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Study area and general observationsFour datasets, equating to four post-whaling timeframes, were used for this study: 1997 (32 years post-whaling), 2003/2004 (38/39 years post-whaling), 2008 (43 years post-whaling) and 2014/2015 (49/50 years post-whaling). Data collection for each timeframe occurred during the annual migration of humpback whales, from breeding grounds in the Great Barrier Reef, to feeding grounds in the Antarctic Ocean. The study site was located off the coast of Peregian Beach (north of Brisbane, in Queensland, Australia), which was approximately one-third of the way along their return migration route. Here, humpback whales were still exhibiting breeding behaviours, such as singing, males joining females as escorts, and males forming competitive groups around a central female. Field work took place in September and October of each year. Generally, the number of migrating groups increased per day to peak during late September and early October. Numbers then gradually fell until the end of the migration.For this study, a group was defined as cluster of whales within approximately 100 m of each other that were diving and surfacing together (as estimated by the land-based visual observers). Groups were constantly changing membership with animals joining and splitting from the group and tend to move at different speeds, and in different directions, whilst making general progress southwards. Groups, unless joining together, were separated by at least 2 km, meaning it was relatively easy to keep a separate track of each group (see below).Acoustic recordings were made from three to five hydrophone buoys moored in 18–28 m of water and arranged in a line or T-shaped array (Fig. 6). Each hydrophone buoy consisted of a surface buoy containing a custom-built pre-amplifier (+20 dB gain) and 41B sonobuoy VHF radio transmitter. A High Tech HTI-96-MIN hydrophone with built-in +40 dB pre-amplifier was suspended approximately 1 m above each buoy’s mooring. Signals were received onshore at a base station 1.5 to 2.5 km away using a directional Yagi antenna and type 8101, four-channel sonobuoy receiver. Singing whales were located by cross-correlating the same song sound arriving at the different hydrophones to determine time-of-arrival differences. These differences, together with an accurate knowledge of the positions of the hydrophones, were then used to determine the most likely location of the singer. Singers generally move slowly and calculating an acoustic position approximately every 10 min produced a detailed track of the singer.Fig. 6: Outline of the study site including the range of visual observations and the position of the acoustic tracking array.Illustrating the study site at Peregian Beach, north of Brisbane, east coast of Australia. The map indicates the position of the land-based station (Emu Mountain) and the acoustic base station along with the position of the 5-buoy hydrophone array. The outline designates the study area. Whales moved in a southerly direction through the area daily. Whale icons illustrate acoustically tracked singing whales (circled in blue) and visually tracked presumed males (black), females (orange), and calves (small black). The 5 km social circle radius for a focal singing (blue circle) and a non-singing (black circle) male are also illustrated. The map is taken from “Google Earth” with permission to print without the need to submit a request (Brand Resource Center | Products and Services – Geo Guidelines (about.google)).Full size imageMigrating groups were tracked visually (7am to 5pm, weather permitting) from a land-based elevated survey point, Emu Mountain (73 m elevation). A theodolite (Leica TM 1100) was used in conjunction with a notebook computer running Cyclopes software (E. Kniest, Univ. Newcastle, Australia) to track the groups in real-time and note group behaviours. The field of view was approximately 20 km in a north/south direction and 10 km offshore (Fig. 6). Humpback whale groups were observed ad libitum and tracked by teams of five people. When whale groups surfaced, the observers called the sighted behaviour, compass bearing, and angle from the group to the horizon (in reticules). Each observation included group identification letter, the time, group size and composition, whether a calf was present, direction of travel, and group location, either by using a binocular reticular measurement or a theodolite measurement. Joining and splitting animals were also noted. A join was defined as one of more animals actively moving towards a group to surface within 100 m and then match the group surfacing times. Examples of this include an individual singing or non-singing whale actively moving towards, and then joining, another individual or group of whales. If more animals subsequently moved in and joined the group, this was termed an additional join to that group. These additionally joined group usually comprised of a female-calf and more than one male escort, or three or more adults, with additional joiners highly likely to be male (21,25,26, supplementary results). On rare occasions a singing whale remained in one place but was joined by another individual. This was termed an additional join given there was no evidence the singer actively moved to join this animal. However, the rarity of these occurrences meant the allocation of this behaviour to additional join, rather than join, had no influence on the results.Some of the migrating animals were biopsied during the day for post-field later sexing. Note biopsied animals were sometimes part of different studies occurring at the field site30,50 and were not necessarily the animals used in this study. However, these biopsy results were used to test assumptions made in this study regarding the sex of joining whales and whales within the observed groups (supplementary results and supplementary note). Weather was noted hourly.Statistics and reproducibilityDefining the proximate effect of male density on individual mating tacticsFor this analysis, a specific period, the 2003/2004 dataset, was chosen as it had the most instances of identified singers and non-singers. Within this timeframe, whales were migrating through the study area at sufficiently low density to avoid confusion. After 2004, it became increasingly difficult to focally follow males.First, for singing males (n = 86), their location within the study area was recorded at the start of singing using the acoustic array. Whilst singing they remained in the same location or meandered slowly within a small area. Non-singing animals that were observed to join a group (n = 31) were assumed to be male (21,25,26,30, supplementary methods and supplementary results). For these joining animals, visual observations were backtracked for 10 to 15 min until they were sighted alone. They were only included in the analysis if they could be definitively backtracked using visual (theodolite) observations, with no opportunity for confusion with other whales in area (i.e., no other whales within 2 km).For each unaccompanied focal male, the number of, and roles, of other presumed males within 5 km radius from the focal whale (Fig. 6) was used as a measure of local male density. The 5 km radius was termed social circle and was chosen as the most likely communication space for their acoustic signals51. For singing focal whales, their social circle was estimated using their location when they began to sing. For non-singing focal males, their social circle was estimated using the backtracked theodolite position to when it was first sighted alone. Next, all groups within the 5 km social circle of the focal whale, along with each group composition (singing animal, lone animal, female and calf pair, female-calf and escort number, adult-only group with the number of adults) were recorded at that timepoint. It was not logistically possible to biopsy and sex all migrating animals, therefore, to estimate the number of males within their social circle several assumptions were made. These assumptions were also tested using a biopsy study carried out in the area (supplementary methods and supplementary results). Female-calf pairs were discounted as it was assumed all adults with a calf were female. It was assumed that female-calf pairs were being escorted by males (21,25,26, supplementary methods and supplementary results). Groups of multiple adults were assumed to be comprised of a likely single female, principal male escort and secondary male escorts or challengers (21,25,26, supplementary methods and supplementary results). Lone animals not involved in any group interactions, and not singing, were given a 70% chance of being male (supplementary note). Animals within adult pairs were given a 70% chance of being male given the likelihood of having a mix of female-male pairs and male-male pairs (21,30, supplementary results and supplementary note).All analysis models were carried out in R (version 3.4.0). The first analysis aimed to determine if the likelihood of first observing the focal individual as a singing or non-singing male was significantly related to local male density, as determined by the number of males within a 5 km radius, termed social circle. Singing whales were allocated a 0 and non-singing whales were allocated a 1. A generalised linear model structure was used, assuming a binomial distribution. Likely males within their social circle were divided into non-singing and singing males (to delineate tactics) and these were included as the two covariates.$${{{{{rm{Singing}}}}}},(0),{{{{{rm{or }}}}}},{{{{{rm{Non}}}}}}{mbox{-}}{{{{{rm{singing}}}}}},(1) sim {{{{{rm{Non}}}}}}{mbox{-}}{{{{{rm{singing}}}}}},{{{{{rm{males}}}}}}, 5,{{{{{rm{km}}}}}}+{{{{{rm{Singing}}}}}},{{{{{rm{whales}}}}}}, 5,{{{{{rm{km}}}}}}$$Each focal male was an independent sample given males were migrating southwards and extremely unlikely to back-track into the study area and therefore be resampled. Significance was set at p  More

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