Ecology

Different proxies for changes in structure and/or function of microbiomes have been developed, allowing assessing microbiome dynamics at multiple levels. However, the lack and differences in understanding the microbiome dynamics are due to the differences in the choice of proxies in different studies and the limitations of proxies themselves. Here, using both amplicon and metatranscriptomic sequencings, we compared four different proxies (16/18S rRNA genes, 16/18S rRNA transcripts, mRNA taxonomy and mRNA function) to reveal the impact of a severe summer drought in 2018 on prokaryotic and eukaryotic microbiome structures and functions in two rewetted fen peatlands in northern Germany. We found that both prokaryotic and eukaryotic microbiome compositions were significantly different between dry and wet months. Interestingly, mRNA proxies showed stronger and more significant impacts of drought for prokaryotes, while 18S rRNA transcript and mRNA taxonomy showed stronger drought impacts for eukaryotes. Accordingly, by comparing the accuracy of microbiome changes in predicting dry and wet months under different proxies, we found that mRNA proxies performed better for prokaryotes, while 18S rRNA transcript and mRNA taxonomy performed better for eukaryotes. In both cases, rRNA gene proxies showed much lower to the lowest accuracy, suggesting the drawback of DNA based approaches. To our knowledge, this is the first study comparing all these proxies to reveal the dynamics of both prokaryotic and eukaryotic microbiomes in soils. This study shows that microbiomes are sensitive to (extreme) weather changes in rewetted fens, and the associated microbial changes might contribute to ecological consequences. More

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The generalist accumulates extracellular nitriteWe first tested whether the generalist accumulates substantial extracellular nitrite under our experimental conditions, and thus creates a niche for the specialist. To accomplish this, we grew the generalist alone in bioreactors with anoxic ACS medium amended with 12 mM nitrate as the growth-limiting substrate and measured the extracellular concentrations of nitrate and nitrite over time. We performed these experiments at pH 6.5 (strong nitrite toxicity) and 7.5 (weak nitrite toxicity).We observed a substantial accumulation of extracellular nitrite regardless of the pH (Fig. 3A, B). When grown at pH 6.5 (strong nitrite toxicity), extracellular nitrite accumulated to a concentration comparable to the initial nitrate concentration (measured maximum extracellular nitrite concentration, 11.8 mM; measured initial nitrate concentration, 12.0 mM) and was subsequently consumed to below the detection limit (Fig. 3A). When grown at pH 7.5 (weak nitrite toxicity), extracellular nitrite again accumulated to a concentration comparable to the initial nitrate concentration (measured maximum extracellular nitrite concentration, 11.7 mM; measured initial nitrate concentration, 12.9 mM) and was subsequently consumed to below the detection limit (Fig. 3B). During growth at pH 6.5, substantial nitrite consumption did not begin until a prolonged period of time after nitrate consumption was complete, resulting in a relatively long duration of nitrite availability (Fig. 3A). During growth at pH 7.5, in contrast, substantial nitrite consumption began immediately after nitrate consumption was complete, resulting in a relatively short duration of nitrite availability (Fig. 3B). The longer duration of nitrite availability at pH 6.5 indicates that the duration of the niche created by the generalist for the specialist depends on pH.Fig. 3: Growth and nitrogen oxide dynamics of the generalist in batch culture.We grew the generalist alone in a bioreactor at A pH 7.5 (weak nitrite toxicity) or B pH 6.5 (strong nitrite toxicity) under anoxic conditions with nitrate as the growth-limiting substrate. Blue squares are measured extracellular nitrate concentrations, yellow triangles are measured extracellular nitrite concentrations, and black circles are measured cell densities. We measured extracellular nitrate and nitrite concentrations with IC and cell densities with FC. C Measured durations of nitrite availability for the generalist growing in batch culture. We grew the generalist alone in 96-well microtiter plates under anoxic conditions with nitrate as the growth-limiting substrate. Open symbols are durations of nitrite availability at pH 6.5 and closed symbols are durations of nitrite availability at pH 7.5. Each symbol is an independent biological replicate.Full size imageTo routinely quantify the duration of nitrite availability, we grew the generalist alone with varying amounts of nitrate as the growth-limiting substrate. We then quantified the length of time from when the growth rate with nitrate was maximum to when the growth rate with nitrite was maximum. This cell density-based proxy measure is valid because the growth of the generalist is directly linked to the consumption of nitrate and nitrite (Fig. 3A, B). The cell density of the generalist was initially linearly correlated with nitrate consumption at both pH 6.5 (strong nitrite toxicity) (two-sided Pearson correlation test; r = −0.96, p = 1.5 × 10–8, n = 15) (Fig. 3A) and 7.5 (weak nitrite toxicity) (two-sided Pearson correlation test; r = −1.00, p = 2.2 × 10–16, n = 30) (Fig. 3B). After nitrate was depleted, the cell density of the generalist became linearly correlated with nitrite consumption at both pH 6.5 (strong nitrite toxicity) (two-sided Pearson correlation test; r = −0.97, p = 3 × 10–4, n = 7) (Fig. 3A) and 7.5 (weak nitrite toxicity) (two-sided Pearson correlation test; r = −0.97, p = 6.8 × 10–10, n = 16) (Fig. 3B). We further validated our cell density-based approach by testing for concordance with our IC-based direct measures of the duration of nitrite availability. We observed a significant positive and linear relationship between the cell density- and IC-based measures (two-sided Pearson correlation test; r = 0.999, p = 0.023, n = 3) (linear regression model; slope = 1.19, intercept = −2.31, r2 = 0.99) (Supplementary Fig. S2), which further validates our cell density-based approach to routinely estimate the duration of nitrite availability.Using our cell density-based approach, we found that the duration of nitrite availability was significantly longer at pH 6.5 (strong nitrite toxicity) than at 7.5 (weak nitrite toxicity) regardless of the initial nitrate concentration (two-sample two-sided t-tests; Holm-adjusted p  0.92, Holm-adjusted p  0.6), and thus followed model predictions (Fig. 4A). However, when the specialist was initially rare (measured initial log rS/Gs of –3.19, –2.65, and –0.88), the relative abundances of the specialist continuously decreased between the third and twelfth transfers (Mann–Kendall trend tests; tau = –0.61 to –0.89, p  0 were dominated by phenotype C (dominant ancestral phenotype with a long time delay between nitrate and nitrite consumption), while generalist isolates from co-cultures with initial rS/Gs  More

Hydrological changes in high-latitude peatlandsWe observed three hydrological pathways, i.e., drying, wetting, and fluctuating, for both peatland clusters, non-permafrost and permafrost peatlands (Fig. 2). Approximately 54% of the studied peatlands have shifted towards drier surface conditions since 1800 CE and more intensively since 1900 CE (Fig. 2a, d), which is in line with the post-LIA warming. The overall change point to drier conditions was dated to ca. 1950 CE for non-permafrost sites and ca. 1890 CE for the permafrost compiled group. Approximately 32% of the studied peatlands have shifted towards wetter conditions (Fig. 2b, e). The overall shifting point to wetter conditions was dated to ca. 1995 CE for non-permafrost peatlands and to ca. 1990 CE for permafrost peatlands. Wetting has been especially intensive since 1900 CE for non-permafrost peatlands and since 1950 CE for permafrost peatlands. Interestingly, the data showed that in permafrost peatlands a significant dry shift always preceded a wet shift (Fig. 2e). Approximately 14% of the studied peatlands indicated no clear trend, with fluctuating hydrological conditions (Fig. 2c, f).Non-permafrost peatlands generally showed spatially extensive drying across the northern high latitudes, apart from northeastern Canada, where a wetting trend was more frequently observed. Permafrost peatlands, however, were more variable, with some drying, some wetting, and no overall coherent regional pattern was visible (Fig.1a, b). It should be noted that peatlands synthesized here have undergone little or no direct human impact, i.e., their surface hydrology was not significantly affected by human disturbances such as drainage, when compared to, for example, central European peatlands discussed in Swindles et al. (2019)5. This implies that climate and/or local topographical forcing are the predominant hydrological drivers in this study. The dataset is to some extent biased as there are more non-permafrost records from northeastern Canada but more permafrost records from northern Sweden and this might result in regional overestimation to either wetting or drying trends. Nevertheless, the pattern of diverse timing of the hydrological shifts between the individual coring points (Fig. 2) indicates the variability in sensitivity of different regions/peatlands to climate changes.Potential links to climate change and permafrost dynamicsThe comparison of the reconstructed water table and climate data suggests that climate, especially summer temperature, has played an important role in shaping the peatland water table (Fig. 1c–f). The pattern detected here for non-permafrost peatlands, an extensive drying, is comparable to that observed for central European peatlands5. In addition to direct climate forcing, a recent acceleration of peat accumulation might partly explain the drying trend by disconnecting the peatland surface from the water table17. However, for northeastern Canada a wetting trend has been observed more often, possibly regulated by the regional climate that shows clearly less warming in the focused period compared to other regions (Fig. 1c, d).Permafrost initiation in the past caused a peat surface uplift and is probably detected as a dry phase (Fig. 2d, e). Post-LIA warming-induced increase in evapotranspiration may have strengthened the surface drying which originally resulted from surface-uplift and probably mitigated the gradual wetting related to permafrost thawing11. The level of warming has varied among the regions. In some areas such as northeastern Canada temperature has increased less and, when combined with higher precipitation or higher effective moisture level, may have caused surface wetting in permafrost peatlands. This is a direct climate forcing rather than permafrost thawing, which is a consequence of climate warming, i.e., more indirect climate forcing. To date, it is yet challenging to estimate any one tipping point of warming that might trigger permafrost thawing, as the local conditions vary from bottom ground soil conditions to hydrology and vegetation. The consequent wetting or drying depends on evapotranspiration and ice richness etc., which further challenges the prediction of hydrological conditions of permafrost peatlands.The divergent three moisture patterns may occur in the same region and even in the same peatland, especially if the permafrost is present. This complex response pattern is well supported by the records from the Abisko region, Sweden, where replicated sampling was carried out, and captured different successional stages of local permafrost peatlands7,18. In contrast to permafrost peatlands, non-permafrost peatlands are more likely to experience a more consistent ecosystem response pattern19 as supported by the replicated records suggesting the same pattern happening simultaneously in several regions (Fig. 1a). The fluctuating pattern of many records reported here suggests that the past and recent climate has not yet caused a state change in hydrological conditions.Insights into carbon dynamics and future perspectiveGenerally, our results suggest that the recent climate warming has caused hydrological shifts in most high-latitude peatlands, highlighting its pronounced effect on shaping peatland moisture balance, and further on driving peatland C balance. It has been reported that a 1-cm water-table drawdown would increase 3.3–5.0 mg CO2 m−2 h−1 and decrease 2.2–3.6 mg CO2-eq m−2 h−1 (CH4) to the atmosphere, and the average sensitivity of CO2 and CH4 combined was 0.8–2.3 mg CO2-eq m−2 h−1 cm−1 according to a global scale analysis, including sites from high-latitudes3. However, it should be noted that the sensitivity of greenhouse gas fluxes to the magnitude of hydrological changes might vary among different regions and peatland types. It appears that most pan-Arctic peatlands are undergoing a drying trend, that may lead to a decreased C sink capacity3,19, if not compensated by increased C uptake from the atmosphere20.It is very likely that over the 21st century warming in high latitudes will continue to be more pronounced than the global average21. Precipitation is projected to increase, albeit with large regional variability. Also, extreme events with heavy rainfall and drought are becoming more frequent and intense22. It is estimated that about 20% of permafrost zone is experiencing accelerated and abrupt permafrost thaw that is likely causing wetting conditions4, while gradual permafrost thaw has been observed across the circumpolar regions23. Both an increase in precipitation and permafrost thaw might mitigate the drying pressure caused by warming and increased evapotranspiration. However, abrupt permafrost thaw in peatlands can result in a rapid (over years to decades) loss of C from the formerly frozen permafrost peat, causing these peatlands to be a net source of C to the atmosphere before post-thaw accumulation returns them to a net sink (centuries to millennia)12,13. The future C sink and source function of peatlands is a key element in contributing to climate change, but the observed divergent pathways of peatland hydrological successions further challenge the projections of high-latitude peatland C sink and source dynamics. Conversely, it clearly highlights the importance of climate forcing in peatland succession scenarios. Our study reveals that the response of high-latitude peatlands to changing climate conditions is complex. We detect variable ecohydrological trajectories, and in the future, these will determine the C sink capacity of northern peatlands. The observed patterns inevitably create challenges for the climate change modelling community. How to capture the highly heterogenic successional pathways of northern peatlands needs to be a key research focus. More

To assess coral holobiont health, we used the commercially available Urinalysis strips (Accutest URS-14 100 strips Urinalysis Reagent Test Paper; ca. $11–35 USD/ bottle) that are designed to detect disease markers in humans, potentially indicating diabetes, metabolic abnormalities, liver diseases, kidney function, and urinary tract infections. There are ten tests on each strip that provide an initial assessment of health using the following standardized markers: leukocytes, nitrite, urobilinogen, protein, pH, blood, specific gravity, ketone, bilirubin, and glucose. To apply this test to coral extracts, we used ambient and stressed nubbins in a comparative approach to identify trends in the data. We presumed that some of the tests are likely not applicable to corals, whereas others such as ketones and leukocytes, which target conserved animal pathways (see below) could prove useful. Samples from three different coral experiments (two bleaching experiments and one environmental survey) were used to assess the response and utility of the different tests on each strip. The first bleaching experiments was done in 2019 on two Hawaiian species: Montipora capitata (stress resistant) and Pocillopora acuta (stress sensitive); this research has been previously described in detail11,12. Briefly, three M. capitata colonies (different genotypes) were selected, with samples collected from each in triplicate at three timepoints (referred to as T1, T3, and T5) that span a period of prolonged thermal stress (16 days). The second bleaching experiment was done in 2021 and included nubbins from M. capitata, P. acuta, and P. compressa. These corals were maintained for 9 days under heat treatment or ambient conditions, with samples collected at the beginning and end of the experimental period from both conditions (see Methods). Finally, the third experiment was done in June 2021 on wild colonies of M. capitata, P. acuta, and P. compressa (Fig. 1A) from Kāneʻohe Bay, Oʻahu, Hawaiʻi (Fig. 1B) and analyzed to assess the extent of natural variability in the test strip results. It should be noted that the test strip results from each experiment are independent (i.e., analyzed separately to measure relative differences within the test population) due to differences in tissue freezing time, storage length, and handling, that affect the results.Figure 1Analysis of Hawaiian corals. (A) The three targeted species in Kāneʻohe Bay. Images created by D. Bhattacharya. (B) Sites of wild coral collection (marked by the yellow circles) in Kāneʻohe Bay in June 2021. Nubbins from two colonies (n = 3) of M. capitata were collected from six reefs: Reef 8, 9, Reef 13, Reef 27, Reef 41, and Reef 43 and from three sites near the Hawaiʻi Institute of Marine Biology (HIMB) on Coconut Island (Moku o Loʻe). This image was adapted from the Pacific Islands ocean observing system (https://www.pacioos.hawaii.edu/projects/coral/)33.Full size imagePortable device for test strip analysisTo facilitate field testing and allow accurate measurement of test strip results in the R, G, and B channels, a combination of 3D printing technology and computer vision was applied to the problem. A custom opaque phone holder was produced using 3D printing (Ultimaker Inc. [https://ultimaker.com]) to control light source quality and quantity during the procedure and for calculating test strip scores (Fig. 2A). This portable phone holder was designed to allow field personnel to conduct experiments and collect results in a convenient and user-friendly manner. Inside the black opaque phone holder, two LED diodes served as a controllable and consistent light source to eliminate noise introduced by any change in light levels (between or during) the test strip reactions, allowing for more accurate and consistent data collection19. Frames of the videos (taken using the smart phone positioned in the holder) were captured for different reagents according to the recommended reading time given by the user manual. For test strip RGB value measurement (Fig. 2B), an automated machine learning method, shown in Fig. 2C, was used as a replacement for traditional, manual methods. Our computer vision workflow, named TestStripDX, uses YOLOv418, which is one of the most mature, accurate, and popular computer vision models available, to isolate a target feature in an image and provide the metadata associated with the object (in this case, each test along the strip), such as position within the coordinates of a rectangular box. Sample pictures of strips were manually annotated and used for training the TestStripDX pipeline (Supplementary Data 1): i.e., these images were used to train a custom detector to identify the different reagent tests along a strip and thereafter, to provide the relevant RGB values for each test (Fig. 2C). Figure 2D shows the comparison between data collected using the manual (ImageJ) versus automated (TestStripDX) methods for a partial list of samples and reagent strips (data shown in Table S1). The very close association of the regression line (R2 = 0.996) with the artificial diagonal line validates the utility and accuracy of the computer vision method.Figure 2Portable instrument for test strip analysis. (A) The 3D-printed phone holder used to analyze the test strips. (B) Example test strip. (C) Flow chart for the training and application of the machine learning method (TestStripDX) used to analyze test strips. (D) Comparison of test strip colorimetric measurement values produced by TestStripDX and ImageJ, for a set of representative images (Table S1). The enforced diagonal matches very closely to the regression line.Full size imageCoral color score measurementsAs described above, color scores provide a proxy for coral health, and are generated by measuring the RGB channels of the bleached (unhealthy) and brown (healthy: i.e., pigmentation provided by the algal symbionts) areas of coral nubbins. For the CoralDX workflow, we trained a custom detector that can recognize coral nubbins, as well as red, green, and blue colored blocks (standards) which are used to normalize the R, G, and B channels in each image (see Supplementary Data 2). The images taken in this case were from a lab environment (Fig. 3A), but this approach could potentially be used in any location provided a background with a uniform color is used in the image. To achieve this goal, a background panel containing the red, blue, and green color blocks would be placed behind (smaller) coral nubbins to make the measurements. It is clear that for large colonies, this approach may prove challenging to apply but we expect that additional testing and modification to the method will allow us to design a better-suited tool for field use. To achieve our goal of automatically obtaining colorimetric measurements of coral nubbins, we needed to devise a method that provides YOLOv4 with areas that are not limited by the standard rectangular boxes used as input for this model. To accommodate irregular nubbin shapes, an additional step (training and testing steps are shown in Fig. 3B) was added to the automated method (Fig. 2C). Our approach uses computer vision-based edge detection to eliminate most of the background surrounding the edges of the coral nubbins, allowing for accurate quantification of the RGB values of the targeted piece of coral. After edge detection, we obtain a picture with a black background highlighting the coral shape as a “mask” (Fig. 3C; 2nd image from left). We then place the mask onto the original coral image, measuring non-zero R, G, and B values (Fig. 3C; 3rd and 4th images from left). This method is superior to selecting coral areas for manual analysis using tools such as the handsfree selection function in ImageJ, which are generally hard to manipulate, have low fault tolerance, and are time-consuming. The RGB values extracted from the coral nubbins and color blocks were investigated using principal component analysis (PCA) to generate Euclidean distances (color scores) among coral nubbins according to treatment, time point, and colony11,16. In Fig. 3D, the correlation between bleaching scores generated using CoralDX and ImageJ for M. capitata and P. acuta are presented for a representative set of nubbins cultured under ambient or thermal stress conditions in the 2019 bleaching experiment (Tables S2, S3). As is apparent, the regression lines show strong correlations (R2 = 0.968 for M. capitata and R2 = 0.991 for P. acuta), supporting the utility of the automated method. The data in both cases are very closely associated with the artificial diagonal line shown in the images, substantiating the strong positive correlation between the scores from the two approaches. The small differences in score values between the methods is primarily explained by difficulties in cropping the edges of coral nubbins that are heavily bleached; the contrast between the coral nubbin and the white background is lessened, creating discrepancies between the nubbin edges identified by CoralDX and ImageJ. This issue can be addressed by testing different color backgrounds to find the optimal set-up. Another potential contributing factor is the differences in the area selected for the color blocks between manual (ImageJ) versus automated methods, although this might only have a minor effect on the results. The CoralDX workflow is not computationally intensive and easily portable to other platforms, such as personal computers and smart phones, allowing for easy deployment in the field.Figure 3Analysis of coral color scores. (A) Example image of M. capitata coral nubbins used for automated color score analysis, with target areas marked with the black (coral nubbins) and yellow (color standards) boxes. The nubbin on the far right is used to demonstrate the masking procedure. (B) Flow chart for the training and application of the machine learning method (CoralDX) used to analyze coral color scores. (C) Example of image processing for one M. capitata coral nubbin showing (from left to right) the original, masked, segmented, and masked RGB nubbin, with the final (right) image used for color score measurements. (D) Comparison of color score values produced by CoralDX and ImageJ, for a set of representative coral nubbins from the 2019 bleaching experiment (Tables S2, S3). The enforced diagonal matches very closely to the regression line in both analyses.Full size imageTest strip resultsArmed with these new tools, we generated the test strip data for different coral samples, where larger “relative enzymatic activity” (REA, measured using the RGB values) values indicate increased reactivity (i.e., increased levels of products targeted by the test). The Accutest URS-14 100 strips test for ketones (using the sodium nitroprusside reaction) measures acetoacetate and assumes the presence of β-hydroxybutyrate and acetone. The former (β-hydroxybutyrate) acts as a signal to regulate metabolism and maintain energy homeostasis during nutrient deprivation. In this process, β-hydroxybutyrate is converted to acetoacetate. Ketone bodies are transported into tissues and converted into acetyl-CoA by thiolases, which then enters the TCA cycle and is oxidized in the mitochondria for energy. Bleaching in corals which are incapable of obtaining adequate energy stores through heterotrophy results in diminished growth rates, degraded reproductive capacity, amplified susceptibility to disease, and elevated mortality rates for the entire colony20. Although ketosis has not been explored in cnidarians, transcriptomic data generated from the M. capitata samples measured in this study12 demonstrate expression of the KEGG pathway for degradation of ketone bodies (Fig. S1). The combination of time-point and treatment (field, T1-AT, T1-HT, T3-HT, T5-HT) was the most significant factor impacting the ketone REA scores (p-value = 0.010) (see details of the PERMANOVA analysis in the “Methods” section). Given this framework, we find that the M. capitata samples remain steady throughout the bleaching period, except for a decrease in enzymatic activity at T3-HT (Fig. 4A). This result is supported by the transcriptomic data, which shows this pathway to be uniformly expressed at all timepoints, except T3-HT, when acetyl-CoA C-acetyltransferase is up-regulated in comparison to T1-HT (fold change [FC] = 1.52) and down-regulated at T5-HT (FC = − 1.84) (Table S4). A possible explanation for this result is that at T3-HT, when the first evidence of bleaching was present, the photosynthetic rate of the symbiotic algae was elevated due to the thermal stress, resulting in greater energy production and a decrease in the abundance of ketone bodies within the coral, but without sufficient stress to cause significant bleaching. During this time, acetyl-CoA C-acetyltransferase enzymatic activity favored the production of acetoacetyl-CoA. However, as dysbiosis continued and the corals no longer had access to the photosynthetic products provided by the symbionts, they produced more acetoacetate and ketosis was detected by the test strips. This response occurs despite the observation that M. capitata can persist heterotrophically and meet much of its energy needs in the absence of algal symbionts21. Interestingly, the three M. capitata field samples show similar amounts of ketone bodies to lab stressed corals, suggesting the presence of stressors in the natural environment.Figure 4Test strip results from the 2019 bleaching experiment. (A) Ketone test strip results for M. capitata, showing genotype-specific (see legend) differences in response. (B) Leukocytes test strip results for M. capitata, showing genotype-specific (see legend) differences in response. These are standard box plots, with the boxes representing the first (Q1) to third (Q3) quartiles. The lines in the boxes are the median (Q2) values and lines (“whiskers”) extending beyond the boxes are the minimum and maximum values, excluding outliers. (C) PCA of the ketone and leukocytes test strip data for the field, ambient, and T1-HT, T3-HT, and T5-HT timepoints.Full size imageThe leukocyte test measures the activity of leukocyte esterase (presence of white blood cells) and other signs of infection in human subjects. This test putatively assesses the coral innate immunity response, which includes the same phases in response to infection and loss of tissue integrity as other invertebrates: recognition, signaling, and effector response22. Corals contain multiple types of immune cells, such as amoebocytes and fibroblasts23. Amoebocytes are amoeboid cells residing in the mesoglea that remove necrotic tissue, encapsulate foreign particles, and generally display phagocytic activity to aid in organism defense against pathogens, which is the cnidarian principal mechanism of immunity24. Amoebocytes can be melanin-containing, agranular, or granular based cells, depending on the signaling pathway22. M. capitata shows an overall increase in enzymatic activity at T1-HT, signaling a heightened immune response (Fig. 4B). This relatively higher level of enzymatic activity decreases at T3 and T5. The field samples show levels that are comparable to the T3-HT and T5-HT thermal stress acclimated colonies and the T1 ambient (Amb) colonies. Again, a combination of time-point and treatment was the most significant factor impacting the leukocyte REA scores (p-value = 0.001). Additional research needs to be done to understand the cause of this response. Nonetheless, the results are consistent with the widely accepted hypothesis that M. capitata adapts well to bleaching conditions12. PCA of the M. capitata test strip results shows a clear separation of the T1-HT coral data from the T3-HT and T5-HT values, with the ambient and field samples intermixed among the latter two timepoints (Fig. 4C). This result again highlights the initial robust response to stress by M. capitata followed by acclimation to the heat treatment that is reflected in the field samples.A noteworthy aspect of the test strip results is the divergence in response to thermal stress among different colonies. This result has also been found for coral metabolomic data11. As described above, each holobiont integrates a complex set of biotic interactions between the host animal and microbiome, explaining the high variation in ketone and leukocytes test results, often between replicate nubbins from one colony and more frequently, between different colonies (Fig. 4A). Existing data using omics methods demonstrate that the stress response of the coral holobiont varies from colony to colony15. The metabolome is controlled by the coral animal genotype, microbial consortium, and environmental conditions, among other factors, and can fluctuate greatly based on individual metabolite turnover rates and the timing of sampling25,26. Therefore, accounting for natural variation in the stress response phenotype and its importance for effective testing methods is a crucial aspect of our work. Our results demonstrate that broad population level sampling (dozens to 100 s of colonies/genotypes) is likely needed to account for the inherent genetic and metabolic variation present in wild coral populations.We also did a more limited analysis of coral stress responses using the ketone and leukocyte test strips with three species (M. capitata, P. acuta, P. compressa) in a 2021 bleaching experiment in which we sampled multiple coral genotypes at time 0 and after 9 days of heat treatment (3ºC increase from ambient; see Methods). These results are based on analysis of 8–9 different coral genotypes (summarized in Fig. 5). Interpreted in the same way as described above, we see that there is substantial genotype-based variation in the stress response. Nonetheless, consistent with the 2019 data, M. capitata shows evidence of a thermal stress response in the ketone and leukocytes tests (Fig. 5A, B). P. acuta shows a more limited response, whereas P. compressa appears to have fully acclimated to the stress regime with lowered reactivity at the end of the experiment. Species identity was the most significant factor impacting the leukocyte and ketone REA scores (p-value = 0.002 and 0.033, respectively), but a combination of species and treatment (AT vs. HT) was found to be significant for leukocytes (p-value = 0.026). PCA of the M. capitata test results shows separation between the ambient samples and some of the high temperature treated samples along PC1; both the ketone and leukocytes tests contribute to the spread of samples along PC1. This reinforces the conclusion that there is evidence for a thermal stress response in the ketone and leukocytes tests of M. capitata however, the significant genotypic variability (particularly apparent when compared with Fig. 4) obscures the differences between the conditions for some of the samples. PCA of the P. acuta and P. compressa test results mirrors our conclusion that the ketone and leukocytes tests in these species show a limited response to stress, with no separation between the samples from the different conditions.Figure 5Test strip results from the 2021 bleaching experiment for three Hawaiian coral species. (A) Ketone test strip results for M. capitata, P. acuta, and P. compressa showing genotype-specific variation in response under the ambient (Amb) and high temperature (HT) treatments. (B) Leukocytes test strip results for M. capitata, P. acuta, and P. compressa showing genotype-specific variation in response under the ambient and high temperature (HT) treatments. These are standard box plots, with the boxes representing the first (Q1) to third (Q3) quartiles. The lines in the boxes are the median (Q2) values and lines (“whiskers”) extending beyond the boxes are the minimum and maximum values, excluding outliers. (C) PCA of the ketone and leukocytes test strip data for the Amb and HT treatments for the three Hawaiian coral species.Full size imageAnalysis of wild populationsTo assess natural variation, we collected apparently healthy M. capitata, P. acuta, and P. compressa nubbins (3 replicate nubbins per colony) from six reefs in Kāneʻohe Bay and from three sites near the Hawaiʻi Institute of Marine Biology on Coconut Island (Moku o Loʻe) (see Fig. 1) and analyzed these tissue extracts using the ketone and leukocytes tests. This analysis shows wide variation in the results with some interesting exceptions. Species identity was the most significant factor impacting the leukocytes and ketone REA scores (p-value = 0.002 and 0.001, respectively), but for leukocytes, colony identity, regardless of species, was also found to be a significant factor (p-value = 0.040). The M. capitata ketone test results are consistent among different reefs and within the same colony with the exception of some colonies (e.g., Colony 8 from Reef 9 and Colony 16 from Reef 43) that show wide intra-colony variation (Fig. 6A). Most of the ketone data for M. capitata fall between REAs of 10–20. In contrast, P. acuta shows more variation in the wild populations for the ketone test, suggesting that many of these coral colonies live under stressful conditions in the field (Fig. 6B). A similar situation to M. capitata, in terms of REAs, holds for the ketone test of P. compressa colonies that show more limited variation (Fig. 6C). The leukocytes test shows high variation for M. capitata (Fig. 6D), P. acuta (Fig. 6E), and P. compressa (Fig. 6F) colonies. These results again point out the complex nature of genome-environment interaction with respect to metabolic syndromes, both at the colony level and among different regions (replicates) of the same colony. For example, P. compressa Colonies 13–15 from Reef 9 show little to no intra-colony variation for the ketone test, yet another colony from this reef (Colony 16) shows high variation among replicates (Fig. 6C). In contrast, P. compressa Colonies 13–15 are far more variable when using the leukocytes test (Fig. 6F). On the basis of the more predictable lab-based results reported above, we interpret these “noisy” field data as evidence of the immense variation in the stress phenome of wild coral populations. Overall, the field results indicate that a starting set of test strip values, followed by repeated field sampling over time of wild colonies may be needed for accurate stress diagnosis, rather than the one-time measurement approach used here. Clearly, more work is needed with wild colony analysis, particularly under varying degrees of thermal stress and apparent bleaching, to fully realize the potential of the technique we present.Figure 6Test strip results from analysis of the 2021 collection of three Hawaiian coral species from the wild. (A and D) Ketone and leukocytes test strip results, respectively, for M. capitata showing intraindividual variation and among the different reefs (see legend) that were sampled (Fig. 1B). (B and E) Ketone and leukocytes test strip results, respectively, for P. acuta showing intraindividual variation and among the different reefs that were sampled. (C and F) Ketone and leukocytes test strip results, respectively, for P. compressa showing intraindividual variation and among the different reefs (see legend) that were sampled. These are standard box plots, with the boxes representing the first (Q1) to third (Q3) quartiles. The lines in the boxes are the median (Q2) values and lines (“whiskers”) extending beyond the boxes are the minimum and maximum values, excluding outliers.Full size imageAnalysis of transcriptomic dataTo identify pathways that may support the M. capitata leukocytes test strip results, which showed the most response in terms of change in REA at T1-HT (Fig. 4B), we analyzed existing transcriptomic (RNA-seq) data derived from the same coral nubbins. The RNA-seq and metabolomic data from these samples have been previously analyzed11,12. Here we searched for co-expression modules that contain genes that are up-regulated at the start of the thermal stress regime (T1-HT) when compared to the ambient treatment. It is at this timepoint that we find a strong cross-reaction with the leukocytes test, followed by loss of cross-reactivity at T3-HT and T5-HT (back down to T1-Amb levels), putatively indicating acclimation (Fig. 4B). As described above, the wound healing response in corals is complex and the (Urinalysis) leukocytes results need to be interpreted as a syndrome involving multiple pathways of stress and immune response. With these considerations in mind, we identified a module (Module 2; see Williams et al.12) of up-regulated genes that contains several markers associated with the coral stress response (Fig. 7). These include a tumor necrosis factor-activated receptor (TNFR)-Cys domain-containing protein (fold-change [FC] = 1.12) that is a well-known mediator of apoptosis and cell death that is functionally conserved in corals. Some members of the TNF family are associated with bleaching27. The most highly up-regulated gene in this module is C-type lysozyme 2 (FC = 2.42) that provides an anti-microbial function (e.g., digestion of peptidoglycan), and is likely expressed as a result of stress-induced dysbiosis in M. capitata. Other markers of stress that are up-regulated in Module 2 include E3 ubiquitin-protein ligase (FC = 1.03) involved in protein degradation, two protein disulfide-isomerase (FCs = 1.32, 1.09) involved in cellular defense against protein misfolding via chaperone activity28, and a metalloproteinase inhibitor 3 (FC = 1.42) which likely functions as a physiological anti-inflammatory molecule29. These data, although not directly substantiating the leukocytes test strip results, provide evidence that the wound healing and immune response pathways were up-regulated in Module 2 at T1-HT (albeit weakly, due to the stress resilience of M. capitata) as suggested by Fig. 4B.Figure 7Gene co-expression analysis. Module 2 representing significantly up-regulated genes in M. capitata from T1-HT in the 2019 differential gene expression analysis12. This module is enriched in genes involved in the wound healing and immune response. The legend for level of up-regulation is shown. Putative gene annotations are also shown.Full size image More

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Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.This is a summary of: Needham, D. M. et al. The microbiome of a bacterivorous marine choanoflagellate contains a resource-demanding obligate bacterial associate. Nat. Microbiol. https://doi.org/10.1038/s41564-022-01174-0 (2022). More

Study systemWe conducted our research at the Jornada Caves, New Mexico, USA from 8 to 29 June 2018. This remote cave site on private land in the Chihuahuan Desert occupies an elevated volcanic plateau at approximately 1500 m altitude, with the remains of collapsed lava tubes forming a deep canyon with cave and arch features. The site was chosen because of the presence of a population of Swainson’s Hawks (Buteo swainsoni) that predates the population of Mexican Free-tailed Bats (Tadarida brasiliensis) that emerge from the caves en masse daily throughout the summer39. The bats migrate to the site during their breeding season from May to September40, and use the caves as a day roost before flying to their feeding grounds at dusk. The population consists of a maternal colony of approximately 700,000 to 900,000 bats which inhabit two connected caves named North and South. The largest and most reliable emergence was from the South cave, occurring every evening without exception. Emergence from the North cave was less reliable, with no bats emerging at all on some nights during the first week of observations. The numbers of bats were topped up in the second week by new arrivals, and emergence from the North cave was reliable thereafter. Emergence began at a variable time between approximately 18:30 and 20:00 MDT and lasted from 10 to 25 min depending on the number of bats emerging. Sunset was between 20:16 and 20:21 MDT, so the bats usually emerged in broad daylight. During the third week of observations, a substantial second emergence usually occurred at each cave, beginning around 0.5 h after the end of the first emergence, when fewer hawks were present. No ethical issues were identified by the Animal Welfare and Ethical Review Board of the University of Oxford’s Department of Zoology. We attended only as observers, and never entered the caves, so the risk of causing disturbance as the bats emerged was low41.Video observationsWe recorded video of the hawks attacking the bats every evening from 8 to 29 June 2018, except for one evening that had to be missed due to bad weather. We used three pairs of high-definition video cameras (Lumix DMC-FZ1000/2500, Panasonic Corporation, Osaka, Japan) to enable reconstruction of the three-dimensional flight trajectories of the hawks and bats, setting the camera lens to its widest zoom setting. We recorded 25 Hz video at 3840 × 2160 pixels for the first three days and 50 Hz video at 1920 × 1080 pixels for the remainder of the study (Movie S1). This higher frame rate proved necessary to facilitate tracking of the bats’ erratic movements but was traded off against lower spatial resolution. Each camera pair was set in widely spaced stereo configuration to enable three-dimensional reconstruction of the attacks, with a baseline distance of 16 to 27 m. The cameras were mounted on tripods which were adjusted to the same height using an optical level kit (GOL20D/BT160/GR500, Robert Bosch GmbH, Gerlingen, Germany). We used the same optical level kit to measure the baseline distance between the cameras.We set up two camera pairs facing approximately north and south across the South cave for the duration of the study. As the swarm’s overall flight direction was variable and influenced by the wind, we positioned the north- and south-facing camera pairs to allow them to be panned from northeast to northwest and from southeast to southwest, respectively. This enabled us to cover most flight directions, except due east (where the bats rarely flew) and due west (which was subject to glare). We set up a third camera pair to view the emergence that occurred from the North cave from the second week onward. When leaving the North cave, the bats usually flew along the lava tube and beneath a rock arch before climbing out of the canyon. We therefore positioned the cameras close to where the swarm began climbing out above the canyon rim, aiming to capture attacks as the hawks swooped low over the canyon.The hawks consistently appeared within a few minutes of the start of emergence, which enabled us to observe the general direction in which the bat swarm was emerging, and to reorient the cameras to view the swarm before the attacks began. As soon as the bats began emerging, the cameras were turned on and left to record. To begin with, all fieldworkers retreated into make-shift hides, but these were gradually phased out for reasons of practicality. The birds quickly became habituated to our presence, venturing close to the cave even when fieldworkers were present. Each attack began with the hawk approaching the swarm in level flight or stooping in from above. This was followed by fast flight through the stream of bats, with one or more attempts made to grab a bat using a pitch-up, pitch-down, or rolling grab manoeuvre with the legs and talons extended (Movie S1). If the first attack was unsuccessful, then the hawks would usually perform further short-range swoops through the stream until they made a catch. Once a bat was caught, the hawk would drift away from the swarm, to consume its prey on the wing.VideogrammetryWe synchronized the videos using the DLTdv5 video tracking toolbox42 in MATLAB R2020a (MathWorks Inc., Natick, MA). To do so, we matched the complex motions involved in the hawks’ attack manoeuvres visually between videos, and applied the relevant frame offset to synchronize them to the nearest frame. To verify the accuracy of this method, we compared the position of the hawk’s wings between the two videos for the three pairs of frames used for synchronization, and again for the three pairs of frames recorded 50 frames later (Fig. S3). This comparison shows that the frame synchronization remains stable as expected over this 1 s time interval, for the randomly selected flight displayed in Fig. S3. Nevertheless, because the cameras’ shutters were not electronically synchronized, this post hoc procedure can only guarantee synchronization of the frames to within ±0.01 s at the 50 Hz frame rate (see Fig. S3). To assess the sensitivity of our trajectory reconstructions to this remaining synchronization error, we compared the flight trajectories that we had already reconstructed with those that would have been reconstructed had the videos been shifted ±1 frame (Fig. S4). This comparison shows that the displacement of the trajectories resulting from a synchronization error of ±1 frame is small in comparison to their path length, and that their shape remains approximately the same, even for the two stooping flight trajectories plotted in Fig. S4.We used the DLTdv5 toolbox to identify the pixel coordinates of the hawk in both videos within a pair, manually tracking the visual centre of the subject’s body from the point at which it appeared in both cameras up to the point of interception. We used the same method to track the bat that the hawk caught or attempted to catch during the terminal attack sequences that we recorded at close range. The bats were too distant to be tracked individually in recordings of the hawks’ long-range approaches, but the point of actual or attempted capture was nevertheless obvious from the hawks’ flight behaviour. We aimed to reconstruct all attack trajectories that were captured by both cameras within a pair. We were able to reconstruct n = 62 terminal attack trajectories, drawn from n = 50 separate attack flights (i.e. n = 12 of these comprised follow-on attack passes, up to a maximum of four consecutive passes made in cases where the first attack pass was unsuccessful; see Supporting Data and Code for details). We were also able to reconstruct n = 26 long-range approaches. Hence, as the population of hawks peaked at approximately 20 birds, there will have been repeated sampling within individuals in both cases.We calibrated the cameras by matching 15 points across both frames, including background features and points on the hawk, which we selected with the objective of covering as much of the capture volume as possible. The image coordinates of these calibration points were exported from the DLTdv5 toolbox into custom-written software in MATLAB, which solved the camera collinearity equations43 using a nonlinear least squares bundle adjustment implemented using the MATLAB Optimization Toolbox R2020a (see Supporting Data and Code). The bundle adjustment routine identifies jointly optimal estimates of the camera calibration parameters and unknown spatial coordinates of the calibration points, by minimizing the sum of the squared reprojection error of the associated image points. The reprojection error of an image point matched across camera views is defined as the difference between its measured image coordinates and those expected under the camera calibration model given its estimated spatial coordinates. This nonlinear approach enabled us to self-calibrate the cameras using identified features of the environment, whilst also incorporating prior knowledge of the intrinsic and extrinsic camera parameters. This in turn avoided the need to move a known calibration object through the very large imaging volume.We set the calibrated baseline distance between the cameras equal to the measurement that we made of this in the field using the optical level. We fixed the focal length of each camera at 1468.9 pixels for the 1920 × 1080 recordings and at 3918.5 pixels for the 3840 × 2160 recordings. These values were estimated using the Camera Calibrator toolbox in MATLAB, from a set of 20 calibration images of a checkerboard pattern held in front of the camera. Lens distortions were found to be minimal, and we therefore assumed a central perspective projection43 in which we assumed no lens distortion and no principal point offset with respect to the camera sensor. The resulting stereo camera calibration was used to solve for the spatial coordinates of the tracked hawk and bat in MATLAB. This is a least squares solution, in the sense that it minimizes the sum of the squared reprojection error for each image point matched across stereo video frames. We therefore report the root mean square (RMS) reprojection error as a check on the accuracy of the calibrations and reconstructions.For the terminal attack trajectories filmed at close range, the mean RMS reprojection error of the 16 calibrations was 0.73 ± 0.35 pixels, whilst for the reconstructed flight trajectories it was 1.22 ± 1.18 pixels for the hawks and 1.87 ± 2.39 pixels for the bats over all n = 62 flights (mean ± SD). For the long-range approaches filmed at a distance, the RMS reprojection error of the 18 calibrations was 0.53 ± 0.61 pixels, whilst for the reconstructed flight trajectories it was 1.08 ± 1.07 pixels for the hawks over all n = 28 flights (mean ± SD). The sub-pixel reprojection error that we achieved in the calibrations is appropriate to the method. The higher reprojection error of the reconstructions is also to be expected, because whereas the bundle adjustment optimizes the camera calibration parameters jointly with the estimated spatial coordinates of the calibration points, the calibration is held fixed in the reconstructions. In addition, any spatiotemporal error in the matching of points across camera frames will manifest itself as reprojection error in the reconstructions.The foregoing calibration reconstructs the spatial coordinates of the matched image points in a Cartesian coordinate system aligned with the sensor axes of one of the cameras. To aid visualization and interpretation of the flight trajectories, we therefore transformed the spatial coordinates of the hawks and bats into an Earth axis system in which the z axis was vertical. To do so, we filmed and reconstructed the ballistic trajectory of a small rock thrown high into the air through the volume of stereo overlap. We identified the image coordinates of the peak of its parabolic path, together with the image coordinates of two flanking points located ±20 or 25 frames to either side. We took the line dropped from the peak of the parabola perpendicular to the line connecting the two flanking points to define the direction of gravitational acceleration. We then used this to identify the rotation needed to transform the spatial coordinates of the hawks and bats into Earth axes with the z axis as vertical. Finally, we made use of the fact that the two cameras in each pair were fixed at the same height to verify the transformation to Earth axes. For the 16 calibrations used to reconstruct the terminal attack trajectories, the inclination of the baseline between the cameras in Earth axes had a median absolute value of just 1.2˚ (1st, 3rd quartiles: 0.8˚, 2.2˚), providing independent validation of the calibration method that we used.Trajectory analysisAll trajectory analysis was done using custom-written software in MATLAB R2020a (see Supporting Data and Code). We used piecewise cubic Hermite interpolation of the reconstructed trajectories to estimate the spatial coordinates of the hawk or bat for any occasional frames in which this was obscured. We then smoothed the trajectories using quintic spline fitting. For the long-range approaches, we used a spline tolerance designed to remove an RMS spatial position error of 0.5 m, corresponding approximately to the wing length of a hawk. For the terminal attack trajectories, we used a tolerance designed to remove an RMS position error of 0.12 m, corresponding approximately to the wing length of a bat. These values were chosen as representative estimates of the accuracy with which it was possible to match points across frames at long and close range, respectively. Finally, we differentiated and evaluated the splines analytically to estimate the velocity and acceleration of the bird and bat at an up-sampled frequency of 2 kHz. This ensured a suitably small integration step size for the subsequent numerical simulations. On average, the hawks flew faster than the bats (Fig. S5A), so were tracked over longer distances (Fig. S5B), but with considerable overlap in their respective distributions.We simulated the hawk’s attack trajectory in the Earth axes using a guidance law of the form:$${{{{{bf{a}}}}}}(t){{{{{boldsymbol{=}}}}}}N{{{{{boldsymbol{omega }}}}}}(t-tau )times {{{{{bf{v}}}}}}(t){{{{{boldsymbol{-}}}}}}K{{{{{boldsymbol{delta }}}}}}(t-tau )times {{{{{bf{v}}}}}}(t)$$
(1)
where a is the hawk’s commanded centripetal acceleration, v is its velocity, ω is the angular velocity of the line-of-sight r from the hawk to its target, and δ is the deviation angle between r and v, written in vector form with δ mutually perpendicular to r and v. Here, t is time, τ is a fixed time delay, and N and K are guidance constants. With K = 0, Eq. 1 describes proportional navigation (PN), whereas with N = 0, Eq. 1 describes pure proportional pursuit (PP). In the case that K ≠ 0 and N ≠ 0, Eq. 1 describes mixed PN + PP guidance. Dividing through by the hawk’s speed (v=left|{{{{{bf{v}}}}}}right|) converts the commanded centripetal acceleration to the commanded angular velocity. It can therefore be seen that Eq. 1 generalizes, in vector form, the PN + PP guidance law that is written as (dot{gamma }(t)=Ndot{lambda }(t-tau )-Kdelta (t-tau )) in the main text, where the magnitudes of the scalar turn rate, scalar line-of-sight rate, and scalar deviation angle are given respectively as (left|dot{gamma }right vert=left|{{{{{bf{a}}}}}}right|/left|{{{{{bf{v}}}}}}right|), (left|dot{lambda }right vert=left|{{{{{boldsymbol{omega }}}}}}right|), and (left|deltaright vert=left|{{{{{boldsymbol{delta }}}}}}right|).Our simulations make use of the kinematic equations:$${{{{{bf{r}}}}}}={hat{{{{{{bf{x}}}}}}}}_{{{{{{rm{T}}}}}}}-{{{{{bf{x}}}}}}$$
(2)
$${{{{{boldsymbol{omega }}}}}}=frac{{{{{{bf{r}}}}}},times left({hat{{{{{{bf{v}}}}}}}}_{{{{{{rm{T}}}}}}}-{{{{{bf{v}}}}}}right)}{{left|{{{{{bf{r}}}}}}right|}^{{{{{{bf{2}}}}}}}}$$
(3)
$${{{{{boldsymbol{delta }}}}}}=left({{{cos }}}^{-1}frac{{{{{{bf{r}}}}}},cdot, {{{{{bf{v}}}}}}}{left|{{{{{bf{r}}}}}}right|,left|{{{{{bf{v}}}}}}right|}right)left(frac{{{{{{bf{r}}}}}},times {{{{{bf{v}}}}}}}{left|{{{{{bf{r}}}}}},times {{{{{bf{v}}}}}}right|}right)$$
(4)
where x is the simulated position of the hawk, and where ({hat{{{{{{bf{x}}}}}}}}_{{{{{{rm{T}}}}}}}) and ({hat{{{{{{bf{v}}}}}}}}_{{{{{{rm{T}}}}}}}) are the measured position and velocity of the target with respect to the Earth axes. Our simulations are implemented in discrete time by coupling the guidance law (Eq. 1) with the kinematic equations (Eqs. 2–4) using the difference equations:$${{{{{{bf{x}}}}}}}_{n+1}={{{{{{bf{x}}}}}}}_{n}+Delta t,{{{{{{bf{v}}}}}}}_{n}.$$
(5)
$${{{{{{bf{v}}}}}}}_{n+1}={hat{v}}_{n+1},frac{{{{{{{bf{v}}}}}}}_{n}+Delta t,{{{{{{bf{a}}}}}}}_{n}}{left|{{{{{{bf{v}}}}}}}_{n}+Delta t,{{{{{{bf{a}}}}}}}_{n}right|}$$
(6)
where the subscript notation indicates the values of the variables at successive time steps, such that ({t}_{n+1}={t}_{n}+Delta t), and where (hat{v}) is the hawk’s measured groundspeed. The simulations were initiated given the hawk’s measured initial position ({{{{{{bf{x}}}}}}}_{0}={hat{{{{{{bf{x}}}}}}}}_{0}) and velocity ({{{{{{bf{v}}}}}}}_{0}={hat{{{{{{bf{v}}}}}}}}_{0}), and were used to predict the trajectory that it would follow under the guidance law (Eq. 1) parameterized by the guidance constants N and K, and time delay τ. Note that Eq. 6 matches the hawk’s simulated groundspeed (v=left|{{{{{bf{v}}}}}}right|) to its measured groundspeed (hat{v}) at all times, such that the guidance law is only used to command turning. We verified that the step size of our simulations ((Delta t=5times {10}^{-4}) s) was small enough to guarantee the numerical accuracy of the fitted guidance parameters and prediction error to the level of precision at which they are reported in the Results.We defined the prediction error η of each simulation as the mean absolute distance between the measured and simulated flight trajectories:$$eta=frac{1}{k}mathop{sum }limits_{n=1}^{k}left|{{{{{{bf{x}}}}}}}_{n}-{hat{{{{{{bf{x}}}}}}}}_{n}right|$$
(7)
where (hat{{{{{{bf{x}}}}}}}) is the hawk’s simulated position, and k is the number of time steps in the simulation. We fitted the guidance constants K and/or N under the various combinations of guidance law (i.e. PN, PP or PN + PP) and target definition (i.e. measured bat position, final bat position, final hawk position) for delays of 0 ≤ τ ≤ 0.1 s at 0.02 s spacing corresponding to the inter-frame interval. In each case, we used a Nelder–Mead simplex algorithm in MATLAB to find the value of K and/or N that minimised the prediction error η for each flight at the given time delay τ. To ensure that we fitted the same section of flight for all time delays 0 ≤ τ ≤ 0.1 s, we began each simulation from 0.1 s after the first point on the trajectory, and ended the simulation at the time of intercept or near-miss. However, as we found the best-fitting delay to be τ = 0, we subsequently re-fitted the simulations with no delay to begin from the first point on the trajectory and report these simulations in the Results. For the terminal attack trajectories, we took the first point on the trajectory to be the earliest point from which it was possible to track the bat that the hawk caught or attempted to catch, and took the time of intercept or near-miss to be the time at which the measured distance between the hawk and bat was minimal. For the long-range approaches, we tested a range of alternative start points from 1.0 s up to a maximum of 20.0 s before the observed grab manoeuvre, in 0.2 s intervals, to accommodate the fact that the hawk could sometimes be tracked for longer than it appeared to be engaged in directed attack behaviour.Statistical analysisAll statistics were computed using MATLAB R2020a. As the hawks could not be individually identified, we were unable to control for repeated measures from the same individual, and therefore treated each attack trajectory as an independent sample. Because the distributions of the model parameters and errors are skewed (Fig. 2), we report their median, denoted using tilde notation, together with a bias-corrected and accelerated bootstrap 95% confidence interval (CI) computed using 100,000 resamples44. For robustness, we use two-tailed sign tests to compare their distributions between different guidance models and target definitions. We state sample proportions together with a 95% confidence interval (CI) computed using the Clopper–Pearson method. We used a two-tailed Fisher’s exact test to compare the odds of success in attacks on lone bats versus attacks on the swarm. Following our previous observational study18, bats classified as lone bats were judged to be flying >5 body lengths from their nearest neighbours and/or appeared to be flying in a different direction to the coordinated members of the swarm (Table S3).Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More