Ecology

Oxygen minimum zones (OMZs) are unique oceanic regions with strong redox gradients. Anoxic zones in OMZs are hotspots for fixed nitrogen loss and production of the greenhouse gas N2O [1, 2]. Microbes in OMZs make important contributions to biogeochemistry, which motivates us to reconstruct metagenome-assembled genomes (MAGs) from the Eastern Tropical South Pacific (ETSP) OMZ (Fig. 1a, b). Among 147 recovered MAGs, we present 39 high- and medium-quality MAGs with completeness >50% and contamination 100 nM d−1) at the same station [6], where MAGs were recovered. Consistently, Thaumarchaeota MAGs (AOAs) were nearly absent (only AOA-2 had a relative abundance higher than 0.01%) and NOB MAGs (NOB-1 and NOB-2) were much more abundant than AOA in the anoxic core (Fig. 1d). MAGs in this study will provide opportunities to discover novel processes and adaptation strategies.Most MAGs had their highest relative abundances in the anoxic zone (Fig. 1c). Many of them contribute to the loss of fixed nitrogen, which occurs by denitrification (the sequential reduction of nitrate to nitrite, NO, N2O, and finally N2) and anammox (anaerobic oxidation of ammonium to N2). Measured nitrate reduction rates at this [5, 8] and other [16, 17] nearby stations were much larger than rates of any subsequent denitrification steps (e.g., nitrite reduction to N2O or to N2). Consistently, preliminary prediction of metabolisms shows that more than half of the MAGs found here contained nar, which encodes nitrate reduction, and one-third of those contained only nar and none of the other denitrification genes (i.e., they are nitrate-reducing specialists) (Fig. 2). Consistently, a previous study found that nar dramatically outnumbered the other denitrification genes in contigs from the Eastern Tropical North Pacific (ETNP) OMZ [18]. Indeed, four of the five most abundant MAGs in the anoxic core were nitrate-reducing specialists (Fig. 2). The fifth was an anammox MAG, which was only assigned to the genus level (Candidatus Scalindua) in GTDB and was not represented at the species level in the Tara Oceans dataset (Table S1). However, this anammox MAG was highly related to 20 anammox single-cell amplified genomes (SAGs) from the ETNP OMZ [19]. The anammox MAG had at least 90% average nucleotide identity (ANI) to the SAGs, with the highest ANI (98.8%) to SAG K21. Consistent with the previous work [19], the anammox MAG also encoded cyanase, indicating its potential of using organic nitrogen substrates. The most abundant nitrate reducer MAG here is Marinimicrobia-1 (Fig. 1), which belongs to the newly proposed phylum Candidatus Marinimicrobia [20]. Notably, one nitrate reducer can only be assigned to phylum level (Candidatus Wallbacteria) and was not present in the Tara Oceans MAGs (Table S1).We also identified a novel archaeal MAG possessing multiple denitrification genes. MG-II MAG-2 encoded Nar alpha and beta subunits, nitrate/nitrite transporters, copper-containing nitrite reductase, and N2O reductase (Fig. 2). Two MAGs from the Tara Oceans metagenomes (Table S1) were identified as the same species as MG-II MAG-2. TOBG_NP-110 (ANI to MG-II MAG-2 = 99.8%) from the North Pacific encoded Nar and nitrate/nitrite transporters, and TOBG_SP-208 (ANI to MG-II MAG-2 = 99.6%) from the South Pacific also contained the same denitrification genes as MG-II MAG-2 (Table S2). In addition, two MG-II SAGs (AD-615-F09 and AD-613-O09) were found at a different station of the ETSP OMZ sampled on the same cruise as this study [21]. Partial 16S rRNA genes of both SAGs are 100% identical to that of MG-II MAG-2 (alignment length = 200 bp for AD-615-F09 and 183 bp for AD-613-O09), but only AD-615-F09 might be the same species as MG-II MAG-2 based on ANI analyses (MG-II MAG-2 had 99.5% ANI to AD-615-F09, and 80.9% to AD-613-O09). Both SAGs also encoded Nar and nitrate/nitrite transporters [21]. The absence of other denitrification genes may be due to the low completeness of the two SAGs (completeness = 5.61% for both SAGs) [21]. Nitrite reductase and N2O reductase genes were located on the same contig in both MG-II MAG-2 and TOBG_SP-208 (Table S2). MG-II MAG-2 and TOBG_SP-208 had low contamination (1.9% and 0.8%, respectively), and their contigs with nitrite reductase and N2O reductase genes contained single-copy marker genes present only once in each MAG (Supplementary Methods). Although these results suggest a nearly complete denitrification metabolism in MG-II archaea, especially N2O consumption metabolism, methods besides metagenomics (e.g. reconstructing SAGs with high completeness) are highly recommended to rule out possible artifacts introduced by metagenomic binning and confirm the presence of these genes and their denitrification activity. Nonetheless, MG-II MAG-2 was present (Fig. 1e) and transcriptionally active in both Pacific OMZs (Fig. S2), indicating its adaptation to low oxygen environments. The MG-III MAG did not have any denitrification genes but was abundant in the anoxic zone (Figs. 1e and 2). It had a GC value (43.2%) distinct from all other known MG-III MAGs [22] and is the most complete (86.0%) and the least contaminated (0%) (Table S1) among all reported MG-III MAGs, indicating that MG-III is a novel archaeon in this group. Bacterial and archaeal MAGs recovered here implied that nitrogen metabolisms were present in more microbial lineages than previously thought. Further analyses of these MAGs will shed light on adaptation strategies in the unique OMZ environment and novel functions related to important element cycles. More

Data source and preprocessingConsidering factors such as amount of cloud and time intervals of image, four remote sensing images with a spatial resolution of 30 m, including Landsat 5 Thematic Mapper (TM) images for 08-21-2000, 09-04-2005 and 09-18-2010, and Landsat 8 Operational Land Imager (OLI) for 09-02-2016,were obtained from the Geospatial Data Cloud Platform (http://www.gscloud.cn). LULC information was extracted from these remote sensing images. In addition, the digital elevation model (DEM) with a spatial resolution of 30 m was obtained from the website. Elevation and slope information were derived from DEM data and used as terrain driving factors for scenario simulation. Other supporting data, such as Weishan County land use data, mine distribution data, general land use planing (2006–2020) and mineral resources planning (2008–2015), Jining City coal mining subsidence land rearrangement planning (2016–2030), were obtained from Weishan Natural Resources and Planning Bureau. These data were used for better data analysis.Considering severe ground subsidence and seeper in the study area, and referring to national standards: Current Land Use Classification (GB/T 21010-2017), remote sensing images were interpreted into six LULC types: farmland, other agricultural land, urban and rural construction land, subsided seeper area, water area, and tidal wetland.In the process of image interpretation, firstly, the remote sensing image was divided into two regions: one region were the lake and the surrounding tidal wetland, and the other region included farmland, other agricultural land, urban and rural construction land, subsided seeper area, etc.In region 1, decision tree classification, combined with the Modified Normalized Difference Water Index (MNDWI), was used to extract lakes. Then we masked them in region 1. The Normalized Difference Vegetation Index (NDVI) was calculated for the remaining image of region 1. Tidal wetland was mainly distributed along rivers and lakes, and NDVI value was higher than that of farmland and other vegetation. By analyzing its geographical distribution and NDVI value, and referring to Weishan County land use data, the appropriate threshold was selected to extract tidal wetland.The spectral signature of rivers, ditches and aquaculture ponds in other agricultural land in region 2 could be easily distinguished from other surface features. They could be extracted step by step by manual visual interpretation and empirical knowledge, referring to Weishan County land use data and water system data. Then we masked them separately in region 2. After extracting rivers, ditches, aquaculture ponds with high water content, the remaining LULC type with high water content in region 2 was subsided seeper area. According to the relationship of spectral signature of different LULC types, it was concluded that among the remaining LULC types in region 2, only TM3 band value of subsided seeper area was higher than TM5 band value. Using this characteristic, subsided seeper area could be distinguished from other LULC types. After extracting subsided seeper area, the remaining LULC types in region 2 were farmland and urban and rural construction land. The spectral characteristics of them were very different. Therefore, they could be distinguished using support vector machine (SVM) classification method, and their respective binary images were generated using decision tree method.The extracted six LULC types were shown in single layer and binary form respectively. Six LULC types were coded and synthesized into one image. We obtained 2000, 2005, 2010, 2016 LULC type maps (Fig. 2). Finally classification post-processing and accuracy evaluation were operated.Figure 2The LULC types maps of 2000, 2005, 2010 and 2016. Maps were generated using ArcGIS 10.1 for Desktop (http://www.esri.com/software/arcgis/arcgis-for-desktop).Full size imageThe accuracy of the interpretation results was verified by confusion matrix and kappa coefficient. The kappa coefficients of the four interpretation maps were 0.84, 0.85, 0.82 and 0.86, respectively (Table 1). The accuracy could meet the needs of further research.Table 1 Accuracy evaluation of the interpretation results (%).Full size tableBy reading previous research results37,38,39,40,41, based on the entropy theory, in the same study area, high spatial resolution data contains more entropy than low spatial resolution data, and reflecting more detailed information, but it will increase the uncertainty of prediction results and reduce the prediction accuracy. Although the prediction accuracy of low spatial resolution data increases, it will lose lots of detailed information. In order to ensure the accuracy of the simulation, considering the area of the study area and data requirement of the CLUE-S model, the interpreted LULC maps with a resolution of 30 m exceed the upper limit of the CLUE-S model data requirement, so the LULC maps were resampled to multiple scales including 60 m, 90 m, 120 m, and 150 m to facilitate logistic regression analysis of LULC types and driving factors.Selection and processing of driving factorsTo interpret the relationship between the LULC and its driving factors in the mining area, we not only need to identify the driving factors that have greater explanatory power for LULC change, but also need to quantitatively describe the relationship between driving factors and LULC types.Considering the accessibility, usability of the data and the actual conditions in the study area, seven driving factors were selected based on the land use map of Weishan County in 2005 and the DEM data5,10,11,13,26,28,29,30. The driving factors included: (1) terrain factors, including elevation and slope factors; (2) five accessibility factors, including the nearest distance between each grid pixel and the main roads, the major rivers, the residential area, the major mines, and the ditches. The 30 m grid data of each driving factor were resampled to 60 m, 90 m, 120 m and 150 m respectively.In this study, BLRM was used to explore the relationship between LULC change and the related 7 driving factors. BLRM is sensitive to multicollinearity. In order to eliminate the influence of collinearity on the regression results, the multicollinearity between independent variables was diagnosed before the regression model was established.The receiver operating characteristic (ROC) curve was used to evaluate the accuracy of regression analysis results at different scales. The results showed that using 60 m resolution provided more accurate regression analysis results and suffered less loss of LULC and driving factor information during resampling. Therefore, we used 60 m × 60 m grid cell data to driving forces analysis.Raster maps of each driving factor at a resolution scale of 60 m are shown in Fig. 3.Figure 3Raster maps of driving factors at a resolution scale of 60 m. Maps were generated using ArcGIS 10.1 for Desktop (http://www.esri.com/software/arcgis/arcgis-for-desktop).Full size imageLogistic regression analysis of LULC types and driving factorsBLRM is often used for regression analysis of explanatory binary variables. The presence and absence of a certain type of LULC in a specific area is set as 1 and 0, respectively, which is characteristic for binary variable. Therefore, we used BLRM to calculate the probability (P) of various LULC types in a specific spatial location, and its mathematical expression is:$$begin{aligned} ln left( frac{P}{1-P}right) = beta _0 + beta _1 X end{aligned}$$
(1)
where (frac{P}{1-P}) is the ’odds ratio’ of an event, abbreviated as ( Omega ), which represents the odds that an outcome will occur given a particular condition compared to the odds of the outcome occurring in the absence of that condition; (beta _0) is a constant; (beta _1) is the correlation coefficient of an explaining variable and an explained variable. Making mathematical transformation of the above expression, we get: (Omega = (frac{P}{1-P}) = e^{beta _0 + beta _1 X}).Regression analysis using BLRM, we divided the study area into many grid cells. Taking each LULC type as the explained variable, and the driving factor causing LULC change as the explanatory variable, we calculated the odds ratio of each LULC type in a specific spatial location, and analyzed the relationship between each LULC type and the driving factors. The calculating equation is:$$begin{aligned} mathrm{Logit} P = ln left( frac{P_i}{1-P_i}right) = beta _0 + beta _1 X_{1,i} + beta _2 X_{2,i} + cdots + beta _n X_{n,i} end{aligned}$$
(2)
Making mathematical transformation of the above equation, we get:$$begin{aligned} P_i = frac{e^{(beta _0 + beta _1 X_{1,i} + beta _2 X_{2,i} + cdots + beta _n X_{n,i})}}{1+e^{(beta _0 + beta _1 X_{1,i} + beta _2 X_{2,i} + cdots + beta _n X_{n,i})}} end{aligned}$$
(3)
where: (P_i) is the probability of a certain LULC type i in a grid cell, (X_{1,i}sim X_{n,i}) are the driving factors of LULC type i, (beta _0) is the constant, (beta _1sim beta _n) are the correlation coefficients of each driving factor and LULC type i.The receiver operating characteristic (ROC) was used to evaluate the accuracy of regression analysis results. The accuracy can be measured by calculating the area under the ROC curve. The area value is between 0.5 and 1. The closer the value is to 1, the higher the accuracy is. In general, the area under the ROC curve is greater than 0.7, which indicates that the selected factor has good explanatory power27,42.CLUE-S simulation and accuracy validationBefore using the CLUE-S model for futural LULC scenario simulation in mining area, the prediction accuracy needs to be verified. Based on the data of LULC in 2005, the spatial distribution pattern of LULC in 2016 was predicted firstly.The modeling accuracy was evaluated based on the Kappa index by comparing the actual LULC map in 2016 with the simulated in 201627,43,44. Equation (4) gives one of the most popular Kappa index equations: i.e.,$$begin{aligned} mathrm{Kappa}=frac{P_o-P_c}{P_p-P_c} end{aligned}$$
(4)
where (P_o) is the observed proportion correct, (P_c) is the expected proportion correct due to chance, (P_c) =1/n, n is the number of LULC types, and (P_p) is the proportion correct when classification is perfect.In order to further verify the accuracy of the model simulation, we also calculated kappa for quantity (Kquantity).Scenario setting of futural LULC simulationDue to the continuous population growth and mineral exploitation in the study area, the land resources, especially farmland resources, have become increasingly scarce and the environment has been deteriorating. Based on the simulation and validated results during 2005-2016, we defined three scenarios—namely natural development scenario, ecological protection scenario, and farmland protection scenario—to predict LULC spatial patterns for 2025.Natural development scenarioIn this scenario, the land use demand of the study area was basically not restricted by policies in near future. We assumed that the change rate of each LULC type in near future was consistent with the change trend from 2005 to 2016. So it is defined as natural development scenario. Using Markov model to obtain the area transition probability matrix of each year from 2017 to 2025, and taking the proportion of each LULC type area in the total study area in 2005 as the initial state matrix, the area of each LULC type in 2025 under the natural development scenario was predicted.Based on the characteristics and trend of the LULC change from 2005 to 2016, after appropriately adjusting the transition probability matrix of different LULC types, we predicted the demands of each LULC type in 2025 under ecological protection scenario and farmland protection scenario using Markov model45,46.Ecological protection scenarioThis scenario emphasizes protecting the ecological environment, restricting the conversion of the LULC types that have more regulatory effects on the ecosystem, such as tidal wetland and water area, to other land use types. Garden land, woodland, grassland, and aquaculture land, belong to other agricultural land, which have regulatory effects on the local ecosystem, so their conversion to other LULC types should be restricted as well.Farmland protection scenarioAccording to the guidelines of “the general land use planning in Weishan County (2006-2020)”, we should maximize the potential use of current construction land, implement intensive and economical utilization of construction land, and use less or not use farmland to economical construction. So in order to ensure the dynamic balance of total farmland amount and the regional food supply security, in the farmland protection scenario, the conversion from farmland to other land use types should be restricted. The projected land use demands for 2025 under the three different scenarios are shown in Table 2.Table 2 Areas of LULC types in 2025 under different scenarios (ha).Full size table More

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Fitting tolerance time versus temperature to build a thermal death time curveThe high coefficients of determination found in the D. melanogaster TDT curves (Fig. 3A) are not uncommon and the exponential relation has consistently been found to provide a good fit of tolerance time vs. temperature in ectotherms3,15,20,22,23,24. Tolerance time vs. temperature data are also well fitted to Arrhenius plots which are based on thermodynamic principles (see for example15,36) and the absence of breakpoints in such plots provides a strong indication (but not direct proof) that the cause of coma/heat failure under the different intensities of acute heat stress is related to the same physiological process regardless whether failure occurs after 10 min or 10 h2,3 (but see “Discussion” section below). Despite the superior theoretical basis of Arrhenius analysis, we proceed with simple linear regressions of log10-transformed tcoma (TDT curve) as this analysis likewise provides a high R2 and is mathematically more straightforward. The physiological cause(s) of ectotherm heat failure are poorly understood37,38 but we argue that they are founded in a common process where heat injury accumulates at a temperature-dependent rate until a species-specific critical dose is attained (area below the curve and above Tc in Fig. 2). Thus, the organism has a fixed amount (dose) of thermally induced stress that it can tolerate before evoking the chosen endpoint. The experienced temperature of the animals then dictates the rate of which this stress is acquired, and accordingly when the endpoint is reached (Fig. 2) It is this reasoning that leads to TDT curves and explains why heat stress can be additive and thus also determines the boundaries of TDT curve modelling.Injury is additive across different stressful assay temperaturesIf heat stress acquired at intense and moderate stress within the span of the TDT curve acts through the same physiological mechanisms or converges to result in the same form of injury, then it is expected that injury is additive at different heat stress intensities. This hypothesis was tested by exposing flies sequentially to two static temperatures (different injury accumulation rates) and observe whether coma occurred as predicted from the summed injury (Fig. 2C). The accumulated heat injury at the two temperatures was found to be additive regardless of the order of temperature exposure (Fig. 3B,C). This finding is consistent with a conceptually similar study using speckled trout which also found strong support for additivity of heat stress at different stressful temperatures13. The exact physiological mechanism of heat injury accumulation is interesting to understand in this perspective, but it is not critical as long as the relation between temperature and injury accumulation rate is known.If injury accumulation is additive irrespective of the order of the heat exposure, we can extend the model to fluctuating temperature conditions. We have previously done this by accurately predicting dynamic CTmax from TDT parameters obtained from static assays for 11 Drosophila species (Fig. 6A, see “Discussion” section below and15). Here we extend this to temperature fluctuations that cannot be described by a simple mathematical ramp function. Specifically, groups of flies were subjected to randomly fluctuating temperatures and the observed tcoma was then compared to tcoma predicted using integration of heat injury based on TDT parameters (Fig. 4). The injury accumulation (Fig. 4C) was calculated by introducing the fluctuating temperature profiles in the associated R-script and the observed and predicted tcoma was found to correlate well (R2  > 0.94) across the 13 groups tested for each sex. These results further support the idea that injury is additive across a range of fluctuating and stressful temperatures and hence that similar physiological perturbations are in play during moderate and intense heat stress. It is important to note that in these experiments, temperatures fluctuated between 34.5 and 42.5 °C and accordingly the flies were never exposed to benign temperatures that could allow repair or hardening (see below).Figure 6adapted from Fig. 4b in15. (B) TDT parameters based on dCTmax from three dynamic tests were used to predict tcoma in static assays. Each point represents an observed vs. predicted value of species- and temperature-specific log10(tcoma). (Inset) Species values of the thermal sensitivity parameter z parameterized from TDT curves based on static assays (x-axis) or dynamic assays (y-axis). The dashed line represents the line of unity in all three panels.Conversion of heat tolerance measures between static and dynamic assays in Drosophila. Data from43. (A) Heat tolerance (dCTmax, d for dynamic assays) plotted against predicted dCTmax derived from species-specific TDT curves created from multiple (9–17) static assays. Data are presented for three different ramping rates (0.05, 0.1 and 0.25 °C min-1). Note that this graph is Full size imageIn conclusion, empirical data (present study;6,13,14,22) support the application of TDT curves to assess heat injury accumulation under fluctuating temperature conditions both in the lab and field for vertebrate and invertebrate ectotherms. Potential applications could be assessment of injury during foraging in extreme and fluctuating environments (e.g. ants in the desert39 or lizards in exposed habitat40) or for other animals experiencing extreme conditions41,42. The associated R-scripts allow assessment of percent lethal damage under such conditions if the model is provided with TDT parameters and information of temperature fluctuations (but see “Discussion” section of model limitations below).Model application for comparison of static versus dynamic dataThere is little consensus on the optimal protocol to assess ectotherm thermal tolerance and many different types of static or dynamic tests have been used to assess heat tolerance. TDT curves represent a mathematical and theoretical approach to reconcile different estimates of tolerance as the derived parameters can subsequently be used to assess heat injury accumulation at different rates (temperatures) and durations13,15,16. Here we provide R-scripts that enable such reconciliation and to demonstrate the ability of the TDT curves to reconcile data from static vs. dynamic assays we used published measurements of heat tolerance for 11 Drosophila species using three dynamic and 9–17 static measurements for each species43. Introducing data from only static assays we derived TDT parameters and subsequently used these to predict dynamic CTmax that were compared to empirically observed CTmax for three ramp rates (Fig. 6A). In a similar analysis, TDT parameters were derived from the three dynamic (ramp) experiments to predict tcoma at different static temperatures which were compared to empirical measures from static assays (Fig. 6B). Both analyses found good correlation between the predicted and observed values regardless whether the TDT curve was parameterized from static or dynamic experiments (Fig. 6). However, predictions from TDT curves based on three dynamic assays were characterised by more variation, particularly when used to assess tolerance time at very short or long durations. Furthermore, D. melanogaster and D. virilis which had the poorest correlation between predicted and observed tcoma in Fig. 6B had values of z from the TDT curves based on dynamic input data that were considerably different from values of z derived from TDT curves based on static assays (Fig. 6B inset). In conclusion TDT curves (and the associated R-scripts) are useful for conversion between static and dynamic assessment of tolerance. The quality of model output depends on the quality and quantity of data used as model input, and in this example the poorer model was parameterized from only three dynamic assays while the stronger model was based on 9–17 static assays (see also “Discussion” section below).Model application for comparison of published dataThermal tolerance is important for defining the fundamental niche of animals1,2,4 and the current anthropogenic changes in climate has reinvigorated the interest in comparative physiology and ecology of thermal limits in ectotherms. Meta-analyses of ectotherm heat tolerance data have provided important physiological, ecological and evolutionary insights5,44,45,46, but such studies are often challenged with comparison of tolerance estimates obtained through very different methodologies.Species tolerance is likely influenced by acclimation, age, sex, diet, etc.47 and also by the endpoint used (onset of spasms, coma, death, etc.27). Nevertheless, we expected heat tolerance of a species to be somewhat constrained45, so here we tested the model by converting literature data for nine species to a single and species-specific estimate of tolerance, sCTmax (1 h), the temperature that causes heat failure in 1 h (Fig. 5). The overwhelming result of this analysis is that TDT parameters are useful to convert static and dynamic heat tolerance measures to a single metric, and accordingly, the TDT model and R-scripts presented here have promising applications for large-scale comparative meta-analyses of ectotherm heat tolerance where a single metric allows for qualified direct comparison of results from different publications and experimental backgrounds. While this is an intriguing and powerful application, we caution that careful consideration should be put into the limitations of this model (see “Discussion” section below).Practical considerations and pitfalls for model interpretationAs shown above it is possible to convert and reconcile different types of heat tolerance measures using TDT parameters and these parameters can also be used to model heat stress under fluctuating field conditions. Modelling and discussion of TDT predictions beyond the boundaries of the input data has recently gained traction (see examples in48,49) but we caution that the potent exponential nature of the TDT curve requires careful consideration as it is both easy and enticing to misuse this model.Input dataThe quality of the model output is dictated by the input used for parameterization. Accordingly, we recommend TDT parameterization using several ( > 5) static experiments that should cover the time and temperature interval of interest, e.g. temperatures resulting in tcoma spanning 10 min to 10 h, thus covering both moderate and intense heat exposure. Such an experimental series can verify TDT curve linearity and allows modelling of temperature impacts across a broad range of temperatures and stress durations13,15,22. It is tempting to use only brief static experiments (high temperatures) for TDT parameterization, but in such cases, we recommend that the resulting TDT curve is only used to describe heat injury accumulation under severe heat stress intensities. Thus, the thermal sensitivity factor z represents a very powerful exponential factor (equivalent to Q10 = 100 to 100,000;15) which should ideally be parametrized over a broad temperature range (see below). We also include a script that allows TDT parametrization from multiple ramping experiments and again we recommend a broad span of ramping rates to cover the time/temperature interval of interest. A drawback of ramping experiments is the relatively large proportion of time spent at benign temperatures where there is no appreciable heat injury accumulation. Thus, dynamic experiments can conveniently use starting temperatures that are close to the temperature where injury accumulation rate surpasses injury repair rate (see “Discussion” section of “true” Tc below, in Supplemental Information and19 for other considerations regarding ramp experiments).A final methodological consideration relates to body-temperature in brief static experiments where the animal will spend a considerable proportion of the experiment in a state of thermal disequilibrium (i.e. it takes time to heat the animal). To avoid this, we recommend direct measurement of body temperature (large animals) or container temperature (small animals), and advise against excessive reliance on data from test temperatures that results in coma in less than 10 min.ExtrapolationMost studies of ectotherm heat tolerance include only a single measure of heat tolerance which is inadequate to parameterize a TDT curve. However, a TDT curve can still be generated from a single measure of tolerance (static or dynamic) if a value of z is assumed (see Supplemental Information). As z differs within species and between phylogenetic groups (Table S115,20), choosing the appropriate value may be difficult and discrepancies between the ‘true’ and assumed z represent a problem that should be approached with care. In Fig. 7A we illustrate this point in a constructed example where a single heat tolerance measurement is sampled from a ‘true’ TDT curve (full line; tcoma = 40 min at 37 °C). Along with this ‘true’ TDT curve we depict the consequences for model predictions if the assumed value of z is misestimated by ± 50%. Extrapolation from the original data point is necessary if an estimate of the temperature that causes coma after 1 h is desired, however due to limited extrapolation (from 40 to 60 min), estimation of sCTmax (1 h) values based on the ‘true’ and z ± 50% are not very different ( 6 h) between heat exposure disrupted additivity, suggesting that injury is repaired at benign temperature50. Injury repair rate is largely understudied but repair rate is generally increasing with temperature51,52,53. It is therefore an intriguing and promising idea to include a temperature-dependent repair function in more advanced modelling of heat injury. Until such repair processes are introduced in the model, we recommend that additivity of heat injury is evaluated critically if it involves periods at temperatures both above and below Tc (i.e. over consecutive days, see also13). An alternative, but not mutually excluding, explanation of increased heat resilience in split-dose experiments relates to the contribution of heat hardening as it is likely that the first heat exposure in a series can induce hardening responses that increase resilience (and thus change the TDT parameters) when a second heat exposure occurs. Such issues of repeated thermal stress have been discussed previously54 but for the purpose of the present study the main conclusion is that simple TDT curve modelling is not applicable to fluctuations bracketing Tc unless this is empirically validated. Future studies could address this issue as inclusion of repair functions would add further promise to the use of TDT curves in modelling of the impacts of temperature fluctuations. More