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• 1
Article
Language: English
In: Ecological Modelling, 24 February 2015, Vol.298, pp.16-23
Description: Chronosequences are a fundamental tool for studying and representing change in Earth surface systems. Increasingly, chronosequences are understood to be much more complex than a simple monotonic progression from a starting point to a stable end-state. The concept of path stability is introduced here as a measure of chronosequence robustness; i.e., the degree to which developmental trajectories are sensitive to disturbances or change. Path stability is assessed on the basis of the largest Lyapunov exponent ( ) of an interaction matrix consisting of positive, negative, or zero entries based on whether existence of a given system state or stage promotes or facilitates (positive), prevents or inhibits (negative), or has no significant effect on transitions to another state. Analysis of several generic chronosequence structures represented as signed, directed, unweighted graphs indicates five general cases: Path-stable reversible progressions ( 〈 0); neutrally path-stable irreversible progressions ( = 0); path unstable with very low divergence (0 〈 〈 1); path unstable with low divergence ( = 1); and complex multiple pathways ( 〉 1). Path stability is probably relatively rare in chronosequences due to the directionality inherent in most of them. A complex soil chronosequence on the lower coastal plain of North Carolina was analyzed as described above, yielding = 0.843, indicating very low divergence. This outcome is consistent with pedological interpretations, and derives largely from the presence of self-limiting early stages, and a few highly developed states that inhibit retrogression back to many of the earlier stages. This kind of structure is likely to be common in pedological and hydrological sequences, but this suggestion requires further testing.
Keywords: Robustness ; Path Stability ; Chronosequence ; Coevolution ; Earth Surface Systems ; Environmental Sciences ; Ecology
ISSN: 0304-3800
E-ISSN: 1872-7026
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• 2
Article
Language: English
In: Geoderma, 01 April 2016, Vol.267, pp.58-64
Description: Soil landscapes often exhibit complex spatial patterns, with some aspects of soil variation apparently unrelated to measurable variations in environmental controls. However, these local, contingent complexities are not truly random or intrinsically unknowable. The purpose of this work is to develop and apply a method for identifying or teasing out causes of soil landscape complexity. Soil spatial adjacency graphs (SAG) represent the geography of soil landscapes as a network that can be analyzed using algebraic graph theory. These SAGs include linear sequential subgraphs that represent sequences of soil forming factors. The number and length of these soil factor sequences (SFS), and their associated spectral radius values, determine whether the SFS are sufficient to explain the spatial pattern of soil adjacency. SAGs and associated graph theory methods provide useful tools for guiding pedological investigations and identifying gaps in knowledge. The methods also allow sources of soil landscape complexity and variability to be determined in a way that can help assess the underlying deterministic sources of chaos and dynamical instability in pedology. The approach is applied to a soil landscape in central Kentucky, producing a SAG with 13 nodes (soil types) and 36 links indicating whether the soils occur contiguously. Five SFS were identified, the sum of whose spectral radius values is 6.35. The spectral radius of the SAG is 6.56, indicating that the SFS can explain most, but not all, of the complexity of the soil relationships. The analysis also points to potential environmental controls that could potentially enable full explanation.
Keywords: Soil Complexity ; Soil Variability ; Spatial Adjacency Graph ; Soil Factor Sequence ; Spectral Radius ; Agriculture
ISSN: 0016-7061
E-ISSN: 1872-6259
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• 3
Article
In: Earth Surface Processes and Landforms, January 2016, Vol.41(1), pp.16-26
Description: Biotic influences on geomorphology (and vice‐versa) are ubiquitous. This paper explores whether landforms may be extended (composite) phenotypes of biota, based on four criteria: process–form relationships between biota and landforms; evolutionary synchrony; selective pressure via ecosystem engineering and niche construction; and positive feedback benefitting the engineer organism(s). Coral reefs, peat bogs, biomantles, insect mounds, grassland soils, salt marshes, mangrove swamps, and some vegetation‐dependent sand dune types clearly meet these criteria. Karst landforms, meandering rivers, and tree uprooting pit‐mound systems meet the first three criteria, but positive feedback to engineer organisms has not been established. Research in biogeomorphology will surely identify other extended phenotypes. Implications are that biological evolution will continue to drive landscape metamorphosis, the appearance of new landform types, and presumably the disappearance of extended phenotypes associated with extinct species. Independently of extended phenotypes, tightly‐coupled geomorphological–ecological interactions such as coevolution, and biogeomorphic forms of ecosystem engineering and niche construction are common. The toposphere, encompassing Earth's landforms, is partly a biotic construct. Some elements would be present in an abiotic world, but the toposphere would not exist in anything resembling its contemporary state without a biosphere. This raises important questions with respect to Earth system evolution. The bio, litho‐, atmo‐, hydro‐, topo‐, and pedospheres coevolve at the global scale. Major biotic events have driven revolutions in the other spheres, but the atmosphere and the global hydrological system seem to have been relatively steady‐state at the global scale. The toposphere and pedosphere have not. This suggests that perhaps landforms and soils provide the major mechanisms or degrees of freedom by which Earth responds to biological evolution. Landforms and soils may thus be the ‘voice’ of the biosphere as it authors planetary change, even if clear biotic signatures are lacking. Copyright © 2015 John Wiley & Sons, Ltd.
Keywords: Biogeomorphology ; Niche Construction ; Extended Phenotype ; Biogenic Landforms ; Toposphere
ISSN: 0197-9337
E-ISSN: 1096-9837
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• 4
Article
Language: English
In: Geomorphology, 01 August 2016, Vol.266, pp.66-74
Description: Scale linkage problems in geosciences are often associated with a hierarchy of components. Both dynamical systems perspectives and intuition suggest that processes or relationships operating at fundamentally different scales are independent with respect to influences on system dynamics. But how far apart is “fundamentally different”—that is, what is the “vanishing point” at which scales are no longer interdependent? And how do we reconcile that with the idea (again, supported by both theory and intuition) that we can work our way along scale hierarchies from microscale to planetary (and vice-versa)? Graph and network theory are employed here to address these questions. Analysis of two archetypal hierarchical networks shows low algebraic connectivity, indicating low levels of inferential synchronization. This explains the apparent paradox between scale independence and hierarchical linkages. Incorporating more hierarchical levels results in an increase in complexity or entropy of the network as a whole, but at a nonlinear rate. Complexity increases as a power of the number of levels in the hierarchy, with and usually ≤ 0.6. However, algebraic connectivity decreases at a more rapid rate. Thus, the ability to infer one part of the hierarchical network from other level decays rapidly as more levels are added. Relatedness among system components decreases with differences in scale or resolution, analogous to distance decay in the spatial domain. These findings suggest a strategy of identifying and focusing on the most important or interesting scale levels, rather than attempting to identify the smallest or largest scale levels and work top-down or bottom-up from there. Examples are given from soil geomorphology and karst flow networks.
Keywords: Scale Linkage ; Scale Hierarchy ; Graph Theory ; Soil Geomorphology ; Fluviokarst ; Geography ; Geology
ISSN: 0169-555X
E-ISSN: 1872-695X
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• 5
Article
Language: English
In: Catena, December 2013, Vol.111, pp.98-103
Description: The spatial pattern of soils and soil properties in soil landscapes is considered here as a function of (1) systematic variation along catenas or associated with spatial patterns of soil-forming factors; and (2) local pseudo-random variations associated with local disturbances or small, unobserved variations in soil-forming factors. The problem is approached at two study sites in the U.S. Atlantic Coastal Plain using algebraic graph theory and the spectral radius of the soil adjacency matrix as a measure of complexity. The matrix is constructed based on the observed spatial contiguity of soil taxa, and soil factor sequences (SFS) are defined for each site based on systematic soil variation associated with variations in parent material, topography, sandy surface thicknesses, and secondary podzolization. The spectral radii of the networks described by the adjacency graphs are compared to those associated with the maximum for a graph of the same size, and the maximum associated with control entirely by variations in soil forming factors. At the Clayroot study site, which is entirely cropland, complexity of the adjacency matrix is less than Λ, the maximum that could be accounted for by the four identified SFS, due to redundant information in the SFS. The Littlefield site, by contrast, has a spectral radius greater than Λ. Here, where about half the site is forested, the contingent variation is likely associated with effects of individual trees on soil morphology. The utility of the adjacency analysis is in identifying whether soil heterogeneity is likely associated with SFS or with contingent factors not captured in SFS.
Keywords: Soil Spatial Heterogeneity ; Soil-Forming Factors ; Soil Factor Sequences ; Adjacency Matrix ; Spectral Radius ; Soil Landscape Complexity ; Sciences (General) ; Geography ; Geology
ISSN: 0341-8162
E-ISSN: 1872-6887
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• 6
Article
Language: English
In: Geomorphology, 15 March 2018, Vol.305, pp.173-184
Description: Geomorphic system resilience is often perceived as an intrinsic property of system structure and interactions but is also related to idiosyncratic place and history factors. The importance of geographical and historical circumstances makes it difficult to generate categorical statements about geomorphic resilience. However, network-based analyses of system structure can be used to determine the dynamical stability (= resilience) based on generally applicable relationships and to determine scenarios of stability or instability. These provide guidelines for assessing place and history factors to assess resilience. A model of coastal wetlands is analyzed, based on interactions among relative sea level, wetland surface elevation, hydroperiod, vegetation, and sedimentation. The system is generally (but not always) dynamically unstable and non-resilient. Because of gradients of environmental factors and patchy distributions of microtopography and vegetation, a coastal wetland landscape may have extensive local variations in stability/resilience and in the key relationships that trigger instabilities. This is illustrated by a case study where dynamically unstable fragmentation is found in two nearby coastal wetlands in North Carolina's Neuse River estuary—Otter Creek Mouth and Anderson Creek. Neither is keeping pace with relative sea level rise, and both show unstable state transitions within the wetland system; but locally stable relationships exist within the wetland systems.
Keywords: Resilience ; Dynamical Stability ; Coastal Wetlands ; Disturbance ; Sea Level Rise ; Geography ; Geology
ISSN: 0169-555X
E-ISSN: 1872-695X
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• 7
Article
In: Earth Surface Processes and Landforms, December 2017, Vol.42(15), pp.2623-2639
Description: Geomorphic and hydraulic units in river channels are closely linked to geodiversity and habitats, and thus to biodiversity. In a ~ 200 km reach of the lower Sabine River, in the northern Gulf of Mexico Coastal Plain, 72 different hydraulic units (HU) were identified in six geomorphic zones or river styles. Richness–area relationships indicate a linear or logarithmic increase of HUs, as opposed to the less steep power functions generally found in biogeographic species–area curves or in soil richness–area analyses. Different results are obtained when starting from the upstream or downstream end of the study area, indicating the importance of directionality in such analyses. These results show that HUs (and related habitats and biotopes) are both richer and more variable than a repeated sequence of units. The number of HUs inundated increases linearly with flow stage categories, indicating the importance of high within‐bank flows in maintaining and activating HUs. Aggregated HUs (AHUs) associated with similar geomorphic units are highly connected, both with respect to patterns of spatial adjacency and potential connectivity at similar flow levels. Spectral graph theory metrics applied to a graph representation of spatial adjacency shows a highly complex network with a high potential for rapid propagation of changes—and even more so for a graph based on flow connectivity. The flow connectivity graph shows far higher synchronization as indicated by algebraic connectivity. Thus suggests more rapid and coherent changes for processes driven by river flow, as opposed to phenomena driven by other factors between flow events. These findings have important implications for understanding relationships between geodiversity and habitat diversity, managing habitat and biodiversity, and linking the latter to instream flows. Copyright © 2017 John Wiley & Sons, Ltd. 72 different hydraulic units (HU) were identified in six geomorphic zones or river styles. Richness‐area relationships indicate a linear or logarithmic increase of HUs, as opposed to the less steep power functions generally found in biogeographic species‐area curves or in soil richness‐area analyses. Spectral graph theory metrics applied to a graph representation of spatial adjacency shows a highly complex network with a high potential for rapid propagation of changes—and even more so for a graph based on flow connectivity.
Keywords: Hydraulic Units ; Geomorphic Units ; Richness–Area Analysis ; Connectivity ; Complexity
ISSN: 0197-9337
E-ISSN: 1096-9837
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• 8
Article
Language: English
In: Mathematical Geosciences, 2016, Vol.48(7), pp.743-765
Description: Evolution of Earth surface systems (ESS) comprises sequential transitions between system states. Treating these as directed graphs, algebraic graph theory was used to quantify complexity of archetypal structures, and empirical examples of forest succession and alluvial river channel change. Spectral radius measures structural complexity and is highest for fully connected, lowest for linear sequential and cyclic graphs, and intermediate for divergent and convergent patterns. The irregularity index $$\beta$$ β represents the extent to which a subgraph is representative of the full graph. Fully connected graphs have $$\beta = 1$$ β = 1 . Lower values are found in linear and cycle patterns, while higher values, such as those of divergent and convergent patterns, are due to a few highly connected nodes. Algebraic connectivity ( $$\mu (\mathrm{G}))$$ μ ( G ) ) indicates inferential synchronization and is inversely related to historical contingency. Highest values are associated with fully connected and strongly connected mesh graphs, whereas forking structures and linear sequences all have $$\mu (G)$$ μ ( G ) = 1, with cycles slightly higher. Diverging vs. converging graphs of the same size and topology have no differences with respect to graph complexity, so complexity change is dependent on whether development results in increased or reduced richness. Convergent-divergent mode switching, however, would generally increase ESS complexity, decrease irregularity, and increase algebraic connectivity. As ESS and associated graphs evolve, none of the possible trends reduces complexity, which can only remain constant or increase. Algebraic connectivity may increase, however. As improving shortcomings in ESS evolution models generally result in elaborating possible state changes, this produces more structurally complex but less historically contingent models.
Keywords: Complexity ; Evolutionary trajectory ; Directed graph ; Algebraic graph theory
ISSN: 1874-8961
E-ISSN: 1874-8953
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• 9
Article
Language: English
In: Geomorphology, 01 January 2014, Vol.204, pp.208-216
Description: The fundamental geomorphic responses to environmental change are qualitative changes in system states. This study is concerned with the complexity of state transition models (STM), and synchronization. The latter includes literal and inferential synchronization, the extent to which observations or relationships at one time period can be applied to others. Complexity concerns the extent to which STM structure may tend to amplify effects of change. Three metrics—spectral radius, Laplacian spectral radius, and algebraic connectivity—were applied to several generic geomorphic STMs, and to three real-world examples: the San Antonio River delta, soil transitions in a coastal plain agricultural landscape, and high-latitude thermokarst systems. While the Laplacian spectral radius was of limited use, spectral radius and algebraic complexity provide significant, independent information. The former is more sensitive to the intensity of cycles within the transition graph structure, and to the overall complexity of the STM. Spectral radius is an effective general index of graph complexity, and especially the likelihood of amplification and intensification of changes in environmental boundary conditions, or of the propagation of local disturbances within the system. The spectral radius analyses here illustrate that more information does not necessarily decrease uncertainty, as increased information often results in the expansion of state transition networks from simpler linear sequential and cyclic to more complex structures. Algebraic connectivity applied to landscape-scale STMs provides a measure of the likelihood of complex response, with synchronization inversely related to complex response.
Keywords: State Transition ; State Transition Model ; Geomorphic Response ; Environmental Change ; Synchronization ; Complex Response ; Geography ; Geology
ISSN: 0169-555X
E-ISSN: 1872-695X
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• 10
Article
Language: English
In: Geomorphology, 15 September 2016, Vol.269, pp.1-7
Description: In some cases biomechanical effects of individual trees may locally deepen or thicken regolith, especially in relatively shallow soils. This biogeomorphic ecosystem engineering phenomenon is at least partly contingent on the geological setting. The purpose of this research was to gain further insight into the biogeomorphic phenomenon, and to assess the relative importance of biomechanical and geological effects. Earlier studies in the Ouachita Mountains of Arkansas showed that individual trees locally thicken the regolith via mechanisms associated with root penetration of bedrock. However, that work was conducted mainly in areas of strongly dipping and contorted rock, where joints and bedding planes susceptible to root penetration were thought to be common and accessible. This project extended the research to the Cumberland Plateau region of Kentucky, where flat, level-bedded sedimentary rocks are dominant. Soil depth beneath trees was compared to that of non-tree sites by measuring depth to bedrock beneath rotted tree stumps and at adjacent sites with 1.0 m. While soil thickness beneath stumps was greater in the Ouachita Mountains compared to the Kentucky sites, in both regions soils beneath stumps are significantly deeper than adjacent soils. Further, there were no statistically significant differences in the difference between stump and adjacent sites between the two regions. This suggests the local deepening effects of trees occur in flat-bedded as well as steeply dipping lithologies.
Keywords: Biogeomorphology ; Soil Depth Variability ; Biomechanical Weathering By Trees ; Tree Rooting ; Soil Thickness ; Geography ; Geology
ISSN: 0169-555X
E-ISSN: 1872-695X
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