apply nosotros determine the carrying capacity of the area, which represents the theoretical maximum number of whales able to occupy Exmouth Gulf during the 2004–2005 seasons. We highlight the implications of having a space-defined carrying capacity in the context of an expanding population given current temporal and spatial apply of the Gulf.

Materials and Methods

Study Surface area

Exmouth Gulf (Fig. ane) is located on the Northwest shelf of Australia, betwixt 21°45'Southward–22°33'S and 114°08'E–114°40'E. This embayment is approximately 3000 kmⁱⁱ in size, with a hateful depth of 9 m and maximum depth of about twenty m. The Gulf is located in the tropical zone and experiences an average SST of 22–23°C during October when whale numbers height. Exmouth Gulf is a recognized resting area for convenance stock D humpback whales as they drift southwards from their calving grounds in Camden Sound (northern Western Australia) to the Southern Ocean each yr between August and November [31]. The Gulf is constrained by coastline on three sides, with a northern opening to the bounding main.

Figure i. The aerial survey rails over Exmouth Gulf.

A typical class flown by the aircraft during surveys. This flight path was split into ix parallel transects spaced approximately 10 km apart.

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Aerial Surveys

A total of 17 aerial surveys were conducted in Exmouth Gulf between 7^thursday July 2004 and fifteen^th October 2005, of which 10 flights included observations of humpback whales (Table 1). Surveys were conducted in a twin-engine, overhead winged aircraft (Cessna 337) maintaining a cruising speed of 222 kmh⁻¹ (120 knots) and an distance of 305 m (1000 anxiety). Data were collected using distance-sampling methods, with the plane post-obit a systematic parallel line transect class across the Gulf (Fig. i) in passing fashion (no deviations from the runway), post-obit Buckland et al. [32]. The parallel transects were spaced approximately x km apart to minimize overlap in the covered strips [29], [33]. Personnel aboard the aircraft included the pilot, two observers and a information recorder. During the survey, the pilot recorded the angle of drift away from the flight path. For each pod sighting the observer measured the vertical and horizontal angles from the plane, as well every bit the GPS location of the plane, and the pod size and composition (number of adults and calves, adamant based on size). At the beginning of each flight the devices were calibrated to ±1sec accurateness. Sea land, glare, wind speed, and visibility were also recorded throughout the survey, to monitor changes in sighting weather. The position of each whale pod was then calculated post-obit the method in Salgado-Kent et al [29].

Abundance

Population transect surveys are subject to availability and perception biases, whereby animals could exist missed if they were non bachelor to be seen, or they were available only not seen by the observer [34]. Therefore, distance-sampling was used to reduce whatever errors caused past perception bias and provide more accurate estimates of abundance [32]. This method models the probability of detection of an animal group equally a office of the perpendicular distance from the transect. The probability detection function can also have into business relationship the variation in sighting conditions, by introducing covariates such as observer and bounding main state. Once a detection function has been fit, it is used to estimate the bodily number of animals in the survey area, including those likely to have been missed by the observer (the perception bias).

The sightings data were correct-truncated at 5 km from the transect line, removing 5% of the information, following the general 'dominion of thumb' to remove extreme values prior to fitting detection functions [32]. In aerial surveys, it is also difficult to brand observations on the transect line every bit information technology lies direct beneath the aeroplane. However, the method of plumbing fixtures a detection function assumes that all animals at the surface (available to exist seen) on the transect line were observed. To business relationship for the discrepancy, a standard left-truncation at 0.one km was set to obtain a better detection office fit, however this did not result in any loss of information as no observations were made within this distance. Distance 6.0 [35] was used to fit dissimilar detection function models (half-normal and risk-rate) for each flight, taking into account covariates that may affect detection probability such as observer, body of water state, pod size, and mean solar day of flight. Model pick for each flying was based on the Akaike'south Data Criterion (AIC), Q-Q plots, and the Kolmogorov-Smirnov and Cramer-von Mises goodness-of-fit tests. If ii or more models were besides similar to brand a option based on the higher up criteria, the parsimonious model was selected. The abundance of whales in Exmouth Gulf for each flight was then estimated in Distance half-dozen.0 using the best probability detection function, and 95% confidence intervals were obtained using a bootstrap.

Availability bias was not accounted for in this analysis, and therefore the model will underestimate affluence. However, nosotros believe this divergence to be small as the Gulf is relatively shallow, and resting whales tend to display passive behaviours such equally surface lying or surface travelling [36]. Therefore pods are more than probable to be at the surface and available to be seen from aerial surveys.

Pods with calves take previously been demonstrated to lag in the migration [37], [38]. By looking at the seasonal variation in calves in the Gulf and comparing this to the total abundance of all whales using the Gulf, nosotros can decide if a lag likewise exists in resting areas. If there were no lag, this would indicate that mainly mothers with calves are probable to exist using resting areas. If a lag does exist, then comparison the length of this lag with those found past Dawbin [38] in the main migration blueprint will point which groups are using the Gulf. The change in the number of pods with calves over times was plotted to test this prediction for this population of humpbacks. As many of the flights independent a modest sample size of pods with calves (<20), altitude sampling was not used in this analysis.

Abundance-Occupancy Relationship

The abundance-occupancy relationship (AOR) describes the relationship between the abundance of a species and the size of their ranges within a region, and reflects the pattern of abundance covarying with the full surface area occupied [39], [forty]. Equally AOR is usually evaluated across many sites within a region, abundance is calculated as the mean density across all occupied patches, and the occupancy as the sum expanse of all the occupied patches [forty]. In the basic AOR design, density remains constant while the occupied area increases, pregnant that abundance increases in proportion to the area. However, for near species the AOR is positive; as the density increases so does the occupied area [40]–[44]. In these cases, the population size is increasing at a greater charge per unit than would be expected only by a range expansion. Alternatively, the AOR design may reflect increases in density while the occupied expanse remains abiding. In this instance, population abundance increases merely the range size stays the same. Understanding the AOR relationship has of import implications for conservation; if there is a positive AOR and so any reduction in habitat will consequence in a greater loss in individuals proportional to the AOR [45]. To investigate the AOR for humpback whales in Exmouth Gulf, the occupancy area for each flight was estimated by a convex hull analysis [46], [47], which calculates the minimum expanse occupied past the population by plumbing equipment the smallest polygon possible that encompasses all the humpback whale sightings. The abundance was then estimated by calculating the density of humpback whales within the convex hull surface area (CHA).

Factors Affecting Pod Density

To calculate the conveying capacity of pods in Exmouth Gulf, it is important to first decide what factors may influence their spatial organisation and nearest neighbour distances. The two factors we investigated here were pod size and pod composition, where a pod is divers as a group of one or more than animals. During the breeding season, humpback whales are usually found in pods of 2–iii animals, however pod size can range from i to 20 animals [48]. Pod size could impact spacing behaviour in that, for example, larger pods may prefer more space. The type of animals present in a pod may as well influence their nearest neighbor distances regardless of pod size. For instance, during the breeding season mother and calf pairs receive the attending of adult males who are looking to compete for and mate with the now receptive female [49], which may alter the spacing of animals around pods with a calf.

To investigate the effect of pod size, the nearest neighbour distance for each pod in each flight was estimated. The pods from all the flights were then grouped together based upon pod size, ranging from 1 to 8 animals. Equally there were less than three observations for pods containing 5 or more animals, these groups were excluded from the analysis. The nearest neighbour distances in each of the remaining four group types were distributed non-normally (Kolmogorov-Smirnov test, p<0.05 for all groups). Therefore, the median nearest neighbor of each grouping size was compared using a Kruskal-Wallis exam.

Pod composition was defined as those with dogie present (wCP) and those without (nCP), due to the limitation of aerial surveys to specify composition in more than detail, such every bit singing males. The nearest neighbor distances for each pod in the two categories were also distributed non-ordinarily (Kolmogorov-Smirnov test, p<0.05 for both groups), and thus the spacing around the dissimilar pod types was tested by comparison the median nearest neighbours using a Kruskal-Wallis exam.

Spacing Behaviour

We defined spacing behaviour as the distance maintained betwixt pods under relatively dense conditions. To determine the spacing of individual whale pods, nosotros first needed to run across if the distribution in the flights followed the same pattern of infinite use. The harmonic mean position of pods for each flight information set was estimated, and the CHA was and then calculated past including increasing percentages of pods closest to the harmonic mean, starting at x% and increasing to 100% in increments of 10%. Two distinct trends of space use emerged with increasing number of pods included in the analysis (Fig. 2): flights 4, five, 6, and 8 used more space for fewer numbers of pods due to the depression number of whales recorded on those days, due to beingness at the offset and the end of the flavour (Table 1) while flights 1, 2, 3, 7, nine and x occupied less surface area per number of pods. Every bit we wanted to summate the distance maintained in relatively loftier density conditions, flights with depression densities (4, 5, 6, 8) were excluded from further analysis.

Figure 2. The area occupied by an increasing number of pods nearest to the centre of aggregation.

The minimum polygon area (convex hull area) around whale pods was repeatedly calculated for each survey flight to include increasing number of pods closest to the centre of aggregation, starting at the nearest x% until all pods were encompassed by the polygon. A scatter plot of these changes in area occupied reveals two patterns in expanse use; the first group of flights are indicated by open symbols (▵ flight 4, ⋄ flying 5, ○ flight half dozen, □ flying eight) and the 2d group by airtight symbols (♦ flight 1, ▪ flight ii, ▴ flight three, +flight seven, – flying nine, ♦ flight x).

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Two singled-out methods were used to summate pod spacing to assess consistency of the estimates. The outset method used the nearest neighbor distances between pods, whereas the second investigated the number of whales inside a given radius of a pod.

Method one.

For each pod in each flight, the distance to the nearest neighbour pod was calculated. A nearest neighbour analysis [50] was conducted for each flying, which calculates the ratio (Rn) between the observed hateful nearest neighbour distance (NND) and the expected hateful NND given a random distribution. Randomly distributed animals will give an Rn value of 1, amassed animals volition have a value less than 1, and uniformly spaced animals will have a value greater than i. This assay indicated that pods in Exmouth Gulf were not uniformly spaced, but had a tendency to cluster (Rn = 0.8; mean across 6 flights). As such, the nearest neighbour distance will vary depending on the distance betwixt the pod and the centre of assemblage. We thus grouped pods based on how close they were to the centre of aggregation because we needed to study the pod arrangement when humpbacks were in relatively high density weather condition, each group included x% of the pods; the 0–10% group contained the x% of pods closest to the harmonic hateful, the x–twenty% group was the next closest 10% to the mean, and so on. We used a i-way assay of variance (ANOVA) to compare the mean nearest neighbor distances for each percentage category. The mean nearest neighbour distances in the ninety–100% grouping were significantly higher than the rest of the groups (p<0.05; Tukey-Kramer. Fig. 3) and so were excluded from this analysis. The nearest neighbour distances of the remaining ninety% of the pods were also non-normal (Kolmogorov-Smirnov examination, p<0.05), so the overall distance maintained between pods was calculated as the median nearest neighbour distance. As there volition exist individual variability in pods, variation in this altitude was estimated past calculating the median absolute deviation (MAD).

Figure 3. A comparing of nearest neighbour distances with proximity to the centre of aggregation.

The nearest neighbour altitude (hateful of flights ± standard error) of groups of pods based on how close they are to the center of aggregation, i.e. the 10% mark contains the closest 10% pods to the mean, the 20% mark contains the closest 10–twenty%, and so on up to the 90–100% grouping. The just group with a significantly unlike nearest neighbour distance was the 90–100%, which was much higher than the rest.

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Method 2.

For each flight, sequential round boundaries at a radial distance of 0.001 km were drawn around every pod from a minimum radius of 0.001 km to a radius where all the pods had some other pod present in the boundary. The proportions of the pods that had at least one pod present within these radii were then calculated. This arroyo produced a cumulative density of the proportion of pods that had other pods present inside a radius of increasing length for each flight. A bend was and then fitted to the information using the least squares method [51] and an exponential model. Here, the distance maintained between pods was estimated to exist at the l% mark, analogous to the utilise of LD50 curves in toxicology [52] and size at maturity curves in fisheries [53]. At this point, half the pods have no other pods within the boundary and half of the pods have at to the lowest degree ane other pod inside the boundary, providing an guess of pod spacing for each flight. Equally a preliminary regression analysis indicated no season trend in the radii (p>0.05), the overall population pod spacing gauge was taken as the mean radius of the six flights, and the error range as the lowest and highest radius over the flights.

Carrying Capacity

Assuming that all pods maintain an area of space, the maximum number of pods able to fit in Exmouth Gulf at whatsoever one fourth dimension can be estimated as the highest density of pods allowing for distance between pods to be maintained within the area utilized by the population. The distances from the two above methods were used as a radius to determine a circular boundary of space effectually a pod. The maximum area used by the population of humpback whales was taken to be the CHA effectually all recorded pods over all the flights. The pods, plus their circular infinite, were arranged in a lattice germination, the densest concentration of circles on a single plane [54], inside the CHA while allowing the circles to overlap to the length of the radius so that the nearest neighbour to a pod was no closer than the spacing radius. This maximum number of pods for each of the methods was then multiplied by the average pod size to obtain 2 estimates of the carrying capacity for Exmouth Gulf. The error range for method 1 was calculated using the median absolute deviation [55] while the error range for method two was estimated by computing the conveying capacity from the maximum and minimum 50% radii of the vi cumulative density curves.

Results

A full of 703 individual whales were sighted in the Exmouth Gulf region during the 2004–2005 aerial surveys (Table 1). The abundance estimates for each flight, using distance sampling, showed a maximum of 459 whales within the Gulf at whatever i fourth dimension, and a total of 1270 whales over the entire menses (CI 670–2080), assuming a maximum two week residency menses for each whale (KCS Jenner, estimated from photo ID re-sights; each whale is represented only in one case in the full judge). The abundance of whales in the Gulf clearly changed over time (Fig. 4a), with whales beginning to enter the Gulf from the north around the first week of August, peaking at the end September, before departing until the start of November. The number of calves within the Gulf follows a similar temporal design, but peaks about a week or ii afterwards the principal migration (Fig. 4b), in early Oct.

Figure 4. The temporal changes in number of A) total whales, and B) calves, in Exmouth Gulf.

A) For each flight, the full number of whales resident in Exmouth Gulf was estimated using distance sampling. The mistake bars marking the 95% confidence interval, calculated using a bootstrap in Distance 6.0. At that place is clear temporal pulse of whales in the Gulf, with the peak occupancy towards the terminate of September. B) The total number of calves observed during each survey flying also displays a temporal pulse to occupancy, just the peak here is slightly later in the first week of Oct.

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Whales in Exmouth Gulf follow an abundance-occupancy relationship whereby the area occupied remains relatively constant as abundance increases (Fig. v; shaded surface area), and consequently density is increasing with abundance. The area of the first value (marked as an open circle) is less than half that of the other areas. This may exist an bibelot in observation, or it may indicate that a constant affluence-occupancy relationship exists simply above a threshold of at least 0.04 whales per km².

Effigy five. The human relationship between density and occupancy of whales in Exmouth Gulf.

The total area occupied was calculated as the convex hull expanse for each flight, and the density every bit number of whales per kmⁱⁱ in this area. The pattern emerging is that of a constant area used with increasing density, as highlighted by the grey shaded surface area. 1 survey (flight 5), marked every bit an open circumvolve, is an outlier to this pattern.

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Estimating the conveying capacity of whales in Exmouth Gulf requires an understanding of how pods spatially organize themselves within the Gulf, which may be influenced past pod characteristics. However, the 2 characteristics we investigated here, pod size and composition, had no upshot on the median nearest neighbour distance of the pods (Kruskall-Wallis test: pod size p = 0.80, pod composition p = 0.58; Fig. 6). Therefore, these variables were not incorporated in analyses to calculate conveying capacity.

Figure half dozen. Boxplots comparing median nearest neighbour of A) the pod size and B) the pod type.

Neither pod size or type showed significant difference in median nearest neighbour distances (Kruskall-Wallis test: pod size p = 0.80, pod limerick p = 0.58). For pod type, 'wCP' are pods with calves nowadays and 'nCP' are pods with no calves observed.

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The get-go method for estimating the spacing between pods, using the median NND of ninety% of the population, generated a radius of 2.16 km (MAD ±0.94 km). In the second method, the saturation curve fit to an exponential model (Fig. 7) estimated the mean distance within which half the population had a pod equally 1.93 km (lowest i.62 km; highest 2.50 km). Fitting the pods into the maximum CHA expanse of 2742 km^two in a lattice formation yielded maximum pod estimates of 698 (method 1; range 345–2160) and 872 (method two: range 523–1242). Given an average observed pod size of 1.7 whales, this equates to conveying chapters estimates of 1187 and 1482 whales, respectively, and density estimates of 0.43 and 0.48 whales km⁻² (Table 2). The ii distinct approaches to estimating the distance maintained betwixt pods were within 0.1 km of each other, translating into a difference in full carrying capacity of approximately 175 pods or 295 whales.

Figure seven. The proportion of the population with a pod inside a fixed radius, and increasing radii.

Cumulative density plots of the proportion of population that have at least one pod within a specified radius, at increasing radii, for A) flight i, B) flight 2, C) flying three, D) flying 7, E) flight 9, and F) flying 10. Each plot was fit with an exponential curve using the least squares method, and the radius at which half the population have a pod inside this radius was calculated from the curves. Theses radii are A) ii.09 km, B) 1.95 km, C) 2.50 km, D) 1.82 km, E) 1.61 km, and F) 1.62 km.

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Word

Our premise is that in limited-space conditions the carrying chapters of an area for resting humpback whales is linked to the infinite requirement of the animals that occupy it, rather than more typically encountered pressures such as contest for food, and predator avoidance. Our results suggest that pods practise maintain a altitude from each other under relatively high-density weather condition, demonstrating that space itself is a resource for these animals and that this space tin can be adamant. Nosotros then used this spacing distance to calculate the theoretical conveying chapters of a humpback whale resting area. The implications of having a chapters limit, under the currently increasing population of WA humpback whales, can merely be assessed once the current use of Exmouth Gulf is understood. Therefore, we also investigated how the humpback whale population before long uses Exmouth Gulf, both spatially and temporally.

In that location is a clear temporal pulse to meridian whale occupancy of Exmouth Gulf, starting from late September to early November, which conforms with the timing of movement of the whale population downwardly the WA declension [31], [37]. This temporal pulse could be acquired by an environmental signal that triggers the whales to exit item areas and go on on their migration, such as a change in temperature or day length, even so the influence of ecology cues on the migration of baleen whales is notwithstanding poorly understood [56]. Equally adult humpback whales need to consummate migration before energy reserves are exhausted, leaving the Gulf may also exist triggered past a certain level of depletion in these reserves.

The number of pods containing calves peaks in the Gulf after the main migration, supporting previous observations that mothers with calves follow the chief migration [37], [38]. The timing starting time betwixt the two peaks in this study was approximately 2 weeks, which is shorter than that estimated past Chittleborough [37]. Nevertheless, the Chittleborough [37] written report used commercial catch data, which reverberate hunting well-nigh migratory areas and thus were probable to capture the timing of the unabridged population of migrating whales, whereas our information were concentrated on a resting area. Therefore, the disparity between peak timings could mean simply a portion of the migrating whales are using Exmouth Gulf to residuum during the southbound migration; if the vanguard of the migrating population are non using Exmouth Gulf so the peak of whale abundance in the Gulf would appear to be subsequently than if sampling the entire population. The match in timing difference between peaks of mature males and lactating females found by Dawbin [38] indicates that it is these groups of whales which are mostly present in the Gulf, supporting the conclusion that resting areas are specially important for mothers with calves [57], merely likewise that it is an surface area where mature males and lactating females are mating. It is important to notation that, every bit distance sampling was not applied to the calf information due to the small sample sizes, the perception bias (the dogie is available to be seen, just is non observed) was non corrected for, and thus the total number of calves within the Gulf could not exist estimated. To further investigate calf presence in this resting area will require more detailed surveys.

The importance of resting areas to migrating whales is still unknown, however during migration a calf requires sufficient food from its mother to enable information technology to grow and proceeds adequate energy reserves to continue migrating towards the Southern Ocean. Mothers are therefore expending their own limited stores to meet both their own energetic requirements and that of the calf. Spending time resting in sheltered embayments, such equally Exmouth Gulf, during migration allows calves to increase energy stores more efficiently, equally they will exist expending less energy when compared to resting and feeding in open ocean conditions, and thus slowing the rate of energy loss. Furthermore, current of air speed is known to influence the energetic surface active behaviours of humpback whales, with rising wind speed increasing behaviours like breaching, pectoral fin slapping, and tail slapping [58]. This correlation is linked to a alter in communication strategies during periods of higher wind-dependant background dissonance [58]. Therefore, the flatter the surface atmospheric condition, the more than the humpback whales tin balance. The air current conditions in Exmouth Gulf are typically characterized by diel changes in speed, creating calmer conditions during the mean solar day and for several hours air current speed can drop to nothing. During the October catamenia in northern Western Australia, these extended low wind, flat water conditions are unique to Exmouth Gulf. These atmospheric condition create the ideal resting environment along the Western Australian declension for whales, particularly mother with calves, at perhaps a disquisitional stage of their migration towards polar waters. In the Australian context, this unique opportunity to boost calf energy reserves mid-migration may increase long term survivability of calves for this population and partly explain the college population growth rate measured in west Australia'south Stock D versus east Australia's Stock E [29], [59]. Considering resting areas are predominately used by mother and dogie pods, we theorise that these pods are driving the spacing behaviour in this resting area, perhaps due to mothers regulating the social stimulus of the dogie. Even so, further research will be required to determine if this is the driver behind the spacing behaviour.

Abundance-Occupancy

The affluence-occupancy relationship of humpback whales within the Gulf demonstrates that the total space used within the Gulf remained abiding regardless of whale abundance. The one exception to this rule is at the lowest affluence observed suggesting there could be a positive AOR below a detail threshold of whales. However this holds little significance to the overall understanding of space utilize as for the majority of the time, the Gulf is occupied at abundance levels above this threshold value.

The AOR analysis uses the average density of whales across the full space used by all the whales (the CHA area) over the duration of each flight, and therefore does non capture any information on the arrangement of whales inside this area. Yet, this spatial arrangement is an important consideration as it has the potential to confound the spacing behaviour analysis. Given that the area used remains abiding, if pods are spacing evenly throughout the area then the altitude maintained between pods will decrease as density within the area increases. Alternatively, if the pods are aggregating within the area, then average maintained distance will remain relatively constant and core area of aggregation volition continue to expand within the limits of bachelor resting area. The nearest neighbor analysis indicated a tendency towards aggregative behaviour, suggesting the second spatial arrangement. As outlying pods, the 90–100% furthest away from the eye for aggregation, were removed from the spacing behaviour analysis, the results are not confounded by having a constant AOR.

The abiding AOR relationship plant for humpback whales in the Gulf is unlike to other cetacean species investigated [44], which tend to show a positive AOR. This could reflect the deviation in the population's situation at the fourth dimension of study; for example, the Minke whales (Balaenoptera acutorostrata) were analysed while they were foraging [44], whereas the humpback whales in this study were not feeding and so distributions were not driven past food patchiness. The issue to having a abiding AOR is that as more whales enter the Gulf, the Gulf becomes increasingly dense. Given that there is a minimum requirement for space between individual pods, at some point maximum density, and thus carrying capacity, volition be reached.

Implications of Spacing Behaviour

The 2 approaches we took to calculate spacing between pods arrived at very similar estimates of approximately 2 km between pods. While both estimates are derived from the same data set, the answers are distinct due to fundamental differences in the approaches used in the estimation of spacing altitude. The offset method full-bodied on just the measured distance to the nearest neighbour for each pod, ignoring any other pods in the vicinity, while the second approach took account of all the pods within a given radius, regardless of which was nearest.

Pod size and composition did not affect the altitude maintained between pods, and so density of pods inside the Gulf volition be the aforementioned regardless of these factors. At that place were very few observations of pods containing more than 4 animals, so an effect on nearest neighbour distance may withal exist at higher pod sizes. However, given the few instances of large pod sizes in Exmouth Gulf over the season, this will have niggling upshot on the overall pod carrying capacity inside the Gulf, bold that a recovering population does not pb to larger pods. Pod composition could besides be further disaggregated to investigate divergence between, for example, singing males or competitive males. However, these aerial survey derived data did non allow us to distinguish such individuals. Other factors that may influence pod density, simply were non able to exist investigated here, are pod activeness, habitat preference, and competitive exclusion. However, the distance maintained between pods calculated hither is representative across the population occupying the Gulf at a indicate in time, and so represents an average over pods in various states of activity and habitat preference. Competitive exclusion is probable to be a factor just in one case the Gulf approaches maximum density and infinite to arriving whales becomes unavailable, which appeared not to be the instance in the 2004–2005 seasons. Some other potentially confounding variable when calculating the spacing distance of pods is movement of and interaction amongst pods. Still any extremes in this variation, such every bit a closer than normal distance between interacting pods, or larger than normal from pods requiring more infinite, would be accounted for in the analysis by looking at the central tendency in distances, resulting in a representative spacing distance across the population occupying the Gulf at that signal in time.

The knowledge that resting humpback whales maintain spacing has implications for their interactions with vessels. Seismic vessels accept strict guidelines when operating effectually and approaching whales, which outline observation, low power, and shutdown zones depending on the distance from the whales [60]. The 2 km spacing of whale pods matches the 2 km low power zone for vessels operating to a higher place 160dB [lx], withal below this source level the depression power zone is reduced to i km, which could be viewed equally an invasion of space for the pod. Tourism vessels also have guidelines when approaching whales [61], with a circumspection zone of 300 grand and a no approach zone of 100 m while fishing vessels take to keep a distance of at least 100 m, all of which are well within the behavioural spacing of humpback pods equally calculated here. A specific humpback whale sanctuary established in Camden Sound, the calving grounds for this population [31], has increased this 100 m no approach zone to 500 m for mother and calf pods, even so this still falls short of the ii km altitude maintained betwixt pods institute in this written report. We do not dispute that these regulations are adequate to avoid disturbance to the whales, indeed the population is recovering at near maximum rate [29], [62], yet vessels spending too long within the boundary of a pods' space may cease up increasing calf interaction and activity levels, and therefore energy consumption, at a time when cyberspace energy levels are intended to exist increasing. So while the immediate touch on of displacement and/or increased activity may not be apparent, there may exist longer term implications to the survivability of the calf mid-migration which is cartoon on fixed energy reserves from its mother. Nosotros would therefore recommend a precautionary approach to management decisions when because increasing vessel density in areas likely to comprise resting whales.

Nosotros calculated the theoretical carrying capacity of Exmouth Gulf to be around 700–850 pods (1200–1500 whales), based on the spacing between pods and the maximum CHA used by the whales. There are moderate errors surrounding the carrying capacity estimates, with ranges calculated equally 345–2160 pods and 523–1242 for methods i and 2 respectively, but our estimates of overall conveying capacity are comparable. Considering the constant AOR relationship, whereby the population is occupying the same amount of area regardless of the number of whales within the Gulf, there will likely be no change in the total surface area used by the whales until carrying capacity is reached. The area the whales are currently occupying (ii,742 km^two) encompasses about of the Gulf. In the context of a currently increasing numbers, there is piddling room within the Gulf for the expansion of whale populations. Therefore, if the response of the population is to aggrandize the resting area, then this expansion will extend outside of the Gulf. Alternatively, the whales will seek other appropriate areas in which to rest forth the coast, which is of particular business concern given the current coastal developments in the northwest of Australia for extractive industries. It is also important to realize that, every bit space is the limiting cistron for carrying capacity, so any reduction of infinite within the Gulf available for whales to residue will outcome either in a reduction to the total carrying capacity of the Gulf or a subtract in spacing between pods. As maximum carrying capacity in the Gulf was non observed in this study, it is difficult to predict the consequence of reaching conveying capacity based on space limitations.

To summate carrying capacity, this report causeless that space limitation exists in the Gulf. The consequent expanse occupied by the whales over varying densities suggests that there are physical constraints with respect to the area used by humpback whales, making space a limited resources. To determine whether the estimate two km spacing altitude found in the 2004–2005 seasons is maintained across years will require additional appropriate aerial surveys such that interannual variability in spacing altitude equally a function of population size can exist evaluated. It may exist that every bit the population off the W Australian coast continues to grow, the average infinite between pods will decrease to conform the increase in whales. Nevertheless, this will depend on the drivers behind spacing behaviour betwixt resting pods. Here, nosotros used the 2004–2005 season to illustrate the concept that space is a resource for resting whales, and distance maintained betwixt pods can be used to calculate carrying capacity at a given point in fourth dimension, which has of import management applications. This study forms the foundation to further work exploring the spacing behaviour of wide-ranging megafauna, and how this may limit carrying capacity in space-limited areas.

Determination

Our written report shows that carrying chapters for humpback whales can be calculated based on their behavioural space requirement nether relatively dense weather condition regardless of pod size or composition, and that this distance tin can be consistently estimated using two separate approaches. Nosotros estimated the carrying capacity of Exmouth Gulf, a migration resting area, to be approximately 1187–1482 whales. Although there has been considerable research into the spacing of other accumulation animals, such as fish and birds, this study is a new approach to agreement the habitat use of large body of water wildlife when they are non feeding, and how the spacing behaviour can make up one's mind a habitat's carrying capacity. The consequence of a conveying capacity in Exmouth Gulf is that, when exceeded, the resting area may aggrandize in fourth dimension or space, or the whales will brainstorm to utilize other areas along the coast for resting. Given that the whale population is sharing the coastal waters with human being activities, such as mining developments, information technology will be important to ensure any expansions in resting area habitat utilize are monitored and that the areas whale populations expand into are disturbance complimentary, in guild to promote the continued good for you population growth for this recovering species.

Acknowledgments

We thank Ben Fitzpatrick for statistical support, Philippe Bouchet for communication on the altitude sampling analysis, and Micheline Jenner and Emily Wilson who assisted with information collection.

Author Contributions

Conceived and designed the experiments: JEB JJM KCSJ. Performed the experiments: JEB JJM KCSJ. Analyzed the data: JEB JJM. Contributed reagents/materials/assay tools: JJM KCSJ. Wrote the paper: JEB JJM KCSJ.

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Source: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0051347

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