Philippa Kaur

Automated tracking of four social insect speciesFifty queenright colonies were used in the tracking experiments (Table 1). Honeybee colonies (subspecies A. mellifera carnica) were housed in the campus apiary of the University of Lausanne. Colonies of L. niger were raised from single mated queens collected on campus. T. nylanderi colonies were collected from the University of Lausanne campus, and L. acervorum colonies collected from Anzeindaz, Switzerland. These four species were chosen because of their abundance and easy availability in Switzerland, and because they – or closely-related species – have previously been used as model systems for the study of spatial organisation in social insects20,21,23,27,44. The colony sizes used in our experiments (Table 1) fell within the natural range of sizes experienced by these species in nature, either as recently founded colonies (L. niger colonies are founded by a single queen and progressively grow from a few workers to mature sizes of up to 40,000 workers over the course of several years; new honeybee colonies are founded by swarms counting 2400–41,000 bees61) or as mature colonies (all colonies of T. nylanderi and L. acervorum used in our experiments were mature colonies collected whole from the field).In all species, a paper tag bearing a unique two-dimensional barcode was glued to the thorax of individuals to allow automated tracking of their movements (Fig. S1). In the ants, tagging of all individuals was performed in a single session two days before the beginning of the experiment, whilst in the bees, newly-emerged workers (one-day-old or less) were tagged every 3 days over the 21 days prior to the beginning of the experiment (Supplementary Note 1).Tagged colonies were kept in glass observation nests with a single entrance (internal nest dimensions, A. mellifera: 69 × 45 × 4 cm, L. niger: 70 × 40 × 8 mm; L. acervorum: 63 × 42 × 2 mm, T. nylanderi: 63 × 42 × 1.5 mm). The honeybee observation nests also included a 64 × 44 cm wooden frame enclosing a double-sided wax comb containing honey, pollen, and developing brood20. Bees were free to move between both sides of the comb. In all species, individuals were allowed to freely exit and enter the nest. Ants were provided with ad libitum food (Drosophila, sugar solution) and water in a foraging arena, while bees foraged on natural resources outside. Both the ant and honeybee observation nests were exposed to diurnal cycles of temperature and light (Supplementary Note 1).High resolution digital video cameras operating at two frames per second were used to identify the location and orientation of each tag across successive images22. All colonies were continuously tracked for three days, which corresponded to the inter-cohort time in the honeybee colonies. The trajectories of each worker, and the physical contacts between workers (Fig. S18 and Supplementary Note 14) were extracted using an existing software pipeline62.Building bipartite site-visit networksTo quantify the spatial preferences of individual ants and bees, the interior of the nest was discretised into a regular hexagonal lattice (Fig. 1a, b). Because the worker body lengths of our four study species span an order of magnitude (from ~ 1.5 mm for T. nylanderi to ~ 15 mm for A. mellifera), the width of the hexagonal bins were defined as 1/4 of the mean worker body-length.To characterise the spatial preferences of different individuals to different parts of the nest, we counted the number of times ({n}_{i}^{s}) that each individual i visited each hexagonal site s. A visit by individual i to site s began when i crossed the border into s, and was terminated when i crossed the border out of s, regardless of the amount of time spent inside. To prevent stationary individuals located on the border between two adjacent sites from rapidly accumulating many single-frame visits to the two sites, successive visits to a same site were only counted when at least 20s elapsed between the end of the previous visit and the start of the next.The site-visit data were used to construct a bipartite network, in which individuals (layer 1) were connected by undirected edges to the sites (layer 2) they visited (Fig. 1c, d). Because individuals typically made multiple visits to the same sites, each edge i–s was weighted according to the total number of times individual i visited site s, that is, ({n}_{i}^{s}).Partitioning site-visit networks into modulesThe extent to which the site-visit networks were partitioned into discrete ‘modules’ (i.e., set of workers with similar space-use patterns and the set of sites that they exhibit strong ties to) was assessed using the DIRTLPAwb+ algorithm for partitioning weighted bipartite networks39. This algorithm searches for the partition that maximises the number and strength of the links within modules, whilst minimizing connections between modules. The number of modules was not specified a priori by the user, but was identified by the algorithm. All site-visit networks had positive modularity (Fig. S3), indicating that they could be partitioned into a set of well-separated modules (Figs. 1e–h, S2, and S4–S5). The modules in each partition were then assigned functional labels according to the following rules. First, the module whose sites were on average closest to the nest entrance was labelled ‘forager’ module. Second, the module or modules with the greatest spatial overlap with the brood pile in the ant colonies or the broodnest(s) in the honeybee colonies were labelled ‘nurse’ module(s). After defining the forager and nurse modules, the remaining modules (if any) were labelled as follows. If there was only one module remaining after identifying the nurse and forager modules, as was typically the case in honeybee colonies, it was labelled ‘peripheral’. If there were two modules remaining, as was typically the case in ant colonies, then the module whose sites were on average closer to the nest borders (i.e., to the periphery of the nest) was labelled ‘peripheral’, and the remaining module labelled ‘intermediate’. In some cases, the DIRTLPAwb+ algorithm identified five or more modules (9.0% of all iterations across all species and colonies). In these cases, the supernumerary modules never contained more than 1 or 2 individuals, and as they could not be unequivocally assigned using our labelling scheme, they were left unclassified for these iterations.Validating network modulesAs a network constructed by a purely random process could exhibit apparent modular structure by chance, we tested whether the discovered modules represent statistically significant entities. To do so, we produced 1000 null model random networks for each observed network using an established permutation method for bipartite networks63 (Supplementary Note 2). Comparisons between the maximum modularity of the observed networks with that of the corresponding random networks showed that, in all four species, the observed modularity was significantly greater than expected by chance (Fig. S3).Constructing worker task profilesA unique labour profile for each ant and each honeybee was constructed by estimating the activity of each worker in the following four tasks:1. Entrance guarding: workers were classed as guarding when they were (i) within two body lengths of the entrance, (ii) roughly facing the entrance, i.e., with a body alignment diverging from the direct heading to the entrance by no more than π/2 radians, and (iii) ‘on station’ at the entrance, as defined by trajectory coordinates with an associated first passage time (ref. 64; time taken for the individual to pass beyond a circle centred on its current location with a radius of two body-lengths) in excess of 500s.2. Patrolling: workers were classed as patrolling65 when they were (i) active, and (ii) ‘roaming’, as defined by first passage times of More

Survey sites and data collectionBenthic and fish surveys were conducted at randomly stratified sites throughout the entirety of the FRT by NOAA’s National Coral Reef Monitoring Program (NCRMP). Sites were categorized into three biogeographic regions, including Dry Tortugas (DRTO, n = 228), Florida Keys (FLKs, n = 322), and Southeast Florida (SEFL, n = 173) (Fig. 1). The Florida Keys were further classified into the following four sub-regions: Lower Keys (LK, n = 103), Middle Keys (MK, n = 46), Upper Keys (UK, n = 140), Biscayne (BISC, n = 33). Within each region/sub-region (except for SEFL), reefs were categorized according to reef types. For DRTO, this included bank, forereef, and lagoon reef sites. For the LK, MK, UK, and BISC, reef types were categorized as inshore, mid-channel, and offshore. Data were collected throughout the region in 2014, 2016, and 2018.Fish and benthic surveys were conducted in accordance with NCRMP methodologies34 (Table S2). The protocol used for the fish surveys was developed from a modified Reef Visual Census (RVC) method35 and was performed using a stratified random sampling design. Divers surveyed two 15 m diameter cylinders, spaced 15 m apart. Fish species were identified to the lowest taxonomic level for a period of five minutes. This was followed by an additional five minutes dedicated to recording species abundances and sizes (10 cm bins).Surveys were used to quantify the benthic cover at each site. The protocol for these surveys followed a standard line point-intercept sampling design. At each site, a 15 m weighted transect was draped along the reef surface. Surveyors recorded benthic composition at 15 cm intervals along the transect (i.e., 100 equidistant points). The benthic composition from these 100 points was then transformed to percent cover of ecologically important functional groups (scleractinian coral [species-specific], gorgonians, hydrocoral, CCA, macroalgae, turf algae, sponges, bare/dead substrate, sand/sediment).Carbonate budget analysisPlanar benthic surveys were adjusted to account for the three-dimensional complexity (i.e., rugosity) of each site using light detection and ranging (LiDAR) data (1 m horizontal resolution; 15 cm vertical resolution) from topobathymetric mapping surveys of the South Florida eastern coastline conducted by NOAA’s National Geodetic Survey. A 15 m x 15 m region of interest (ROI) was placed around the GPS coordinates of each site using ArcGIS Pro with 3D and Spatial Analyst extensions (ESRI). The ROI was then overlaid with existing multibeam echosounder (MBES) and LiDAR bathymetry data. Within the ROI, LiDAR was extracted using the Clip Raster function from ArcPy (ArcGIS’s python coding interface), and the Surface Volume tool was used to calculate the 3D surface area. Rugosity was calculated by dividing the 3D surface area by the 2D surface area of the ROI.The methodology for standardizing reef carbonate budgets to topographic complexity (i.e., rugosity) diverged from that of the ReefBudget approach by using site-specific rugosity rather than species-specific rugosity17. This was a necessary limitation of this analysis as transect rugosity at 1 m increments was not measured using the NCRMP benthic survey protocol. To ensure that reef topographic complexity was still accounted for, however, rugosity of the entire reef site, calculated from LiDAR bathymetry data, was used in this analysis. While rugosity of the site rather than of each benthic component, specifically for corals, can lead to an under or overestimation of carbonate production rates, we note that site and species rugosity (i.e., encrusting and massive coral morphologies) was low for the vast majority of sites and species surveyed, thereby reducing the probability of an under or overestimation.Reef carbonate budget analysis was performed following a modified version of the ReefBudget approach17. Coral carbonate production was derived from species-specific linear extension rates (cm year−1), skeletal density (g cm−3), coral morphology (branching, massive, sub-massive, encrusting/plating), and percent cover. Carbonate production by CCA and other calcareous encrusters was similarly calculated as a function of surface area, literature reported linear extension rates, and skeletal density17. Gross carbonate production at each survey site was measured as the sum total of carbonate production by all calcareous organisms found at each site and was standardized to site-specific reef rugosity.Gross carbonate erosion for each survey-site was calculated as the sum total of erosion by four bioeroding groups: parrotfish, microborers, macroborers, and urchins. The calculations roughly followed the ReefBudget methodologies17 (Table 1). Parrotfish size frequency distributions from NCRMP surveys were multiplied by size and species-specific bite rates (bites min−1), volume removed per bite (cm3), and proportion of bites leaving scars to calculate total parrotfish erosion17. The substrate density (1.72 g cm−3) used in these calculations followed that of the ReefBudget protocol17. Microbioerosion was calculated from the percent cover of dead coral substrate, which was multiplied by a literature-derived rate17 of − 0.240 kg CaCO3 m−2 year−1. Macroboring was calculated as the percent cover of clionid sponges multiplied by the average erosion rate of all Caribbean/Atlantic clionid sponges17 (-6.05 kg CaCO3 m−2 year−1). External bioerosion by urchins was calculated using Diadema urchin abundance collected from the benthic surveys. Due to the lack of test size data from the NCRMP benthic surveys, urchin abundance was multiplied by the bioerosion rate of an average test sized36 (66 mm) Caribbean/Atlantic Diadema urchin (-0.003 kg CaCO3 m-2 year−1). While using an average test sized Diadema urchin for this analysis may have led to an under or overestimation of urchin erosion, the abundance of Diadema urchins measured in the surveys was minimal, as they appeared to be functionally irrelevant across the FRT.Model validationAs the survey methodologies and data sources employed in this analysis were modified from that of the standard ReefBudget approach17, we chose to validate our model through a fine scale temporal comparison of annual ReefBudget surveys conducted by NOAA at Cheeca Rocks (UK) to three nearby NCRMP sites used in our analysis. Since the NCRMP surveys were performed in 2014, 2016, and 2018, this study focused exclusively on these three survey years from the NOAA Cheeca Rocks dataset. Temporal trends related to reef growth/erosion were visually compared to see if survey types provided comparable results (SI Figure S6).Statistical analysisAll model calculations and statistical analyses were performed using R37 with the R Studio extension38. Generalized linear models (GLMs) were run on response variables involved in habitat production (i.e., net carbonate production, gross carbonate production, and gross carbonate erosion) to evaluate spatial trends related to reef development across sub-regions and reef types. Each GLM was performed with reef type being nested within sub-region. The best fit distribution for each variable was determined using the fitdistrplus R package39. Linear regression analysis was used to evaluate the relationship between net carbonate production and both live coral cover and parrotfish biomass. All plots were created using ggplot2 R package40 and edited for style with Adobe Illustrator41. More

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Selection of surveys and extraction of dataWe selected published surveys that produced estimates of sperm whale population size or density (see Supplementary Information for methodology; surveys listed in Table 1). We extracted: the type of survey (ship, aerial; acoustic, visual), the years of data collection; the coordinates of the boundary of the study area; the estimates of g(0) and CV (g(0)) used to correct for availability bias, if given; and an estimate of sperm whale population or density in study area with CV. From these we calculated for each survey the survey area with waters greater than 1000 m deep (typical shallow depth limit of sperm whales3). When no value of g(0) was used (8 ship visual surveys) we corrected the population/density estimate using an assumed generic value of g(0) and recalculated the CV to include uncertainty in g(0) (as in Eq. 1 of8). Three ship visual surveys did calculate a single g(0) estimate: 0.62 (CV 0.35)32; 0.57 (CV 0.28)35; 0.61 (CV 0.25)37. These are consistent and suggest a generic g(0) = 0.60 (CV 0.29), also agreeing with g(0) = 0.60 estimated from pooled surveys in the California Current10.Global habitat of sperm whalesTo extrapolate sperm whale densities from surveyed study areas to the sperm whales’ global habitat, we created a one-degree latitude by one-degree longitude grid. We removed the following grid points as not being prime sperm whale habitat1,3,40: points on land or with central depths less than 1000 m; largely ice-covered points in the Beaufort Sea, and the waters north of Svalbard and Russia; the Black Sea and Red Sea both of which have shallow entrances that appear not to be traversable by sperm whales.Generally, food abundance is a good predictor of species distribution. However, this is not possible for sperm whales as we have no good measures of the abundance or distribution of most of their prey, deep-water squid57. Instead, oceanographic measures have been used to describe sperm whale distributions over various spatial scales with a moderate level of success13,14. We follow this approach. Measures that might predict sperm whale density were collected for each grid point, some at just the surface, others at the surface, 500 m depth, 1000 m depth or an average of the measures at the different depths (Supplementary Table S2). Water depth was the strongest predictor in Mediterranean encounters, when compared to slope and distance to shore13. Temperature and salinity have been used as predictors for the distribution of fish and larger marine animals, which could translate into prey availability and thus density for sperm whales58,59. Primary productivity and dissolved oxygen generally dictate the biomass of wildlife in an area, while nitrate and phosphate levels limit the amount of primary productivity in an area60. Eddy kinetic energy is a measure of the dynamism of physical oceanography which is becoming a commonly used predictor of cetacean habitat61. We did not use: latitude and longitude as these primarily describe the general geographic distribution of the study areas, and geographic aggregates of sperm whale catches62 as these proved to have no predictive power. The mean values of the 14 predictor measures were calculated over calendar months for each grid point, and then over the grid points in each study area.To obtain predictors of the sperm whale density at each grid point, we then made quadratic regressions of the density of sperm whales in each study area (i), d(i), on the mean values of the predictor measures, weighting each study area by its surface area. Because the surveys were conducted over different time periods, the densities were corrected based on the estimated trajectory of global sperm whale populations by multiplying d(i) by the ratio of the global population in 1993 over that in the mid-year of the survey (as in Fig. 4). Predictor variables were selected using forward stepwise selection based upon reduction in AIC.Sperm whale population sizeThe population of sperm whales globally, N, was then calculated as follows:$$N=sum_{k}dleft(kright)cdot aleft(kright),$$
(1)
where a{k} are the parameters of the regression; the summation is over k, the grid points; d(k) is the estimated sperm whale density at grid point k from the habitat suitability model; and a(k) is the area of the 1° cell centred on grid point k. Population estimates for other ocean areas (North Atlantic, North Pacific, Southern Hemisphere) were calculated similarly.The CVs of these population estimates were calculated following the methodology in8, (although there is an error in Eq. (3) of8 such that the squareroot symbol covers both the numerator and denominator rather than just the numerator). The error due to uncertain density estimates for the different surveys is:$$CVleft({D}_{T}right)=frac{sqrt{sum_{i}{left(CV({n}_{i})cdot {n}_{i}right)}^{2}}}{sum_{i}{n}_{i}}.$$
(2)
This is combined with the uncertainty in the extrapolation process (output from the linear models), CV(extrap.), to give an overall CV for the population estimate:$$CVleft(Nright)=sqrt{{CV({D}_{T})}^{2}+{CV(mathrm{extrap}.)}^{2}.}$$
(3)
Post-whaling trend in population sizeWe compiled a database of series of surveys producing population estimates of the same study area during the period 1978 (by which time most commercial sperm whaling had ceased) and 2022. Each series had to span at least 10 years, and all of the surveys in the series had to be comparable in terms of area covered throughout the time span. There also had to have been at least 3 surveys for a data set to be included.The data consisted of the survey area, A, the estimated population in area A in year y (for multi-year surveys, y would be the midpoint of the data collection years), nE(A,y), and the provided CV of that estimate, CV(nE(A,y)). The data series used for these analyses are summarized in Table 3.For each survey area, A, we calculated the trend in logarithmic population size, r(A), over time using weighted linear regression:$${text{Log}}left( {n_{E} left( {A,y} right)} right) , sim {text{ constant}}left( A right) , + rleft( A right) cdot y. left[ {{text{weight }} = { 1}/left( {{1} + {text{ CV}}left( {n_{E} left( {A,y} right)} right)} right)^{{2}} } right]$$
(4)
Table 3 also includes other published estimates of sperm whale population trends, from sighting rates or mark-recapture analyses of photoidentification data, with these estimates also having to span at least 10 years of data collection, and include data collected in three or more different years.Population trajectoryTo examine possible trajectories of the global sperm whale population following the start of commercial whaling in 1712, we used a variant of the theta-logistic, a population model that has been employed in other recent analyses of the population trajectories of large cetaceans45,63. The theta-logistic model is:$$nleft(y+1right)=nleft(yright)+rcdot nleft(yright)left(1-{left(frac{nleft(yright)}{nleft(1711right)}right)}^{theta }right)-fleft(yright)cdot cleft(yright).$$
(5)

Here, n(y) is the population of sperm whales in year y, r is the maximum potential rate of increase of a sperm whale population, and θ describes how the rate of increase varies with population size relative to its basal level before whaling in 1711, n(1711). The recorded catch in year y is c(y) and f(y) is a correction for bias in recorded catches.Whaling reduced the proportion of large breeding males64, likely disrupted the social cohesion of the females3, and may have had other lingering effects which reduced pregnancy or survival, and thus the rate of increase. Poaching has been found to reduce the reproductive output of African elephants, Loxodonta Africana, which have a similar social system to the sperm whales3, and this effect lingers well beyond the effective cessation of poaching46. There is some evidence for these effects of what we call “social disruption” on sperm whale population dynamics20,46,65. We added a term to the theta-logistic to account for such effects:$$nleft(y+1right)=nleft(yright)left[1+rcdot left(1-{left(frac{nleft(yright)}{nleft(1711right)}right)}^{theta }right)-qcdot frac{sum_{t=y-T}^{y}f(t)cdot c(t)}{nleft(y-Tright)}right]-f(y)cdot c(y).$$
(6)

Here, (frac{sum_{t=y-T}^{y}f(t)cdot c(t)}{nleft(y-Tright)}) is the proportion of the population killed over the last T years, and q is the reduction in the rate of increase when almost all the whales have been killed. This reduction is modelled to fall linearly as the proportion killed declines to zero.The global sperm whale population has some geographic structure18. Females appear to rarely move between ocean basins, and males seem to largely stay within one basin. Furthermore, sperm whaling was progressive, moving from ocean area to ocean area as numbers were depleted4. We model this by assuming K largely separate sperm whale subpopulations of equal size. Exploitation in 1712 starts in subpopulation 1 and moves to subpopulations 1 and 2 when the population 1 falls to α% of its initial value, and so on for the other ocean areas. The catch in each year in each area being exploited is pro-rated by the sizes of the different subpopulations being exploited. The population model for subpopulation k, which is one of the KE subpopulations being exploited in year y, is:$$nleft(k,y+1right)=nleft(k,yright)left[1+rcdot left(1-{left(frac{nleft(k,yright)}{nleft(k,1711right)}right)}^{theta }right)-qcdot frac{sum_{t=y-T}^{y}C(k,t)}{nleft(k,y-Tright)}right]-Cleft(k,yright),$$
(7)
where the estimated catch in year y in subpopulation k is given by: (Cleft(k,yright)=f(y)cdot c(y)cdot n(k,y)/sum_{{k}^{mathrm{^{prime}}}= More

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