Philippa Kaur

Model: network structureCommunities are simulated using a modified version of the evolutionary food web models developed in Allhoff et al. (2015) and Allhoff & Drossel (2016), which build on previous models25,26 to show that biodiversity can be maintained in multitrophic networks despite ongoing species turnover when feeding traits are allowed to evolve independent of body mass. The model includes consumptive and competitive interactions, where interaction strengths are determined by the traits of consumer species and their resources. All species possess three traits, a body mass or size ((m)) (used interchangeably), which places them on a body size trait axis, a feeding center ((f)) and feeding range ((s)), which determine the shape and placement of their feeding curve along the axis (Fig. 1a). While the (s) parameter specifically represents one standard deviation of a species’ feeding curve, we refer to (s) throughout as simply the feeding range. The feeding curve represents the hypothetical, fundamental feeding niche of species and shows the potential strength of a consumer’s attack rate for a given resource located along the body size trait axis. Because interactions are determined through these Gaussian curves, our networks are technically fully connected. However, when resources are far from consumer’s feeding centers, interaction strengths become asymptotically small, having a negligible effect on dynamics. Additionally, a basal resource drives energy flow in the food web (Fig. 1a). A summary of all model parameters and variables is provided in Table 2.Model: population dynamicsDynamics are governed by a bioenergetics consumer-resource model, where parameters are scaled to the body mass of species, following previous developments in Yodzis & Innes (1992) and Brose et al. (2006). The rate of change of consumer biomass (({B}_{i})) is given by:$$frac{{dB_{i} }}{dt} = mathop sum limits_{j = resources} e_{j} g_{ij} B_{i} B_{j} – mathop sum limits_{j = consumers} g_{ji} B_{i} B_{j} – mathop sum limits_{j = competitors} c_{ij} B_{i} B_{j} – x_{i} B_{i}$$
(1)
where ({e}_{j}) represents the efficiency of biomass conversion of resource (j) by consumers, ({g}_{ij}) is the mass-specific consumption rate of resource (i) by consumer (j), ({c}_{ij}) is the interference competition between consumer (i) and (j), and ({x}_{i}) is the mass-specific biomass loss from respiration and mortality for consumer (i). The rate of change in basal resource biomass (({B}_{0})) is described by:$$frac{{dB_{0} }}{dt} = n_{0} – mathop sum limits_{j = consumers} g_{j0} B_{j} B_{0} – lB_{0}$$
(2)
where ({n}_{0}) represents the constant influx of resource biomass and (l) the outflow rate. The time scale of the whole system is therefore defined by setting the constant resource influx rate ({n}_{0}=1), meaning that all other rates in the system, and consequently also consumer lifespans, must be interpreted in relation to ({n}_{0}). The basal resource is given a constant body mass trait value of ({m}_{0}=1) which does not evolve. The mass-specific consumption rate is given by:$${g}_{ij} = frac{1}{{m}_{i}} frac{{a}_{ij}}{1+{sum }_{k=prey}{h}_{i}{a}_{ik}{B}_{k}}$$
(3)
where,$${a}_{ij}= {m}_{i}^{0.75}cdot {N}_{ij}={m}_{i}^{0.75}cdot frac{1}{{s}_{i}sqrt{2pi }}cdot mathrm{exp}left[-frac{{left({log}_{10}left({f}_{i}right)-{log}_{10}({m}_{j})right)}^{2}}{2{s}_{i}^{ 2}}right]$$
(4)
describes the mass-specific attack rate of consumer (i) on resource (j), given the feeding kernel (({N}_{ij})) of consumer (i). Gaussian feeding kernels are calculated from consumer (i)’s feeding range (({s}_{i})), feeding center (({f}_{i})), and resource j’s body mass (({m}_{i})), such that resources which occur close to consumer feeding center on the body size trait axis result in the highest attack rates (Fig. 1a). The mass-specific handling time for consumers is given by ({h}_{i}=0.4cdot {m}_{i}^{-0.25}). Interference competition between consumer (i) and (j) is described by:$${c}_{ij}= {c}_{0}cdot frac{{I}_{ij}}{{I}_{ii}} text{ for }ine j$$
(5)
where,$${I}_{ij}= int {N}_{ik}cdot {N}_{jk}dleft({log}_{10}{(m}_{k})right)$$
(6)
describes the overlap in resources (k) between two competing consumers (i) and (j), such that consumers with similar feeding traits will have greater overlap between their feeding kernels resulting in higher competition coefficients.Model: community assembly & network evolutionCommunity assembly of food webs occurs through a combination of ecological and evolutionary dynamics (Fig. 1b). All ecological dynamics are described by the consumer-resource model above, where species with viable biomass densities persist in communities and species whose biomass falls below a fixed extinction threshold ((varepsilon = {10}^{-8})) are removed from the network. New species are introduced probabilistically into the network at fixed intervals through either mutation events ((p)) or as invaders ((1-p)), where (p) can be manipulated to increase the frequency of either mutation or invasion events. The traits of new mutant species are drawn probabilistically from a Gaussian distribution set around the traits of a selected extant parent species in the network. Invader species traits are generated in a similar fashion but using a Gaussian distribution with a greater standard deviation. The standard deviation of this trait range is set with the invader strangeness parameter (z), which can be manipulated to increase the range of potential traits for invader species. Thus, a larger (z) value increases the probability that new invader species will appear “strange” compared to other species already in the community. For mutant species, (z) is always set to 0.1.Parents of mutants are chosen probabilistically, where species with greater individual density (species biomass/body mass) are more likely to generate new mutant species. The parents of invader species are chosen randomly, with equal probability given to all extant species in the community. Both mutants and invaders are introduced into the system at the extinction threshold biomass ((varepsilon ={10}^{-8})). For mutants the initial biomass is removed from the biomass of the parent species’ populations, while for invaders this biomass is added into the system without affecting the parent species’ biomass pool; however, this difference did not significantly impact our results.Communities are initialized with a single ancestor species (starting biomass (varepsilon ={10}^{-8})) and the basal resource (starting biomass (=frac{{n}_{0}}{l}=2.0)) (Fig. 1b). The ancestor species is given a body mass of (m=100), feeding center of (f=1), and feeding range of (s=0.4). Upon initialization, the system is a run with only the ancestor species consuming the basal resource until a new species is introduced at 100 time steps. Thereafter, new species are introduced every 100 time steps, with ecological dynamics occurring between each species introduction. Additionally, species biomass is assessed at each 100 time step interval and non-viable species populations that fall below the biomass extinction threshold are removed. This process is repeated cyclically over the course of simulations (Fig. 1b), with many new species being generated and many removed due to extinction. The persistence of individual species is thus determined by their individual traits and overall resource availability given the composition of the rest of the community. With this dynamical approach to simulating evolving food webs, similar models have been shown to generate viable communities with both multi-trophic diversity and constant species turnover27,28, making this framework useful for testing the evolutionary impacts of species invasion and disturbance on community composition.Simulation experimentsSimulations were conducted in C, where numerical integration of differential equations was performed using the Runge–Kutta–Fehlberg algorithm from the GNU Scientific library29. Simulations were run for 25 million time steps, with 250,000 novel species introductions (mutants or invaders) for each simulation. To test if invasion would increase disturbance and variability in communities and drive the evolution of more generalized species, we conducted simulations where invaders were introduced with an increased probability of having trait values that were divergent from parent species. We controlled this by manipulating the invader strangeness parameter ((z)) across a range from (z=0.1) (invader and mutant trait values are equivalent) to (z=5.0). Invasion frequency ((p)) was fixed at 0.2 for all simulations, making mutation events more likely to occur than invasion.We hypothesized that introducing invaders with traits that are very different from parent species and from the community should result in greater disturbance in food webs because these species would be more likely to occupy novel niche space along the body size trait axis, which could result in the overexploitation of resources either through superior feeding strategies or by allowing invaders to avoid consumption by other consumers. Together, this should increase the probability of disrupted consumer-resource dynamics and secondary species extinction occurring with the introduction of strange invaders, both resulting in increased variability of biomass in the community. As a result, this increased variation should favor the survival of more generalist species in the community if they can buffer variability by consuming a greater range of resources.This is tested against the assumption that specialist consumers are more efficient than generalist consumers (generalist trade-off hypothesis2,12), which is built into our model given the formulation of the attack rate parameter ((a)), where specialist species achieve higher optimal peaks in attack rates, given their smaller feeding ranges ((s)). Thus, under conditions of low variability, our model results in communities being composed of mostly very specialized species, with narrow feeding ranges. To counter this trend toward extreme specialization, we set a floor for minimum feeding range values for all species of (s=0.3). Given these tendencies, we expected the persistence (lifespan) of more specialist species to be greatest under conditions of low variability (low invader strangeness) and that the relative persistence of more generalist species compared to specialists should increase with disturbance due to increasingly strange invaders.To test the robustness of these predictions, we replicated the (z) parameter sweep 100 times using random initial seed sets, resulting in 5000 simulations total, which collectively generated over 1.25e+09 unique species across all simulations. Data from these simulations was extracted at three different time intervals. We assessed species traits and lifespan data for all species generated in simulations at every 100 time steps, excluding data from the first 50,000 time steps to avoid including transient dynamics. Community level data, including community biomass and basal resource biomass were extracted at every 50,000 time steps (excluding time 0 from analysis). Species turnover data was extracted at every 10,000 time steps. In the infrequent event that simulations did not complete (community level extinction or crashed runs) we reran simulations with different random seed sets but identical parameter values.Data & statistical analysisDo resource and community variation increase with invader strangeness?To assess whether the addition of increasingly strange invaders into food web communities resulted in increased variation we analyzed several metrics of community and resource variability. We calculated the standard deviation (SD) of the basal resource biomass across time for each simulation and pooled these data for all simulation replicates across the invader strangeness parameter sweep. To assess variation at the community level, we used a similar approach to calculate variability in community biomass. For this metric, we summed the population biomasses of all species in the community for each given time interval output (excluding species introduced at that time step) and calculated the SD of these values across time for each individual simulation.Finally, to further assess community variability and to determine if increasing invader strangeness drives increased extinction in communities, we calculated species turnover for each time output. Species turnover was measured as the percentage change in the composition of species in communities between each time output (10,000 time steps). We then calculated mean species turnover over time for each simulation replicate and pooled all data together. To account for the non-linearity observed in our variation data (see “Results”) we conducted generalized additive models (GAM) to determine if increasing invader strangeness resulted in a significant increase in variability. GAMs were fit using a gamma error distribution with a log link function to account for continuous data constrained to positive values.Does the degree of generalism in communities increase with invader strangeness?To determine if the degree of generalism and the proportion of generalist species in food webs increased as invader strangeness increased, we calculated the mean and median feeding range ((s)) (Table 1) of species which occurred in communities for each simulation. We included all species that were generated and that survived for at least 100 time-steps in simulations, to remove the many non-viable species which immediately go extinct. Additionally, we included only mutant species for this metric to avoid the influence of the traits of invaders species, which we directly manipulated through the invader strangeness parameter. We reasoned this would provide a more independent metric of feeding range trends in communities. Mean and median feeding range were calculated for all simulation replicates and the impact of invader strangeness was assessed with GAMs (gamma error distribution with a log link function) to account for non-linear data (see “Results”).Additionally, we calculated a measure of the realized feeding range of consumers (distinct from the fixed fundamental feeding range ((s)) (Table 1)) to determine if more species were functioning as feeding generalists in communities. For this metric, we calculated the attack rate of each consumer on all other species in the community (including the basal resource and the focal consumer) for each time output (every 50,000 time steps from our community data, excluding species introduced at that time step). We then calculated the proportion of the attack rate on each species compared to the focal species’ maximum possible attack rate (an ideal prey at the exact center of the consumer’s feeding kernel). We then excluded all values below a threshold of 0.1 and from this calculated the proportion of species consumed out of the total number of species in the community. This metric correlated positively with the fundamental feeding range ((s)) of consumer species (Supplementary Fig. S3) and we refer to it throughout as the realized feeding range (Table 1) of consumer species. For our statistical analysis, we calculated the mean realized feeding range of species per simulation across invader strangeness ((z)) and ran a GLM with a quasibinomial error distribution and logit link function to account for proportional data.Does the persistence of generalist species increase with invader strangeness?To determine the persistence of species in our simulations we assessed the lifespan of individual species in simulated communities across time. For a given species, lifespan was measured as the number of time steps it persisted in a simulation after its initial introduction. We used this data to determine the relationship between species persistence and feeding range traits in two ways. First, we assessed the lifespan of all species in individual simulations continuously given the feeding range trait values across species. From this, a regression coefficient was calculated from the log10-scaled data, using a GLM with a gamma error distribution (log link), to determine the trend or “lifespan slope” for each simulation under different levels of invader strangeness (Fig. 4b). These lifespan slope values were then assessed for all simulation replicates across the full range of the invader strangeness parameter. Because more specialized species have higher maximal attack rates and are typically more efficient in our model, we expected that the lifespans of specialist species would be longer than more generalized species and that lifespan slopes should be negative under conditions of low variation. Given this, we expected to observe a positive trend in lifespan slope values across the invader strangeness parameter sweep if disturbance was increased in simulations as (z) became higher. We tested for this positive trend in the lifespan slope data by conducting a GAM (Gaussian distribution and the identity link function) to manage the observed non-linear trend in our data (see “Results”).For the second approach, we aimed to determine the relative persistence of species by binning “generalist” and “specialist” species based on feeding range traits and comparing species lifespans between these groups. For this analysis we split species into bins, where specialist species included all species with feeding range (sle) 0.32 and generalists as all species with feeding range values (sge) 0.39 (species with intermediate feeding range values were excluded from the analysis). We performed a robustness check of bin cutoffs but found no qualitative or statically significant differences in our results for a range of bin cutoff values. To assess how the relative persistence of generalists compared to specialists was influenced by invader strangeness, we then calculated the mean life span of all species falling into either of these categories per simulation and determined how these values were influenced by (z) for all simulation replicates. To assess whether mean lifespan was different between each of these groups across the invader strangeness sweep, we conducted a GLM with species type (generalist or specialist) and invader strangeness ((z)) as fixed effect terms and tested for the statistical significance of their interaction on mean species lifespan. The GLM was run using a Poisson distribution to account for discrete lifespan count data with a log link function. All GLMs and GAMs were performed in R using the “glm” and “mgcv” functions30, respectively, and all non-linear parameters in GAMs were fit using generalized cross validation (GCV). More

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A framework to estimate unowned cat abundanceIn the following sections, we describe the application of an IAM, a hierarchical modelling approach, which estimates unowned cat abundance in discrete geographical units from spatially replicated citizen data, in combination with expert data obtained from 162 sites across five urban areas in England. In doing so, we explored key predictors of unowned cat abundance. We then estimated unowned cat abundance across urban areas in England and the UK with respect to the modelling results. We used WinBUGS53 and R54 for all data analysis via the R package R2Winbugs55 and QGIS56 for plotting maps.Data collation and preparationA database of unowned cat count data were compiled from citizen science data and expert data collected throughout a one-year period that began between 2016 and 2018 across five urban areas in the UK. Areas included Beeston, Bradford, Bulwell, Dunstable & Houghton Regis and Everton (Fig. 1). These data were collected as part of Cat Watch, a community partnership project set-up by Cats Protection, a UK feline welfare charity, to control cat numbers39,57. Two distinct forms of citizen science data were collected: (1) the first consisted of an initial cross-sectional random-sample door-to-door survey carried out with approximately 10% of households. At that stage, residents were asked how many cats they know of locally and how many they think were owned in the form of a multiple-choice question with the following options; none, 1–2, 3–4, 5–9, 10 or more, from which the number of unowned cats were derived. When a range was selected the central value was taken; for ten or more we used 15 (the average from reports when 10 or more was specified was 14.7). Location data were available for 3101 survey responses, within which there were estimates of 4411 unowned cats; (2) throughout the project, residents were able to report unowned cats in their area directly via social media or through a mobile application. During the study period, 877 reports were received reporting on the locations of 2790 unowned cats. These data were collected according to the study protocol approved by University of Bristol Faculty of Health Science Research Ethics Committee approval number 38661. All methods were performed in accordance with the relevant guidelines and regulations. Informed consent was secured in advance of survey participation. Residents provided report data voluntarily, with no identifying information collected. No experimental protocols were used.Expert data were obtained from an experienced community team (CT) that recorded when and where an unowned cat was found or confirmed the lack of presence of an unowned cat. The CT carried out extensive door-to-door surveillance across both reported hot spot and cold spot areas. These data are considered of higher quality, due to the ability of the CT to correctly identify an unowned cat and with no risk of double counting the same individual. Unowned cats can be either stray or feral. Protocols to accurately identify a stray cat included; scanning for a microchip, attaching a paper collar to notify potential owners, advertising online, door-to-door notifications, local posters and contacting other animal welfare organisations, including veterinary practices. If no owner was found during this process it was identified as unowned. Feral cats were more likely to be identified via behavioural means; as they have not been socialised to humans, they will be more fearful and will not approach humans47. If they have already been neutered they may also have their left ear “tipped”. During the study period, there were 601 records from the CT, reporting on the location of 605 confirmed unowned cats. All three of these data sources provided detailed location data (postcodes and/or addresses) enabling geo-referencing of unowned cat location data.To account for duplicate sightings, the citizen science data required clustering to account for neighbours in close-proximity reporting the same cats. There is limited understanding of urban unowned cats in the UK, however studies of urban unowned cats in other areas indicate home range sizes between 3.7 and 10.4 ha for urban areas58,59. Studies on unowned cats in the UK indicate that home ranges vary between 10 and 15 hectares60. We assume a maximum 20 ha home range, equivalent to a circular area with a diameter of 504 m. Consequently, we apply a 500 m cluster function in R that derives clusters of cat sightings that are within 500 m of each other. The individual records were maintained as replicate counts within each cluster. Clustering of 500 m has also been shown to provide reasonable estimates in an urban area with high expert coverage (91%), where you would not anticipate cat numbers to be significantly inflated above those observed by experts25. In the absence of expert data, the effect of violating this assumption (i.e. reporting them as replicate sightings when they are not) would result in lower estimates of cats. However, where expert data is available, the effect of violating this assumption would result in bias in the observation parameters, not estimates of the cats themselves, which are also inferred from the expert data that do not contain duplicate sightings.Data analysisWe applied an integrated abundance model (IAM) within a Bayesian framework that combines count data across sites from two forms of citizen science data and expert data25. The hierarchical structure of the IAM enables it to borrow strength from the sites with expert data to inform detection biases of citizen science data, including detection probability of an unowned cat and false positives due to misidentification of an owned cat as unowned. The goal of the inference is to estimate the abundance of unowned cats within each site and explore covariates as predictors of population density.Specifically, observed citizen science counts at each site i and during each replicate survey j are linked to true site-specific population sizes (Ni) via a detection probability (p) and the expected number of misidentifications (m). We apply a Poisson distribution to account for additional stochasticity in spatial replicates not accounted for in the systematic biases (m and p). Each type of citizen science data is modelled separately to account for the different biases in collection methods between the survey data (y) and report data (u):$$ {y_{i,j}}sim {text{ Poisson }}({N_i}{p_y} + {m_y}) $$$$ {u_{i,j}}sim {text{ Poisson }}({N_i}{p_u} + {m_u}) $$Expert consensus (wi) was available on the abundance of individuals for 104 sites and linked to true population sizes via a Poisson observation error.$$ {w_i}sim {text{ Poisson }}left( {N_i} right) $$We additionally assume that where expert counts are available they are accurate at the level of presence or absence.$$ {z_i}sim {text{Bernoulli}}left( Omega right) $$$$ {N_i}_= {z_i}{lambda_i} $$whereby zi is a binary measure of occurrence, with each of the i sites occupied or not, that is modelled as a Bernoulli random variable determined by occupancy probability (Ω). True site-specific population sizes (Ni) are therefore a function of whether a site is occupied or not and a site-specific mean λi. When expert data on occurrence can be inferred from expert consensus this was included in zi.We extend the original development of an IAM25 described above to model the log the site specific mean (λi) as a linear function of covariates (x) using the following linear relationship:$$ log{lambda }_{i} = mu +sum_{j=1}^{n}{beta }_{j};{x}_{j,i}+{varepsilon }_{i}$$$$varepsilon sim N(0,{sigma }^{2})$$where xj, I are the values of the jth covariate across sites i, βs are the regression coefficients for each covariate and ɛ is the residual site-specific variation providing estimates of unexplained variance. We also fitted a model without covariate effects to gain an estimate of total site-specific variance. The proportional reduction in the residual site-specific variation component is a measure for the proportion of the site-specific variance in abundance explained by that covariate or covariates.To assess the credibility of covariate effects we calculated the probability that their effects were positive [P(β  > 0)] or negative [P(β  More

With S1GBM’s characteristics as a global, PLIA-normalised, high-resolution C-band backscatter dataset, a direct validation experiment is not feasible since we lack matching reference backscatter data collected during airborne or ground based radar campaigns. Other existing global mosaics were generated based on different time-spans, polarisations17, frequencies18, or do not share the novel feature of the PLIA-normalisation20.On these grounds, we prefer to assess the characteristics of the S1GBM layers with respect to different land cover types on a global scale, and to incorporate the gained knowledge into an easy-to-use classification algorithm for permanent water bodies (PWB). This simple mapping experiment acts as an example and should on the one hand demonstrate the integrity and quality of the S1GBM mosaics (and document its limitations), and on the other hand, stimulate more advanced applications and ingestion-models by the remote sensing- and the wider user -communities. Our validation of the obtained PWB-map compares—over a representative and diverse set of eight world regions (see Fig. 1b)—the S1GBM mosaic with a reference water body map, as well as with true-colour imagery from the Sentinel-2 optical sensor. This arrangement should also portray the shape and texture of the S1GBM mosaic and help the audience with the interpretation of the SAR imagery, which as stated at the outset, allows a unique view on the Earth’s surface.In the following, 1) we examine in detail the appearance and spatial features of the S1GBM VV- and VH-mosaics over the region of Bordeaux, also investigating the effect of the PLIA-normalisation. Then, 2) we derive the characteristic C-band backscatter signature for global land classes. Finally, 3) we perform the PWB-experiment in eight world regions a) to evaluate the dataset’s integrity, b) to demonstrate its spatial information and exemplify its use, and c) to comment on the S1GBM’s assets and caveats.Detail example BordeauxFigure 2 gives an example of the land cover signal in the S1GBM VH and VV mosaics over Bordeaux, France. Comparing it with the recent PROBA-V-based Land Cover dataset of the Copernicus Global Land Service (CGLS LC10052), several surface features are apparent in the mosaics, including urban areas with varying density in both VV- and VH-channels. In the VH mosaic, a clear discrimination of forest areas (cf. with LC100’s broadleaf in brighter green, needle leaf in darker green) against crops (brighter yellow) and vineyards (darker yellow) is apparent. The cross-polarised VH-backscatter is more sensitive to vegetation-density, -structure, and -status, as multiple scattering between branches and volume scattering increases the share of backscattered microwaves with changed polarisation. Most prominent, in both VH and VV, is the very large contrast between land surfaces and open waters with significant lower backscatter signatures. This is the basis for our PWB-mapping experiment discussed in detail in the subsequent section.We would also like to draw the attention to the spatial detail carried by the S1GBM mosaics, with various features at deca- and hectometric scale shown for example in Fig. 2. For instance, one can see bridges, highways, railways, and airports in the Bordeaux metropolitan area in the south-west corner of the here displayed T1-tile (100 km extent). Also, in the west, from north to south, the shorelines of the Gironde estuary and its downstream rivers are clearly mapped, resolving small islands and narrow straits. Agricultural plots and forest sections may be differentiated especially in the VH mosaic, e.g. with particular structures in the north-west corner. For further exploration, users may visit the open web-based S1GBM viewer51 offering a pan-and-zoom exploration of the full S1GBM VV- and VH-mosaics.Figure 2b,d allows the comparison of the S1GBM VV backscatter mosaic (which underwent the PLIA-normalisation) against the mean of non-normalised Sentinel-1 VV backscatter from the same observation period (not part of the dataset publication; just for comparison). As discussed above, radar backscatter is strongly dependent to PLIA, and hence Sentinel-1 SAR images are subject to the observation geometry defined by the mission’s relative orbit configuration and the overlapping pattern (cf. global map in Fig. 1b). One can clearly see this impact in Fig. 2d, where data from all local orbits are averaged in their native orbit geometry (i.e. mean of σ0 (θro, t), resulting to characteristic linear artefacts of backscatter discontinuities along the limits of the (repeating) orbit footprints. The mini-map of the Bordeaux-T1-tile in Fig. 2d plots the number of input Sentinel-1 scenes, also reflecting the heterogeneous coverage pattern induced by the different number of overlapping relative orbits (from 2 to 4 in this area), each with a different local PLIA-range, generally. Notably, the triangular zone covered by only 2 orbits (yellow, 194 scenes) is a zone that features a PLIA-spread that is not large enough to reliably estimate the local PLIA-slope β. This zone is part of the pixel domain where we applied the static slope value of −0.13 dB/° to the S1GBM mosaic, with a resulting backscatter image that is free from orbit-related artefacts (Fig. 2b). We note that the sections covered by 3 or 4 orbits in this example are normalised with the regular regression slope, letting us conclude that our approach yields a smooth mosaicking impression in areas of mixed coverage density.Backscatter signature analysisDelving into above concept that SAR backscatter characteristics in the S1GBM are determined by land cover, we analysed the backscatter signature for the global land surface for each major land cover class (LCC). We globally aggregated data from the normalised S1GBM VV and VH mosaics per LCC and formed the backscatter distribution within each LCC, allowing the discrimination of typical SAR backscatter signatures for a specific land cover class.Land cover definitionsAs land cover dataset, we selected the above-mentioned PROBA-V-based CGLS LC100 for its full global coverage and the (for global datasets) relatively high spatial resolution with a pixel spacing of 100 m. To allow a fast pixel-by-pixel comparison, we resampled the CGLS LC100 to the Equi7Grid at 10 m using nearest-neighbour-downsampling. After a first inspection of backscatter signatures, we grouped the 23 LCC of the LC100 to 13 major LCC, accounting for the similarity between certain classes: Respective open and closed forest classes were aggregated to evergreen needle leaf forest, evergreen broad leaf forest, deciduous needle leaf forest, and deciduous broad leaf forest, and herbaceous wetland was grouped with herbaceous vegetation. Table 2 lists the main statistics per land cover and the group aggregations.Table 2 Sentinel-1 backscatter statistics per land cover class (LCC) of the CGLS LC100 dataset, mean and standard deviation, for the S1GBM mosaics in VV and VH polarisation.Full size tableC-band backscatter signaturesThe C-band backscatter signatures of our major 13 LCC are plotted for VV- and VH-polarisation as distribution-density-“heatlines” in the upper part of Fig. 3, illustrating the global average backscatter levels of each surface class, and the variance within. Forest and water-body classes have a very narrow distribution, whereas snow and ice and bare vegetation have a greater spatial backscatter variability. Snow and ice packs often have a heterogeneous structure from its complex genesis involving melting and freezing phases, leading to a mixture of surface- and volume-scattering when observed by radar. Likewise, the LCC bare vegetation comprises very different surfaces dominated by rocky, sandy, or mountainous surfaces, each governed by a distinct backscatter behaviour and hence create the wide spread within this LCC.Fig. 3Results from the S1GBM C-band backscatter signature analysis for major land cover classes, which are provided by the 100 m Land Cover Version 2.0 product of CGLS. The heatlines in (a) and (b) show the S1GBM’s normalised backscatter distribution within the total area of each major land cover class, for VV and VH, respectively. In preparation for the mapping of permanent water bodies (PWB), (c) and (d) show the distributions for the globally combined water- and land- surfaces, with the combined classes indicated by blue and brown bars in (a) and (b) legends. For the PWB-mapping, three land cover classes have been excluded due to the lack of clear separability against the water classes, i.e. due to largely overlapping distributions. The selected thresholds for VV and VH mosaics used in our PWB-mapping algorithm are indicated as red lines.Full size imageThe LCC-heatlines in Fig. 3a,b are approximately ordered by the mean backscatter value. On top, one can find the two water LCCs with a very low backscatter level that is caused by mirror-like-reflection away from the sensor, followed by bare and herbaceous vegetation LCCs that are dominated by dry conditions and hence are generally weak scatterer. The LCCs moss & lichen, shrubs, and agriculture feature medium backscatter and variation thereof. Higher backscatter levels are observed over the forest LCCs, where volume and multiple scattering become more dominant, as well as over the LCC urban & built up, where corner reflections acting as echo cause the strongest radar backscatter.When comparing VV and VH polarisation, the biggest difference is in the overall level of backscatter, with about 7 dB between both polarisations across all LCCs. The order of LCCs as a function of mean backscatter is mostly the same for VV and VH, except for the water and ice classes. Interestingly, the open sea class shows a steeper drop from VV to VH, whereas shrubs show a comparatively small drop. We found that the strongest changes in the backscatter distributions are apparent in the non-forest vegetation classes, e.g. for bare vegetation and agriculture, supporting our initial assumptions on the sensitivity of Sentinel-1 VH backscatter to complex vegetation dynamics and crop varieties.Permanent water body mappingFollowing up to what we have already seen along the rivers in Fig. 2, water bodies (represented by the LCCs open sea and permanent water bodies) show a most distinctive backscatter signature in relation to other land cover classes (cf. 3a-b). Effectively, water surfaces show in radar images a strong contrast with land surfaces. The reason for this are the different microwave scattering mechanism over water- and land-surfaces and the side-looking geometry of SAR systems. A specular reflection of the radar pulses by the water surfaces leads to backscatter intensities received by the sensor that are much lower than for most other land cover types. With the S1GBM VV- and VH-mosaics at hand, we exploited this discriminative feature of water bodies and employed a simple permanent water body mapping method. Unlike the backscatter mosaics of the S1GBM, the obtained PWB map can be validated directly, as we have available matching global water body maps as a reference. Moreover, the experiment should demonstrate the ease of realising a land cover mapping application in short time, exploiting the novel S1GBM data and its high-resolution radar imagery of the Earth’s land surfaces.Based on above insights from the Sentinel-1 backscatter signature analysis, our first step was to spatially merge all water- and all land-LCCs and build the combined backscatter signatures for VV and VH (Fig. 3c,d). The water distribution (all water classes; bright blue) is plotted for both polarisations next to the non-water distribution (all land classes, bright brown), already demonstrating an acceptable feature separation. However, as one can see in the heatlines above, water has still some significant overlap with some land LCCs, e.g. with bare vegetation, herbaceous vegetation, and moss & lichen. Naturally, this translates to a considerable overlap in the merged distributions below, especially in the VH case and for moss & lichen. We concluded that for these LCCs no robust separability against water bodies is given in the S1GBM data and excluded the three classes from further PWB-mapping. Also, we dropped the LCC open sea in further processing as we limit the PWB experiment to inland surfaces (that are also covered by the reference dataset). The backscatter distributions of the PWB LCC and the selected land LCCs are shown in dark blue and brown (permanent water bodies and selected land classes in Fig. 3c,d), with a noticeably improved separability, especially in VH polarisation.As a next step, evoking the theory of Bayesian inference with equal priors for binary classification, we obtained a statistically optimal global threshold for VV and VH, each. In this respect, we identified two thresholds, −15.0 dB for VV and −22.9 dB for VH polarisation, which we applied in a third step as an upper-bound backscatter-value on the complete S1GBM mosaics to map the global PWBs. Note again that the LCCs bare vegetation, herbaceous vegetation, moss & lichen, and open sea are not included in the PWB-mapping and are masked in all later results.Although the VV and VH mosaics are redundant to some degree, the consideration of both channels is most advantageous for the PWB-mapping. First, the classification based on Bayesian inference is more robust when resulting from two discriminations. Second, while the VH mosaic offers a better separability between water and non-water (having less overlap in the distributions and hence less false positive and negative classifications), and the heatline of the PWB-LCC is better defined in VH, the VV mosaic offers in general a higher spatial detail due to its stronger backscatter signal and hence more favourable signal-to-noise ratio.By applying the obtained thresholds to the normalised S1GBM mosaics as simple classification rules$${sigma }_{0}^{{rm{VV}}}(38)le -15.0;{rm{dB}}$$
(2)
$${sigma }_{0}^{{rm{VH}}}(38)le -22.9,{rm{dB}}$$
(3)
and through joining them with logical “AND”, we were able to produce a global PWB map in less than two hours, using 70 parallel cores on the VSC-3 supercomputer.Evaluation of S1GBM mosaics and PWB mapTo evaluate our S1GBM permanent water body (PWB) map, we chose as a reference dataset the Global Surface Water (GWS23) from the European Commission’s Joint Research Centre (JRC-EC). The GSW offers globally at a 30 m native sampling different variables on water bodies, e.g. annual seasonality, occurrence, recurrence, or maximum extent, and is based on 36 years of Landsat data in its newest version (GSW1_2). Although the annual seasonality for 2015 or 2016 was not accessible from version GSW1_2 at the time of writing this manuscript, we found the Seasonality 2015 dataset of the GSW1_0 version suitable as a reference. Pixels valued with seasonality “12” (i.e. all months) are labelled permanent water and constitute our reference PWB map, which we warped by means of bilinear resampling to the Equi7Grid at a 10 m pixel spacing.The evaluation presented in this paper was carried out on a representative and diverse set of eight world regions (see locations in Fig. 1b). For each region, classification results were assessed by a pixel-by-pixel comparison between the PWB map from S1GBM and from the GSW reference. Having such binary maps (water vs. non-water) it was straightforward to generate an “accuracy layer” representing the four elements of the commonly used confusion matrix, i.e. true positives, false positives, false negatives, and true negatives, to discuss the skill of the S1GBM to map PWBs. Areas belonging to the four excluded LCCs were masked in the result plots. Furthermore, to give some visual guidance in the evaluation regions, we acquired from the Copernicus Sentinel-2 Global Mosaic (S2GM) service the RGB-composite for the year 201953 (the mosaic for 2015 was available only over Europe).In the following, we present results for four large-scale regions (500 km × 500 km) in Fig. 4, and for four small-scale regions (120 km × 120 km) in Fig. 5. For each region, the S1GBM VV mosaic is displayed on the left panel (space-saving/omitting the VH mosaic, which contributes likewise to the PWB mapping), the accuracy maps showing the performance against the GSW reference in the centre panel, and the Sentinel-2 RGB-composite to aid visual interpretation on the right panel. The accuracy maps are annotated with the respective User’s Accuracy (UA) and Producer’s Accuracy (PA), as the percentage of the agreement between the two PWB-maps.Fig. 4For four example sites at the large scale (500 km extent), the S1GBM VV mosaic (left) is contrasted with classification results from the S1GBM PWB mapping against the PWB taken from JRC Global Surface Water (GSW) in 2015 (centre), and with the RGB-composite of the Copernicus Sentinel-2 Global Mosaic (S2GM) for the year 2019 (right). Box outlines are shown in global overview in Fig. 1b.Full size imageFig. 5For four detailed example sites (120 km extent), the S1GBM VV mosaic (left) is contrasted with classification results from the S1GBM PWB mapping against the PWB taken from JRC GSW in 2015 (centre), and with the RGB-composite of the Copernicus S2GM for the year 2019 (right). Box outlines are shown in global overview in Fig. 1b.Full size imageLarge-scale examinationsFigure 4a–c shows the southern part of Finland, an area accommodating a multitude of small and large post-glacial lakes. Those are clearly visible in dark colours representing low backscatter values in the S1GBM mosaic, while the other parts of the country (which is dominated by vast forests) shows rather uniform medium backscatter. The optical RGB-composite from Sentinel-2 does not feature the same accentuation of the lakes, troubled by remainders of cloud coverage in the yearly mosaic. The PWB accuracy map shows perfect agreement between S1GBM and GSW, with an UA and PA of 100% each. We identified two reasons for the excellent performance: First, the C-band backscatter signatures of the predominant land covers in Finland, such as forests, cities, agriculture, are well distinguishable against water bodies and hence allow an almost sterile PWB-mapping. Second, northern Europe is well covered by the Sentinel-1 mission and the S1GBM has been built with a high data density, letting us expect the best mosaic quality.Moving to the region of the Lake Superior Basin in Canada and USA presented in Fig. 4d–f, we encounter a very similar, cold-temperate environment, but with a substantial higher share in spacious inland water bodies. Also here, the accuracy map shows a perfect agreement between S1GBM and GSW, which, in our interpretation, is clearly because of good feature separability in the SAR image. Particularly remarkable is that North America is much less covered by Sentinel-1 than Europe and that the imperfect modelling of the PLIA-dependency over water surfaces (as apparent e.g. in the east section of Lake Superior) does not impair the S1GBM PWB-mapping. Generally, imperfect PLIA-normalisation of SAR images is prominent over water bodies, whose specular reflection regime is characterised by a very strong PLIA-gradient (i.e. the slope β). However, we note that also the Sentinel-2 mosaic has striping artefacts bound to orbit footprints, and additionally suffers from cloud cover. The latter is a common problem in optical observation of higher latitudes, but is without effect in SAR imagery.Figure 4g–i depicts the situation for a section of the Albertine Rift Valley in eastern Africa with its lake system. Reflecting to a great deal the region’s diverse flora, which is displayed in many green and brown tones in the RGB-composite, the S1GBM VV mosaic shows a much more heterogeneous pattern than in the above examples. The forested sections in the west show distinct higher backscatter values than the savanna sections in the east, and also other geomorphological features correspond well with the radar and optical mosaic. Concerning the PWB-mapping, we see again perfect agreement, but with one large exception: the eastern end of Lake Albert is entirely labelled in red as false land, suggesting that these water areas are missed in the S1GBM PWB map (what can be confirmed after a quick check with common thematic maps). In this area we see the impact of the relatively poor input data density of about only 50 Sentinel-1 scenes (cf. Figure 1b), and apparently, we overlooked the impact of a few images with outlying backscatter levels during the manual quality curation. Moreover, the three Sentinel-1 relative orbits covering this area create almost identical viewing angles and yield a very small PLIA-range, troubling our backscatter normalisation. As a result, striping artefacts appear not only over water bodies (cf. Canada example) but also over land (in north-west part Fig. 4g), while, however, the Sentinel-2 mosaic is likewise affected by striping issues (cf. Figure 4i), for other reasons, though.The last row in Fig. 4(j–m) is centred at Bangladesh and displays the confluence of the Ganges and Brahmaputra streams, which are joined downstream by the Meghna river and ultimately discharge into the Bay of Bengal. Also in this region, the geomorphological features perceivable in the RGB-composite are reflected well by strong textural patterns in the S1GBM mosaic, promoting its broader use in land cover applications (note also the zoom-in plotted in Fig. 5j–m). The PWB-mapping results are inconclusive, as rivers of all sizes are correctly mapped, but many pixels are labelled in yellow as false waters. We consider this disagreement between S1GBM and GSW to be most likely a result of the different temporal resolutions of the two datasets, as the S1GBM is a two-year data aggregation reduced to single layers, whereas the GSW allows monthly snapshots of water bodies. For example, the Hoar ecosystem—which appears as yellow bulb in the north-east of Fig. 4k—is a large monsoon-fed lagoon system that is labelled by the GSW with seasonality-values ranging from 9 to 12 months. In the S1GBM mosaics, which are built using temporally averaged backscatter, these areas are obviously dominated by the high occurrence of water surfaces and act therefore as “most-of-the-time water bodies”. Some more vindication comes from the Sentinel-2 yearly mosaic, which also draws the Hoar area with a water texture. We conclude on this matter that seasonal water bodies are not properly modelled by our simple approach with Eq. 3, and it would need additional inputs from variance measures like the backscatter standard deviation.Small-scale examinationsFigure 5 depicts the small-scale example regions with respect to the PWB-mapping experiment. The first row in a-c) zooms to the Swiss lakes in central Europe and both, the radar and the optical mosaic, feature a high level of heterogeneity and detail, with many individual forests, cities, valleys, rivers, alpine lakes, and with the airport north of Zurich resolvable (in the centre-left of the box). The results from the PWB-mapping are very good with high UA- and PA-values, but with two anomalies: First, the southern arm of Lake Lucerne (in the south-west) shows some red segments of false land along the mountain flanks reaching into the lake. After inspection of the S1GBM mosaics we can state that this is clearly an artefact from the terrain modelling with the rather coarse, 90 m-sampled VFP SRTM Digital Elevation Model (DEM) during the Sentinel-1 preprocessing. At the time of the project, we selected the VFP DEM35 for its complete global coverage and its manually-checked quality, and accepted the coarse resolution (with respect to the 10 m-sampled Sentinel-1 SAR data). The second small anomaly can be found in the Alps in the south of the image, with the west-end of the Klöntalersee labelled in yellow as false water. The S1GBM is artefact-free at this location, and after checking the GSW’s seasonality, we hypothesise that ice covers this mountain lake during winters and leads to the different interpretation.Figure 5d–f presents the area around the confluence of the Amazon and Tapajós streams in central Pará in Brazil. Here, the rivers ramify into a multitude of lagoons and channels at various sizes, forming a complex system of water bodies. Fortunately, while the Sentinel-2’s RGB mosaic appears impure and rugged from contamination with the frequent cloud coverage in the central tropics, the Sentinel-1 mosaic offers a clear image that fully resolves the capillary structure of the water bodies and its shorelines. We consider this a remarkable feature, also recognising the very low input data density of the S1GBM mosaics in this area (cf. Figure 1b). Concerning the PWB-mapping, we obtained a good agreement with the GSW’s reference, labelling most PWBs correctly and misclassifying only small sections of the lagoons and river-arms. The false-water deviations are bound again to the seasonality of those segments that are most of the time under water, much alike to the situation in Bangladesh discussed around Fig. 4j–m. The red-labelled areas highlight water bodies which are mapped by the GSW but not by the S1GBM, and are of particular interest, as they exemplify that water surfaces seen by optical sensors are not necessarily identical to those seen by radars54. Swamp-like structures and waters with out-growing vegetation show a completely different SAR signature and hence might be distinguishable from open waters within a SAR image.The third small-scale example is the Great Salt Lake in Utah, USA, as displayed in Fig. 5g–i. The S1GBM offers many details of Salt Lake City’s structures in the south-east, and of the mining facilities at the eastern shorelines of the lake, as also visible in the RGB-composite. Obviously, the radar image does not account for the difference in salinity between the north- and south-section of the Great Salt Lake that is visible in the optical image. However, our S1GBM PWB method maps correctly—contrary to the GSW reference—the east-west rail causeway splitting the lake, which one can see as a red line in the accuracy map in Fig. 5h. With its pronounced semi-arid climate, this region shows a different behaviour than above examples. The dry conditions and the sparse vegetation with its weak scattering trouble seriously the S1GBM PWB-mapping, with many false water pixel all around the area. Here, we see the weak performance of the simple threshold approach with Eq. 3 in regions with a general low backscatter from land, and hence small contrast to water bodies.Figure 5j–m zooms into the Sundarbans at the southern shorelines of Bangladesh, with its multifaceted surface and its complex river-deltas. Both, the true-colour image from Sentinel-2 and the VV-mosaic from Sentinel-1 produce a feature-rich image and highlight the mangrove forest in the southern section with strong green colour or high backscatter, respectively. Adjacent to the north, the rice and bean agriculture draws large contrast patterns in the satellite images. For the PWB-mapping, a similar result as from the larger view on this region (cf. Figure 4k) is obtained, with all rivers and channels correctly classified, but with a substantial overestimation of permanent water bodies in areas of high water seasonality. To what extent rice fields and its managed inundations play a role here is left unanswered by the data, though, as managed rice fields typically show significant jumps in seasonal backscatter time series. More

Population genomicsDNA was sourced from fin clips or gill tissue sampled from 223 individuals of Siganus fuscescens from 2013 to 2017. From the northwest to the southwest of Australia, 40 individuals were sampled from the Kimberley, 36 from the Pilbara, nine from Exmouth Gulf, seven from Coral Bay, 40 from Shark Bay, 51 from Cockburn Sound, and 40 from Wanneroo Reef (Supplementary Data 3). However, following quality filtering of these DNA sequences, three rabbitfish individuals were excluded (see below), resulting in 220 rabbitfish individuals used in all remaining analyses (Supplementary Table S4). These tissue samples were extracted using the DNeasy Blood & Tissue Kit (Qiagen, Germany) based on a modified protocol, which included an in-house binding buffer, 1.4× volume of both wash buffers, and a partial automation of the extractions on a QIAcube (Qiagen) platform to minimize human handling and cross-contamination.SNP genotyping was conducted using the DArTseq protocol at the Diversity Arrays Technology (University of Canberra, Australia), which is a reduced representation genomic library preparation method that uses two restriction enzymes46,47. Genomic DNA was digested with the enzymes PstI–SphI and PstI–NspI and small fragments (0.75) or rare (allele frequency 1% and those 620. OTUs not assigned to bacterial or eukaryotic kingdoms were removed from the dataset and the accuracy of taxonomic assignment was assessed through the use of Australian databases for marine flora and diatoms25,26. This resulted in a table containing 86 OTUs, but we only retained OTUs with at least 10 read sequences given that these are less likely to be erroneous sequences that can arise from index-tag jumping. These 78 OTUs—used in downstream statistical analyses—corresponded to cyanobacteria (Cyanophyceae), unknown Eukaryota, dinoflagellates (Dinophyceae), diatoms (Coscinodiscophyceae and Fragilariophyceae), microalgae (microscopic algae of cell size ≤20 µm including Cryptophyceae, Haptophyceae, Mediophyceae, and Chlorarachniophyceae), green macroalgae (Chlorophyta with cell size >20 µm), red macroalgae (Rhodophyta with cell size >20 µm), and brown macroalgae (Ochrophyta with cell size >20 µm) and were represented by silhouettes from PhyloPic (http://phylopic.org/about/) on Figs. 4 and 5, and Supplementary Fig. S2. We then calculated the relative abundance of the 78 OTUs (based on the total number of sequence reads from each individual stomach content, which was visualized in the figure) using a circular plot that was generated with the R-package Circlize57. We also represented the 30% most abundant OTUs across all stomach content samples with a heatmap using a Bray–Curtis distance matrix, which was computed with the R-package phyloseq73 (Supplementary Fig. S2).To investigate differences in stomach contents between tropical residents and vagrants to temperate environments, we performed a non-metric multidimensional scaling ordination (nMDS) in two dimensions based on the Bray–Curtis dissimilarity of individuals. The nMDS plot, whose stress value was 0.12, was plotted using the R-package ggplot274. To further test the dissimilarity in diet composition among tropical residents and temperate vagrants, a permutational analysis of variance (PERMANOVA) was conducted on the same distance matrix with 100,000 permutations. We also tested the homogeneity of group dispersions using the PERMDISP2 procedure with 100,000 permutations as well. The nMDS plot, PERMANOVA, and PERMDISP2 were done with the R-package Vegan60. Finally, to highlight food sources that were unique or significantly associated to a single region or a combination of regions, we used the indicator species (IndVal) analysis in the R-package Indicspecies75 with 100,000 permutations and a significance level corrected with the Benjamini and Hochberg (BH) method76 (Supplementary Data 1 and 2). Significant results were illustrated using colored Venn diagrams on Fig. 5.The 23S rRNA sequence of the kelp species, Ecklonia radiata, from the Western Australian region was not available in the NCBI database, and so three samples were collected in November 2018 at Dunsborough (southwest Australia) and their DNA was extracted with the Miniplant Kit (Qiagen) according to manufacturer’s instructions. Prior to extraction, kelp tissues were rinsed with a continuous flow of tap water for 30 min, then soaked in a solution of 70% ethanol, and finally thoroughly rinsed with Milli-Q water. Tissues were also bead-bashed twice with the Tissue Lyzer II (Qiagen) for 30 s on each cycle. The optimal yield of template DNA was estimated with qPCR following the same method as described above. Each kelp sample was prepared for single‐step fusion‐tag library build using unique index tags following the methods of DiBattista et al.77 and pooled to form an equimolar library. Size selection was also conducted with a Pippin Prep instrument using the same size range as above, and cleaning was done with QIAQuick PCR purification kit (Qiagen). Final libraries were quantified using a Qubit 4.0 Fluorometer (Invitrogen) and sequenced on the Illumina Miseq platform using 500 cycles and V2 chemistry (for paired-end sequencing).Paired-end reads were stitched together using the Illumina Miseq analysis software (MiSeq Reporter V. 2.5) under the default settings. Sequences were assigned to samples using MID tag combinations in Geneious v.10.2.6 and reads strictly matching the MID tags, sequencing adapters, and template-specific primers were retained. Each of the three samples was dereplicated into unique sequences. The unique sequence with the highest number of reads (86,000–120,000) was identical in the three samples, and it did not match any 23S rRNA gene sequences available in the NCBI database based on BLASTn. This sequence was thus designated the 23S rRNA voucher sequence of Ecklonia radiata from southwestern Australia, blasted against all OTUs found in the stomach of rabbitfish individuals in this study, and deposited on GenBank (accession number MW752516).Past and current observations, and climate modelsHistorical sea surface temperature (SST) data were acquired from two sources, each with different temporal coverage and spatial resolution. The present-day (2008–2017) and 1900–1909 SST climatologies were calculated from HadISST78, which is resolved monthly and at 1° spatially. Additionally, the National Oceanic and Atmospheric Administration (NOAA) Coral Reef Watch “CoralTemp v1.0” (daily and 5-km resolution)79 was used to assess SST anomalies during the 2011 marine heatwave.Historical and projected SST data were extracted from outputs of a suite of Coupled Model Intercomparison Project Phase 5 (CMIP5) models. We used the monthly-resolution SST model outputs that included historical greenhouse gas (Historical GHG), and representative concentration pathways of 4.5 and 8.5 W m−2 forcings (“RCP4.5” and “RCP8.5”) runs of the r1i1p1 (designation of initial conditions) ensemble member80. These models included ACCESS, CanESM, CMCC, CNRM, CSIRO, GFDL, GISS-E2-H, INMCM, MIROC, MRI, and NorESM80. The model SST data for each run (historical GHG, RCP4.5, and RCP8.5) were converted to anomalies relative to a 2008–2017 base period, and these anomalies were added to the HadISST 2008–2017 climatology. This analysis was conducted separately for both mean annual and minimum monthly mean (MiMM). Finally, we calculated ensemble means by averaging the SST anomalies from the 11 models. Ensemble means are plotted in Fig. 1 as decadal averages (thick lines) and decadal ranges (shading) of the mean annual 20 °C contour and the MiMM 17 °C contour. The historical GHG run is used to compare the observed and GHG-forced rates of warming between 1900–1909 and 2018–2017, while the two RCP runs are used to project future (2090–2099) SST scenarios. The observed 1900–1909 contours (from HadISST) fall within the ranges of those from the CMIP5 historical GHG ensembles, indicating that anthropogenic emissions are responsible for warming in this region over the past century.Surface ocean currents during the 2011 heatwave were assessed using Simple Ocean Data Assimilation (SODA) v.3.3.181, a state-of-the-art ocean model constrained by observations when and where they are available. We calculated the near-surface (0–25 m) current anomalies (relative to 1980–2015 mean) for the austral summer (January, February, March, or “JFM”) of 2011, which was the peak of the 2010–2011 Western Australia marine heatwave7. These current anomalies are plotted on top of SST anomalies in Fig. 1b. All climate analyses were performed in MATLAB2012b.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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