Philippa Kaur

Having introduced our novel explore-and-fuse method and the Physarum Steiner Algorithm we shall dedicate this section to discussing how the algorithm’s parameters influence the model, and how the method can be used towards diverse applications.In what follows we shall consider how different parameters such as the different shapes of cells, as well as their number, influence the results obtained by the Physarum Steiner Algorithm. We shall then conclude the section by studying different applications that our methods have.Cell shapeAlthough13 and6 considered diamond shaped CELLs, we shall consider here CELLs with other shapes. The primary benefit of square cells is that their shape allows for more cytoplasm to be placed on the grid. As a result, the foraging phase is very fast so using square cells tends to result in shorter run times than using diamond-shaped cells. In addition, large square cells are able to more completely cover the standard square grid than diamond-shaped cells. On the other hand, diamond-shaped cells result in less cytoplasm and more time spent in the foraging stage. This gives the cytoplasm time to move towards a centralized location which results in better solutions.Example A In order to illustrate the above point, in Fig. 3a.i., we begin with squares that are tightly packed. Since the squares are so tightly packed (1 apart), if any piece of cytoplasm in a square is moved, it will lead to a connection with a neighboring cell. As a result, all the points are found very quickly. In fact, many of the squares are connected and part of the network even if they are not close to any of the points, as shown in Fig. 3 (a.ii.). Shrinking these extra squares takes a long time and can also result in long paths which are far out of the way as seen in Fig. 3a.iii.Example B In contrast to Example A, in Fig. 3b, we consider diamond-shaped cells. The cells start off diamond-shaped and with less overall cytoplasm than the square cells. The cells then spend quite a few iterations in the foraging phase. Although this does take time, it allows the cytoplasm to move towards a centralized location around the active zones as seen in Fig. 3 (b.ii.). When the cell finally proceeds to the shrinking phase, there is less cytoplasm to remove and no out of the way paths, resulting in shorter solutions. The downside to this is the increased time which in some cases can be very long (over 100 million iterations) and in some cases the algorithm may not even complete.The effect of multiple cellsIn what follows we shall examine the effects of the number of cells used. We run 10 trials on 10 grids for a total of 100 trials on each cell size and number of cells. For each trial, we measure the total amount or area of cytoplasm that is initially spawned. This is used to normalize the search area which is the number of squares in the grid (for example a (100 times 100) grid has search area 10,000).Success rate: The algorithm may sometimes be unsuccessful at connecting all the points. For example, the cells may miss a point early on and move far away from that point, making it almost impossible to ever find that point. There may also simply not be enough cytoplasm for two far away cells to fuse into one. For each number of cells (1, 9, 25, 100), we try various sizes/amounts of cytoplasm and compute the proportion of trials (out of 100) that successfully terminate within 10 million iterations.Figure 4(a) Proportion of trials that are successful versus the search area as a percentage of cytoplasm for trials with 1, 9, 25, and 100 cells. (b) Length of solutions versus the search area as a percentage of cytoplasm. (c) Number of iterations versus the search area as a percentage of cytoplasm. Failed trails excluded from graphs.Full size imageIn Fig. 4a, we see that the black line (100 cells) extends much further to the right than the cyan line (one cell). Thus, the more cells there are, the larger of a search area we can explore. This is mainly because with more cells, we can spread out our cytoplasm instead of having it be concentrated in certain areas.Solution length Another important metric to consider is the solution length. We measure how good the solution is by counting the amount of cytoplasm when the algorithm terminates. We ignore any cytoplasm that is part of a disjoint cell that does not contain an active zone, or in other words is separate from the cell that actually forms the tree. In Fig. 4b, we see that as the search area as a percentage of cytoplasm increases, the quality of the solution improves. This is because there is comparatively less cytoplasm to begin with. In addition, we see that as the number of cells increases, it is possible to find a better solution. This correlates with the earlier result shown in Fig. 4a that using more cells allows solutions to be found with less cytoplasm. Trials with 100 cells found the shortest solutions (rightmost data point).Run time The last metric we consider is the run time. We consider the true number of iterations the algorithm runs for. By true iterations, we account for the fact that in a parallel algorithm or set of real-world Physarum organisms, multiple cells will be introducing and moving bubbles at the same time. As a result, the iteration count is scaled by the number of disjoint cells. In Fig. 4c, we see that the more cells there are, the lower the number of iterations. This may be because with more cells, the cytoplasm is more spread out and therefore there are less out of the way points which may take a very long time to find. From the above analysis, we see that using more cells allows us to explore bigger search areas, find shorter solutions, and solve problems faster.ApplicationsThe behavior of Physarum and the models it has inspired have found many different uses among which are drug repositioning, developing bio-computing chips, approximating highways layouts, and designing subway systems2,8,9,10. In order to illustrate the operation of the Physarum Steiner Algorithm and demonstrate its applicability to real world problems, we consider the following:

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Network design We use the algorithm to develop a road network in the United States.

Obstacle-avoidance We use the algorithm to solve the obstacle-avoiding Euclidean Steiner tree problem.

VLSI routing We use the algorithm to route connections between pads in chip design.

Topological surfaces We discuss the algorithm’s adaptability to varying surfaces and boundaries by considering topological surfaces such as the sphere, torus, Klein bottle, and (mathbb{RP}mathbb{}^2).

Road networks The Physarum Steiner Algorithm can be used to build a road network between the largest one hundred cities in the lower 48 United States (excluding Alaska and Hawaii). We use data32 containing the longitude and latitude of the 100 cities with the highest population to generate a rectangular grid of active zones.We spawn diamond-shaped cells of size 7 with a spacing of 1 as shown in Fig. 3. After many iterations, the final road network is shown in Fig. 5a. The algorithm is particularly suited to the problem of designing transportation systems because it first connects all the points before optimizing the network into a tree. The algorithm can thus be terminated early depending on how much redundant connectivity is desired in the transportation network.For example, in Fig. 5b, we have a network that still contains loops in high-traffic routes between the Bay Area, Los Angeles, and Las Vegas. If we allow the algorithm to continue running, we will get networks with fewer loops and eventually a tree.Figure 5Road network generated by the algorithm. (a) shows the final solution with no loops while (b) displays a solution that has some redundancy resulting from terminating the algorithm early.Full size imageWe believe that this algorithm can be applied to many similar problems such as designing fiber optic or electric cable networks. Moreover, as discussed in the last section, it will be very interesting to compare this study to that of33, where in vitro slime mold is used to investigate the construction of transportation networks over a USA map.Obstacle avoidance Due to the cellular automaton nature of this algorithm, it is straightforward to define boundaries or other obstacles that need to be avoided. This is very useful in cases where certain areas need to be avoided such as a lake or the boundary of a county. And, unlike the current standard obstacle-avoiding Euclidean Steiner algorithm27 which takes multiple hours for graphs with only 150 points, the run time of the Physarum Steiner Algorithm is not affected by the need to avoid obstacles.As an example, consider the boundary given in Fig. 6a. Here, the grey area represents the search area and the 100 white squares outlined in dark grey are the points. There are many possible real world situations similar to this. For example, the grey area could be a county and all the points represent homes that subscribe to a certain Internet service provider (ISP). The big white area in the center could be a lake and the smaller white area could be a dog park. The ISP company could utilize the Physarum Steiner Algorithm to find networks to lay fiber optic cables.Figure 6(a) Sample boundary map. Grey area is search area and small white squares are points. (b) Initial deployment of Physarum. (c) Solution at the end of the foraging stage. (d) The final network.Full size imageWe begin by deploying square Physarum cells of size 7 in Fig. 6b. In Fig. 6c, the cells begin to fuse, share intelligence, and find all the points. We choose a solution that still has some loops to increase reliability and ease of future modification to the network. Our final solution is shown in Fig. 6d. This solution is generated in 300,000 iterations and less than 30 seconds.VLSI Routing for VLSI (very large-scale integration) chip design19 is one of the largest real-world manifestations of the Steiner tree problem, especially as modern chips may contain upwards of 10 billion transistors. Solving the VLSI problem would require additional modification to the Physarum Steiner Algorithm since VLSI design is typically presented as a group Steiner tree problem and has very large problem sizes, the Physarum Steiner Algorithm. Due to the usage of a square grid in the Physarum Steiner Algorithm, the algorithm is easily applied to find rectilinear networks such as those required for routing chips. In addition, our empirical results suggest that it should scale well to the large problem sizes common in chip design. Using data from34, we consider a set of pads that need to be connected. In Fig. 7, we represent the pads as active zones and generate a tree between them.Figure 7(a) Graphical representation of 131-point VLSI data set34. (b) Routing solution obtained by the Physarum Steiner Algorithm.Full size imageTopological surfaces Finally, the Physarum Steiner Algorithm is easily applicable to finding Steiner trees on other topological surfaces. Given the nature of the algorithm, we are able to map coordinates on one edge to another. In Fig. 8, we use square identification spaces to find Steiner trees on the torus, sphere, Klein bottle, and (mathbb{RP}mathbb{}^2). These solutions on identification spaces can be seen on a torus and a sphere in Fig. 8a,b.Figure 8Steiner trees on topological surfaces we defined by identification space and obtained through our code. (a) Torus. (b) Sphere. (c) Klein Bottle. (d) (mathbb{RP}mathbb{}^2). Images generated using manim35.Full size imageConcluding remarksWe have presented here a novel explore-and-fuse approach to solve problems that cannot be solved by traditional divide-and-conquer.Our approach is inspired by Physarum, a unicellular slime mold capable of solving the traveling salesman and Steiner tree problems. Besides exhibiting individual intelligence, Physarum can also share information with other Physarum organisms through fusion. These characteristics of Physarum inspire us to spawn many Physarum organisms to independently explore the problem space and collect information in parallel before sharing the information with other organisms through fusion. Eventually, all the organisms fuse into one large Physarum that can then globally optimize using the knowledge collected earlier. Explore-and-fuse can be seen as a less rigid form of divide-and-conquer that can better handle problems that cannot be decomposed into independent subproblems.We demonstrate the explore-and-fuse approach on the Steiner tree problem by creating the Physarum Steiner Algorithm. This algorithm has the ability to incrementally find Steiner trees. The first solution tends to contain many loops that are removed with additional iterations of the algorithm. This incremental improvement is particularly useful for applications such as road and cable networks where some degree of redundancy in the connectivity is desired. In particular, it will be very interesting to compare our work to the the one done in33 where a protoplasmic network created by in vivo Physarum is considered to study and asses show the slime mold imitates the United States Interstate System. We foresee several applications of our algorithm in this direction, leading to similar findings to those appearing in the studies done in33.The algorithm operates on a rectilinear grid and is particularly applicable to rectilinear Steiner tree problems such as those that often arise in VLSI design. In addition, the algorithm performs well on the obstacle-avoidance Euclidean Steiner tree problem.In comparison to the existing Physarum-inspired Steiner tree algorithms described in Section “The Steiner tree problem”, the Physarum Steiner Algorithm uses a completely different mechanism. While the existing algorithms use a system of equations modeling the thickening of tubes as protoplasm flows through them, the Physarum Steiner Algorithm is based on modeling Physarum spatially moving around a grid and finding a tree between squares of the grid. In addition, it should be noted that the approach taking in existing algorithms would not work on the Euclidean Steiner tree problem as in the Euclidean Steiner tree problem, there are an infinite number of possible points that could be part of the Steiner tree (essentially any point in the plane). It would not be possible to write a system of equations representing the infinite possible points and edges. In the future, we believe further work could be done to improve the Physarum Steiner Algorithm. Since the Physarum Steiner Algorithm is an approximate algorithm, future improvements could be made so its approximations are closer to the actual optimal solution. In addition, it would be interesting to see this approach applied to other problems Physarum has been able to solve such as the traveling salesmen problem. More

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Study subjectsWe conducted foraging experiments on strepsirrhines (Nindividuals = 18) at the Duke Lemur Center (DLC), North Carolina, from February to November 201513. Our sample includes six fat-tailed dwarf lemurs (3–16 years of age, 3 males, 3 females), six gray mouse lemurs (3–7 years of age, all female), and six aye-ayes (17–32 years of age, 2 males, 4 females). Because these species are solitary and nocturnal, most animals were housed singly and were kept on a reversed light cycle such that they were active and could be tested during the day. Housing conditions were similar for all individuals, and they were all fed daily in a similar manner with a diet that included fruits, vegetables, meal worms, and monkey chow (details in13).All vervet data were collected on wild animals (Nindividuals = 12) at Lake Nabugabo, Uganda (0°22′–12° S and 31°54′ E) during four separate field seasons (April-June 2013, Double Trapezoid array, M group15; June–September 2013, Pentagon array, M group24; August–September 2015, Z-array, M group12; July–August 2017, Pentagon array, KS group25). M group was composed of between 21–28 individuals, containing 2–3 adult males, 7–9 adult females, 2 subadult males, 1–3 subadult females, and 9–12 juveniles and infants. KS group was composed of 39–40 individuals including 5 adult males, 11 adult females, 3 sub-adult males, 5 sub-adult females, and 15–16 juveniles and infants. All individuals were reliably identified based on natural features (details in12,15,24,25). Outside of foraging experiments, wild vervets were not provision fed.All Japanese macaque data (Nindividuals = 10) were collected at the Awajishima Monkey Centre (AMC), Awaji Island, Japan (34°14′43.6″ N and 134°52′59.9″ E) between July and August 2019 (Z-array26). AMC is a privately-run tourist and conservation center visited by a large group of free-ranging Japanese macaques (~ 400 individuals) called the “Awajishima group”47. The group is composed of different-aged individuals of both sexes, with bachelor males and bachelor male groups living around the periphery48. The Awajishima group forages on wild foods for much of their dietary requirements but is also provision-fed a combination of wheat and soybeans, supplemented with peanuts, fruits, and vegetables twice daily for ~ 10 months of the year (details in47,49,50).Study designNavigation arraysThe strepsirrhines and vervets were tested on a “double-trapezoid” shaped multi-destination array with six feeding platforms13,15, modified from17 (Fig. 1a), where there were 720 possible routes (6!). Three different double-trapezoid arrays were built to account for differences in body size: one for the smaller dwarf and mouse lemurs, one for the mid-sized aye-ayes, and one for the larger, wild vervets. Arrays were scaled such that the distance from platform 1–2 (the shortest distance between targets) was approximately twice the body length of the subject species. Vervets were additionally tested on a Z-shaped array with six feeding platforms (720 possible routes, Fig. 1b12), and a pentagon-shaped array with five feeding platforms (120 possible routes, Fig. 1c24,25,46). Japanese macaques were tested on an identically sized Z-array26.Figure 1Design of the navigational arrays used, with (a) the Double Trapezoid array used for Cheirogaleus medius, Microcebus murinus, Daubentonia madagascariensis, and Chlorocebus pygerythrus. Three different arrays were built and scaled to the body size of animals (see “Methods”). (b) The Z-array used for C. pygerythrus and Macaca fuscata. The same size array was used for both species because they are similar in adult body lengths (vervet mean range from four sites: 34.5–42.6 cm51, Japanese macaque mean range from six sites: 48.9–59.7 cm52. (c) The Pentagon used for C. pygerythrus. Distances here are unitless but roughly proportional to the body size of each species tested. Created in R version 4.0.4 and ProCreate.Full size imageFor strepsirrhine trials, DLC staff captured individuals in their enclosures and transported them in padded crates to the testing room. The dwarf and mouse lemur array was set up in a specially designed box (0.91 × 1.83 m) with a small compartment to contain strepsirrhines for rebaiting between trials. The aye-aye array was set up on the ground in a room measuring 2.44 × 4.27 m, where subjects stayed during the duration of their daily trials13. Vervet and macaque trials occurred when individual monkeys voluntarily left their group to participate in foraging experiments alone. Vervet arrays were set up using wooden feeding platforms (0.75 m long, 0.75 m wide × 0.75 m high) placed in an outdoor clearing measuring roughly 10 × 14 m in the home range of the study group. Japanese macaque arrays were also set up using small wooden feeding tables (0.40 m long, 0.30 m wide, 0.21 m high), covered in green plastic labeled with the platform number. Two identical arrays were built in neighbouring provision-feeding fields at the AMC (Near Lower Field: ~ 10 × 35 m, and Far Lower Field: ~ 15 × 45 m).In these studies, all platforms were baited with a single food item. The reward used varied by species (strepsirrhines: grape piece, apple piece, honey, agave nectar, or nut butters, vervets: slice of banana, piece of popcorn; macaques: single peanut or piece of sweet potato). Strepsirrhines have sensory adaptations for using olfaction to locate food53, while the cercopithecoids are heavily reliant on vision to locate resources54, so we ensured that each platform was baited with identical food items within a trial that smelled and looked the same to avoid biasing where the animals chose to go. Platforms for the wild monkeys were not rebaited between trials until all animals were ≥ 20 m away and the entire sequence could be rebaited before their return15,24,25,26.For all species, we started a trial when the tested individual entered the array and took the reward at a platform. We then recorded each successive platform visit (including revisits to empty platforms) until all rewards had been collected ending the trial. In our analyses, we included a total of 852 trials collected over six navigational experiments, completed by 40 unique individuals (18 lemurs, 12 vervets, 10 macaques) (Table 2).Table 2 Individuals and trial sample size included in the analysis.Full size tableData simulationsIn addition to empirically collected data, we simulated agents learning to travel efficiently in the same set of arrays using a simple iterative-reinforcement learning model based on the one used by Reynolds et al.6 to test for traplining behavior in bumblebees. In this model, agents move randomly between locations in an array until they visit all locations, then reset for another trial. If the agent completed a trial by travelling less distance than on previous trials, the probability of the agent repeating location-to-location transitions that occurred in that trial increased for future trials by a reinforcement factor. Initial transition probabilities were inversely proportional to the distance between two locations. Unlike Reynolds et al.6 our simulated agents started at a random location and were not required to return to that location to complete the trial. This matches the trial structure used in our experiments (open-TSP), and reflects multiple central place foraging patterns in primates55. Finally, agents could not return to the location they had just come from, using an “avoid the last location” behavioral heuristic observed in nectivores56,57, which prevented agents from getting stuck in “loops” between two locations (S1 Simulation Validation).Within each of the arrays used to collect empirical data, we ran simulations with reinforcement factors of 1 (no reinforcement), 1.2 (mild reinforcement), and 2 (strong reinforcement). For each array and reinforcement factor combination, we ran 100 agents that each completed 120 trials, where there was an equal probability of starting each trial at any location. Then, for each array and reinforcement factor combination, we ran 100 additional simulations per species tested in the given array, where the probability of starting a trial at any location was equal to the empirically observed location-starting probabilities of the respective species.These simulations were designed to help us test predictions of our two hypotheses regarding primate learning and decision making within the arrays. If primates learn to solve navigational arrays efficiently by reinforcing movements between platform pairs, they should exhibit overall greater receptiveness in their sequences of location visits than reinforcement factor 1 simulations, and a greater decrease over time in total distance travelled to complete the arrays. If primates are pre-disposed to navigate arrays using heuristics, they should exhibit shorter distances travelled on initial trials than in simulations.Data analysisFrom the raw sequences of locations visited in each trial, we calculated two metrics: minimum distance traveled, and the proportion of platform revisits that occurred within identical 3-platform visit sequences (determinism-DET)18. All calculations were done using R version 4.0.458 and packages rstan59 and tidyverse60. A fully reproducible data notebook containing this work, as well as all analyzed data, is available at https://github.com/aqvining/Do-Primates-Trapline. All figures were created by AQV in R version 4.0.4 and ProCreate.Distance traveledTo calculate minimum distance traveled, we created a distance matrix for each resource array containing the relative linear distance between any two resource locations. These minimum linear distances approximate the distances traveled by the animals, which may not necessarily be linear. We then summed the linear distances for all transitions made in a trial. Because resource arrays were scaled to the subject species’ body size, these relative distances were standardized.DeterminismGiven a sequence of observations, Ayers et al.63 defines determinism (DET) as the proportion of all matching observation-pairs (recurrences) that occur within matching sub-sequences of observations (repeats) of a given length (minL). This metric has been previously used to distinguish sequences of resource visitation generated by traplining behaviour from sequences generated by known processes of random movement within a given resource array18,61,62. It has several advantages in the analysis of foraging patterns, including the ability to detect repeated sequences between non-consecutive foraging bouts, imperfect repeats in sequences (i.e., omission or addition of a particular site), and distinguishing between forward- and reverse-order sequence repeats63.We adapted the methods of63 to calculate the number of recurrences and repeats generated by the sequence of location visits in each trial of our experiments and simulations. Based on an analysis of the sensitivity of DET scores to the parameterization of minL, we set minL to three for our calculations (S2 Sensitivity Analysis).Statistical analysesLearning ratesWe modelled distance travelled as a function of trial number, species, and individual. Metrics of animal performance on learned tasks are known to follow power functions over time and experience64, so we a priori applied log transformations to distance travelled and trial number, then fit a linear model. Thus, in the resulting model, the intercept can be interpreted as an estimated distance travelled on the first trial and the slope can be interpreted as the exponent of a learning curve. We modelled species and individual effects on the intercept by summing an estimated grand mean (µ0), species level deviation (µsp,j), and individual level deviation (µid,i). We treated species and individual level effects on the learning rate parameter (slope) the same way, summing a grand mean (b0), species level deviation (bsp,j), and individual level deviation (bid,i). We estimated additional parameters for the variance of individual level deviations in intercept and slope (σµID and σbID, respectively). Finally, after finding residuals in an initial analysis to have variances predicted by trial number and species, we estimated a separate error variance for each species (σε,sp) and weighted the standard deviations of the resulting error distributions by dividing them by the square root of one plus the trial number.We set regularizing priors on the model parameters, assuming distances travelled would remain within one order of magnitude of the most efficient route, but not setting any strict boundaries. For the grand mean of the intercept, we used a normal distribution centered around twice the minimum possible distance required to visit all platforms in the array, with a variance of one. For the grand mean of the slope and all species and individual level deviations to the slope and intercept, we used normal distributions centered at zero with variance of one. For all error terms, we used half-cauchy priors with a location parameter of zero and a scale parameter of one. The full, hierarchical definition of the model is given in Eq. (1).$$Distance sim {mu }_{0}+ {mu }_{sp,j}+ {mu }_{id, i}+left({b}_{0}+ {b}_{sp, j}+ {b}_{id,i}right)Trial+ epsilon$$$${mu }_{0} sim mathrm{N}(4.78, 1)$$$${mu }_{sp}, {b}_{0}, {b}_{sp} sim mathrm{N}(mathrm{0,1})$$$${mu }_{id} sim mathrm{N}(0, {sigma }_{mu ID})$$$${b}_{id} sim mathrm{N}(0, {sigma }_{bID})$$$$epsilon sim mathrm{N}(0, {sigma }_{epsilon ,sp}/sqrt[2]{1+Trial})$$$${sigma }_{mu ID}, {sigma }_{bID}, {sigma }_{epsilon } sim mathrm{Half Cauchy}(mathrm{0,1})$$DeterminismTo compare DET between species, and between empirical and simulated data, we created a binomial model of expected repeats generated in a trial given the number of recurrences (Eq. 2).$$Repeats sim binom(Recursions, DET)$$$$DET= {logit}^{-1}(alpha)$$$$alpha={a}_{0}+Sp+Src+ Int+ID$$$${a}_{0}, Sp, Src, Int sim mathrm{N}(0, 1)$$$$ID sim mathrm{N}(0, {sigma }_{ID})$$$${sigma }_{ID}sim mathrm{Half Cauchy}(mathrm{0,1})$$where a0 is the mean intercept, Sp is one of four coefficients determined by the species (simulations are of the “species” which was used to assign its starting-location probabilities), Src is one of four coefficients determined by the source (empirical data and each level of reinforcement factor), Int is one of 16 interaction coefficients (each possible combination of Sp and Src), and ID is a varying effect of the individual. Because the length of a sequence affects DET, we limit our analysis of DET to the sequences generated by a subject’s or an agent’s first ten trials. Subjects that completed fewer than ten trials were excluded from this portion of the analysis. More

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

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

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