The optimal hydrolysis conditions were pH 7.11, 4300 U/g enzyme concentration, 50 °C hydrolysis temperature, and 3.95 h hydrolysis time. Under these conditions, the α-glucosidase inhibition rate of CSCPH was 58.70% (IC50 8.442 ± 0.33 mg/mL). The peptides with high α-glucosidase inhibitory activity were isolated from CSCPH by ultrafiltration and Sephadex G25. Leu-Leu-Val-Leu-Tyr-Tyr-Glu-Tyr (LLVLYYEY) and Leu-Leu-Leu-Leu-Pro-Ser-Tyr-Ser-Glu-Phe (LLLLPSYSEF) were identified and synthesized for the first time by Liquid chromatography electrospray ionisation tandem mass spectrometry (LC-ESI-MS/MS) analysis and virtual screening with IC50 values of 0.33 and 1.11 mM, respectively. Lineweaver-Burk analysis and molecular docking demonstrated that LLVLYYEY was a non-competitive inhibitor of α-glucosidase, whereas LLLLPSYSEF inhibited α-glucosidase, which displayed a mixed inhibition mechanism. The study suggests the possibility of using peptides from Camellia seed cake as hypoglycaemic compounds for the prevention and treatment of diabetes.In recent years, food-derived hypoglycemic peptides have received a lot of attention in the study of active peptides, but their anti-diabetic mechanism of action is not yet clear. In this study, camellia seed cake protein (CSCP) was used to prepare active peptides with α-glucosidase inhibition. The optimization of the preparation of camellia seed cake protein hydrolyzed peptides (CSCPH) was conducted via response surface methodology (RSM) using a protamex with  The inhibition of α-glucosidase activity is thought to be a useful method for diabetes management. In light of this, an increasing number of researchers are concentrating their efforts on discovering more efficient α-glucosidase inhibitors in natural substances  as the horizontal coordinate and 1/V as the vertical coordinate, to plot straight lines at different concentrations to determine the type of inhibition and calculate the relevant parameters, and the double inverse equation is shown in Equation (4). Secondary graphing is calculated as shown in Equations (5) and (6).With minor modifications, a recent study determined the kinetic parameters of hibition . In brieV is the reaction rate. [S] and [I] are the concentrations of substrate and inhibitors, respectively. mK is the Michaelis-Menten constant, maxV is the maximum reaction rate, icK is the competitive inhibition constant, and iuK is the uncompetitive inhibition constant.Which v/v) and digested at 37 °C for 120 min. SIFs  was then mixed and the mixture was incubated for 120 min. After 120 min of incubation, the pH was adjusted to 7 by NaOH (1M) to stop the simulated gastric digestion (SGD) phase; after 240 min of incubation the simulated intestinal digestion (SID) phase was stopped by a boiling water bath for 10 min.The method of simulated gastrointestinal digestion (SGID) follows the previous method with slight modifications . Simulatp < 0.05. All data are reported as mean ± SD. All experiments were repeated in triplicate.The results were analyzed using SPSS version 26. Statistical analysis was performed using one-way ANOVA and Duncan’s multiple-range test. Differences were considered significant at α-glucosidase is one of the key enzymes for the fine regulation of insulin function, it is a target for delaying glucose absorption and inhibiting postprandial hyperglycemia. Some α-glucosidase inhibitors can inhibit carbohydrate digestion by competitively inhibiting various α-glucosidases in the small intestine; therefore, the rate of α-glucosidase inhibition is used as an indicator for selecting the optimal protease. It was discovered that protamex’s hydrolysate was noticeably (p < 0.05) more effective than the other aforementioned enzymes  [α-glucosidase was reduced, resulting in a decrease in the overall inhibitory activity of the hydrolysis product. When the degree of hydrolysis was stabilized, the inhibitory activity also stabilized, indicating that the composition of the peptides in the hydrolysis product remained unchanged, and the content and structure of the peptides with an inhibitory effect on α-glucosidase did not change. The inhibitory activity of CSCPH α-glucosidase was also affected by enzyme concentration, with the maximum inhibitory activity reaching 4000 U/g and no significant change in inhibitory activity as the enzyme concentration continued to increase , hydrolysis time (B), protease concentration (C), and temperature (D). As shown in igestion B. The DH. (2019) . The duractivity .α-glucosidase inhibition rate of CSCPH: pH, enzymatic digestion time, enzyme concentration, and temperature. The center point values for the four independent variables had already been fixed at 50 °C, pH 7.0, 4000 U/g, and 240 min in previous studies , and A, B, C, and D is the pH of the enzymatic digestion solution, the enzymatic digestion time, the protease concentration, and the temperature of the enzymatic digestion solution, respectively.Further optimization of four variables using BBD-based RSM based on an initial assessment of single-factor trials to achieve the best  studies . The des studies . The expshown in . The pre2) was used in conjunction with the lack of fit test and probability (p) values to assess model fitness. α-glucosidase inhibitory action, which showed F-values of 21.37 and an extremely low p-value (p < 0.0001), implying that the variables in the model were very significant. Meanwhile, the respective p-values of the lack of fit test for the model of α-glucosidase inhibition activity were 0.0614, demonstrating that the model was capable of accurately predicting the α-glucosidase inhibitory activity for all combinations of the independent variables investigated at the significance level (p > 0.05). Furthermore, the purpose of the lack of fit test is to establish whether the experimental data can be adequately described by the model or whether a more complicated model is required. The model of α-glucosidase inhibitory activity gave an R2 value of 0.9553, suggesting that according to the prediction equation, the model would describe the response variability quite well. Closer R2 values approaching 1.00 indicate that the model has a better capacity to predict the response with more accuracy [2 values for α-glucosidase inhibition activity were 0.9553, suggesting that only 4.47% of the α-glucosidase inhibitory activity in this model was not explained. These results demonstrate that the fitting model is a satisfactory mathematical description of the hydrolysis process.The coefficient of determination  were generated using a quadratic equation in which the α-glucosidase inhibitory activity of the enzymatic digestion product was considered. The enzyme concentration had the greatest effect on the α-glucosidase inhibitory activity of the enzymatic digestion product (p < 0.0001), followed by pH (p = 0.0041), while there was no significant effect of enzymatic digestion time (p = 0.5701) and enzymatic digestion temperature (p = 0.6741) on the α-glucosidase inhibitory activity. To illustrate the calculated interaction of the respective variables on the α-glucosidase inhibition activity of the enzymatic digestion products, the interaction of pH, temperature, protease concentration, and time on the α-glucosidase inhibitory activity of the enzymatic digestion products is depicted in α-glucosidase inhibition rate is indicated by the steepness of the upper spatial surface of the network plot, and the elliptical eccentricity of the contour plot in the lower part of the image reflects the effect of the independent variables on the α-glucosidase inhibition response values. The optimum conditions for the factors influencing enzymatic digestion are represented at the peak of each curved surface. The model produced a desirability value close to 1, which implies that the recommended settings are optimal for obtaining the maximum α-glucosidase inhibition activity at CSCPH [α-glucosidase inhibition were estimated to be 50.23 °C, pH 7.07, 4267 U/g protease concentration, and 3.95 h. These conditions may result in a 58.70% inhibition of α-glucosidase activity. Experiments were carried out in triplicate using the expected optimal conditions to confirm the validity of the model. According to the data, the experimental value obtained was a little higher than the predicted value, 59.36 ± 0.69%, with an error value of 0.66%. As the experiments produced results close to the predicted values, the model was considered to anticipate the best-case scenario for the production of the α-glucosidase inhibitory peptides.The effect of independent variables on the at CSCPH . The ideα-glucosidase inhibitory peptides on an industrial scale [α-glucosidase inhibitory activity was selected for further fractionation and ultrafiltration separation into CSCPH-I (<1 kDa), CSCPH-II (1–3 kDa), CSCPH-III (3–10 kDa), and CSCPH-IV (>10 kDa). α-glucosidase inhibitory activity, which is clearly molecular weight dependent. CSCPH-II had the strongest α-glucosidase inhibitory activity (IC50 3.896 ± 0.148 mg/mL), while CSCPH-III had the least inhibitory effect on α-glucosidase (IC50 62.44 ± 0.965 mg/mL). In general, peptides with lower molecular weights have higher potential inhibitory activity [α-glucosidase inhibitory effect, possibly due to the abundance of free amino acids and salt ions in it, resulting in a reduced positive effect. These findings suggest that reducing the molecular weight of the hydrolysate fraction may increase the maximum α-glucosidase inhibition of the peptide. It is also worth noting that the α-glucosidase inhibition of peptides of different molecular weights is influenced by the amino acid composition and sequence.Considering that the molecular weight of protein hydrolysates is so important in the generation of bioactive peptides, ultrafiltration is used to separate the hydrolysate into various fractions with varied molecular weights. Different MWCO (molecular weight cut-off) membranes are often used for this process. This is a method that can be easily scaled up to produce al scale . In thisactivity ; howeverα-glucosidase being IC50 13.641 ± 0.37 mg/mL, 11.376 ± 0.122 mg/mL, 7.021 ± 0.096 mg/mL, and 2.033 ± 0.093 mg/mL, respectively  found that after molecular weight grading, peptide mixtures with low molecular weight showed stronger effects [Sephadex G25 (1.6 × 80 cm) was used to separate CSCPH-II. Four fractions were collected based on varied elution times: CSCPH-II-1, CSCPH-II-2, CSCPH-II-3, and CSCPH-II-4 A, with tectively B. The efpeptides . The α-g effects , which aAs shown in α-glucosidase inhibitory activity, the sequence peptides in CSCPH-II-4 were identified using LC-ESI-MS/MS. Peptide sequence resolution of the mass spectrometry raw files using the software PEAKS Studio (8.5) ‘de novo score’ resulted in the identification of 469 peptides. Molecular docking is now becoming a common tool for fast and effective virtual drug screening and design. Peptides with higher scores were further validated for in vitro activity through docking performed by the Glide/XP scoring function [To identify peptides with function  for de nα-glucosidase with high accuracy (resolution of 1.90 Å) and used acarbose as the initial ligand to ascertain the ligand’s method of binding to the α-glucosidase active site , who utilized in silico-designed peptide sequences with binding energy scores ranging from −6.3 to −8.7 kcal/mol [α-glucosidase was strongly influenced by two hydrophobic amino acids: Pro and Leu [α-glucosidase inhibitor [The first five promising peptides were screened and scored for in vitro activity validation , and thepeptides . Similarkcal/mol . The res and Leu . For insnhibitor , and thiα-glucosidase by LLVLYYEY and LLLLPSYSEF, the kinetics of inhibition of α-glucosidase were determined using the Lineweaver-Burk plot analysis. maxV gradually decreased and the double inverse plotting line nearly intersected the X-axis, indicating that the mK value remained unchanged. This indicates that the type of inhibition of α-glucosidase by LLVLYYEY is non-competitive, that is, the peptide is not structurally similar to the substrate and does not occupy the active center of the enzyme with the substrate, but rather inhibits the enzyme activity by binding to an essential group other than the active center. α-glucosidase in a mixed manner, including both competitive and non-competitive inhibition, as both mK and maxV values increased with the increasing substrate concentration. In addition, we performed a secondary plot of the peptide concentration I using slope and 1/maxV (min/∆OD), respectively, and the fits all yielded a simple straight line, indicating a single inhibition site or a single inhibition-like site on α-glucosidase [iuK for LLVLYYEY was 0.547 mg/mL, as previously reported by Wu et al. (2020) [icK) and 3.76 mg/mL in the non-competitive inhibition (iuK)  complex. The inhibition mechanism could indicate that LLLLPSFSEF first binds to α-glucosidase to form a competitively inhibited enzyme inhibitor (EI) complex, and due to the non-competitive inhibition of LLLLPSFSEF, it can further bind to ES complex to form an enzyme-substrate inhibitor (ESI) complex. These results suggest that LLVLYYEY is a non-competitive α-glucosidase inhibitor, whereas LLLLPSYSEF is a mixed α-glucosidase inhibitor.To further investigate the potential mechanism of inhibition of cosidase . As show. (2020) , indicaton (Kiu) F. For LLα-glucosidase , who discovered that WVYY (seven bonds) had greater ACE inhibitory action than WYT (four bonds) [α-glucosidase [α-glucosidase crystal active sites used in this study included ASP203, THR205, ASP542, and ARG526 [Molecular docking is a bioinformatics approach that assesses potential interactions between receptors and ligands by studying their sites of action and key residues . Sites, cosidase . As noter bonds) . It is acosidase . The α-gα-glucosidase inhibitory activity after simulated gastric digestion for LLVLYYEY and LLLLPSYSEF, but after SGID they both demonstrated a significant loss of activity. Similar results indicated that YPVEPF was only slightly degraded during SGD, whereas after SGID, YPVEPF was substantially degraded [α-glucosidase inhibitory peptides are highly resistant to SGD and still have α-glucosidase inhibitory activity after SGID.Simulated physiological digestion is a very useful tool for evaluating the stability of bioactive peptides against digestive enzymes . The resdegraded . This reα-glucosidase inhibiting active peptides. CSCPH was isolated and purified using ultrafiltration and Sephadex G25 to obtain CSCPH-II-4. Two bioactive peptides, LLVLYYEY and LLLLPSYSEF, were identified from CSCPH-II-4 for the first time by LC-ESI-MS/MS and virtual screening. Inhibition kinetics and molecular docking results indicated that LLVLYYEY was a non-competitive inhibitor, whereas LLLLPSYSEF was a mixed inhibitor. These peptides have not been found in any natural sources up to this point. Future research will focus on these peptides’ antidiabetic efficacy and toxicity features, paving the way for the creation of these peptides as dietary supplements or anti-diabetic medications.CSC is a by-product of the production process of Camellia seed oil, and the use of these by-products to produce high-value-added functional food ingredients is a timely and popular area of research in this field. In this study, we developed a model to optimize CSCP for the preparation of


Traditional minimally invasive fluoroscopy-based techniques for pedicle screw placement utilize guidance, which may require fluoroscopic shots. Computerized tomography (CT) navigation results in more accurate screw placement. Robotic surgery seeks to establish access and trajectory with greater accuracy.This study evaluated the screw placement accuracy of a robotic platform.Demographic data, preoperative/postoperative CT scans, and complication rates of 127 patients who underwent lumbosacral pedicle screw placement with minimally invasive navigated robotic guidance using preoperative CT were analyzed.On the GRS scale, 97.9% (711/726) of screws were graded A or B, 1.7% (12/726) of screws graded C, 0.4% (3/726) of screws graded D, and 0% graded E. Average offset from preoperative plan to final screw placement was 1.9 ± 1.5 mm from tip, 2.2 ± 1.4 mm from tail and 2.9 ± 2.3° of angulation.Robotic-assisted surgery utilizing preoperative CT workflow with intraoperative fluoroscopy-based registration improves pedicle screw placement accuracy within a patient’s pedicles. Minimally invasive (MI) techniques have been integrated into spine surgery in a number of ways, including the placement of percutaneous pedicle screws. As the most common anchor point in posterior spinal fusion procedures, high level of accuracy in screw placement is paramount. Despite relatively low clinically adverse complications associated with malposition, a misplaced screw may still result in neurological/neurovascular injury , 2, duraThe major modalities for MI spine surgery are fluoroscopic guidance, computed tomography navigation (CTnav), and robot-assisted surgery. The level of evidence in all 3 fields has grown substantially, with several systematic reviews available –11. FluoFurther data are needed to describe the accuracy and safety of such systems, particularly in a field in which the robotics technologies operate with different hardware, software, and clinical implementation. The aim of present study was to quantitatively assess the accuracy of pedicle screws placed with the guidance and navigation of a robot.This retrospective chart review was exempt from the Italian Ethics Committee. Data were collected from 3 surgeons at a single site. All three surgeons are experienced neurosurgeons who have been doing robotic-assisted surgery since its adoption at their surgical center. Patients who were included in the analysis were between 21 and 85 years of age and required surgery that includes screws to be inserted in thoracic, lumbar spine or sacrum. Demographic data , operative data , preoperative/postoperative computerized tomography (CT) scans, and complication rates of 127 patients treated with lumbosacral pedicle screws through a minimally invasive robotic assisted technique were analyzed. The methods for this publication are similar to those described in a previously published manuscript by the same principal investigators .The surgical technique employed in this study utilized a robotic positioning system  Fig.  in whichOnce the patient was placed on the table, the dynamic reference base was then placed by making a small incision and anchoring the base to the posterior superior iliac spine. An attachment to the C-arm was used while fluoroscopy shots were taken in view of the robotic system’s positioning camera to merge the patient positioning to the preoperative CT scan. Anterior–posterior and lateral shots were taken to ensure registration of each targeted vertebral level. To confirm successful registration, landmark checks were performed with tracked instruments.The robotic arm was controlled by the surgeon through a foot pedal, which when pressed caused the arm to move to the preplanned screw trajectory. Through the guide tube attached to the robotic arm, stab incisions were made using a scalpel. Navigated instruments were passed through the guide tube to maintain the planned trajectory, and screws were inserted with these instruments. This process was repeated for all screws. Based on the surgeons’ discretion, 81/127 (63.8%) patients underwent a laminectomy and/or discectomy. Once the screws were placed, rods were placed and held in place with locking caps. Implant position was confirmed with fluoroscopy.Postoperative CT scans were used to perform a Gertzbein and Robbins System (GRS) evaluation of pedicle screw accuracy. In this scale, screws were graded as A (no breach), B (breach of less than 2 mm), C (breach of less than 4 mm), D (breach of less than 6 mm), or E (breach of more than 6 mm). Screws graded to have a less than 2 mm breach (Grade A or B) were considered clinically acceptable, while those screws with a greater than 2 mm breach were considered inaccurate, as in other studies –21. The Statistical analysis was performed using SPSS Statistics Version 25 software . Data were presented as mean ± standard deviation. Pearson correlation coefficients were calculated for the relationship between body mass index (BMI) and screw offset . The lev2 (range 18.8–40.8 kg/m2). Patients were most commonly diagnosed with degenerative disc disease (DDD) (47/127) and degenerative spondylolisthesis (47/127) (Table There were 127 patients included in this investigation. The average age was 51.5 ± 11.9 years (range 23–81 years) with 65.4% (83/127) of the patient population being male. The average BMI was 25.5 ± 3.9 kg/mThere were 732 posterior screws placed with robotic navigation in the 127 patients included in this study. However, 6 screws were not placed with the robot under surgeon discretion and were not included in the analysis, leaving a total of 726 screws analyzed. Average intraoperative set up time was 15.7 ± 8.5 min. Average screw insertion time was 25.4 ± 15.1 min, an average of 4.4 ± 2.2 min per screw. The mean operative time was 121.8 ± 46.8 min, mean blood loss was 44.5 ± 61.6 cc, and mean radiation time was 18.3 ± 13.3 s  of screws graded A or B, 1.7% (12/726) of screws graded C, 0.4% 3/726) of screws graded D, and 0% graded E. GRS grade by level is presented in Table /726 of sThere was 1 reported complication out of 127 patients. During 1 case, a dural laceration caused the surgeons to open and reposition 4 screws intraoperatively. These 4 screws were excluded from the offset and accuracy analysis. There were no reported returns to the OR. Out of 726 posterior screws placed, 11 (1.5%), including the 4 previously mentioned, were repositioned intraoperatively.Accurate placement of pedicle screws is essential to avoid complications directly related to screw placement, including dural tears, vascular injury, and compression of the neural elements leading to neurological deficit, among others . MalposiPlacement of the screw within the boundaries of the pedicle is dependent on the accuracy of the screw to the plan developed by the surgeon. Utilizing preoperative CT, the surgeon creates a plan for the placement of each pedicle screw which is registered to the intraoperative fluoroscopy. Close matching to the preoperative plan indicates that the navigation system is accurate in guiding the surgeon during the procedure. Jiang et al.  have shoThe strengths of this study include the large patient size and the addition of surgical/accuracy data to a relatively disparate amount of data that exists for the 3 currently marketed robotic systems, of which the Mazor system  has been most heavily studied. Limitations of this study are the lack of long-term clinical outcomes to demonstrate the impact of robotic surgery and pedicle screw accuracy on patient health. The current study is from a single location, which impacts the generalizability of the results. Future studies with long-term follow ups from multiple sites under multiple surgical workflows are required to resolve these limitations. Also, future studies can investigate the factors affecting the accuracy of screw placement with the robots.Robotic-assisted surgery is highly accurate for the placement of pedicle screws within the patient’s pedicles and according to preoperative planning. In this study, 97.9% of screws were rated either A or B on the Gertzbein–Robbins Scale and tip and tail offset values were an average of 1.9 ± 1.5 mm and 2.2 ± 1.4 mm respectively. Mean intraoperative radiation time was 18.3 ± 13.3 s. Screw placement accuracy is unaffected by patient BMI, a potential benefit of this procedural approach.


Topography change caused by melting ice in Arctic soils has the potential to accelerate permafrost thaw and trigger abrupt and large-scale change in the Arctic. We extended a site-scale permafrost thermal hydrology model to represent ground subsidence and combined it with new and existing data from a well-characterized tundra site to better understand the consequences of thaw subsidence in a warming Arctic. Our spatially resolved simulations of a representative carbon-rich tundra site indicate that subsidence will not accelerate permafrost thaw significantly and cause abrupt permafrost thaw over large areas. However, thaw subsidence will likely lead to more runoff and significantly accelerate drying of the tundra landscape in a warming climate with important effects on sensitive Arctic ecosystems. We used a model for permafrost hydrology informed by detailed measurements of soil ice content to better understand the potential risk of abrupt permafrost thaw triggered by melting ground ice, a key open question associated with permafrost response to a warming Arctic. Our spatially resolved simulations of a well-characterized site in polygonal tundra near Utqiaġvik, Alaska, agree well with multiple types of observations in the current climate. Projections indicate 63 cm of bulk subsidence from 2006 to 2100 in the strong-warming Representative Concentration Pathway 8.5 climate. Permafrost thaw as measured by the increase in active layer thickness (ALT)—the thickness of the soil layer that thaws each summer—is accelerated by subsidence, but the effect is relatively small. The ALT increases from the current-day value of approximately 50 cm to approximately 180 cm by 2100 when subsidence is included compared to about 160 cm when it is neglected. In these simulations, previously identified positive feedbacks between subsidence and thaw are self-limiting on decadal time frames because landscape runoff and increasing evapotranspiration result in drier tundra with weaker surface/atmosphere coupling. These results for a tundra site that is representative of large swathes of the Alaska North Slope suggest that subsidence is unlikely to lead to abrupt thaw over large areas. However, subsidence does have significant effects on the hydrology of polygonal tundra. Specifically, subsidence increases landscape runoff, which helps maintain streamflow in the face of increased evapotranspiration but also causes drier tundra conditions that could have deleterious effects on sensitive Arctic wetland ecosystems. Arctic permafrost regions are warming significantly faster than the rest of the Earth and are already experiencing widespread environmental change . These t2medium confidence to that assessment because models required for quantitative projections are limited . The column submodels use ATS’s detailed representation of surface energy balance, subsurface transport of water and energy, and water accumulation on the surface including phase change. The columns are not directly coupled to each other, but all are sequentially coupled to a common two-dimensional surface system representing overland nonisothermal flow. The effects of microtopography on overland flow are represented through a subgrid model that was developed from microtopography-resolving simulations over individual polygons  (ATS)  in a mulpolygons . The subThe ATS model has been evaluated  against SI Appendix, Fig. S1). We addressed this uncertainty by conducting simulations that used median, 20th percentile, and 80th percentile ice content profiles.New spatially averaged, depth profile estimates of permafrost ice content (volume percent) for transects across entire ice-wedge polygons (from trough center to trough center) were generated by intensive sampling of low- and flat-centered polygons (three of each type) located near the Utqiaġvik study site . Ice conMethods). Soil and snow properties are from previous parameter estimation and model evaluation studies (ngee-arctic.ornl.gov).We used the new measurements of ice content and previously published data from our site in the multiscale configuration  of ATS t studies , 22, whiMethods). Projections were then run from 2006 through 2098. Meteorological forcing data for that period were projected for the site by adding long-term trends from Community Earth System Model . The projected ALT at 2100 is about 1.8 m when subsidence is included and about 1.6 m when subsidence is neglected. That relative insensitivity is the net result of competing effects, as described below. It is important to note, however, that the effect of subsidence on carbon mass thawed each year is larger than the effect on ALT because the thaw front goes through higher-density consolidated soil after the excess ice has melted. In simulations that neglect consolidation and subsidence, the simulated thaw front passes through the same ice-rich soil every year. Because the ice-rich soil has lower carbon density on a bulk volume basis, neglect of consolidation and subsidence underestimates the amount of carbon thawed each summer. The specific volume of thawing soil solids—volume of soil solids experiencing thaw each summer, per unit area—is a more relevant metric than ALT because the amount of soil solids is positively correlated with the quantity of organic carbon that is vulnerable to potential decomposition. The specific volume of thawing soil solids with and without subsidence is shown in The effect of subsidence on ALT is relatively minor. The ALT for subsiding and nonsubsiding cases nearly overlaps for much of the century and only starts to separate around 2060 . To clearly separate trends from the interannual variability, we divide the simulation period from 2006 to 2098 (inclusive) into early-, mid-, and late-century periods, and show box-whisker plots statistics for each  . The upper permafrost boundary was identified by the examination of cryostructures and their positioning , where the boundary at 0.45 m corresponds to the average ALT of the sampled polygons .Two-dimensional profile estimates of ice content to 3-m depth (aset S1)  were deraset S1) . Soil piitioning , 37. TheDataset S1, ref. . Porosity determined from the water content (volume percent) of the observed horizons located above the permafrost table  was then assumed  to represent the structurally competent porosity for each soil type. Structurally competent porosity for each depth interval below the permafrost table was then determined as an average of the porosities of each soil type weighed by the relative cross-sectional area of each type within the depth in question. We calculated excess ice content this way for each of the flat- and low-centered polygons  and useThe cold-region hydrology processes represented in ATS are summarized here and described in detail elsewhere , 16. Then in the diffusion wave equation provided n is sufficiently small; we use n = 0.1 s·m−1/3, which is in the insensitive range identified by those studies.Subsurface water movement in variably saturated conditions is represented by a two-phase  extension of Richards equation . Constitutive relationships among temperature, liquid pressure, unfrozen water content, and total water content are based on thermodynamic constraints  and standard soil moisture/pressure relationships measured in unfrozen conditions . In thisTotal evapotranspiration (ET) in the cold-region configuration of ATS results from the surface energy balance, which includes latent and sensible heat transfers and surface radiative balance. ET is not partitioned between evaporation and transpiration, effectively relocating transpiration losses from the root zone to the near-surface soil region. This is an appropriate approximation for our study site which is dominated by evaporation losses  and for The constitutive relationships and the soil thermal hydrology models in ATS have been evaluated against multiple laboratory experiments on freezing soils , 38, 40.SI Appendix, Fig. S5). Each column submodel includes a representation of two-phase soil thermal hydrology, snow thermal processes including compaction, surface water ponding and evaporation, and surface radiative energy balance. The columns are not directly coupled to each other, but all are sequentially coupled to a common two-dimensional surface system representing overland nonisothermal flow. This spatial configuration was motivated by the results of fine-scale simulations. Those simulations showed that significant variations in temperature and moisture content among center, rim, and trough positions in ice-wedge polygons are relatively short lived. On seasonal time scales, lateral subsurface flow and heat transport are sufficient to equilibrate temperature and water table across each polygon . Low-centered values are assigned to polygons that have not experienced subsidence, high-centered values are assigned to polygons that have experienced subsidence of 40 cm or more, and linear interpolation is used between those end member cases. All the four subgrid parameters are interpolated this way. However, Jan et al. , mid-century (2037 to 2067), and late century (2068 to 2098) are identical except for the long-term secular trend in air temperature (and incoming long-wave radiation), allowing for direct comparisons for the three periods.Bottom boundary conditions for the simulation are no water flow and specified temperature (−6 °C) based on borehole measurements in the area . BoundarA two-step spinup process was used to initialize the simulation. The first step was to simulate one high-centered polygon and one low-centered polygon using the looped “typical year” DayMet data as forcing. This step placed each column in a cyclic steady state. The results of those simulations were then mapped into the 3D primal mesh to provide an initial condition for the second spinup step. The second spinup step used that 3D state as initial condition and was forced by historical DayMet data for the period 1985 to 2005. Results from that spinup step were then used as initial conditions for the projections.Soil and surface parameters needed in the simulation were taken from previous modeling studies of the site , 19, 22 Appendix 01 (PDF)Click here for additional data file.


Allosteric regulation of multi-domain protein kinases provides a common mechanism to acutely control kinase activity. Protein kinase C serves as a paradigm for multi-domain proteins whose activity is exquisitely tuned by interdomain conformational changes that keep the enzyme off in the absence of appropriate stimuli, but unleash activity in response to second messenger binding. Allosteric regulation of protein kinase C signaling has been optimized not just for itself: Alessi and colleagues discover that protein kinase C phosphorylates LRRK1, a kinase with even more domains, at sites on its CORB GTPase domain to allosterically activate LRRK1. Protein kinase C (PKC) is no stranger to allosteric regulation. The newly synthesized protein undergoes a series of ordered phosphorylations both by other kinases (mTORC2 and PDK1) and by autophosphorylation in order for it to adopt an autoinhibited conformation [Identifying bona fide substrates of PKC has been challenging given the multiplicity of isozymes (nine genes encode PKC isozymes) which have similar substrate specificities and, for the diacylglycerol-regulated conventional  and novel  isozymes, similar regulatory mechanisms. Phorbol esters, functional analogs of diacylglycerol, have proven to be powerful pharmacological tools to interrogate PKC signaling because, unlike diacylglycerol, they are not readily metabolized and thus lock PKC at the membrane in an active conformation. However, few of the plethora of phosphorylation changes resulting from phorbol ester treatment of cells have been mechanistically connected to direct phosphorylation by PKC, and functional impacts are largely uncharacterized. Yet PKC isozymes are well known to play important roles in cellular homeostasis, with aberrant activity associated with diverse diseases. Even small changes in levels of activity can be pathogenic, as epitomized by Alzheimer's Disease germline variants in PKCα that increase activity by a modest 30% yet have been shown to be sufficient to drive cognitive decline in a mouse model . UnderstIn a series of beautifully executed biochemical experiments, Malik et al. have now shown that many PKC isozymes phosphorylate and activate LRRK1, but not the related isozyme LRRK2. LRRK1 and LRRK2 are multi-domain Ser/Thr kinases whose deregulation causes severe but distinct pathologies . Rare gein vitro to increase its phosphorylation of Rab7A -sensing C2 domain and novel PKC isozymes translocating primarily to Golgi [A hallmark of PKC activation is that it occurs at the membrane, with Cato Golgi . UnsurprAs the authors note, LRRK1 may be only the second kinase demonstrated to be directly phosphorylated and activated by PKC. Protein kinase D (PKD) is phosphorylated by novel PKC isozymes on its activation loop, a segment near the entrance to the active site that stabilizes the active conformation upon phosphorylation . Thus, tAs discussed above, phorbol esters such as PMA have been powerful tools to study the activity and roles of PKCs, as these non-metabolizable diacylglycerol analogs maximally and irreversibly activate PKC isozymes to reveal downstream pathways. While in this study PMA was used to activate PKC, it would be interesting in future work to determine whether natural agonists of PKC, for example activation of phospholipase C through GPCRs also resulted in the phosphorylation and activation of LRRK1. Additionally, LRRK2 phosphorylation in the switch II domain of substrate Rabs has been shown to alter Rab effector interaction and therefore downstream signaling ,17–19, hIn summary, the work from Malik et al. identifies a unique on/off switch of the LRRK1 kinase domain that is distally controlled by CORB domain phosphorylation catalyzed by protein kinase C. This elegant allosteric mechanism exemplifies the diverse methods nature uses to exquisitely control kinase function, and underscores how a small change in structure confers regulation by the PKC pathway to LRRK1 but not LRRK2, creating regulatory specificity between these two enzymes.


Water is one of the most important elements for life on earth. Water's rapid phase‐change ability along with its environmental and biological compatibility also makes it a unique structural material for 3D printing of ice structures reproducibly and accurately. This work introduces the freeform 3D ice printing (3D‐ICE) process for high‐speed and reproducible fabrication of ice structures with micro‐scale resolution. Drop‐on‐demand deposition of water onto a −35 °C platform rapidly transforms water into ice. The dimension and geometry of the structures are critically controlled by droplet ejection frequency modulation and stage motions. The freeform approach obviates layer‐by‐layer construction and support structures, even for overhang geometries. Complex and overhang geometries, branched hierarchical structures with smooth transitions, circular cross‐sections, smooth surfaces, and micro‐scale features  are demonstrated. As a sample application, the ice templates are used as sacrificial geometries to produce resin parts with well‐defined internal features. This approach could bring exciting opportunities for microfluidics, biomedical devices, soft electronics, and art. A freeform 3D printing process (3D‐ICE) is presented to print 3D complex microscale ice structures rapidly and reproducibly with circular cross‐sections, smooth walls, hierarchical branched geometries, and overhang features. As a sample application, the printed ice templates are used as sacrificial geometries to produce resin parts with well‐defined internal features. Although water has been used as a resource for many applications, the use of ice as a structural material is relatively uncommon. However, the simple and rapid phase transition of liquid water to ice and ice to liquid water or water vapor can provide exciting opportunities to use water as an environmentally friendly and biocompatible structural material for many advanced applications. In particular, ice can be used to create sacrificial templates that later form conduit and other open features inside fabricated parts. Taking advantage of the intriguing benefits of water as a structural material requires developing reproducible techniques for fabricating complex, multi‐scale, and high‐resolution structures of ice. This work introduces a freeform 3D printing process (3D‐ICE) for fabricating ice structures with micro‐scale resolution that can also be used for reverse molding. Originally developed as a 2D process for printing graphics, inkjet printing has since evolved into a 3D printing process for diverse applications, including patterning of wax, binders for ceramic 3D printing, and biological inks for tissue engineering. In tissue engineering, 3D inkjet printing has enabled the precision placement of cells in scaffolds and facilitated co‐printing of cells and hydrogels. 3D inkjet printing of polymers involves the controlled deposition of liquid ink in the form of droplets. The deposited ink is then solidified, commonly through ultra‐violet (UV) curing or solvent evaporation, to create the final structures. Generally, 3D inkjet printing is performed through layer‐by‐layer deposition: a thin layer of liquid polymer is deposited onto a platform in a specified pattern and then cured/dried before another layer is deposited. This layer‐by‐layer process significantly limits processing speed and print resolution and necessitates incorporating support structures in fabricating complex geometries, including undercuts and overhangs.We follow the 3D droplet‐on‐demand (inkjet) printing approach with water as the printing ink. Inkjet printing is a non‐contact, maskless, scalable, and high‐resolution process that has found extensive applications in the electronics, pharmaceutical, and biomedical industries.1 Orig The inkjet ice printing method was first introduced by Zheng et al. The authors used a voxel‐based ice printing method, where a voxel was frozen before the next voxel was deposited above it. Each independent voxel can either be an individual droplet or an agglomeration of multiple droplets deposited by using a high‐frequency burst, referred to as “the trigger mode.” Using this approach, Zheng et al., demonstrated the fabrication of various ice structures, including straight and overhung geometries with cross‐sectional diameters equal to the diameter of individual deposited voxels, as well as interesting and challenging geometries such as the letters in the alphabet. However, the voxel‐based approach poses challenges in the fabrication of structures with smooth surfaces and hierarchical geometries with smooth transitions, especially when the cross‐sectional dimensions are different from the droplet size. In another recent work, researchers used a multi‐nozzle inkjet printing system to fabricate ice structures. A layer‐by‐layer approach was used, enabling 2.5D (extruded geometry) ice structures to be fabricated.Recently, a few works have demonstrated droplet‐based inkjet printing of water to print micro‐scale ice templates.8, 9 Although the continuous stream enabled high‐speed printing of large‐scale ice structures, it impeded the ability to print small or precise features. Further, support‐free printing could not be realized due to the significant time delay between the deposition and freezing. At an architectural scale, ice construction has been proposed as a possible solution for building human habitats on Mars. Several groups have also attempted to print structures at freezing temperatures, including liquid metal, aerogels, and hydrogels. Other researchers have proposed using water ice as a positive resist for 3D nanofabrication using ice‐assisted electron‐beam lithography . A thin film of ice, deposited and selectively etched inside an electron microscope, is used as a sacrificial mask layer for fabricating 3D nanostructures with complex features including overhanging geometries. By stacking multiple layers, the process can also be used to fabricate multi‐layered structures in fewer steps compared to conventional techniques.Other works have explored the 3D printing of diverse materials under freezing temperatures at larger size scales. Rapid‐freeze prototyping was used to fabricate centimeter‐scale ice sculptures using a steady stream of water deposited on a cold build platform.11 AltWe present a support‐free, freeform 3D ice‐printing process for the high‐speed fabrication of complex, mesoscale ice structures with micro‐scale resolution and smooth surfaces. The dimension and resolution of the printed ice features are dictated by essentially controlling the droplet deposition frequency (frequency modulation) and the X–Y motions of a high‐precision motion system. Experimental studies are performed to determine the printing path, motion‐stage speed, and droplet frequencies that enable the reproducible fabrication of smooth ice structures with straight, inclined, branching, and hierarchical geometries. Several sample ice structures are printed to demonstrate the proposed technique. Finally, we demonstrate an innovative reverse‐molding application of the freeform 3D ice printing technique by printing sacrificial ice templates to fabricate parts with well‐defined internal features/voids.2freeform 3D printing of ice structures without requiring support structures. We used 3D‐ICE to fabricate structures with smooth surfaces, continuous (non‐discrete) variations in diameter, and overhanging features. Such structures are very challenging or impossible to fabricate using the voxel‐based methods and are uniquely enabled by our freeform 3D fabrication method with the droplet‐ejection frequency modulation synchronized with stage motions  as the pillar length grows. Modulating the droplet discharge frequency allowed us to continuously vary the width of the printed geometry within a broad size range (≈50–400 µm here), unlike the discrete nature of the layer‐by‐layer or droplet‐wise deposition modes.To determine the droplet frequency required to print the desired pillar diameter, we considered the dynamics of the freezing process. Conservation of mass dictates that the sum of the ice and liquid water cap masses is equal to the total mass of the deposited water. For the layered deposition at 5 Hz, the mass of the ice structure is equal to the total deposited water mass (up to a certain height) since each droplet freezes before the next one arrives. At higher deposition frequencies, we calculated the volume of the liquid pool from the difference between the total deposited mass and the mass of the ice . Note that reduced heat flux at longer pillar lengths affects the droplet frequency needed to produce a required width. For instance, at sufficiently long pillar heights, 5 Hz frequency also produces continuous structures with smooth surfaces Figure . We calcThe repeatability of the 3D‐ICE approach is critical to its utility as a broadly applicable fabrication process. To this end, we performed a repeatability/reproducibility analysis on fabricated ice pillars. First, we fabricated 25 pillars with 100 µm target diameter size and measured their width from the images. The details of this study are included in Figure 2.2In addition to the droplet ejection frequency, the print geometry is dictated primarily by the X–Y stage motions during printing. Using controlled stage motions coordinated with the droplet dispensing allowed us to print ice forms with complex geometries, such as steep overhang angles or arch‐type structures. Precise synchronization of stage motions and droplet dispensing is critical to enable free‐form 3D printing without sacrificial support structures.Figure Y‐axis motions, the results are equally applicable for any stage motions in the X–Y plane. Thus, the resulting motion can be used to generate complex ice geometries with 3D features.At a given pillar length, the rate of the freeze front rotation depends on the offset of the incoming droplet from the heading axis at the pillar tip Figure . We used2.3Figure X– Y stage motions. In most cases, the stage remained stationary during droplet ejection, and stage motions occurred in the time interval between ejection of individual drops. For these prints, the nozzle Z‐height was held constant. For the helical coil, the helix structure was first printed in one continuous step, followed by the thinner central pillar . Alternatively, when the process is used to make channels in hard materials, the ice can be melted into water and easily removed via expulsion or evaporation. However, using a similar process for soft and delicate positive forms can damage these materials and collapse the fabricated channels due to surface tension forces. In this case, our approach to directly sublimate away the sacrificial (ice) templates causes minimal disruption to the positive form. Potential applications of reverse molding include, but are not limited to, soft matter and electronics manufacturing, biomedical device fabrication, tissue engineering, and even art. Previously, ice has been used as a sacrificial support material for fused deposition modeling and stereolithography. Alternatively, cryogenic printing has also been used in tissue engineering for printing layered scaffolds with aqueous polymer slurries. After printing, these constructs were freeze‐dried to sublimate the water, leaving behind a porous scaffold. However, layered deposition during the printing process results in a striated scaffold structure, which is generally undesirable. Furthermore, the existing approaches only demonstrated simple, grid‐based geometries. Recently, sacrificial ice printed templates dip‐coated in extracellular matrix proteins have been used for fabricating personalized tissue grafts with hierarchical vascular branches. However, this method could only be applied to produce large freestanding ice structures with minimum dimensions greater than several millimeters.An exciting and compelling application of 3D ice printing is its use for fabricating sacrificial templates. Such ice templates can be used for reverse molding, that is, to create internal (negative) channels and other void features in a solid (positive) part.19 TheFigure  Therefore, to prevent melting the submerged ice structures, we actively cooled the resin and slowly ramped the curing UV lamp intensity over 20 min. This maintained the temperature of the encapsulant well below the melting temperature of ice ‐curable resin. As described in Figure 32 Thee Figure . Figurese Figure .We performed a repeatability study for the inverse molding process. Five ice pillars with nominally the same diameter (100 µm) and spacing (500 µm) were fabricated and used to create internal channels in UV‐curable resin. The average internal channel diameter was measured as 98 µm with a standard deviation of 3 µm. The spacing between the channels was measured as 507 µm with a standard deviation of 5 µm  process to fabricate ice structures with micro‐scale resolution. Our freeform printing strategy eliminates the need for support structures and layer‐by‐layer construction, enabling high‐speed and reproducible fabrication of complex 3D ice structures with micro‐scale resolution, continuously varying circular cross‐sections, smooth surfaces, and branched hierarchical geometries with smooth intersections. The dimension and resolution of the printed ice features were dictated by modulating the droplet deposition frequency and the X–Y motions of a high‐precision motion system. Experimental studies were performed to determine the printing path, motion‐stage speed, and droplet frequencies to reproducibly fabricate smooth ice structures with straight, inclined, branching, and hierarchical geometries. Notably, the knowledge of freeze‐front progression allowed continuous and rapid variation of the printed feature size even when the X–Y stages were stationary. We printed several sample 3D ice structures to demonstrate the proposed technique.An innovative application of the freeform 3D ice printing technique was realized by printing sacrificial ice templates to fabricate parts with well‐defined internal features/voids. The printed 3D ice templates were submerged into a UV curable resin. The water was then sublimated or flowed out to create the final solid components with internal features. This ability to rapidly and easily remove the sacrificial structure from ice to liquid or directly to vapor provides a great advantage, for example, for soft elastomer parts for microfluidics. For parts with medium‐to‐low volume of internal features/voids, this freeform inside‐out 3D printing approach (reverse molding) is orders of magnitude faster than the traditional, layer‐by‐layer positive 3D printing approaches and enables considerable time and cost savings compared to 3D printing of the positive forms. Such components are commonly encountered in 3D microfluidic devices, complex mechanical systems with embedded cooling channels, vascularized engineered tissue scaffolds, and pneumatic actuators for soft robotics. Furthermore, our freeform approach eliminates stepping patterns on surfaces, creating high‐quality parts without time‐consuming and costly finishing processes. The use of water–an abundant, biocompatible, and environmentally friendly resource–as the negative ink makes this technology especially attractive for biomedical applications, 3D microfluidic device fabrication, manufacturing biocompatible soft and flexible electronics, and even for creating artistic structures.4 A piezoelectric droplet‐on‐demand printhead with a 50 µm nozzle  was used to produce the water microdroplets for printing. Inkjetting was performed using a sinusoidal waveform with a period of 10 µs and amplitude of 17.0 V, resulting in 50 µm diameter droplets. The nozzle was mounted onto an Z‐axis stage  tubing. A custom‐built manually‐controlled pneumatic system was used to adjust back pressure at the printhead to achieve stable ejection of water droplets. Additionally, the pneumatic system was also used to apply positive pressure to the water to purge it from the nozzle for cleaning the nozzle prior to printing.Inkjet ice printing was accomplished by modifying the previously described custom inkjet‐based printer.37 A pPrinting was done on a 12 × 15 mm copper print plate. The print plate was attached to the cooled print platform using a vacuum chuck to prevent unintended relative lateral motion between the motion stage and build surface. The platform was cooled using a two‐stage system consisting of a Peltier cooler  sandwiched between a heat exchanger  and the copper vacuum chuck. Indium foil  was used to ensure good thermal contact between the layers. A recirculating chiller (Vevor USA) was used to cool HC‐50 coolant  to −20 °C, which was circulated through the heat exchanger for the first stage of cooling. The Peltier cooler provided the next stage of cooling. A thermal controller  was used to switch the Peltier cooler on and off in response to platform temperature measured using a thermistor , allowing to control the temperature of the build stage to within +/−1 °C.The cooling assembly was mounted onto an X–Y stage  through a thermally insulating Teflon block. The XYZ stages and droplet dispenser were controlled using a single A3200 Npaq motion controller . To eject a single droplet, the motion controller sent a high‐speed digital pulse to the JetDrive controller , which applied the analog jetting waveform to the piezoelectric nozzle to eject a droplet.To prevent frost formation on the cold build plate, the entire setup was contained inside a custom‐built acrylic enclosure. Before starting the printing, the chamber was purged with dry nitrogen for at least 15 min to eliminate ambient humidity. The nitrogen inlet was specifically designed to prevent the formation of recirculation zones and allow uniform dispersion of dry nitrogen gas throughout the chamber  computer aided design (CAD) software and then transferred into MATLAB . Spline functions were fit to individual print segments. Print stage motions were then generated from segment centerlines, and a correction factor was calculated based on the local segment curvatures. Droplet ejection frequencies were calculated based on desired local segment width and height above the build surface . Final print paths were compiled in the AeroBasic language  and were uploaded to the controller to print the desired shapes. Running the code in real‐time on the motion controller allowed coordination between the stage motion and high‐speed droplet ejection.The printing process was observed using a color camera  coupled to a long working distance objective , resulting in a 3.7 × 4.9 mm field of view. A bright white laser‐emitted diode (LED) bulb was used to illuminate the scene, and a gray back‐drop was used for imaging. An LED strobe synchronized to droplet ejection was used to view the jetted droplets and ensure consistent jetting of water droplets before the start of the printing. Acquired images were processed using Fiji.38The printed ice templates were submerged into a UV‐curable resin  using a custom‐built automated mechanism  under a combination of ring and coaxial illumination.The resin was contained inside a custom‐fabricated well with quartz walls , Painesville Twp., OH, USA) and a thin aluminum base. The high level of transparency of the quartz glass at the UV wavelength facilitated efficient curing of the contained resin and clear optical imaging post‐fabrication. The encapsulation process was observed with a microscope camera  with a wide field of view. The resin was cured using a high power 400–410 nm ultraviolet LED  controlled by an LED driver  for statistical analysis was chosen as n = 5. In one case, 25 repeated experiments were conducted to better understand the nature of statistical distribution of data. MATLAB  was used to calculate the mean and standard deviation (SD). Error bars were reported as measured range. Repeatability of the printing and reverse molding process are further characterized in Figure The sample size (The authors declare no conflict of interest.Supporting InformationClick here for additional data file.Supplemental Movie 1Click here for additional data file.Supplemental Movie 2Click here for additional data file.Supplemental Movie 3Click here for additional data file.Supplemental Movie 4Click here for additional data file.Supplemental Movie 5Click here for additional data file.Supplemental Movie 6Click here for additional data file.Supplemental Movie 7Click here for additional data file.Supplemental Movie 8Click here for additional data file.Supplemental Movie 9Click here for additional data file.


The rate and consequences of future high latitude ice sheet retreat remain a major concern given ongoing anthropogenic warming. Here, new precisely dated stalagmite data from NW Iberia provide the first direct, high-resolution records of periods of rapid melting of Northern Hemisphere ice sheets during the penultimate deglaciation. These records reveal the penultimate deglaciation initiated with rapid century-scale meltwater pulses which subsequently trigger abrupt coolings of air temperature in NW Iberia consistent with freshwater-induced AMOC slowdowns. The first of these AMOC slowdowns, 600-year duration, was shorter than Heinrich 1 of the last deglaciation. Although similar insolation forcing initiated the last two deglaciations, the more rapid and sustained rate of freshening in the eastern North Atlantic penultimate deglaciation likely reflects a larger volume of ice stored in the marine-based Eurasian Ice sheet during the penultimate glacial in contrast to the land-based ice sheet on North America as during the last glacial. Stalagmites from NW Iberia record the rapid demise of large ice sheets during the penultimate deglaciation, and reveal decadal-scale feedbacks between warming and ice melting. The rapid retreat of ice sheets which yields high meltwater fluxes, can be caused by marine ice sheet instability, ice sheet saddle collapse and marine ice cliff failure2. While the timing and associated deglacial feedbacks have been extensively studied for the last deglaciation 3, knowledge of the insolation thresholds, rate of ice sheet melting, and feedback sequence of previous terminations is more limited due to the lack of direct absolute chronology for ice retreat and deglacial warming. Some studies suggest that the sequence of millennial feedbacks may be different in previous terminations5. The penultimate deglaciation, Termination II (TII), is of particular interest because orbital boundary conditions were different, and the termination was followed by an interglacial with a + 1.2 to 5.3 m sea level highstand - suggesting both Greenland and Antarctic ice sheets retreated further than during TI6, despite similar highs in atmospheric CO27. To fully understand the last interglacial highstand, clear knowledge of the ice sheets melting time and retreat rates during TII is needed9.During glacial terminations, retreating ice sheets release large meltwater fluxes into the ocean. This leads to rising sea level and can initiate strong climate feedbacks when sufficiently large meltwater fluxes reach regions of deepwater formation in the North Atlantic. These ocean-atmosphere interactions, together with associated ocean CO18O lower than the mean ocean, meaning the deglacial melting of the Northern Hemisphere (NH) ice sheets lowers the δ18O of the surface ocean (δ18Osw). For regions proximal to release of glacial meltwater, such as the North Atlantic, the rate of δ18Osw depletion and freshening can exceed the global average11, which has been useful in diagnosing meltwater routes during TI14. We propose that the evolution of the North Atlantic δ18Osw can be recorded in coastal European speleothems through the transfer of the δ18Osw signal of the ocean moisture source to the δ18O of rainfall, and thereby the δ18O of dripwater15 from which the speleothem is formed. We report on the North Iberian Speleothem Archive (NISA) from caves within 10 km of the Atlantic coast  with the δ18Osw on the Irish Margin16 and a low standard error indicates a consistent relationship throughout the deglaciation despite the potential for variation in atmospheric and surface ocean boundary conditions . Multiproxy process modeling suggests that this correlation arises because higher temperature strongly increases vegetation productivity in this biogeographic regime, enhancing soil CO2 production and oversupply of CO2 to karst waters, both factors which produce more negative δ13C in speleothems (δ13Cspeleo)31. We infer that the specific slope of the temperature vs δ13CNISA relationships may be specific to a given cave systems and host lithology, and may be sensitive to the degree of smoothing of millennial-scale changes which is affected by the speleothem growth rate and the years aggregated in each drilling increment.Additionally, we confirm that over TI, the δ18ONISA and δ13CNISA over TII as indicators of δ18Osw and temperature, respectively. Three 230Th–dated NISA stalagmites replicate the main features of the TII deglaciation between 135 and 129 ka  and its relationship with regional warming (δ13CNISA)  Fig. .32, we infer that the addition of meltwater is the main driver of rapid deglacial freshening and declines in the δ18Osw in the eastern North Atlantic. Both abrupt freshening pulses began during a period of rapid warming, then, after several decades of rapid freshening, temperatures cooled rapidly, consistent with freshening-induced AMOC slowdown  and AMOC slowdown, a North Atlantic freshwater δ18O anomaly persisted. Unusually, for ~ 3000 years, the δ18ONISA remained lower than the final interglacial state. The maintenance of a freshwater δ18O anomaly for so long in the surface eastern North Atlantic requires addition of meltwater at rates greater than it can be distributed through mixing with the global ocean. Thereafter, starting around 131 ka, the North Atlantic freshwater δ18O anomaly diminishes rapidly, which suggests that the rate of addition of meltwater into the eastern North Atlantic had slowed sufficiently so that ocean circulation homogenized the deglacial meltwater anomaly to the global ocean average. This decline coincides with a rapid decrease in IRD delivery in the Northeast Atlantic and Labrador Sea  on the Iberian margin also slowed significantly at 131 ka  for the Red Sea curve39, and our chronology implies the potential for an earlier and even more concentrated meltwater pulse than estimated from the derivative of the Red Sea sea level curve  , remains below −1‰ only between 16.4 and 15.2 ka (1.2 ky duration), whereas during TII it remains below −1‰ from 134.7 to 131.2  Fig. . Yet, th TI Fig. . During 18Osw anomaly coincides with the interval of fast melt rate of the Eurasian ice sheet according to recent sea level reconstructions41  would be diluted during advection across the Atlantic by the North Atlantic Drift42. These model simulations, albeit limited, suggest the potential for higher amplitude δ18Osw anomaly in the eastern North Atlantic during EIS melt than NAIS melt, given similar δ18Oice as assumed in previous studies43. Therefore, one explanation for the longer duration surface ocean δ18Osw anomaly during TII is a larger proportion of EIS-derived meltwater in TII compared to TI.During TI, this period of greatest regional δs41 Fig. . One int45. The potential for a larger PGM EIS ice sheet has been explored in dynamical ice sheet models with total EIS ice volumes of up to 70 m sea-level equivalent, nearly triple that of the LGM EIS46. Because of similar estimated PGM and LGM sea level and benthic δ18O, this simulated large PGM EIS likely coexisted with a smaller than LGM NAIS46. The ice sheet reconstruction featuring a large TII EIS46 encompasses a 2.5–3.5x greater volume of marine-grounded  EIS ice at the PGM, compared to the LGM (Methods) with thickest ice in the Fennoscandian sector. Because of isostatic loading and higher relative sea level caused by self-gravitation, the larger PGM EIS would have been even more sensitive to ocean forcing and marine ice sheet instability which could have contributed to a rapid retreat. Although the onset of modeled TII EIS retreat differs slightly from our record8, its duration is broadly consistent with the here documented duration of eastern North Atlantic δ18O anomaly.In support of this explanation, Eurasian PGM deposits are found well beyond the limit of ice extent from the LGM, with the largest expansion in the Barents-Kara sectors of northern Russia Fig. . However49. Based on our records, we cannot confirm nor rule out disintegration of such an ice shelf as a contributor to freshening at the onset of TII, leading the retreat of Northern sectors of the EIS. However, the modest magnitude of Arctic shelf ice volume suggests that this cannot be the only factor responsible for differences in the meltwater anomaly and rate of change in δ18Obenthic and sea level rise over TII  also coincides with a period of AMOC reduction inferred from proxies such as Pa/Th50 . Nonetheless, the temporal coincidence of reduced AMOC and the phase of most rapid EIS retreat in TI may not be coincidence. Simulations suggest that meltwater release from the Northern and western margin of the EIS (and the Mackenzie River outlet of the North Americans), is more effective at decreasing AMOC compared to North American melt routed through the Gulf of Mexico, Hudson Bay, or St. Lawrence outflows52, because the former meltwaters reach the locations of northern North Atlantic convection with lesser dilution by other surface waters53. Therefore, the strong surface meltwater δ18Osw between 16.4 and 15.2 ka in the eastern north Atlantic may be both a direct consequence of high EIS melt rates releasing water in the eastern North Atlantic, and an indirect consequence of the high EIS melt rates on AMOC stability and concomitant amplification of the surface meltwater δ18Osw. In and of itself, reduced AMOC intensity, such as that inferred to have occurred during the Younger Dryas according to Pa/Th   Model (Version 4.8)71 NW Iberian caves: Pindal Cave , La Vallina Cave , and Cueva Rosa . These stalagmites cover TI, Greenland Stadial 22 (GS22), and TII72. Additional growth phases have been studied in the stalagmite Candela since earlier publication72, and we report additional dates and higher resolution geochemical data. In Candela, A ~10 cm long basal growth phase (CANB) has been sampled along its main growth axis and redated, contrasting with strongly off-axis and condensed sampling of this phase in earlier work. Additionally, within the Bølling-Allerød, a transient 1.5 cm shift in growth axis has been resampled along its expanded central growth axis for 2.5 cm, expanding by 5-fold the record previously sampled in a lateral portion at only 0.5 cm thickness.Stalagmite samples were analyzed from the following previously described73 between 230Th dates, for intervals of rapid freshening in TI and TII, we refine age models by estimating stalagmite growth rates from the width of growth bands defined by fluorescent layers74 which have been described to result from seasonal delivery and/or incorporation of fluorescent organic substances in dripwater75.To account for variation in growth ratesStalagmite slabs were mounted in low-viscosity Laromin C260 epoxy , ground flat with SiC paper, and then polished with a diamond suspension to 0.25 µm in preparation for Confocal laser scanning microscopy (CLSM) and laser ablation ICP-MS. Imaging by CLSM was performed at the Scientific Center for Optical and Electron Microscopy (ScopeM) at ETH Hönggerberg using an OIympus Fluoview 3000. Here, a series of overlapping images were obtained under 100–200x magnification using an incident wavelength of 488 nm and measuring fluorescence in a 490–590 nm window. Images were obtained at 1024 × 1024 or 2048 × 2048 resolution, corresponding to 1.2 to 0.6 µm/pixel (respectively) under 100x magnification. Images were processed using Fiji/ImageJ, where the exact distances between growth layers were recorded on an absolute length scale and later cross-referenced to laser ablation and drilling  data. Confocal images were counted in stalagmite Garth section from 177.5 to 269.5 mm from the tip. Growth layer thickness was used to determine rates of isotopic change in sections which could be layer counted, and to develop accurate interpolation of ages between U/Th dates. In areas where annual layers were not immediately visible, typically when layer thickness was less than 3 µm, an average growth rate for that section was assigned in order to be consistent with the sequence of U/Th ages.230Th dating. New dating was completed using standard methods and analysis on MC-ICP-MS (Thermo-Finnigan Neptune)76 at Xi’an Jiaotong University and the University of Minnesota; some previously published aged used in this study also include determinations on SF-ICP-MS (Thermo-Finnigan ELEMENT77); results are given in Supplement Tables 14C ages were measured at ETH Zurich with a gas ion source in a Mini Carbon Dating System at the Laboratory of Ion Beam Physics, ETH, via on-line acid digestion78 and calibrated with INTCAL 202079 and results are given in Supplement Table 27. Because agricultural and pasture land uses became widespread in Northern Spain after 5.5 ka BP80 which may decouple the natural relationships between climate and vegetation over cave sites, we do not present or discuss speleothem records younger than 5 ka BP.Absolute chronology is based on subsamples drilled for 230Th ages are interpolated using the Bchron software82  whereas linear interpolation was employed for short growth phases bracketed only by basal and top U/Th dates . Two approaches are used to refine the age model within the 18 to 14 ka interval in Candela. Where visible growth laminae are present, their thickness is used to constrain growth rates , and advanced upwards ~90 year using width of fluorescent growth layers to constrain growth rate. Growth layers are not countable in the following 7.7 mm of stalagmite  interval at the end of the δ13C maximum. The precision of the age model is lowest between 17.85 and 16.1 ka, and improves by 16 ka due to a 15.4 ka 230Th date and the 16.1 and 14.5 ka tie points with Laura. Following these tie points, the age model until the hiatus at 11.6 ka is established from 230Th tie points, with interpolation between dated points further constrained by counting of 600 annual layers (14.5 to 13.9 ka) during the Bølling-Allerød. This set of speleothem records chronicles the changes across TI in higher detail than previous records from the region, with the following average absolute 95% CI age uncertainties 20–18 ka ; 18–16 ka , 16–14 ka ; 14–12.5 ka (Candela +/− 260 years).Age models for stalagmites younger than 30 ky are illustrated in Supplementary Fig. Age models for stalagmites spanning TII and the Bchron uncertainty windows, are illustrated in Supplementary Figs. 83 and are reported in ‰ relative to the Vienna PDB Standard. Analytical uncertainties for calibration with two in-house carbonate standards and NBS-19 and NBS-18 international standard and were 0.08 ‰ for both isotopes. Samples for isotopes were micromilled at 0.1 to 0.5 mm increments, or drilled at 1 to 5 mm increments, from the central axis of stalagmites. Stalagmite δ18O and δ13C were screened for the coupled effects of CO2 degassing and prior calcite precipitation, as detailed below. A spliced record of δ18ONISA and δ13CNISA is compiled from stalagmites spanning 26–5 ka BP. Where multiple stalagmites grow synchronously, we employ for the splice, the stalagmite with best constrained chronology and the stalagmite in which there is the least variation in Mg/Caindex over the included time interval. The goal of this approach is to limit the potential influence of PCP on the inferred trends in δ18ONISA and δ13CNISA.New stable isotope determinations were measured at Scientific and Technologic Centers from the University of Barcelona with a Thermo-Finnegan MAT-252 coupled to a CarboKiel-II and at ETH Zürich with a Thermo-Finnegan Delta V Plus coupled to Gas Bench II72, and with similar standardization approaches at ETH Zürich (Agilent QQQ 8800); all ratios are reported in mmol/mol. Mg/Ca is widely used indicator of variation in PCP84 and we use speleothem Mg/Ca and the Mg/Caindex as a qualitative indicator of the influence of the coupled process of CO2 degassing and prior calcite precipitation (PCP) on isotope trends, hereafter referred to as PCP. To facilitate comparison across stalagmites from different portions of the cave, which sample stratigraphically distinct portions of the host limestone, we normalize the measured Mg/Ca in each sample (Mg/Casample) to the minimum Mg/Ca of that stalagmite (Mg/Camin), where high index suggests little loss of Ca due to PCP and a low index suggests significant loss of Ca due to PCP.Mg/Ca was measured on splits of the isotope samples, at the University of Oviedo (Thermo ICAP DUO 6300)13C of dripwater acquired through rain equilibration with soil gas and bedrock dissolution is the primary signal of interest, we plot stalagmite δ13C coded by the Mg/Caindex  mmol/mol)  and peak MIS 5e (127–123 ka) are less influenced by PCP in Gael. At the same time, the trend in δ13CNISA at the termination onset may be amplified in Gael by decrease in PCP between 135 and 134 ka. In stalagmite Neith, Mg/Ca and δ13CNISA correlate strongly within glacial and termination time windows  using crossplots of isotopic records with Mg/Ca  mmol/mol), suggesting that variation in PCP is not a significant influence on the trend in δ18ONISA in this time interval. Over the termination there is also no correlation between growth rate and δ18ONISA in Garth, the stalagmite for which growth rate is most precisely resolved due to annual layer counting. .During TII, we evaluate whether deglacial δ18O of surface seawater (δ18Osw) is commonly estimated from coupled Mg/Ca and δ18O of planktic foraminifera89. We compare published marine δ18Osw with δ18ONISA over the time interval from 25 to 5 ka BP in fixed 500 year time bins  relative to the benthic δ18Ocalcite on the Iberian margin, which can be precisely and independently tuned to speleothem chronology for TII. This metric is denominated (δ18ONISA-BC) or (δ18OSW-BC). Although the decrease in benthic δ18Ocalcite is driven by both deep ocean warming and decreasing deep ocean water δ18O components, high resolution OA GCM model simulations show that in the depth range of our Iberian Margin North Atlantic records, decreasing deep ocean δ18O and warming are closely temporally coupled when meltwater release decreases AMOC intensity, because shallowed North Atlantic winter mixed layer depth lead to mid-depth warming11.The calculation of regional surface ocean δ18Osw records for TII91 based on Mg/Ca SST and δ18Ocalcite and align the major depletion in both δ18Osw of ODP 97791 and in δ18ONISA in Garth, as illustrated in Supplementary Fig. 10, we extend the NW Iberian speleothem chronology by the additional alignment of three key cooling events in the δ13CNISA record with events identified in the alkenone-SST record also from ODP 97792. ODP 977 is the primary tuning target because is the only available δ18Osw record that matches exactly the amplitude of the initial speleothem freshening in both TI and TII  is somewhat attenuated, potentially due to low biogenic productivity and foraminiferal growth periods which are biased against extreme conditions98.The ODP 977 marine chronology is transferred to ODP 97699 and 984100 we align the major reduction in %N. pachyderma sinistral with the deglacial temperature rise in the Alkenone SST record from ODP 977, a clear structure that correlates well all along the Iberian margin cores, as well as a subsequent local maximum in %N. pachyderma sinistral evident as a local minimum in alkenone SST  is known to lead that of deep N Atlantic and S Atlantic and Pacific over the TI103 and the applied tuning suggests a similar pattern in the TII 93 exhibit divergent millennial structure and amplitude of SST change across H11 likely reflecting a seasonality control in the H11 temperature signal. More intense winter cooling but summer warming104 during cold reversals may lead to differences in rate of winter vs annual or summer warming, which may enhance discrepancies among proxies which may have differing influence of summer and winter seasons. An additional factor which has been documented to slow the manifestation of deglacial SST rise in alkenone records on the Iberian Margin is the transport of glacial-aged alkenones into sediments of deglacial and early interglacial age29.Within H11, we have not relied on temperature records for tuning, because the alkenone temperatures exhibit a slower rate of warming than implied by δ18Osw record during the termination and using its δ18Oplanktic record during the interglacial. δ18Osw tuning of TII is based on observed lags during TI. During TI, the δ18Osw of ODP 99967 is based on 14 C age model, updated to INTCAL2013 with constant 400 year reservoir age. During TI the W Iberian margin δ18Obenthic105 is on chronology tuned to GRIP106 and Hulu90. We observe that depletion of δ18Osw at ODP 999 lags that of W Iberian margin δ18Obenthic by an average of 1100 years  and western Caribbean (no cooling from AMOC shutdown). However, during the interglacial, these two subtropical locations may be expected to have similar evolution of SST and δ18Osw.Therefore we use the combined signal of δ18Oplanktic to serve directly for correlation during MIS 5e (Supplementary Fig. We tune ODP 999 using its δ61 and an ice history that is the same as ICE6G for T2108. The sea level history and glacial isostatic adjustment modelling is from8, using the same ice sheet histories. ‘Marine’ ice is defined here simply as the volume of ice that is grounded below the reconstructed sea level.We approximate the ‘marine’ proportion of the T1 and T2 Eurasian ice sheet using the ice sheet reconstructions ofFurther information on research design is available in the Supplementary informationReporting Summary


Panthera leo) feeding data and show that preference vs prey size follows a bell-curve. Using just two estimated parameters, this curve can be used as a general way to describe predator feeding patterns. Our method can be used to: test hypotheses about what factors affect prey selection, predict preferences in new sites, and estimate overall prey consumed in new sites.Most natural ecosystems contain animals feeding on many different types of food, but it is difficult to predict what will be eaten when food availabilities change. We present a method that estimates food preference over many study sites, even when number of food types vary widely from site to site. Sampling variation is estimated using bootstrapping. We test the precision and accuracy of this method using computer simulations that show the effects of overall number of food types, number of sites, and proportion of missing prey items per site. Accuracy is greater with fewer missing prey types, more prey types and more sites, and is affected by the number of sites more than the number of prey types. We present a case study using lion ( Most natural ecosystems contain animals feeding on many different types of food, but it is difficult to predict what will be eaten when food availabilities change. Ecologists face this issue all the time. For example, if we introduce a biocontrol agent then will it escape regulation by predators? Or if climate change shifts the range of a plant species then how will that affect feeding on other plants eaten by a common herbivore? Or if an invasive species appears then how will its predators respond? We need to be able to predict food preference for any combination of food types.At the moment, theories of predator behaviour explain processes in current study sites but do not predict preference in new study sites. Such theories include optimal foraging –3 and moThere have also been some excellent studies looking at how dietary preference varies with factors such as amounts of food , 13, seaOne main reason for this general paucity in predicting preferences is methodology. While there is a mature field of study about ways to estimate prey preference in one study site –25, therThe difficulty in combining prey preferences over many sites arises from the fact that all measures of preference are relative to the prey items present at individual sites. Just adding or subtracting one prey type may completely change preferences for the other prey; thus, it is difficult to combine preferences among sites that have different types of prey.For example, suppose a predator prefers 4 prey items in this order A>B>C>D. In a site containing only prey items C & D, the predator would select for C. In a site containing prey items A, B, C, the predator would select against C. It is not known how to combine data from those 2 sites to predict selection when all prey are present. One would estimate that both C and B have intermediate selection values but it is not known how to estimate overall preference for B vs C. The problem is much more difficult when 20 prey species exist in 40 different sites.Previous studies have calculated prey preference values for each prey type within each study site, then averaged these individual preference values over all study sites for each prey type , 27. ThePanthera leo) feeding.We present a method that estimates overall prey preference by combining data over many study sites, even when not all sites contain all prey items. Our method adjusts for the relative nature of preferences at individual study sites, allowing one to predict feeding preferences in new study sites, or when prey items change. This method also produces estimates of sampling variation, and thus, confidence intervals for preference estimates. We show how to increase precision by weighting the estimates by both prey densities and sampling effort. We then illustrate the method with a simple numerical example and test the method’s accuracy and precision using simulations. Finally, we show an example application using data from lion  method. Note that, following convention, we refer to foods as “prey”, and the feeder as the “predator”. However, our method applies to all types of animals, not just predators, and the selected items could be vegetation, or even non-food items, such as types of habitat. All analyses were carried out using the Wolfram Language , and R cAt each site there is a list of prey items that the predator eats, and for each prey item we have estimates of abundance and consumption. Abundance estimates can originate by any means . At each site we estimate within-site preferences for those prey that are available:ij all sum to 1 for each site, and j is summed over all prey types present in site i, . This preference estimate is the Manly’s ∝ [Note that the ∝anly’s ∝ , 23.pj = overall prey preference for prey item j. This is equivalent to an overall ∝j when all prey types are present.We want to estimate:We explain the procedure with an example.Suppose we have m = 4 sites and n = 6 prey types. The within-site preferences (∝) are given by the following matrix, where columns are prey types and rows are sites. The dashes show when the prey type is not present at that site.Step (ii). We are estimating overall prey preferences iteratively. We start with some initial values of overall prey preference , and then update these at each iteration k. For the first iteration we choose equal values that sum to 1, and for the kth iteration, we use the averages summed over all sites.Step (iii). The α values at each site initially sum to 1. These are then scaled to the values you would expect if all prey were at that site—this step is the key to the whole method. This scaling is done because preferences cannot be simply averaged over sites, because at each site they are relative to each other—i.e. they sum to 1, even though some prey are missing. Thus, in order to combine them, we rescale the preferences so that they would sum to 1 if all prey items were present.We calculate this scaling constant by the following. Since all prey items are not present, we replace the missing prey items with the overall prey preference estimates. Then we choose the constant so that the new preferences sum to one.th iteration of the estimation process,Let th iteration of the estimation process,th iteration of the estimation process,th iteration of the estimation process,i = the set of prey items that are available in site i,Ai = the set of prey items that are missing in site i,Mi = the constant that rescales all preferencescThese new preferences in each site all sum to 1—i.e.:ij sum to one, and solve for ci, we get that the scaling constant for each site isIf we re-arrange For example, in site 1 prey types {1,2,4,5} are present, and thus all of the preference values in site 1 are scaled by:Step (iv). The missing values in matrix . The overall prey preferences for the next iteration are estimated by the means of the columns in matrix (n matrix . E.g. thStep (vi). Compare the new estimate for overall preference to the one used in step (ii). If there is a change in the estimates, then repeat steps (ii)–(v) with the same initial table of preferences but with the new vector of overall prey preferences. The result is a set of overall preference estimates. These preferences range from 0 to 1 and sum to 1, and the important aspect is their values relative to each other, not their absolute values.Step (vii). Ecological estimates should always have a measure of their error [ir error . This cair error , treatinir error , and thePreliminary simulations showed that using this transformation significantly increased accuracy of the estimates.These estimates can be improved by appropriate weighting, since variances among prey preference estimates are not equal. Typically these variances are not known, however they are decreased by sampling more predators and in areas of higher prey density. For example, the preference estimate would be very variable for rare prey types. Thus we can use inverse-variance weighting  to minimi = sample size used to estimate prey consumption—e.g. number of individuals eaten, number of scats, etc.fPrey consumption effort weighting is carried out as follows. For each prey type the precision of overall preference would be affected by the total number of feeding samples collected at each site. Let:Weighting i = the set of prey items that are available in site i, andAi = number of prey types present at site i—thus, ni = |Ai|.nDensity weighting is carried out as follows. Letij. We handle them by imputation—i.e. by substituting the mean density of all other prey at that site. Thus, if prey type s is not present at site i, then for it’s density we use:Since not all prey types are at each site, there are some missing values in the densities dWeighting Weighting by both prey consumption effort and prey densities is carried out by weighting In this toy example, there are 6 prey types at 4 sites.Step (i). The values in each cell are within-site preferences—note that rows sum to 1 for each site.Step (ii). We start with initial estimates of equal values of overall preference for the first iteration:Step (iii). We rescale the ∝ij values by multiplying (for each site) by Step (iv). We replace the missing values by the overall preferences from Step (v). We estimate new overall values of overall preference by the mean of the values at each site. Thus overall preferences for all prey types at iteration #2 are:For example, the overall preference for prey type 1 (0.197) is the mean of the values in column 1 in matrix .Repeating steps (ii)–(iv)Step (v).Repeating steps (ii)–(iv)Step (v).rd and 4th iteration ..rd and 4i) were generated using a uniform distribution. Then mean prey density for each site was generated using a normal distribution with a mean of 100 and a coefficient of variation of 0.5, truncated to a minimum value of 5. Then the density of each prey type within each site was generated using a normal distribution with a mean of the site prey density and a coefficient of variation of 0.5. “Preference” was treated as the probability of choosing a prey item each time it was encountered. Thus the number of prey consumed for each prey type within each site was generated using a binomial distribution with a mean of pi and an n of prey density. Finally, sites with incomplete collections of prey were simulated by using a binomial random number generator to randomly drop prey types from each site.We tested the accuracy and precision of IPA using simulations. We varied the number of prey types, number of sites and the proportions of prey types missing per site. For each simulation, overall preferences . We calculated those indices for prey types at each site, and then calculated the mean for each prey type over all sites (while ignoring the missing prey types at each site).IPA gave more accurate and precise estimates of overall prey preference compared to the averaged preference. For example, The IPA estimates are more precise when they are weighted by both prey densities and number of feeding samples for most combinations of parameters . ConfideAccuracy of bootstrapped estimates of confidence intervals varies with prey characteristics. The proportion of missing prey types, and the number of prey types and sites, all interact to affect accuracy. Generally, accuracy is greater with fewer missing prey types, more prey types, and more sites, for most combinations of parameters . There ik1, k2, k3 = fitted parametersWe illustrate the IPA method with lion feeding data  that incpref = overall prey preference estimated by IPAwt = log(prey weight).Since the preferences are relative to each other, we scaled them so that the maximum function value would be 1—i.e. the preferences are all scaled relative to the maximum. We did not estimate the weighted IPA estimates because prey density and consumption surveys were not carried out in the same manner among sites.1) and standard deviation of the feeding curve (k2) . k1 is a measure of average size of prey eaten, and k2 is a measure of feeding specialization (the width of the curve). If other predators fit similar curves, we can use those parameters to compare different predators and to estimate competition among predators living in the same system.Analysing overall preference by prey weights in this way yields several biological insights. First, we can describe feeding preferences by just using two parameters, representing the mean  more than any other prey species  and Jacobs’ index from .“No preference" for Manly’s ∝ is 1/(# of prey types), while for Jacobs’ index it is 0. Consequently, for Manly’s ∝ the range of prey preferences for avoidance is smaller than for selection whereas for Jacobs’ the range of prey preferences for avoidance vs selection is the same.Jacob’s index is affected by relative prey densities when there are more then two prey types , 45–thusThe total of Manly’s ∝ for all prey types is 1 but there is no constant total for Jacobs’ index.All preference indices are relative. If preferences are estimated for a large suite of prey items, then one cannot just apply those values directly in a different situation with fewer prey. However Manly’s ∝ can be re-normalized to take into account the dropping of prey itemsIPA uses Manly’s α for the index of prey preference. Many other studies have used the Jacobs’ index e.g. , 41, 44), 4441, 4IPA uses Manly’s α because IPA hinges on scaling the preference measures to those you would expect if all prey types were present in each site (Step 1). The scaling requires that prey preferences range from 0 to 1, and sum to 1 in each site—and Manly’s α is the only published index that does this.However, Manly’s α has a weakness in that it is sensitive to variations in densities of rare prey. IPA minimizes this problem in two ways: first, mean preference (Step 3) is weighted by prey density, and second, when estimating sampling error during bootstrapping, the preferences are transformed by arcsine(2 x − 1).On the other hand, Manly’s ∝ is useful when predicting total biomass of prey consumed—one simply multiplies Manly’s ∝ by prey density and body mass. In addition, Manly’s ∝ is biologically relevant in that it represents the relative probability of eating a prey once it is encountered .When organism densities are estimated, several availability biases can occur, and these can potentially affect preference estimates. False absences occur when individuals are present but undetected, and false presences occur when individuals are not present but are wrongfully identified to be present . If suchIf important ecological differences exist among sites, then this might affect the accuracy of overall estimates of prey preference, and thus of conservation interventions. There are two ways of dealing with this. First, find out if preferences do differ among sites, by comparing standardized preferences within each site (i.e. step (iv)) to overall preferences. Currently this would be done visually, and thus work is needed to develop statistical tests for this. Sites that are different would then be treated separately. Second, instead of analyzing preference based on prey species, one could use prey weights. Many predators select prey mostly based on size, not prey species . The lioet al. [IPA can be generalized. In the description of IPA, we use the term “prey types”; prey can be categorized in many ways. For example, Lungdoh et al.  classifiLepus americanus)–lynx (Lynx canadensis) system [Canis lupus) -moose  system [et al. [Acinonyx jubatus) prey requirements in 12 South African game reserves in order to manage re-introductions of cheetah. To combine data from many sites, the researchers had to focus on only the two most important prey types. Using IPA, we can estimate relative prey preferences for all prey types and thus combine them into one overall measure of prey consumption. Also, if we include prey weight, we can estimate overall biomass of prey consumed. This flexibility will make it easier to build predator-prey models with many varied prey types.In studies of predator-prey relationships, IPA can also be used to estimate overall prey consumption. Many of the key studies of predator-prey relationships have focused on systems with a limited number of main prey types  system ), becaus [et al.  comparedOne can use IPA to test hypotheses about factors that affect prey preference. The type of test depends on whether the factors are inherent properties of the prey types or ones that can vary among sites. For example, some properties that are inherent are handling time, risk of injury during capture, taste and size of the prey . Some prCanis latrans) change prey preference in response to changes in snowshoe hare (Lepus americanus) density. Such comparisons were possible because Prugh worked within one study site over several years, with a relatively constant number of prey types. Such an analysis can now be carried out using IPA over a wide range of study sites that differ in prey types. As of July 2019, there are at least 109 studies of coyote feeding habits that could be used in such a comparison.We can test for the varying properties by analyzing the differences between estimated and observed preferences for each prey type and site. IPA preferences are estimated under the assumption of constant preferences among sites, and thus can be viewed as a null hypothesis. Models can be tested predicting the differences between estimated and observed preferences as a function of prey density, prey diversity, or various habitat features. This allows us to test hypotheses that had previously been limited to a narrow range of study sites. For example, Prugh  showed tApplication of IPA allows us to: test hypotheses about what factors affect prey selection, predict preferences in new sites, and estimate overall prey consumption in new sites. The method’s robust flexibility could lead to a general theory of feeding preference that will allow us to understand and predict food choice.S1 Appendix(DOCX)Click here for additional data file.