Björklund, J., Rydval, M., Schurman, J. S., Seftigen, K., Trotsiuk, V., Janda, P., ... & Svoboda, M. (2019). Disentangling the multi-faceted growth patterns of primary Picea abies forests in the Carpathian arc. Agricultural and Forest Meteorology, 271, 214-224.
Lábusová, J., Morrissey, R. C., Trotsiuk, V., Janda, P., Bače, R., Cada, V., ... & Mateju, L. (2019). Patterns of forest dynamics in a secondary old-growth beech-dominated forest in the Jizera Mountains Beech Forest Reserve, Czech Republic. iForest-Biogeosciences and Forestry, 12(1), 17.
Cailleret, M., Dakos, V., Jansen, S., Robert, E. M., Aakala, T., Amoroso, M. M., ... & Camarero, J. J. (2018). Early-warning signals of individual tree mortality based on annual radial growth. Frontiers in Plant Science, 9, 1964.
Friess, N., Müller, J. C., Aramendi, P., Bässler, C., Brändle, M., Bouget, C., ... & Gossner, M. M. (2019). Arthropod communities in fungal fruitbodies are weakly structured by climate and biogeography across European beech forests. Diversity and Distributions.
Janda, P., Tepley, A. J., Schurman, J. S., Brabec, M., Nagel, T. A., Bače, R., ... & Frankovič, M. (2019). Drivers of basal area variation across primary late-successional Picea abies forests of the Carpathian Mountains. Forest Ecology and Management, 435, 196-204.
Sommerfeld, A., Senf, C., Buma, B., D’Amato, A. W., Després, T., Díaz-Hormazábal, I., ... & Harvey, B. J. (2018). Patterns and drivers of recent disturbances across the temperate forest biome. Nature communications, 9(1), 4355.
Rydval, M., Druckenbrod, D. L., Svoboda, M., Trotsiuk, V., Janda, P., Mikoláš, M., ... & Wilson, R. (2018). Influence of sampling and disturbance history on climatic sensitivity of temperature-limited conifers. The Holocene, 28(10), 1574-1587.
Mikac, S., Žmegač, A., Trlin, D., Paulić, V., Oršanić, M., & Anić, I. (2018). Drought-induced shift in tree response to climate in floodplain forests of Southeastern Europe. Scientific reports, 8(1), 16495.
Vítková, L., Bače, R., Kjučukov, P., & Svoboda, M. (2018). Deadwood management in Central European forests: Key considerations for practical implementation. Forest Ecology and Management, 429, 394-405.
Kozák, D., Mikoláš, M., Svitok, M., Bače, R., Paillet, Y., Larrieu, L., ... & Frankovič, M. (2018). Profile of tree-related microhabitats in European primary beech-dominated forests. Forest Ecology and Management, 429, 363-374.
Bosela, M., Lukac, M., Castagneri, D., Sedmák, R., Biber, P., Carrer, M., ... & Roibu, C. C. (2018). Contrasting effects of environmental change on the radial growth of co-occurring beech and fir trees across Europe. Science of The Total Environment, 615, 1460-1469.
Sabatini, F. M., Burrascano, S., Keeton, W. S., Levers, C., Lindner, M., Pötzschner, F., ... & Debaive, N. Where are Europe’s last primary forests?. Diversity and Distributions.
Schurman, J. S., Trotsiuk, V., Bače, R., Čada, V., Fraver, S., Janda, P., ... & Seidl, R. (2018). Large‐scale disturbance legacies and the climate sensitivity of primary Picea abies forests. Global change biology.
Bače, R., Schurman, J. S., Brabec, M., Čada, V., Després, T., Janda, P., ... & Nagel, T. A. (2017). Long‐term responses of canopy–understorey interactions to disturbance severity in primary Picea abies forests. Journal of Vegetation Science, 28(6), 1128-1139.
Després, T., Vítková, L., Bače, R., Čada, V., Janda, P., Mikoláš, M., ... & Svoboda, M. (2017). Past disturbances and intraspecific competition as drivers of spatial pattern in primary spruce forests. Ecosphere, 8(12).
Zemanová, L., Trotsiuk, V., Morrissey, R. C., Bače, R., Mikoláš, M., & Svoboda, M. (2017). Old trees as a key source of epiphytic lichen persistence and spatial distribution in mountain Norway spruce forests. Biodiversity and Conservation, 26(8), 1943-1958.
Meyer, P., Janda, P., Mikoláš, M., Trotsiuk, V., Krumm, F., Mrhalová, H., ... & Svoboda, M. (2017). A matter of time: self-regulated tree regeneration in a natural Norway spruce (Picea abies) forest at Mt. Brocken, Germany. European Journal of Forest Research, 136(5-6), 907-921.
Nagel, T. A., Mikac, S., Dolinar, M., Klopcic, M., Keren, S., Svoboda, M., ... & Paulic, V. (2017). The natural disturbance regime in forests of the Dinaric Mountains: A synthesis of evidence. Forest ecology and management, 388, 29-42.
Meigs, G. W., Morrissey, R. C., Bače, R., Chaskovskyy, O., Čada, V., Després, T., ... & Mikoláš, M. (2017). More ways than one: Mixed-severity disturbance regimes foster structural complexity via multiple developmental pathways. Forest Ecology and Management, 406, 410-426.
Mikoláš, M., Svitok, M., Bollmann, K., Reif, J., Bače, R., Janda, P., ... & Coppes, J. (2017). Mixed-severity natural disturbances promote the occurrence of an endangered umbrella species in primary forests. Forest Ecology and Management, 405, 210-218.
Janda, P., Trotsiuk, V., Mikoláš, M., Bače, R., Nagel, T. A., Seidl, R., ... & Jasík, M. (2017). The historical disturbance regime of mountain Norway spruce forests in the Western Carpathians and its influence on current forest structure and composition. Forest Ecology and Management, 388, 67-78.
Mikoláš, M., Tejkal, M., Kuemmerle, T., Griffiths, P., Svoboda, M., Hlásny, T., ... & Morrissey, R. C. (2017). Forest management impacts on capercaillie (Tetrao urogallus) habitat distribution and connectivity in the Carpathians. Landscape Ecology, 32(1), 163-179.
Kulakowski, D., Seidl, R., Holeksa, J., Kuuluvainen, T., Nagel, T. A., Panayotov, M., ... & Wohlgemuth, T. (2017). A walk on the wild side: disturbance dynamics and the conservation and management of European mountain forest ecosystems. Forest Ecology and Management, 388, 120-131.
Čada, V., Morrissey, R. C., Michalová, Z., Bače, R., Janda, P., & Svoboda, M. (2016). Frequent severe natural disturbances and non-equilibrium landscape dynamics shaped the mountain spruce forest in central Europe. Forest Ecology and Management, 363, 169-178.
Cailleret, M., Jansen, S., Robert, E. M., Desoto, L., Aakala, T., Antos, J. A., ... & Čada, V. (2016). A synthesis of radial growth patterns preceding tree mortality. Global change biology.
Trotsiuk, V., Svoboda, M., Weber, P., Pederson, N., Klesse, S., Janda, P., ... & Mateju, L. (2016). The legacy of disturbance on individual tree and stand-level aboveground biomass accumulation and stocks in primary mountain Picea abies forests. Forest Ecology and Management, 373, 108-115.
Bače, R., Svoboda, M., Janda, P., Morrissey, R. C., Wild, J., Clear, J. L., ... & Donato, D. C. (2015). Legacy of pre-disturbance spatial pattern determines early structural diversity following severe disturbance in montane spruce forests. PloS one, 10(9), e0139214.
Primicia, I., Camarero, J. J., Janda, P., Čada, V., Morrissey, R. C., Trotsiuk, V., ... & Svoboda, M. (2015). Age, competition, disturbance and elevation effects on tree and stand growth response of primary Picea abies forest to climate. Forest Ecology and Management, 354, 77-86.
Mikoláš, M., Svitok, M., Tejkal, M., Leitão, P. J., Morrissey, R. C., Svoboda, M., ... & Fontaine, J. B. (2015). Evaluating forest management intensity on an umbrella species: Capercaillie persistence in central Europe. Forest Ecology and Management, 354, 26-34.
Jonsson, B. G., Pe'Er, G., & Svoboda, M. (2015). Forests: not just timber plantations. Nature, 521(7550), 32-32.
Trotsiuk, V., Svoboda, M., Janda, P., Mikolas, M., Bace, R., Rejzek, J., ... & Myklush, S. (2014). A mixed severity disturbance regime in the primary Picea abies (L.) Karst. forests of the Ukrainian Carpathians. Forest Ecology and Management, 334, 144-153.
Svoboda, M., Janda, P., Bače, R., Fraver, S., Nagel, T. A., Rejzek, J., ... & Čada, V. (2014). Landscape‐level variability in historical disturbance in primary Picea abies mountain forests of the eastern Carpathians, Romania. Journal of vegetation science, 25(2), 386-401.
Knorn, J. A. N., Kuemmerle, T., Radeloff, V. C., Keeton, W. S., Gancz, V., BIRIŞ, I. A., ... & Hostert, P. (2013). Continued loss of temperate old-growth forests in the Romanian Carpathians despite an increasing protected area network. Environmental Conservation, 40(02), 182-193.
FULL VERSION ABOVE
Disturbances shape forest structure and composition, but the temporal dynamics of disturbance patterns, their influence on dynamics of forest structural complexity, and the potential impacts of ongoing climate changes are not fully understood. We addressed these issues by focusing on (1) long-term, landscape level retrospective analysis of disturbance dynamics of mountain Norway spruce (Picea abies) forest; (2) testing for the prevailing disturbance agent; and (3) the detection of disturbance drivers, particularly site conditions, using a dendrochronological approach.
We had a unique opportunity to sample a large area of natural forest (in otherwise altered region) in Bohemian Forest, that was recently affected by extensive and severe wind and bark beetle disturbances raising management concerns. Tree-ring series of a minimum of 35 trees on each of the 26 study plots were analysed for signals of past disturbances that were indicated either by release from suppression (rapid growth increase) or rapid early growth rate (gap origin).
A broad range of disturbance severities were detected across the landscape, but severe disturbances (>50 % trees responded), with a short rotation period of 174 years, best characterize the area. Reconstructed disturbances were associated with historically documented windstorms and bark beetle outbreaks. They were distributed across the landscape and affected its large portions with spatially variable severity. Over the last five centuries, disturbances peaked in the 1820s, but were rare after 1880. This non-equilibrium dynamics resulted into mature landscape structure at the end of 20th century and contributed to the large extent of disturbances in the last two decades. Disturbances were more frequent on wind-exposed locations such as mountain ridges and flatter terrain.
Frequent disturbances did not allow the forest to develop into an old-growth phase; rather disturbance events of variable severities created structures important for biodiversity and could also preserve key early-seral phases in the landscape. We anticipate that potential future increase of disturbance intensities will not lead to comparable regime shifts in forests shaped by high-severity disturbances that kill largely mature trees (e.g., wind and bark beetle), because such disturbances are followed by resistant forest structure. Conservation areas should be large enough to allow for a wide range of disturbances. Emphasizing ecological functions needs understanding of biological legacies of natural disturbances and managers could partly rely on natural events to restore natural features into cultivated forests.
Description of attachments: On the first picture you can see annual resolution of chronologies of growth releases only showing the synchronization of disturbances at the level of individual trees; and (b) summary of peaks (indicating individual disturbance events) in the same chronologies at the plot level referred to disturbances and severe disturbances, >10 % and >50 % released trees, respectively. Peaks in 5-year running sum (blue dots) were calculated proportional to sample depth. For example, during the 5-year period around 1780, 56 % of available plots (5 out of 9 plots) indicate disturbance by growth releases. Reconstructed disturbance events (peaks) were significantly associated with known windstorms and bark beetle outbreaks evidenced in the archived documents of the surrounding region.
The second one shows location of the study area within the National Park and Protected Landscape Area Šumava in the Czech portion of the Bohemian Forest. The contour of 1150 m a.s.l. corresponds to the distribution of mountain Norway spruce (Picea abies) forest type restricting the study area and individual localities. We did not analyse two central localities because one was disturbed in 1990th (impossible core extraction) and second was likely harvested in late 19th century. Groups of plots obtained by cluster analysis of disturbance histories are shown.
FULL VERSION ABOVE
Severe canopy-removing disturbances are native to many temperate forests and radically alter stand structure, but biotic legacies (surviving elements or patterns) can lend continuity to ekosystém function after such events. Poorly understood is the degree to which the structural complexity of an old-growth forest carries over to the next stand. We asked how predisturbance spatial pattern acts as a legacy to influence post-disturbance stand structure, and how this legacy in fluences the structural diversity within the early-seral stand.
Two stem-mapped one-hectare forest plots in the Czech Republic experienced a severe bark beetle outbreak, thus providing before-and-after data on spatial patterns in live and dead trees, crown projections, downlogs, and herb cover.
Post-disturbance stands were dominated by an advanced regeneration layer present before the disturbance. Both major species, Norway spruce (Picea abies) and rowan (Sorbus aucuparia), were strongly self-aggregated and also clustered to former canopy trees, predisturbance snags, stumps and logs, suggesting positive overstory to understory neighbourhood effects. Thus, although the disturbance dramatically reduced the stand’s height profile with ~100% mortality of the canopy layer, the spatial structure of post-disturbance stands still closely reflected the pre-disturbance structure. The former upper tree layer in fluenced advanced regeneration through microsite and light limitation. Under formerly dense canopies, regeneration density was high but relatively homogeneous in height; while in former small gaps with greater herb cover, regeneration density was lower but with greater heterogeneity in heights.
These findings suggest that pre-disturbance spatial patterns of forests can persist through severe canopy-removing disturbance, and determine the spatial structure of the succeeding stand. Such patterns constitute a subtle but key legacy effect, promoting structural complexity in early-seral forests as well as variable successional pathway sandrates. This influence suggests a continuity in spatial ekosystem structure that may well persist through multiple forest generations.
Description of attachments: On the first picture you can see spatial patterns of regeneration. A) Spatial patterns of saplings (small: 50–90cm, large: 90–200 cm); B) spatial relationship between spruce and rowan saplings; C) spatial relationship between saplings and canopy living trees and D) spatial relationship between saplings and snags or stumps evaluated with univariate and bivariate pair correlation function. Both strongly self-aggregated spruce and rowan saplings are clustered to canopy (>25m) trees, snag and stumps.
On the second one you can see the conceptual figure illustrates how the structural complexity of an old-growth forest carries over to the next stand, inspite of a severe canopy-removing bark beetle disturbance. Structurally simple patches dominated by a dense overstory tend to be replaced by a young simple cohort (high density, more evenly spatially distributed, shorter and more uniform heights). Structurally complex patches that include gaps tend to be replaced by with a similarly complex young cohort (lower density, larger patches of open space, greater maximum and wider variability in heights). This difference in post-disturbance early-seral structural development pathways is attributed to light conditions and microsite availability when the advance regeneration bank was formed: Under densely closed canopies, there are suitable microsite conditions (sparse herb layer) for seedling establishment but not enough light for sustainable height growth over a certain threshold. In contrast, under moderate canopy cover, the establishment of new seedlings is inhibited by a dense herb layer. Seedlings and saplings that do manage to establish in these patches are subject to mortality due to resource competition by the herb layer, resulting in lower advance regeneration density, larger patches of open space and wider height variability under moderate canopy cover.
FULL VERSION ABOVE
Tree-related microhabitats (TreMs) are important features for the conservation of biodiversity in forest ecosystems. Although other structural indicators of forest biodiversity have been extensively studied in recent decades, TreMs have often been overlooked, either due to the absence of a consensual definition or a lack of knowledge. Despite the increased number of TreM studies in the last decade, the role of drivers of TreM profile in primary forests and across different geographical regions is still unknown.
To evaluate the main drivers of TreM density and diversity, we conducted the first large-scale study of TreMs across European primary forests. We established 146 plots in eight primary forests dominated by European beech (Fagus sylvatica L.) in the Carpathian and Dinaric mountain ranges. Generalized linear mixed effect models were used to test the effect of local plot characteristics and spatial variability on the density and diversity (alpha, beta, and gamma) of TreMs.
Total TreM density and diversity were significantly positively related with tree species richness and the proportion of snags. Root mean square tree diameters were significantly related to alpha and gamma diversity of TreMs. Both regions reached similarly high values of total TreM densities and total TreM densities and diversity were not significantly different between the two regions; however, we observed between the two regions significant differences in the densities of two TreM groups, conks of fungi and epiphytes. The density and diversity of TreMs were very high in beech-dominated mountain primary forests, but their occurrence and diversity was highly variable within the landscapes over relatively short spatial gradients (plot and stand levels). Understanding these profile provides a benchmark for further comparisons, such as with young forest reserves, or for improving forest management practices that promote biodiversity.
Description of attachments: On the first picture you can see eﬀect plots showing the results of GLMMs testing for the eﬀect of tree species richness, RMS DBH, proportion of snags, and region on diversity (alpha, beta and gamma) and density of TreMs. Predicted values (lines, circles) are displayed along with 95% conﬁdence intervals (gray polygons, error bars).
On the second one you can see comparison of densities of TreM groups between snags and living trees.
FULL VERSION ABOVE
Distribution and connectivity of suitable habitat for species of conservation concern is critical for effective conservation planning. Capercaillie (Tetrao urogallus), an umbrella species for biodiversity conservation, is increasingly threatened because of habitat loss and fragmentation.
We assessed the impact of drastic changes in forest management in the Carpathian Mountains, a major stronghold of capercaillie in Europe, on habitat distribution and connectivity.
We used ﬁeld data surveys with a forest disturbance dataset for 1985–2010 to map habitat suitability, and we used graph theory toanalyse habitat connectivity.
Climate, topography, forest proportion and fragmentation, and the distance to roads and settlements best identiﬁed capercaillie presence. Suitable habitat area was 7,510 km2 in 1985; by 2010, clear-cutting had reduced that area by 1,110 km2. More suitable habitat was lost inside protected areas (571 km2) than outside (413 km2). Habitat loss of 15 % reduced functional connectivity by 33 % since 1985.
Forest management, particularly largescale clear-cutting and salvage logging, have substantially diminished and fragmented suitable capercaillie habitat, regardless of the status of forest protection. Consequently, larger areas with suitable habitat are now isolated and many patches are too small to sustain viable populations. Given that protection of capercaillie habitat would beneﬁt many other species, including old-growth specialists and large carnivores, conservation actions to halt the loss of capercaillie habitat is urgently needed. We recommend adopting policies to protect natural forests, limiting large-scale clear-cutting and salvage logging, implementing ecological forestry, and restricting road building to reduce forest fragmentation.
Description of attachments: On the first picture you can see forest disturbance patterns between 1985 and 2010, which almost exclusively represent clear-cutting and postdisturbance salvage logging, compared to capercaillie habitat in the Carpathians. Frames A and B focus on the Low and High Tatra Mountains and the Maramures region in Romania, respectively.
The second one shows change in the importance of individual capercaillie habitat patches between 1985 and 2010, measured by importance of habitat patch based on probability of connectivity index (dPC) based on a dispersal distance of 2.5 km. The importance of the habitat patches is classiﬁed into ﬁve levels based on dPC value: 0–1 (very low); 1–3 (low); 3–9 (medium); 9–27 (high).
FULL VERSION ABOVE
Quantifying the patterns and consequences of natural disturbance is vital for conserving biodiversity and ecosystem services. Mixed-severity disturbance regimes are prevalent in temperate forests worldwide, but key uncertainties remain regarding the variability of disturbance-mediated structural development pathways. This study investigates the influence of disturbance history on current structure in primary, unmanaged Norway spruce (Picea abies) forests throughout the Carpathian Mountains of central and eastern Europe, where windstorms and native bark beetle outbreaks are the dominant natural disturbances.
We inventoried forest structure on 453 plots (0.1 ha) spanning a large geographical gradient (1000 km), coring 15–25 canopy trees per plot for disturbance history reconstruction (tree core total n=11,309). Our specific objectives were to: (1) classify sub-hectare-scale disturbance history based on disturbance timing and severity; (2) classify current forest structure based on tree size distributions (live, dead, standing, downed); (3) characterize structural development pathways as revealed by the association between disturbance history and current forest structural complexity.
We used hierarchical cluster analysis for the first two objectives and indicator analysis for the third. The disturbance-based cluster analysis yielded six groups associated with three levels of disturbance severity (low, moderate, and high canopy loss) and two levels of timing (old, recent) over the past 200years. The structure-based cluster analysis yielded three groups along a gradient of increasing structural complexity. A large majority of plots exhibited relatively high (53 %) or very high (26 %) structural complexity, indicated by abundant large live trees, standing and downed dead trees, and spruce regeneration.
Consistent with conventional models of structural development, some disturbance history groups were associated with specific structural complexity groups, particularly low-severity, recent (very high complexity) and high-severity, recent (moderate complexity) disturbances. In other cases, however, the distribution of plots among disturbance history and structural complexity groups indicated either divergent or convergent pathways. For example, multiple disturbance history groups were significantly associated with the high complexity group, demonstrating structural convergence. These results illustrate that complex forest structure – including features nominály associated with old-growth – can be associated as much with disturbance severity as it is with conventional notions of forest age. In addition, natural disturbances can induce relatively high levels of tree mortality while simultaneously contributing to the development of structural complexity at sub-hectare scales.
This study in primary forests can inform policy and management initiatives intended to emulate natural forest dynamics across mountain landscapes, particularly given projections of increasing disturbance aktivity under global change.
Description of attachments: On the first picture you can see transition plot showing associations between disturbance history groups and current forest structure groups. Box height corresponds to number of plots in each group. Line thick-ness corresponds to the relative number of plots associated with each pairwise combination. We tested these transitions quantitatively with indicator analysis.
The second one shows conceptual model of disturbance-mediated structural development in primary Norway spruce forests shaped by a mixed-severity disturbance regime.
FULL VERSION ABOVE
Disturbances, both natural and human induced, influence forest dynamics, ecosystem functioning, and ecosystem services. Here, we aim to evaluate the consequences of natural disturbances on the magnitude and dynamics of tree- and stand-level biomass accumulation from decadal to centennial scales. We use tree-ring data from 2301 trees and biometric data from 4,909 trees sampled in 96 plots (each 1000 m2) to quantify the influence of mixed severity disturbance regimes on annual aboveground biomass inkrement (AGBI) and total aboveground biomass accumulation (AGB) across a mountainous monotypic Norway spruce (Picea abies (L.) Karst.) primary forest.
We hypothesise that the multiple internal and external factors constraining tree growth will cause differences in tree and stand-level biomass trajectories in these natural forests. Although we found that tree-level AGB growth increases with tree size,we also found that tree age and disturbance legacies plays a crucial role for AGB in the investigated Norway spruce forests. Importantly, while younger trees of the same diameter class have an average current AGBI rate that is ~225 % higher than older trees (300–400 years), we find trees that have been suppressed for up to 120 years can respond vigorously when competition is reduced. On average, post disturbance AGBI was ~400 % greater than pre-disturbance AGBI. Growth of suppressed trees, independent of their age, followed similar trajectories after canopy accession. While aboveground biomass generally increased through time, the time since disturbance and disturbance severity are important co-predictors for stand-level AGBI and AGB. These forests regained most of the above ground living biomass over short interval (~50 years) after low intensity disturbances.
The highest stand-level living AGB was observed on plots that experienced >40% canopy removal 160–190 years ago, whereas the highest AGBI occurred in plots disturbed recently within the past 40–50 years. Our results emphasize the importance of including both individual tree age and disturbance legacies to accurately characterize biomass dynamics and trajectories in forest ecosystems. Importantly, the period of time that a tree is in the canopy, and not tree age, modulates the trajectory of tree level AGBI. Growth rates begin to decline after ~30 years (tree-rings width) and ~100 years (AGBI) in the canopy. We demonstrate that even late-seral forests can rapidly regain biomass lost to low intensity disturbance.
Description of attachments: On the first picture you can see geographical location and period of occurrence of maximum disturbance severity (colour gradient) of the 96 study plots (0.1 ha each). The reconstructed disturbance history is based on the growth pattern of 23–25 randomly selected trees per plot. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.) Source of digital elevation model: http://www.reverb.echo.nasa.gov; country boundaries: http://www.diva-gis.org. Updated from Trotsiuk et al. (2014).
The second one shows tree-level aboveground biomass increment (AGBI)andring-width increment (TRW)in relation to age (a,c) and time since main canopy accession event. (b, d). All trees were grouped based on the duration of suppression period into 10 years step classes (colour gradient) and the average chronology was truncated when the sample depth drops below 15 individuals. Trees show similar growth trends in both AGBI and tree-ring increment after main canopy accession event (b, d). Dashed lines (c) were ﬁtted to the TRW values shortly before and after the canopy accession event from each curve, and show a steady potential for growth increase over tree age. (For interpretation of the references to colour in this ﬁgure legend, the reader is referred to the web version of this article.)