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OverviewWe used data from the national forest inventory conducted by the US Department of Agriculture, Forest Service, Forest Inventory and Analysis (FIA) program to quantify tree biomass and growth along forest edges and within the forest interior. We estimated the causal impact of the forest edge environment on patterns of tree biomass and growth, while accounting for potentially confounding variables. We then used the regression models to estimate the aggregate difference in growth attributable to forest edges throughout the northeastern U.S. Finally, to better understand the implications of our findings, we quantified the degree of forest fragmentation throughout temperate and tropical forest biomes world-wide, using a 30 m forest cover map.Study areaOur analyses of edge impacts on forest biomass and growth were conducted throughout twenty-states (1.7 million km2) in the northeastern and upper mid-west of the United States (Supplementary Fig. 1). This region contains 765,000 km2 of forest and encompasses gradients of dominant land-uses, climatic conditions, and forest composition while remaining within deciduous, coniferous, and mixed temperate forest ecosystems.Identifying edges in forest inventory dataThe FIA collects measurements of tree size, growth, and land-use within a nested plot design across the country19. Each FIA plot is composed of four individual subplots; within each subplot, the diameter at breast height (dbh) of every tree >12.7 cm is measured during each measurement period. The re-measurement frequency for FIA plots in our study area is between 5 and 7 years, but this can differ between Forest Service regions. In addition to tree measurements, the database details land-use condition data that includes the proportion of the area that is forested and, on some plots, the land-cover class of the non-forest area (FIA User’s Manual, Condition Table). FIA plots are considered forested if some portion of the plot includes a contiguous forest patch (including potentially outside of the plot area) of greater than 4047 m2 that has more than 10% canopy cover. With a memorandum of understanding between the USFS and Harvard University, we had access to the true, unfuzzed plot coordinates, which are not publicly available. Evaluating >48,000 plots in the USFS Northern Region sampled from 2010 to 2020 and selecting the most recent measurement cycle for each plot, we identified subplots that contained both a forest and a non-forest condition and categorized these as edges (Supplementary Table 1). Only subplots that included a forest condition in both the most recent and previous measurement were included. Subplots where the mapped condition changed from forest to non-forest were excluded. Changes in the amount of mapped forest condition were included and are incorporated into the calculation of response variables using the most recent condition area. We identified FIA plots where all four subplots were fully forested as interior plots to be used for comparison. Subplots located within the same plot as an edge subplot (i.e., edge-proximate subplots) were excluded from this study due to limitations in our ability to quantify their distance from an edge. The spatial configuration of subplots is such that a fully forested subplot may be up to ~65 m away from an identified forest edge within another subplot. Studies suggest that the distance of edge influence in temperate forest does not extend more than 30 m into the forest interior15,33. Since the FIA does not contain information about the geometry of non-forest conditions beyond the subplot boundary, we deemed that the large uncertainty in the relationship between these subplots to a non-forest edge precluded their inclusion in the study. The FIA plot configuration prevented quantification of the distance of edge influence in our analysis; the exclusion of subplots adjacent to edge-subplots may limit direct comparisons with other fragmentation studies.We used the FIA condition data to characterize the non-forest land use in edge subplots. Information on adjacent non-forest land cover is not collected on all FIA plots (4327 of 6607 edge subplots). We aggregated FIA land-cover classification to a binary anthropogenic or unknown edge type designation and present results from all edge subplots and the anthropogenic edge subset (FIA User’s Manual Condition Table, Section 2.4.50).For each subplot (168 m2 in area), we calculated two primary response variables of interest: total live tree BA and BAI. Notably, trees smaller than 12.7 cm dbh) in m2. BAI was calculated on a per-tree basis as the difference in radial growth of live adult trees between the most recent and previous measurements, and then divided by the number of years between measurements (m2 yr−1). In addition, we aggregated individual tree diameter measurements to calculate mean stem density (stems ha−1) and mean tree diameter for each subplot (Fig. 2).We accounted for variable subplot area by normalizing both BA and BAI to a per-hectare of forested area basis, resulting in units of m2 ha−1 and m2 ha−1 yr−1, respectively. To account for potential small-area bias, we performed a sensitivity analysis on the relationship between BA and subplot forested area (Supplementary Fig. 2). We subsequently excluded 1284 subplots under 30 m2 in area as the area to BA relationship asymptotes relationship above this threshold. Finally, we accounted for errors in field dbh measurements, sometimes resulting in negative BAI values, by excluding the 97.5% quantiles of both BA and BAI distributions.Given their spatial configuration, FIA subplots are not fully independent measurements, potentially introducing issues with pseudo-replication and spatial autocorrelation within our dataset. To test for spatial autocorrelation we examined the semivariance of model residuals36, and found that there was high correlation only at distances of less than 1 km. The spatial stratification of the FIA plot design minimizes issues of plot–plot proximity within our study. However, to account for autocorrelation between subplots, we filtered our pre-matched dataset to only including one subplot from each FIA plot. For plots containing multiple edge subplots, we selected the subplot with the largest forested area. For interior plots, we selected the central subplot and excluded all others.Isolating the effect of edges on growthAbiotic controlsTo account for environmental controls on forest growth we included the most critical abiotic predictors of terrestrial vegetation productivity (light, water, temperature, and nitrogen deposition) as covariates in the regression models (Supplementary Fig. 4, Supplementary Table 2). Light, water, and temperature data were drawn from spatial raster maps (0.5° resolution) as unit-less indices of relative limitation on vegetation productivity, ranging from 0 to 13. Nitrogen data were drawn from the 2018 NADP gridded inorganic wet nitrogen deposition product (4 km spatial resolution; kg of N ha−1)37. To interpolate across small gaps in the raster data (usually along water bodies), we used the Nibble tool from ArcGis Pro (ESRI Team). We then used FIA plot locations to extract values from each raster layer for all FIA subplots.Forest compositionTree species may vary in their responses to biogeochemical changes that occur on forest edges. Overall forest community response emerges from complex interactions between species. We used aggregations of tree species, termed forest composition groups (or forest types)38, to assess if species composition influenced the response to altered edge condition. Forest type classifications for each subplot are provided by the FIA (FIA User’s Manual, Condition Table) and are defined in Appendix D therein. We aggregated the FIA forest types into eight broader species groups, following Thompson et al.23, and defined in Supplementary Table 1.Matching, GLM regressions, and model selectionAll statistical analyses and most of the data processing were conducted in R, version 3.439. Using a causal inference framework, we created a quasi-experimental statistical design that included pre-matching followed by a GLM regression analysis40. Matching emulates an experimental design using observational data by identifying control groups of untreated (forest interior) plots that were as similar as possible to treated (forest edge) plots in terms of observable confounders. By capturing key differences in abiotic variables we control for the fundamental drivers of forest productivity, allowing for a direct estimation of the average treatment effect of edges. Similarity was defined by nearest-neighbor covariate matching determined by Malahanobis distance, implemented in the MatchIt library in R41, the simplest and best method when the dataset is robust enough to find a match for every treated plot20. This method excludes forest interior plots that are not matched with an edge plot. Given differences in sample size between the full edge dataset and the subset designated as anthropogenic edges, we performed matching separately on the two datasets. To assess the efficacy of matching on reducing the differences in covariate distributions, we used summary statistics calculated with the MatchIt library and report the pre- and post-matched covariate balance in Supplementary Table 4 and Supplementary Table 5 (sensu Schleicher et al.42). Matching was highly successful, largely eliminating differences in all covariate distributions in both datasets.Our primary response variables of interest, BA and BAI, were right-skewed, non-normally distributed and violated the assumptions of normality necessary for ordinary least squares regression43. We, therefore, used a GLM to better fit the structure of our data. GLMs are an extension of linear regression that allow more freedom in the choice of probability distribution function through the use of a link function to model relationships between predictors and response variables44. The gamma probability distribution is frequently chosen to model BA, given its assumptions of positive, continuous values and flexible model form23,45. We performed a series of GLM regressions on our post-matched datasets, using a gamma probability distribution with an inverse link function to model the relationship of BA and BA with a suite of predictor variables, using the glm function as implemented in the R Core stats package39. Due to differences in sample size between the all-edge dataset and the anthropogenic-edge subset, we modeled these two datasets separately for each of BA and BAI, resulting in four separate regression analyses. We used a model selection framework to identify the most parsimonious model within each of the model sets based on the Akaike Information Criterion (AIC) and residual deviance statistic46,47. We report the model-selection and model-fit results for each of our separate analyses, including model forms, AIC, Nagelkerke Pseudo-R2, and residual deviance in Supplementary Table 2. Across all four regression analyses, the best-performing model was one that included an interaction between the edge-status and forest type categorical variables, as well as the variables of temperature-limitation, light-limitation, water-limitation, and nitrogen deposition.We then used the best performing model from each analysis to compare the differences in BA and BAI between forest edge and interior across each forest type. We estimated the treatment effect of edge-state within each forest type using the ggeffects package48 to calculate marginal effects with the continuous predictors (temperature, light, water, and nitrogen deposition) held at their within-forest type regional means. The results of this analysis are displayed in Fig. 1 and Supplementary Table 3; primary error bars on the interior point show the 95% confidence interval of the marginal effect from the full edge model, while secondary error bars show the CI from the anthropogenic edge model. Due to the smaller sample size in the anthropogenic model, estimates of the mean marginal effect of the interior plots vary slightly (though non-significantly) from those from the full dataset. The main text description reports outputs from both models, calculated from separate interior mean estimates. For visual clarity, we only display one set of interior means in Fig. 1.Mortality and timber harvestIn tropical forests, large reductions in productivity along edges are associated with increased tree mortality.9 To assess differences in tree mortality across our study region, we applied a simplified GLM analysis, including edge-state as our only predictor variable. The FIA differentiates between mortality attributed to timber harvest and that attributed to other, non-harvest causes. The results of this analysis are presented as marginal effects of each edge category in Supplementary Fig. 3. There are no significant differences in biogenic mortality between edge groups and no difference in overall mortality (combined biogenic and anthropogenic); there is a small, but statistically significant (p  More

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The Chaihuín stratigraphyCore transects (Fig. 2b) reveal three sand layers, intercalated between herbaceous peats, that are laterally extensive over 600 m across the marsh (Fig. 3a). In all cases, the sand layers have sharp lower contacts and transitional upper contacts. Ten accelerator mass spectrometric (AMS) radiocarbon dates modelled using a Bayesian phased sequence model provide the chronology (Fig. 3c and Supplementary Table 1). The age of plant macrofossils immediately beneath the upper layer, sand A, are consistent with burial by the 1960 tsunami. The age model places the deposition of the middle sand B at 1600–1820 and lower layer, sand C, at 1486–1616 CE. The calibrated age ranges for sands B and C are reasonably broad due to plateaux in the radiocarbon calibration curve, which affect dates from the seventeenth to twentieth centuries21.Fig. 3: Geological evidence from Chaihuín.a Stratigraphy of selected coring transects showing three laterally extensive sand sheets. Transect locations X–X’ and Y–Y’ shown on Fig. 2; b sedimentology of sand sheets, including grain size, sorting and clastic composition (%) classified relative to six modern environments established by discriminant analysis (see Supplementary Discussion), with images of sands A and B in CN17/8. Box-and-whisker plots show the statistical parameters measured in sand samples with the horizontal line inside the box representing the median, the box representing the upper and lower quartiles, the whiskers representing the minimum and maximum values excluding any outliers and the crosses the extreme outlier values. The number within each box indicates the number of samples in each group; c probability density functions (95.4%) of radiocarbon dates and modelled ages for the three earthquakes. Full radiocarbon results in Supplementary Table 1.Full size imageThe sedimentology and mineralogical signatures of the sand sheets are described in detail elsewhere based on over 100 hand-driven cores22 and summarised in Supplementary Discussion; here we analyse diatoms in three representative cores and present reconstructions of marsh surface elevation change over time from a diatom-based transfer function (Fig. 4 and Supplementary Data 1). From diatom analysis of the three cores, we identified 170 species indicative of differing tolerances to tidal inundation. Only 14 species were absent from a previously published modern training set that includes 29 samples from Chaihuín20, and 9 of these species constituted 2% of any sample (comprising 4–5% in 2 non-sand samples).Fig. 4: Diatom assemblages and estimates of land-level change derived from a regional south-central Chile transfer function for three cores from Chaihuín.a–c Diatom assemblage summaries and dominant taxa in cores CN14/5 (a), CN17/8 (b) and CN18/11 (c) at elevations of 0.88, 0.89 and 1.10 m above mean sea level (MSL), respectively. Elevation optima of diatom species are classified based on weighted averaging of the modern training set and reported relative to mean higher high water (MHHW). The modern analogue technique was used to calculate the squared chord distance to the closest modern analogue, and the threshold for a fossil sample having a close modern analogue is defined as the 20th percentile of the dissimilarity values (MinDC) for the modern training set44. Reconstructed palaeomarsh surface elevations (PMSE) and coseismic subsidence are shown from the weighted averaging partial least squares (WA-PLS) model only. d Estimates of coseismic subsidence in 1737 from three cores and three different diatom-based transfer function approaches, showing 95.4% uncertainties.Full size imageThe laterally extensive uppermost coarse to medium-grained sand sheet (A) is mid grey, varies in thickness between 1 and 19 cm, has a median grain size of 0.49 mm and is upwards fining (0.27–0.71 mm) in 61 cores (80% of those in which A is preserved, massive in the others). The marsh grades steeply into freshwater scrub, and there is no sand unit in cores just above the high marsh limit. There is an abrupt contact between the sand and dark brown silty herbaceous peat below, which contains plant material including below-ground stems (rhizomes) of Scirpus americanus. In many cores, there are rip-up clasts (~2 cm) of peat encased in the sand sheet, as well as vegetation rooted in the peat below. The peat below the sand sheet contains a diatom assemblage that is almost entirely composed of species found on the contemporary high marsh above mean higher high water (MHHW) (e.g. Eunotia praerupta, Nitzschia acidoclinata), with higher elevation optima than the diatoms found in the herbaceous peat above the sand unit (e.g. Rhopalodia constricta) (Fig. 4a). The overlying peat also contains low, albeit important, percentages (5–24%) of taxa with elevation optima below MHHW. By contrast to the peats, sand A is dominated by species with lower elevation optima (59–72% of the total assemblage have optima below MHHW), including Achnanthes reversa and Planothidium delicatulum.The middle brown-grey to dark grey mica-rich coarse to medium-grained sand sheet (B) is similarly laterally extensive across the entire marsh, varying in thickness between 2 and 32 cm. It has a median grain size of 0.47 mm and is upwards-fining (0.38–0.68 mm) in 31 cores (50% of those in which B is preserved, massive in others), but rip-up clasts of peat were only occasionally observed. In some cases, we observe a 2–4-cm-thick cap of horizontally bedded detrital plant fragments and wood at the top of the sand layer. The sand sheet abruptly overlays a red-brown to dark brown silty herbaceous peat with variable silt content and humification. Humidophila contenta dominates the diatom assemblage in the peat below sand B (up to 37% of the assemblage) and is also present in the peat overlying the sand sheet, which remains dominated by species with elevation optima above MHHW. In the core from the lowest contemporary marsh elevation (CN14/5, Fig. 4a), there is an increase in low marsh diatom species (elevation optima below MHHW) above the sand compared to below (e.g. A. reversa, P. delicatulum). Diatom assemblages are relatively consistent across the five samples from the sand unit, with 54–76% of the assemblages being species with elevation optima below MHHW, including A. reversa, Fallacia tenera and P. delicatulum.A third sand deposit (C) is found in 16 cores at the southern end of the marsh, although still traceable over 200 m and across most cores that penetrated deep enough to potentially sample sand C. The deposit is a dark grey fine to medium-grained massive sand (median grain size 0.25 mm, range 0.22-0.29 mm), with a maximum thickness of 51 cm and contains occasional rip-up clasts from the buried organic unit below encased in the sand. The basal contact is abrupt, with the sand overlying a brown clayey silt with occasional herbaceous plant remains, humified organic matter and woody plant material. The organic horizon below sand C contains more diatom species typically found at lower elevations in the tidal frame than the peats below A and B (Fig. 4a). There is also a change in species composition approaching the top of the peat, with abundances of Opephora pacifica and Pseudostaurosira perminuta decreasing and H. contenta and E. perpusilla increasing from the base to top of the peat below sand C. Also in contrast to the other two buried organic deposits, there is a change in species composition approaching the top of the peat and samples immediately above and below sand unit C have very similar diatom assemblages, dominated by H. contenta and E. perpusilla. Diatom preservation in the sand unit was very poor, and it was not possible to obtain representative counts from this unit.Brown silty herbaceous peats separate the three sand sheets, deposited intertidally on the basis of their diatom composition. In addition to the relative variations in freshwater and brackish diatom composition of peats described above, the peat units also vary in their degree of humification. While peats below sands A and C contain humified organic matter, the peat below sand B is unhumified. Additionally, two layers of highly humified black peat were observed immediately above and below sand A in low marsh cores from the southwest of the marsh, varying in thickness between 1 and 15 cm.Evidence for a locally sourced tsunamiWe interpret all three sand sheets as being deposited by locally sourced tsunamis, rather than far-field tsunamis or non-seismic processes (e.g. storms, river floods or aeolian processes). This is based primarily on coincident land deformation, and also upon their lateral extent, diatom composition, and sedimentological signatures. Dealing first with the latter lines of reasoning, sands A and B are not only dominated by marine sublittoral and epipsammic diatom species but also contain substantial numbers of benthic silty intertidal mudflat and freshwater taxa, which also dominate the underlying peats. This is consistent with mixed diatom assemblages in tsunami deposits worldwide and indicative of tsunamis eroding, transporting and redepositing diatoms from diverse environments as they cross coastal and inland areas23,24,25,26. The presence of marine and tidal flat diatoms excludes deposition of sand by river flooding25,27, and statistical comparison of the sedimentological and mineralogical signatures of the sands with modern depositional environments, reported by Aedo et al.22 and summarised in Supplementary Discussion, further supports a seaward rather fluvial sediment source. We observe a maximum sedimentary contribution of 12% from upstream fluvial sources (Fig. 3b) and do not observe erosional or depositional features characteristic of fluvial flood deposits, such as a high basal mud content reflective of suspended loads during the initial stages of flooding or inverse grading as energy increases28.Meteorologically driven deposition of the sands, either during storm surges or other transient sea-level fluctuation events (e.g. El Niño), is discounted as the diatoms in the overlying organic units demonstrate lasting ecological change27,29. While a non-tsunamigenic earthquake followed closely in time by a large storm surge may impact diatom assemblages in the same way, there are several further characteristics of the three sand sheets which are consistent with a tsunami origin, even though these, in themselves, are not diagnostic. These include the lateral extent (traceable across 230 m), upwards-fining grain size of sand sheets A and B, and clasts of underlying peats observed within sands A and C and occasionally within B. The absence of extreme climatic phenomena, such as hurricanes and tropical storms, in the Chaihuín area during the historic period also minimises the possibility of finding storm deposits. However, while it is recognised that the above criteria cannot be used individually to confirm tsunami deposition, it is the combination of all sedimentological and diatom evidence that we use here in support of the most compelling evidence for tsunami deposition, which comes from the accompanying abrupt land-level change. The latter rules out deposition by tsunamis sourced in the far-field, storms or aeolian processes.Evidence for coseismic land-level changeFollowing established criteria30,31, we use the sedimentary and diatom evidence to propose that the Chaihuín sequence records three earthquake events, associated with vertical coseismic deformation and tsunami deposition. Diatom assemblages from immediately below sand layers A and B are characterised by species with higher elevation preferences than those found immediately above the sands, suggesting decreases in marsh surface elevation consistent with coseismic subsidence (Fig. 4). Diatom assemblages show minimal change across sand layer C; instead a transition occurs prior to event C whereby species with lower elevation preferences are replaced by those with higher elevation preferences, indicating net emergence prior to event C followed by minimal coseismic subsidence.The transfer function reconstructs 0.35 ± 0.42 m of subsidence occurred in event A, which local testimony and radiocarbon dating confirm to be the 1960 earthquake. Compared to our previous estimate for this event20, refining the transfer function method and expanding the modern training set here, reduces the uncertainty by 0.26 m. Reconstructed subsidence agrees with observations of 0.7 ± 0.4 m19. By contrast, the transfer function reconstructs very minor subsidence of 0.10 ± 0.36 m occurred in event C, but this needs confirmation from analyses of additional cores.The transfer function predicts that coseismic subsidence occurred in event B, with reconstructions varying between 0.10 ± 0.33 and 0.52 ± 0.39 m, and averaging 0.22 ± 0.38 m (Fig. 4d). While this is close to the detection limit of coseismic land-level change30 and the error term is large compared to the amount of deformation, we interpret event B as being associated with net submergence for two reasons. First, changes in diatom-inferred marsh elevations between pre- and post-earthquake samples are greater than other sample-to-sample changes. Second, all nine reconstructions, regardless of core location or transfer function approach, indicate submergence rather than a mixture of submergence and emergence (Fig. 4d).Linking the geologic and historical recordsDespite the broad modelled age ranges for events B and C of 1600–1820 and 1486–1616 CE, respectively, each range only includes one historically reported earthquake. If the historical catalogue is complete, sands B and C represent tsunamis accompanying the 1737 and 1575 earthquakes, respectively. Although other great tsunamigenic earthquakes occurred in the time range of event B (1657, 1730, 1751), their rupture areas have been placed much further north8,32 and therefore are very unlikely sources for the observed deformation. Age ranges do not include 1837; therefore, absence of evidence for this earthquake at Chaihuín supports the chronicle-based interpretation that the 1837 rupture area lies further south11,16. The preservation of turbidites from 1837 at sites to the north of Chaihuín14 is consistent with observations of earthquake-triggered turbidites some distance outside the rupture zone, as observed for the Mw 8.8 2010 Maule earthquake14.Implications for the rupture depth in 1737The Chaihuín record provides the first evidence for crustal deformation during the 1737 earthquake and the first evidence for the earthquake being tsunamigenic. While the nearshore bathymetry and orientation of the coastline may amplify tsunami inundation and the abundant sediment source may enhance the potential for evidence creation during even moderate tsunamis, the direction of land-level change at Chaihuín (subsidence) calls for reconsideration of the associated rupture depth. While correlation with evidence of shaking-induced turbidites from Calafquén and Riñihue lakes14, along with the absence of a 1737 event in sedimentary records from Río Maullín and Chucalén to the south9,11, supports the hypothesis that a smaller section of the plate interface ruptured in 1737 (between 39 and 41°S) than in 1960 and 157514, the Chaihuín record also forms an important constraint on the depth of local slip in 1737.By combining deformation and tsunami modelling, we show that our evidence of coastal subsidence and tsunami inundation at Chaihuín is better explained by offshore, shallow megathrust slip rather than by deeper slip below land as previously suggested16 (Fig. 5 and Supplementary Fig. 1). This is demonstrated by a simple numerical experiment designed to find the most likely depth range of the causative earthquake rupture that can explain the coastal subsidence inferred at Chaihuín and also the tsunami inundation.Fig. 5: Results of model tests to show that the 1737 rupture must have been confined to the offshore region at shallower fault depths than previously proposed.a The lower panel shows the trench-normal section of the megathrust and seafloor geometry at the latitude of Chaihuín used in the modelling experiment. The upper panel shows the bell-shaped slip distributions for a suite of eight earthquake ruptures and the middle panel shows the modelled vertical surface deformations using an elastic dislocation model (see “Methods”). The red and blue curves are the deep and shallow ruptures used as illustrative examples in the text. In this suite of models, the rupture width and peak slip are fixed at 100 km and 1 m, respectively, and the rupture location is systematically shifted horizontally in the trench-normal direction to represent ruptures at different depths. b Summary plot showing the modelled coastal uplift (left vertical axis) and tsunami runup (right vertical axis) predicted by the suite of models. Note that coastal subsidence can only be produced by offshore ruptures, with slip shallower than ~20 km. Ruptures deeper than this produce uplift at the coast. This opposing pattern of coastal deformation between shallow versus deeper ruptures is insensitive to how much slip is prescribed at the fault. Supplementary Fig. 1 shows the results for two different suite of models, in which the rupture width varies by fixing the updip (Supplementary Fig. 1a) and downdip (Supplementary Fig. 1b) limits.Full size imageOur numerical approach (see also “Methods”) leverages the sensitivity of the deformation sign (uplift or subsidence) and tsunami size at the Chaihuín coast to the depth of megathrust slip33 (Fig. 5). An earthquake rupture with maximum slip at 33 km fault depth (Fig. 5a, red model), as previously inferred from historical records16, will result in coastal uplift and a relatively small tsunami. Instead, if the rupture occurs offshore (Fig. 5a, blue model), the deformation will result in coastal subsidence and a much larger tsunami. From a systematic analysis in which the hypothetical rupture models are shifted horizontally in the trench-normal direction or vertically in the depth direction (Fig. 5a, upper panel), we conclude that subsidence at the Chaihuín coast could only be produced by ruptures placed mainly offshore, at average megathrust depths shallower than 20 km (Fig. 5b, downward triangles). Deeper ruptures will produce coastal uplift and consequent smaller tsunamis (Fig. 5b). The same conclusion is reached by varying the rupture width with fixed updip and downdip limits (Supplementary Fig. 1).Our conclusions are independent of the use of a normalised unit displacement in all models (i.e. 1 m at the centre of its corresponding bell-shaped rupture) because the opposing effects of deep versus shallow ruptures at Chaihuín are insensitive to the magnitude of slip involved and depend on its locus. The amount of slip determines the magnitude of deformation but not its sign due to the elastic response of the crust during earthquakes34. However, with evidence at only one location we only feel confident to constrain the depth range but not the magnitude nor along-strike extent of the causative slip. Therefore, from our numerical experiment we conclude that to produce subsidence at the Chaihuín coast, an offshore rupture likely shallower than 20 km is required as a deeper source would result in coastal uplift. This is also consistent with the inferred tsunami heights (Fig. 5b), which are larger for a shallower rupture and therefore more likely to produce inundation on land independent of the local topography. This geologically-based inference of an offshore rupture (blue curve in Fig. 5b) contrasts with the deeper rupture below land (red curve in Fig. 5b) previously inferred from historical observations alone16.Implications for tsunami recurrence intervalsThe average interval between the three events preserved at Chaihuín, 193 years, is shorter than the interval proposed for full segment 1960-style ruptures of 270-280 years9,11,14. This supports the notion that the Chilean subduction zone displays a variable rupture mode, in which the size, depth, tsunamigenic potential and recurrence interval vary between earthquakes10. Of greatest importance, however, is the shorter average recurrence interval of tsunami inundation than previously reported. With the addition of the 1737 tsunami alongside previously known events in 1960, 1837 and 1575, the historical recurrence interval for tsunamis generated anywhere along the Valdivia segment of the Chilean subduction zone is reduced to 130 years. This holds even if the inferred tsunami inundation is not associated with the 1737 earthquake, but with another earthquake of similar age missed in the historical catalogue. More