A regime shift from erosion to carbon accumulation in a temperate northern peatland

Peatlands are globally important ecosystems but many are degraded and some are eroding. However, some degraded peatlands are undergoing apparently spontaneous recovery, with switches from erosion to renewed carbon accumulation—a type of ecological regime shift. We used a palaeoecological approach to investigate and help understand such a switch in a blanket peatland in North Wales, UK. Our data show: (a) a rapid accumulation of new peat after the switch from the eroding state, with between 5.2 and 10.6 kg/m2 carbon accumulating since the beginning of the recovery which occurred between the late 1800s and early to mid‐1900s CE, with an average carbon accumulation rate in the new peat between 46 and 121 g C m−2 year−1; (b) three main successional pathways in peat‐forming vegetation and (c) hydrological changes with an increase to moderately high water‐tables after the switch that promoted new carbon accumulation as well as protecting vulnerable old carbon. External factors, including changes in climate and industrial activity, can only partially explain our results. Following previous studies, we suggest that internal ecosystem processes offer a substantial part of the explanation and interpret the switch to renewed carbon accumulation as a bifurcation‐type tipping point involving changes in the physical form of the eroded landscape. Synthesis. Our long‐term ecological data reveal a switch from a degraded peatland with active erosion and loss of carbon to a revegetated, wetter peatland accumulating carbon. The switch can be interpreted as a bifurcation tipping point. We suggest that external factors such as climate and pollution levels are important for setting suitable boundary conditions for peatland recovery, but internal mechanisms can explain the change in peatland state. Our study is the first of its kind to apply tipping point theory to the internal mechanisms linked to peat erosion and recovery and may help improve understanding of the trajectories of other peatlands in a changing climate.

Because they are large carbon (C) reservoirs-storing twice as much C as all the world's forests-there is growing interest in how peatlands function, so that their behaviour and C sink strength under a changing climate and different land uses may be modelled (Page & Baird, 2016). It is widely documented that many peatlands are degraded. In blanket peatlands, degradation frequently occurs as erosion, which results in loss of C and loss of important peatland habitats over centennial time-scales (Gallego-Sala & Prentice, 2013).
It is sometimes assumed that, once initiated, erosion will continue until all of the original peat mass has been removed (e.g. Wishart & Warburton, 2001). However, some blanket peatlands are undergoing apparently spontaneous recovery, switching from erosion to renewed C accumulation. Recent work has shed light on factors affecting peatland initiation (e.g. Morris et al., 2018), their responses to climate change (e.g. Charman et al., 2013) and the relative importance of autogenic and allogenic factors in controlling changes in the composition of peatland vegetation and rates of peat accumulation (e.g. Belyea, 2009;Belyea & Baird, 2006). Peatland initiation and re-initiation (the latter being synonymous with revegetation as shown in Figure 1) are types of ecological regime or state shift (Andersen, Carstensen, Hernández-García, & Duarte, 2009;Beisner, Haydon, & Cuddington, 2003;Folke et al., 2004), as is the switch from an intact peatland to an eroding one. In ecology, a regime shift may be defined as 'a sudden shift in ecosystem status caused by passing a threshold where core ecosystem functions, structures and processes are fundamentally changed' (Andersen et al., 2009). Compared to many ecosystems, such as shallow lakes and coral reefs where the causes of sudden changes have been revealed (see Folke et al., 2004), regime shifts in peatlands are poorly understood.
Blanket peatlands occur in oceanic and hyper-oceanic high-latitude regions where precipitation (mostly rainfall) is abundant throughout the year, causing water-logged conditions in which peat-forming plants (principally Sphagnum mosses and the cotton sedges Eriophorum spp.) thrive (Gallego-Sala & Prentice, 2013;Lindsay, 2010). Although some blanket peatlands may have formed in response to forest clearance in the Neolithic and Bronze Age, or earlier (e.g. Tallis, 1998), there is strong evidence that they are also natural phenomena as a result of climate shifts or soil-forming processes (Gallego-Sala, Charman, Harrison, Li, & Prentice, 2016;Lawson, Church, Edwards, Cook, & Dugmore, 2007;Tipping, 2008), with initiation dates extending as far back as 8,000-12,000 cal BP (calibrated years before present, with present defined as 1950). Erosion has been a feature of blanket peatlands in the United Kingdom for centuries and was reported as long ago as the early 19th century (e.g. Aiton, 1811).
Erosion may be associated with the developmental phase of the peatland-that is, it may be an autogenic phenomenon-but may also arise from natural and human-induced changes in environmental conditions (climate, land use and atmospheric pollution; Bower, 1962;Bowler & Bradshaw, 1985;Bragg & Tallis, 2001;Conway, 1954).
Blanket peatland erosion is characterized by the formation of gullies apply tipping point theory to the internal mechanisms linked to peat erosion and recovery and may help improve understanding of the trajectories of other peatlands in a changing climate.

K E Y W O R D S
bifurcation tipping point, blanket bog, carbon accumulation, palaeoecology and land-use history, peatland dynamics, peatland erosion, regime shift, spontaneous recovery F I G U R E 1 Landscape of erosion and revegetation. Photographs of the study site (see Figure 2) showing (a) actively eroding haggs and inter-hagg gullies. The haggs are ~1 m high. (b) Revegetation in wider gullies between haggs, acting to stabilize previously eroding peat. (c) Erosion of gully down to the mineral substrate (see mid and lower right of image) with revegetation, here a combination of mostly Juncus spp. and Sphagnum spp. (Bower, 1962;Clement, 2005;Wishart & Warburton, 2001), and gully networks may be linear (gullies subparallel to each other), dendritic or anastomosing. The last type of landscape is often termed a 'hagged peatland' (Figures 1 and 2), and usually occurs on lower gradient areas such as hilltops and plateaus ('hag' or 'hagg' usually denoting the 'islands' of uneroded peat found between gullies; e.g. Bowler & Bradshaw, 1985;Foulds & Warburton, 2007).
Many erosion complexes are showing signs of recovery, with peat-forming vegetation re-establishing, (a) on previously eroding bare-peat surfaces, (b) in areas where eroded peat has been deposited and (c) in areas of mineral ground exposed by the complete removal of peat in gully bottoms ( Figure 1). However, it is unclear whether revegetation is a temporary phenomenon in a landscape where erosion will ultimately remove all of the peat mass (Wishart & Warburton, 2001) or whether it can lead to the restabilization of the peatland and the infilling of gullies (Crowe, Evans, & Allott, 2008;Evans & Warburton, 2007). Recent work by Harris and Baird (2019) has shown that the location of the principal plant types in a recovering hagged peatland in North Wales (UK) can be predicted with some accuracy using hydrological and micrometeorological metrics derived from a fine-scale topographic model of the peatland. Although useful in indicating the conditions required for revegetation to occur, such an approach is necessarily 'static' because it does not reveal when revegetation started or those factors unrelated to the topography that may have been involved in the change in system state: the switch from erosion to renewed C accumulation. Similarly, successional changes following the switch, and the degree to which revegetation has led to C accumulation, cannot be obtained from a study of current vegetation distribution. To address these limitations, and in the absence of long-term monitoring, we took peat cores from the same peatland studied by Harris and Baird (2019) and used a high-resolution palaeoecological approach similar to that of Taylor, Swindles, Morris, Gałka, and Green (2019) and Swindles et al. (2015) to reconstruct the recent ecohydrological history of the peatland. Specifically, we sought to address the following key questions: (a) When did the recovery start and what are the possible mechanisms? (b) What successional processes have occurred? (c) Have water levels relative to the ground surface changed or remained stable since the start of the recovery? and (d) How much peat (and associated C) has accumulated since recovery started?

| MATERIAL S AND ME THODS
The study was carried out on a hagged area of blanket bog in the Migneint in the Upper Conwy catchment, North Wales, UK (latitude 52.97°N, longitude 3.84°W). The peatland site ( Figure 2) lies at an altitude of approximately 500 m a.s.l. Average rainfall is 2,100 mm/year, and average January and July temperatures are 2.2 and 12.8°C respectively (Green et al., 2017;Swindles et al., 2016).
The peat overlies thin glacial deposits, and Cambrian mudstones and Ordovician siltstones (Lynas, 1973). Little is known about the historical management of the area other than the site has been used for grazing, and some areas just beyond the study site were drained with shallow (~50-70 cm deep) ditches constructed between the 1940s and 1970s  and Polytrichum commune Hedw. There are two main revegetation areas (Figures 1 and 2): wide gullies in which new peat has established mostly on mineral ground, and the areas around the edge of the main hagged area, where new peat has established in some places on bare, formerly eroding peat, and in some places on mineral ground. We collected four peat cores from the two areas (MIG1 from a wide gully and MIG2, MIG3 and MIG4 from the edge of the main hagged area, Figure 2). Large diameter cores of 15 cm were collected using the scissor method described by Green and Baird (2013), to avoid compaction and disturbance of the loosely consolidated peat. The MIG1 and MIG4 cores were collected from areas where visual evidence suggested all of the old peat had been stripped away and new peat had formed directly on mineral ground: exposed peat faces at the edges of the gully near to the coring locations showed subpeat mineral material (Figure 1c), while depth probing with an auger suggested the peat was 40-50 cm deep. However, the 40-to 50-cm cores did not reach the mineral material and neither could we be certain that there were no traces of old peat between the new peat and mineral material, although we think it is likely that new peat formed directly on mineral material at MIG1 and MIG4. More information is provided on this point in Appendix S1. Initial visual inspection of MIG2 and MIG3 cores suggested that they consisted of newly accumulated peat on top of a former erosion surface, which marked the top of old, Holocene peat. The dating (discussed below) was used to check this interpretation. The dating was also used to ascertain whether there was old peat at the base of cores MIG1 and MIG4 or whether the samples contained new peat only.
We analysed the cores in several ways to address the research questions. To help answer the first question, we dated the cores using 210 Pb (contiguous 1-cm intervals) and Accelerator mass spectrometry (AMS) 14 C. 210 Pb ages were calculated using the Constant Rate of Supply model (Appleby, 2001;Appleby & Oldfield, 1978).
We obtained additional dates using AMS 14 C, particularly to confirm the date of uneroded peat below the newly forming peat.
We applied the age-depth model package rbacon v.2.4.2 using Bayesian modelling to integrate 210 Pb and 14 C dates (Blaauw & Christen, 2011;R Core Team, 2020). Contiguous, 1-cm down-core samples were analysed for plant macrofossils to characterize vegetation development and address the second question. The method used follows Gałka et al. (2017), with seeds and fruits assessed using counts, and other plant remains (e.g. leaves, roots) estimated as volume percentages. To answer the third question, we analysed 1-cm thick samples taken every 4 cm for testate amoebae to reconstruct changes in water-table depth. Analysis followed Booth, Lamentowicz, and Charman (2010), and the water-table reconstruction was calculated using the pan-European transfer function (Amesbury et al., 2016). To answer the fourth question, we measured the dry bulk density and the C content of the peat for contiguous 1-cm samples. Analysis for peat dry bulk density, organic matter content through loss-on-ignition and the carbonnitrogen quotient through elemental analysis followed Chambers, Beilman, and Yu (2011). Apparent C accumulation rates in the newly formed peat were calculated by multiplying the mass per unit area of each depth increment by its C concentration and then dividing by the difference between the bounding dates of the increment, as obtained from the age-depth model (Tolonen & Turunen, 1996). Apparent C accumulation rates were not calculated beyond the limit of 210 Pb dating. Full information on the methods is provided in Appendix S1.

| RE SULTS
Below, we discuss the results in relation to each of the research questions and with reference to Figure 3.

| When did spontaneous recovery start and what are the possible mechanisms?
Radiocarbon dates for MIG2 and MIG3 confirm that the lower part of the peat profile in each case formed around 7,000 cal BP, and represents the remains of the original Holocene peat mass, with younger peat from that mass removed by erosion. The agedepth model indicates that the oldest 'new' peat formed in 1875 CE ± 45 years in MIG2 and 1906 CE ± 23 years in MIG3 (both record the boundary between old and new peat). Taking a conservative approach, and assuming the basal new peat may represent 'false starts' in the system before continued revegetation (see conceptual model and accompanying discussion in Section 4.3), spontaneous recovery started sometime between 1875 ± 45 and 1931 ± 21 for MIG2, and between 1906 ± 23 and 1934 ± 10 for MIG3. The oldest peat in MIG1 is 1922 ± 14 years, and in MIG4 it is 1950 CE ± 26 years, suggesting all of the peat at these locations is new and that revegetation started at, or sometime before, these dates. However, because the boundary between the new peat and underlying mineral material or old peat was not recorded at MIG1 and MIG4, estimates of the timing of the switch are conservative. Combined, the data suggest that the majority of the new peat started accumulating from around the late 1800s and early to mid-1900s CE, with an apparent acceleration in the last 40 years (see Section 3.4 and 4.1 for discussion on C accumulation). We searched for regional events occurring around the date of spontaneous recovery and this onset of more rapid C accumulation, and briefly outline them below.

| Change in climate
Climate warming occurred in mid-to high-latitudes in the Northern Hemisphere after the Little Ice Age from the middle of the 19th century to the present, which reversed the long-term cooling trend of the past 5,000 years (Ljungqvist et al., 2019;Masson-Delmotte et al., 2013). The Central England Temperature record-the longest record in the United Kingdom-shows an increase in annual average temperature of approximately 1.5°C since 1850 CE (Parker, Legg, & Folland, 1992), and centennial trends show increased temperatures in all seasons since the record began in 1659 CE, with greatest increases in winter and autumn, and associated increases in growing degree days (Kendon, McCarthy, Jevrejeva, Matthews, & Legg, 2019; see Appendix S1). The timing of the post-Little Ice Age and 20th century warming broadly coincides with the switch seen in our data, suggesting that there may be some climatic influence on the recovery and increase in rates of C accumulation.

| Change in industrial activity
There is a long history of below-ground and open-cast mining in north-west Wales, with mining of the Ordovician slate veins predating the Medieval Period. Activity increased substantially at the end of the 18th century; quarry output peaked in the late 19th century, decreased by the 1920s, and the majority of quarries had closed by the 1960s (Hughes, Horak, Lott, & Roberts, 2016;Prichard, 1942).
The nearest quarry to the site (~1.5-km away) was worked from 1870 for about 50 years. Given the timing of the regional industrial activity, it is possible that dust fertilization from mining contributed to the shift to peat accumulation. Elemental analysis of the peat cores (data not shown here) revealed low concentrations of Fe and F I G U R E 3 Peat characteristics and palaeoecological data for (a) MIG1, (b) MIG2, (c) MIG3, (d) MIG4. For each core, organic matter content (%), dry bulk density (g/cm 3 ) and C accumulation rate are shown alongside the core photograph; also shown are key taxa from the plant macrofossil data (displayed as percentage or count data); charcoal abundance; and water-table depth reconstructions from testate amoebae. All data are plotted against depth (cm) with an age scale (cal. BP) shown for reference. The dashed grey bar in MIG2 and MIG3 represents the boundary between old (below) and new (above) peat. The location of the radiocarbon dates are shown by squares (black for old, Holocene peat in MIG2 and MIG3; and grey for recent peat in MIG1 and MIG4)

| Change in grazing regime
Sheep farming in the Welsh uplands was a major industry from the 13th century onwards. Since the 1850s, there has been an increase in Welsh sheep populations from 2.5 million in 1867 to a peak of ~12 million at the end of the 1990s (Welsh Government, 2018).
Estimates of wild animal densities are not available, and although cattle are important domestic livestock in Wales, they are less commonly grazed in the uplands. Given that sheep densities were still increasing in the 18th, 19th and 20th centuries, changes in grazing are unlikely to have contributed to the shift to peat accumulation and we dismiss it here as a possible primary factor in the switch.
Other possible external factors were also dismissed. For example, there is no evidence of historical peat cutting in the region until the 1970s (Evans, Young, & Jenkins, 2008), and there is low charcoal abundance in the macrofossil data and no unconformity in peat accumulation (beyond the unconformity observed between old and new peat), indicating minimal impact of fire on peat accumulation. Therefore, apart from potential climate amelioration and a fertilization effect from quarry activity, we could not identify any obvious cause for the switch.
Further details on external factors are provided in Appendix S1.

| What successional processes occurred?
We identified three successional pathways in the macrofossil data that differed according to whether the revegetation occurred on mineral ground or bare, formerly eroding peat. MIG2 and MIG3 record the same broad successional pathway after the shift, with E. vaginatum succeeded by S. fallax with a later increase in Cyperaceae ( Figure 3). Both cores represent revegetation on formerly eroding bare peat. MIG1 and MIG4 represent revegetation on mineral ground (probably-see Section 2) and both record broadly similar successional pathways, but with a difference in dominance. MIG1 shows a transition from Juncus with S. fallax to dominance by P. commune; and MIG4 records a transition from herbaceous species to dominance by S. fallax, with an almost continuous presence of Juncus. The complete macrofossil record for each core is provided in Appendix S1.

| Have water levels changed or remained stable since spontaneous recovery?
When revegetation first occurred, water-tables were relatively deep at ~25-10 cm meaning they were deep within the existing peat mass or fell into the mineral material below. After recovery, water-tables were moderately high and stable with some evidence of standing water (e.g. Arcella discoides (Ehrenberg 1843) in MIG4) and nutrient-poor conditions, typical of blanket peatlands.

| How much peat and associated C has accumulated since spontaneous recovery?
There was a rapid accumulation of peat after the switch, with a peat is underlain by older remnant peat, as is the case at MIG2 and MIG3, the decay losses from this older peat (even if protected to some extent by a rising water-table following the switch) need to be combined with the rates of new peat addition to obtain net rates of C accumulation. However, such losses are difficult to estimate retrospectively (Young et al., 2019). At MIG1 and MIG4, it is likely that all old peat was eroded away before the new peat developed (see Section 2 and Appendix S1). Therefore, our figures for net C addition for these locations are the same as new C accumulation, and are conservative because we did not reach the base of the new peat. Uncertainty in the age models for all four cores means that there is associated uncertainty in the C accumulation rates (see Appendix S1). Nonetheless, combined, our data show that new peat is rapidly accumulating, while at the same time, older remnant peat is now protected from rapid aerobic decay by a higher water-table.

| D ISCUSS I ON
Palaeoecological studies from peatlands are common but these typically focus on long-term changes in the peatland or on using the peat as an archive of regional climate change (e.g. Blundell, Hughes, & Chambers, 2018;Milner et al., 2016). Instead, we use a fine-scale palaeoecological approach that allows us to understand recent peatland behaviour and regime shifts. The only similar study done on blanket peats that we are aware of is by Crowe et al. (2008) which provided useful insights into revegetation after erosion, but the cores were not dated, and the analysis focused mostly on vegetation changes rather than water-table and C accumulation. Our work complements other fine-scale palaeo studies such as Swindles et al. (2015) and Taylor et al. (2019) but differs from them in the type of peatland studied and the nature of the ecological dynamics (neither looked at recovery from erosion).

| Recent carbon dynamics
Our data show that new peat is rapidly accumulating after the switch from the eroding state, while at the same time, older remnant peat is becoming protected from rapid aerobic decay by a higher watertable. The timing of the switch to new C accumulation between the late 1800s and 1930s is earlier than other UK sites where revegetation has been occurring from the 1950s to 1970s CE onwards (e.g. the Pennines, UK- Evans & Warburton, 2007), although evidence of the onset of revegetation in these other areas is partly anecdotal (M. Evans, pers. comm.). We have identified when revegetation first occurred in parts of our site, but the revegetating area is expanding and some areas of bare peat have yet to undergo a switch to the revegetated state (e.g. areas to the south of our core sites, Figure 2).
The transition from erosion to revegetation, and the accumulation of new C, is therefore an ongoing process. It can be misleading to compare the rates of C addition, as new peat, with rates of net C accumulation reported from other studies because the latter includes decay losses from older, underlying peat. However, as we note above, the rates of C addition recorded for the two cores with no remnant old peat are equivalent to net C accumulation (MIG 1 and MIG4). Therefore, it is possible to compare our data from these cores  Loisel et al., 2014). In our cores, the average C accumulation was between 46 and 121 g C m −2 year −1 . Estimates of more recent apparent rates of C accumulation in northern peatlands are often higher, for example 51-149 g C m −2 year −1 (Piilo et al., 2019); however, these higher rates are, in part, due to an artefact known as the 'acrotelm effect'. Even under a constant climate, rates of C accumulation calculated for near-surface peat layers produce an apparent increase (Clymo, Turunen, & Tolonen, 1998;Turner, Swindles, & Roucoux, 2014;Young et al., 2019). This is caused by the younger litter and peat near the peatland surface having undergone less decay and decomposition than deeper layers. Unfortunately, this effect is very difficult to correct for (Young et al., 2019).

| The effects of changes to the climate and of industrial activity
Of the external factors that we considered, only two-climate change and quarrying-could plausibly explain our results, but even then, probably only partially. The timing of changes in climate and quarrying approximately coincide with the switch and rapid peat growth, but both factors require additional mechanisms to fully explain the data as we discuss below. This led us to consider whether a loss of resilience of the eroding state, due to changes in the way rainwater collects and flows through the erosion gullies, might also offer an explanation for the switch.
Our data meet the requirements of the definition of a shift to a different regime or state given in the introduction; that is, they suggest a wholesale change in how the system functions (it is 'qualitatively different'-see Lenton, 2013). In some peatlands, yearon-year changes between C accumulation and loss may occur (e.g. Roulet et al., 2007) but these reflect an essentially stable system responding to variability in driving (boundary) conditions (e.g. meteorological), and, possibly, internal system noise (stochasticity-see Lenton, 2013). In contrast, at our study site we see a fundamental change in how the peatland behaves, from a condition of long-term C loss, with bare eroding surfaces and a patchy vegetation cover vulnerable to 'wash out' (see below), to one with a spatially continuous vegetation cover, higher water-tables and sustained (year-on-year) peat and C accumulation.
At large spatial scales, climate is the dominant control on peatland initiation and peat accumulation (Charman et al., 2013;Morris et al., 2018). For example, a widespread increase in C accumulation rates over the past millennium has been attributed to increased plant productivity linked to climate warming (Charman et al., 2013;Gallego-Sala et al., 2018;Loisel et al., 2014;Piilo et al., 2019;Yu, Beilman, & Jones, 2009;Zhang et al., 2018). However, simply matching an increase in rates of C accumulation with recent changes in climate can be misleading because of the acrotelm effect noted above. Therefore, while it is possible that a warming climate from the middle of the 19th century to the present has provided favourable conditions for plant growth, leading to plant productivity exceeding decomposition, we cannot unequivocally attribute the switch and period of rapid peat accumulation to this amelioration. In addition, especially at smaller scales, for peat to accumulate, site-specific factors need to be suitable (e.g. local topographic conditions creating suitable hydrological conditions; Zhang et al., 2018) and peat accumulation at the site scale cannot therefore be explained solely by climate.
It is also possible that mining activities in the 19th and 20th centuries provided a mild fertilization effect and increased plant productivity, contributing to the switch to peat accumulation. As we note above, mining activity in the region around the field site coincided with revegetation and peat accumulation, and an increase in Fe and K concentrations in the peat. Mining dust can increase the base mineral input and nutrient supply to peatlands (Gałka, Szal, Broder, Loisel, & Knorr, 2019;Ireland, Clifford, & Booth, 2014), and there is evidence of high C accumulation rates related to dust supply (Kylander et al., 2018). On bare, eroding peat surfaces, input of mineral-rich dust can promote the growth of minerotrophic wetland plant species (e.g. Juncus, Carex) or species with high nutrient-use efficiency (e.g. McGraw & Chapin, 1989), both of which can stabilize the peat surface for Sphagnum to re-establish (cf. Paal, Vellak, Liira, & Karofeld, 2009). Indeed, peatland restoration programs often include fertilization of bare peat to encourage nurse species to reestablish (e.g. Alderson et al., 2019;Yorkshire Peat Partnership, n.d.).

E. vaginatum;
The successional pathways at the study site show initial colonization by E. vaginatum and J. effusus, which may have acted as nurse species before S. fallax dominates (Figure 3). However, given that the erosion had exposed the mineral ground in places, it is unlikely that external nutrient enrichment would be needed for these vascular plants to establish. Continued dust input through mining activities would not be conducive to Sphagnum growth because particulate pollution slows growth through a range of physiological and morphological responses (Farmer, 1993;Ireland et al., 2014). However, S. fallax-the dominant Sphagnum species at the site-is a common species in drained and damaged peatlands (e.g. in Central Europe; Gałka & Lamentowicz, 2014;Marcisz et al., 2015;Šímová et al., 2019) and there is evidence that it can tolerate higher mineral levels, increased nutrient supply and some pollution (Kooijman & Kanne, 1993;Limpens, Tomassen, & Berendse, 2003), and mining activity in the region slowly declined from the turn of the 20th century. Changes in climate and quarrying, although probably implicated in the switch, do not therefore provide simple and conclusive explanations for our findings.

| The loss of resilience of the eroding state caused by changes in the landscape and its hydrological behaviour
In addition to climate and quarrying, internal ecosystem processes might explain why the change in system state occurred. After gullies first formed, the erosion state would have been maintained because rainwater, concentrated by narrow gullies, would have eroded peat from the gully floors and sides and 'washed out' any vegetation trying to establish there. Over time, however, gullies would have widened until reaching a critical width, after which rainwater was no longer sufficiently concentrated to wash out new, peatforming vegetation. Our data do not allow us to say for certain if the shift between states was discontinuous, as is the case in systems exhibiting bi-stability or multiple stable states (e.g. Lenton, 2013;Petraitis, 2013), or whether it occurred as a continuous change in a monostable system (e.g. Lenton, 2013;Petraitis, 2013;Scheffer et al., 2009). However, as discussed below, the shift to a new state is consistent with a type of tipping point called a bifurcation. To paraphrase Lenton (2013), a bifurcation may be defined as the situation where a small, 'smooth', change to a control parameter-the width of an erosion gully in our case-causes a sudden qualitative or topological change to a system's behaviour (i.e. a fundamental change in its functioning). As the system approaches a bifurcation tipping point, it may exhibit critical slowing down (recovery from perturbation takes longer) and a greater variance in its properties (known as 'flickering'; Lenton, 2013). These indicators can act as an early warning that a system is approaching a tipping point (Scheffer et al., 2009).
In Figure 4 we envisage the study site undergoing morphological changes that reduce the resilience of the eroding state to perturbation (see below) until the switch occurs. We also propose the selfamplifying (positive feedback) mechanisms responsible for the change to renewed peat and C accumulation. In the left-hand column of Figure 4, we adapt a figure from Lenton (2013) that uses the analogy of a ball in a 'stability landscape' to illustrate how the system moves towards a bifurcation-type tipping point. The x axis on the landscape represents the system state, which initially has two depressions or bowls, also called 'potential wells'. Although a continuum of states or positions along the x axis is possible, the ball (representing the state of the system at any particular time) tends to settle in the base of a bowl, which may be considered an attractor. The two attractors here are the two states being considered (erosion as the right-hand potential well, and revegetation combined with peat accumulation as the well on the left). As erosion gullies in the real landscape deepen and widen, the erosion attractor weakens, shown by its potential well in the stability landscape becoming shallower and slightly narrower (i.e. it is becoming less resilient to perturbation). Eventually, the system reaches a point where the potential well representing the erosion state disappears and the ball moves to the alternative attractor representing the revegetated, peat-accumulating state.
As noted in Figure 4, perturbations are the periods of lower intensity rainfall. The erosion state is maintained by vegetation being washed out. During periods where less intense rainfall occurs, vegetation may establish from seedbanks or plant fragments originating from bare peat or neighbouring intact peatland, moving the ball in the direction of the left-hand state in Figure 4 (peat accumulation state); a perturbation occurs. After the resumption of more intensive rainfall events, vegetation is removed and erosion resumes.
However, after the gully reaches a critical width, a similar-sized perturbation may cause the system to switch to the new state (Stage 4: peat accumulation). Periods of lower intensity rainfall can occur in a system that is essentially static climatically; that is, they may simply represent variability within a given climate.

F I G U R E 4
The weakening of the resilience of the peatland as it moves towards a bifurcation-type tipping point. The peatland is represented by a theoretical stability landscape (following Lenton, 2013) in the left-hand column, and by a cartoon of a cross section of peatland in the right-hand column In Figure 4 we consider how the switch might occur in gullies that have eroded down to a more erosion-resistant mineral substrate. In two of our cores-MIG2 and MIG3-the switch occurred before the mineral substrate had been reached, which suggests that other tipping point mechanisms were involved in these cases. However, gullies may become wider before an erosion-resistant layer has been reached. In peatlands on shallow slopes, such as our study site, lateral retreat of gully walls occurs via slumping and block failure (mass movements) and processes such as wind erosion, frost heave and rain splash erosion.
Peat derived from these processes is deposited in the gully base and removed by running water (Evans & Warburton, 2007).
The stages described in Figure 4 essentially use tipping point theory to formalize a similar idea presented by Wishart and Warburton (2001), with one important and substantial difference. In their study of eroding blanket peatlands in the Cheviot Hills of southern Scotland, they envisaged the system becoming stuck at Stage 3; they suggested that channels or small streams in the widening gully would periodically erode newly established vegetation and continue to undercut the gully walls until all of the original peatland had been eroded away. They also note that there are no feedback mechanisms in their conceptual model that see the system return to a state of 'undisturbed blanket peat' (Wishart & Warburton, 2001). This view contrasts with our conceptual model where the streams disappear, and infilling becomes self-reinforcing. Our model fits observations at our study site. We have visited all of the revegetating gullies at our site and most small channels or streams, where they occur, have become clogged with vegetation; that is, they do not conform to the scenario depicted by Wishart and Warburton (2001). More recently, Evans and Warburton (2007) hypothesized a sequence essentially the same as depicted in Figure 4. They propose a conceptual 'cut and fill' model of cycling between erosion and revegetation in blanket peatlands. In their model, they also consider other revegetation mechanisms such as natural damming of gullies by blocks of eroding peat falling from the gully sides.
Based on the above discussion we propose that a non-reversible shift takes place between the two equilibrium C states (eroding and accumulating) found in gullies within hagged blanket peatlands ( Figure 5). As we have already noted, our down-core data do not allow us to say if this switch relates to a monostable or bistable system, but the system shifts states in a way that is consistent with a bifurcation tipping point, and our observations lead us to believe that the shift from C loss to C accumulation is not reversible. That is not to say that erosion cannot restart, but once the gully has begun to accumulate C it does not become progressively narrower, reversing the sequence shown in Figure 4 ( to Stage 1 (Figure 4). Nevertheless, until a gully completely infills, it will receive water from higher, uneroded, areas between gullies; that is, it will remain a site of flow concentration. For this reason, it may be more prone to new gully formation than the uneroded areas, and this possibility would tend to support the cyclical model of Evans and Warburton (2007).
Our model of events in Figures 4 and 5 shows how the shift is driven by internal morphological changes in the system under a stable climatic forcing. However, changes in state are also affected by boundary conditions. For example, climatic changes may combine with internal morphological changes to cause a shift. If the climate warms and dries, vegetation may grow more rapidly on the floor of the gully during periods with less intensive rainfall (such as the periods of low rainfall identified across England and Wales in recent centuries-see Appendix S1), and damaging flows of water will be less common because of the drier climate, meaning that a state shift may occur for a narrower gully than would be the case if the climate did not change. Therefore, it is possible for the changes in climate that we discuss earlier to modify the internal mechanisms causing a regime change. Finally, our model does not preclude switches occurring at different times across a landscape.
Gullies vary in width and stage of development within a peatland (including along individual gullies), and this variability can be expected to be reflected in differences in the timing of switches from the eroding to accumulating states as observed in our cores.

| Nonlinearity and thresholds in peatland behaviour
Our study provides a clear example of threshold behaviour in a peatland system, and points to an additional way in which we might investigate peatlands and conceptualize their behaviour. Explicitly thinking in terms of a tipping point framework helps reveal possible internal mechanisms by which sudden and fundamental changes in system Wide Narrow functioning may occur. Studies such as that of Charman et al. (2013), who suggest that northern peatlands may become stronger C sinks under a warming climate, show that peatlands can display essentially linear behaviour over centennial time-scales, and it is tempting to assume that such linear behaviour will continue into the future as the climate continues to warm. However, as we show above, internal 'evolution' of a peatland can bring about fundamental, step-like, changes in peatland behaviour. In this context, it is notable that peatland development models such as DigiBog (Baird, Morris, & Belyea, 2011) and HPM (Frolking et al., 2010) tend to include strong negative feedbacks (stability within a single state). For example, as shown in the modelling study by Swindles, Morris, Baird, Blaauw, and Plunkett (2012), a drying of the climate causes an initial deepening of water-tables in a peatland but also causes a reduction in peat permeability (hydraulic conductivity) through aerobic decay that reduces rates of water flow from the peatland, so that the water-table position relative to the peatland surface returns to its pre-drying position. While such strong negative feedbacks certainly occur in peatlands, and perhaps even dominate (see Belyea, 2009), other possibilities exist and are worth considering.
For example, under future climates, with an increase in drought frequency and duration, a peatland may start to crack. Although the peat between cracks may decay and undergo a reduction in its permeability, the effect of cracks as conduits for rapid water flow may override this reduction, causing water-tables to fall further below the surface, to a new deep water-table state, that could in turn lead to changes in peatland vegetation and its C balance. In other words, threshold behaviour may occur, and peatlands may undergo topological changes in state as the climate warms.

| Management implications
We have shown how peatlands can 'self-repair' from an eroding state, both in terms of their vegetation and hydrological functioning. Eroded blanket peatlands are priority sites for conservation in the United Kingdom (IUCN, 2018), and efforts are often made to reduce or halt erosion by placing dams across gullies (e.g. Armstrong et al., 2009;MoorLIFE, 2020;Parry, Holden, & Chapman, 2014). Our tipping point model (Figure 4) shows why such efforts are generally successful but also points to alternative interventions that might be considered. A series of dams along a gully will reduce water-level gradients in the stretches between the dams. Flow will deepen but flow velocities will be reduced, lowering the probability of washout of any vegetation that may establish. Damming gullies would not generally change flow discharge along them, because that is controlled by upstream catchment area and net rainfall. Although effective at reducing erosion or stimulating revegetation, a series of dams may be undesirable because of erosion downstream of a dam caused by a plunge pool, although measures may be taken to prevent this (e.g. using permeable dam materials that decrease flow velocities rather than create a watertight seal, Armstrong et al., 2009). Pools also tend to form behind dams and these may be undesirable because of the higher CH 4 emissions associated with them (e.g. Laine, Wilson, Kiely, & Byrne, 2007;Waddington & Roulet, 1996). An alternative to damming is to widen gullies artificially so that a state transition to revegetation and C accumulation is more likely, or to reduce water flow down a gully by rerouting water flow pathways in its upper catchment. Both alternatives require regrading of the peatland landscape using mechanical diggers, but such large-scale works already take place in some degraded UK peatlands (Yorkshire Peat Partnership, n.d.). Of course, another alternative is to do nothing, especially if the peatland looks like it is close to a tipping point already (e.g. a partially vegetated gully containing patches of new peat). Through reconstructing a trajectory of peatland self-recovery, our results provide an additional perspective on management options for eroding blanket peatlands.

| CON CLUS IONS
Much of the literature on peatlands is focused on how peatlands become degraded and switch from C sinks to sources. Similarly, much of the literature on tipping points focusses on shifts from a 'good' to a 'bad' state. Unusually, we find the opposite and set out to understand what causes a peatland to switch from active erosion with exposed peat, loss of vegetation and loss of C, to revegetation, higher water-tables and renewed C accumulation over short time-scales. Between 5.2 and 10.6 kg/m 2 of new C has accumulated since the switch, occurring between the late 1800s and early to mid-1900s, with average C accumulation rates as new peat between 46 and 121 g C m −2 year −1 . Our palaeoecological data reveal a switch in system functioning that can be explained as a bifurcation tipping point. External factors, such as climate and pollution levels, are likely to be important for setting suitable boundary conditions to shift a peatland towards recovery, but internal mechanisms (i.e. evolution of gully network) also offer an explanation for the changes we observe in the system's functioning. Of course, recovery may not last as the climate changes, and new types of degradation may occur such as the cracking of peat mentioned above. Nevertheless, for both recovery and degradation, we show how application of tipping point theory can help improve understanding of some important aspects of peatland behaviour.

ACK N OWLED G EM ENTS
We are grateful to the National Trust and Natural Resources Wales for access and permission to work on the site; Andrew Roberts

PE E R R E V I E W
The peer review history for this article is available at https://publo ns. com/publo n/10.1111/1365-2745.13453.

DATA AVA I L A B I L I T Y S TAT E M E N T
The peat core data, including the palaeoecological and peat properties data, are available in the Dryad Digital Repository https://doi. org/10.5061/dryad.sbcc2 fr3r (Milner et al., 2020).