Soils, regoliths, and the landforms and surfaces they occupy change and evolve over time. A key issue is the extent to which their development is convergent or divergent. Whereas convergent development leads to less complexity over time, divergent development increases complexity, as initially similar soils become increasingly more differentiated. Traditionally, pedological theory has focused on divergent evolution in the vertical dimension, as initially undifferentiated parent materials develop horizonation and layering due to pedogenesis. At the same time, convergence in evolution of the soil cover has been emphasized, whereby soils evolve toward some attractor state (e.g., zonal, mature, or climax soils). This paper is a review and synthesis of recent research on changes in complexity of soilscapes over time, focusing on convergent and divergent development. Special attention is given to evidence of divergent pedogenesis (as historically, the emphasis has been on convergent trends) and methods to detect and analyze changes in soil complexity.
Convergent pedogenesis at the landscape scale (as well as analogous concepts of landscape evolution and ecological succession) has long been recognized and traditionally considered normative. Thus, its implications and associated conceptual frameworks are well understood by pedologists. Divergent pedogenesis (as a fairly common occurrence rather than an occasional aberration) has a much more recent scientific history. Thus, outstanding questions remain: Under what circumstances is soil development convergent or divergent? What are the implications for soil (and landscape and ecosystem) evolution where divergence is dominant? How do mode shifts (c.f. Phillips, 2014) occur between convergent and divergent pathways?
Divergent versus convergent evolution is directly related to soil complexity from two general perspectives. With respect to evolutionary trajectories, convergence or divergence implies changes in complexity over time in the form of decreasing or increasing variability, irregularity, differentiation, and diversity. Thus, measuring, estimating, or assessing convergence and divergence entails measuring or modeling changes in complexity. From the perspective of soil complexity more broadly, complexity has many important aspects and implications, including pedodiversity, spatial variability, and pedometrics, as well as evolutionary pathways. However, with respect to pedogenesis, questions about convergence and divergence are arguably the most fundamental. Specifically, changes in complexity over time are relevant to the following:
- Models and understanding of soil formation and development: These provide the lenses through which we evaluate soils. Viewing the soil from different perspectives can lead to quite different conclusions, and as discussed below, some frameworks are explicitly linked to convergent (especially) and divergent development. If only convergence or divergence is dominant, then it is important to choose an appropriate conceptual model. If both are significant, it implies a need to use multiple frameworks or one that allows for either convergence or divergence. This also applies to genesis and development of landscapes, ecosystems, and hydrologic systems, because pedological, geomorphic, ecological, and hydrologic system development is inextricably intertwined.
- Linking pedological change to changes in soil forming factors: To what extent is pedological change attributable to changes in factors of soil formation, disturbances, or intrinsic feedbacks? Is pedological change proportional to that of environmental controls? This is particularly relevant for soil (and other Earth surface system) responses to climate, anthropic, and other environmental changes, as potential changes in complexity have profound implications for the methods, context, and uncertainty of predictions.
- Interpretation of paleosols, soil stratigraphy, and soil memory: Are observed features attributable to single or multiple potential causes or developmental trajectories? Is the magnitude or variability of preserved features likely to be disproportionately small or large compared with the driving factors? How does convergence/divergence influence the preservation of soil features or properties?
- Explaining soil heterogeneity: Convergent and divergent pedogenesis imply fundamentally different hypotheses and assumptions (and therefore eventually different conclusions and interpretations) about variation of soils in space and over time.
There exist multiple aspects of soil complexity, including complexity of individual pedons or weathering profiles (e.g., Phillips, 2000 ; 2001a ; Peh et al., 2010 ; Montagne et al., 2013), or complexity of the soil cover (soil maps or landscapes; e.g., Fridland, 1976 ; Hole and Campbell, 1985 ; Ibáñez et al., 1995). One can also consider complexity of soils as holistic entities (e.g., soil types or series) or of more specific soil properties or features. Soil complexity is inextricably intertwined with soil variability, irregularity, and predictability. Soil complexity is also fundamental to pedodiversity (Richter and Babbar, 1991 ; Ibàñez et al., 2013 ; Phillips, 2013a), which itself has multiple aspects, including richness (number of different entities present) and evenness (relative abundance of entities). Complexity is also linked to some aspects of soil memory (Phillips and Marion, 2004 ; Targulian and Goryachkin, 2008).
This synthesis will not attempt a comprehensive review of all aspects of soil complexity, although they are all interrelated. The focus will be on changes in complexity and convergent versus divergent evolution and on complexity of soil landscapes, with soil types or taxa (generally at the series level) as the fundamental units.
Convergent and Divergent Soil Development
Dominant ideas about soil formation, ecological succession, and geomorphic landscape evolution in the 20th century (and earlier) developed in a common intellectual milieu and all focused on convergent evolution toward, for example, a mature or climax soil, climax vegetation community, or a peneplain (or later steady-state equilibrium) landscape (Osterkamp and Hupp, 1996 ; Huggett, 1998). Other developmental pathways were acknowledged, but in the prevailing conceptual models, they were interpreted as abnormal exceptions or as the result of disturbances or interruptions of normal patterns. In pedology, this was expressed as development toward a mature, climax, zonal soil, characterized by dominantly progressive pedogenesis (promoting increased levels of pedogenic development) and proisotropic (increasingly differentiated) vertical or stratigraphic development (Schaetzl and Thompson, 2015).
In the late 1980s, Johnson and colleagues promoted a view of pedogenesis that gave regressive pedogenetic pathways and proanisotropic processes equal conceptual weight and recognizing that either or both sets of pathways and processes (progressive/regressive and proisotropic/proanisotropic) may be common and “normal” in different soils (Johnson et al., 1987; 1990 Johnson and Watson-Stegner, 1987). My own early research into pedogenetic complexity was based on linking these ideas to complex nonlinear dynamics and divergent development of soil landscapes (e.g., Phillips, 1993a;b;c ; 1995).
Soil formation and development, and variation of soil properties, may be dominated by extrinsic (allogenic) controls (e.g., the classic soil forming factors of climate, biota, topography, parent material, and age or time), intrinsic (autogenic) factors involving processes and phenomena within the soil, or some combination. Intrinsic soil relationships may be dynamically stable or unstable. For example, under some circumstances, feedbacks between weathering and soil thickness may produce a steady-state thickness, whereby surface removals are approximately balanced by soil production through weathering (e.g., D'Odorico, 2000). Although these conditions are often unmet (e.g., Johnson et al., 2005), where they do obtain soil thickness is closely related to topography, and are minimally variable in similar slope positions. By contrast, interactions among vertical moisture movement, material translocation, and hydraulic conductivity are often dynamically unstable, resulting in extreme local spatial variability in the depth to illuvial layers and the wetting front geometry (e.g., Montagne et al., 2013). Denoting extrinsic controls as soil-forming factors (SFFs), soils dominated by extrinsic factors, or by intrinsic factors that are mainly dynamically stable, lead to convergent pedogenesis with soil variation that is less than the variability of SFF. Likewise, soils dominated by stable intrinsic phenomena will be convergent, with variation proportional to, or less than, that of the SFF. Where soil development is dynamically unstable, pedogenesis will be divergent, with variation greater than that of SFF.
Recent studies on the role of initial conditions in landscape and ecosystem development, in contrast to approaches that implicitly or explicitly assume convergent development, postulate divergent development. More homogeneous conditions exist in early stages, with increasing heterogeneity over time. For instance, in their review of the role of initial development processes as key factors in landscape development, Raab et al. (2012) identified a common pattern of lower complexity initially, with complexity increasing over time because of sensitivity to initial conditions and amplification of variations. A study of interrelationships among substrate, topography, and vegetation in early stages of development by Biber et al. (2013) also assumed increasing complexity. However, as Maurer and Gerke (2016) pointed out, such studies are in their infancy and are based on a notion (tacitly assumed, as they are focused on young systems) that whatever the pathways of early soil and landscape development, a state of dynamic equilibrium tends to be approached. Note, however, that the latter may simply be a deceleration of change or a relaxation time in response to disturbance rather than a normative steady-state attractor.
A mode is defined as the way or manner in which something occurs. It is not unusual for soils and other Earth surface systems to shift between convergent and divergent modes of evolution as the processes involved reach various limits or thresholds (Phillips, 2014). For example, consider pedon-scale chemical weathering as shown in Figure 1. Parent material properties (e.g., structure, lithology, mineralogy) or microtopography may create initial variations in weathering susceptibility that are often exaggerated because of positive feedbacks (Nahon, 1991 ; Twidale, 1991, 1993). This divergence increases the weathering contrast until weatherable minerals are depleted in the more strongly weathered zones. Then geochemical kinetics rather than moisture availability becomes the major limiting factor for weathering rates. This switch results in eventual convergence of weathering rates and the stage or extent of weathering (Phillips, 2001a ; 2014). Conceptual models of initial codevelopment of topography, soils, and vegetation often tacitly, if not explicitly, assume divergence in early stages with eventual convergence (Raab et al., 2012 ; Maurer and Gerke, 2016).
Just as divergent systems may switch to convergent modes, soils formed under extended periods of convergent evolution can transition to divergent development by tectonic, geomorphic, climatic, biological, and anthropic disturbances. Small, localized disturbances can also precipitate divergence because of unstable growth of disturbance effects. A number of examples are available from the literature on woody vegetation invasions of grasslands, typically driven by climate change, human agency, and/or disturbances. The ecological transition often results in increasing spatial fragmentation that may be expressed in soil morphology as well as soil chemical and ecological properties (e.g., Daryanto et al. 2013 ; Verboom and Pate, 2013 ; Podwojewski et al., 2014). Similar divergence may occur because of shrub or tree removal in woodlands (e.g., Shankey et al., 2012).
DETECTION AND MEASUREMENT OF CONVERGENCE AND DIVERGENCE
Because convergence and divergence are closely related to dynamical instability and deterministic chaos, methods for detecting and analyzing dynamical instability and chaotic dynamics are relevant. Reviews and syntheses of these methods in the contexts of pedology, geosciences, and ecology are given elsewhere (Phillips, 1999; 2004; 2006 ; Sivakumar 2009; 2017 ; Turcotte, 2012). Divergence and convergence also imply either increasing or decreasing spatial variability over time. Thus, methods of assessing spatial variation, which are highly advanced in soil science, are also relevant when applied in a historical or change-over-time context (Phillips, 2004; 2006). This includes applications of fractal analysis to soils (see overview by Pachepsky et al., 2000), which is closely linked to complex nonlinear dynamics and scaling properties. While most applications of fractals have addressed problems in soil physics, hydrology, taxonomy, and soil structure, these methods have also been used to quantify heterogeneity at broader scales.
Convergence or divergence in a soilscape can be considered in terms of the mean difference between any two randomly selected points initially, δ(ο), and at time t, δ(t). These differences can relate to the soil as a whole (e.g., a profile development index or taxonomic distance) or specific properties (e.g., soil thickness, cation exchange capacity). In the latter case, different portions or properties of a soil could show different trends (c.f. Phillips, 2000 ; Richter and Markewitz, 2001). If δ(ο)/δ(t) or δ(t)/δ(t + i) > 1, this indicates convergence; δ(ο)/δ(t) or δ(t)/δ(t + i) < 1 divergence. That is, differences are either being reduced or exaggerated (on average).
Rosenstein et al. (1993) explicitly related δ and its changes to deterministic chaos (or the absence thereof) and dynamical stability in nonlinear dynamical systems. Phillips (1993a, 1999) adapted the method to soil and other Earth surface systems. Thus, when soils are treated as dynamical systems, there is a direct equivalence among dynamical stability, absence of deterministic chaos, convergence, and a decrease in complexity. Likewise, a direct equivalence exists between instability, chaos, divergence, and increasing complexity.
Table 1 shows studies demonstrating or suggesting instability and chaos in development of soils. This is not to imply that all studies applying such methods find evidence of divergence (see, e.g., Ryzhova, 1996 ; Phillips, 2016a). Most do (Table 1), but this is largely because many of the earlier studies were specifically looking for evidence of chaotic pedogenesis, and many others applied the methods to cases where observed soil complexity could not be readily explained otherwise.
A number of studies that do not explicitly mention complexity theory, nonlinear dynamics, chaos, and instability provide empirical evidence of divergent pedogenesis (Table 2). The remainder of this section will focus on techniques developed since (roughly) 2000 and that do not necessarily fit obviously into broad categories of stability analysis, chaos detection, or analysis of spatial variability.
Richness-area analysis as an approach for assessing potential divergence was developed by Phillips (2001b) to examine the relative importance of extrinsic (SFF) versus intrinsic (local instabilities) factors in pedodiversity. Where the latter are prominent, divergent development is present. Denoting S as the number of different soil types (richness) and A as area, S = f(A), a power function has generally been found to be the best fit; that is,
If the relationship is developed by successively sampling larger or additional areas, the c represents richness in the smallest area, whereas b indicates the rate of increase of richness with area. For this type of curve (as opposed to a relationship developed by sampling discrete units of varying area), c ≥ 1, and b > 0.
A can be divided into n homogeneous elementary units A i, i = 1, 2,…, n, such that A = ΣA i and S i = c i A i bi. If the elementary units are indeed constant (within observational precision) with respect to SFF, soil variability within an A i must be due to intrinsic rather than extrinsic factors. If no intrinsic variability is present, c i = 1; b i = 0. Therefore, c i reflects inherent richness of unit i, and b i the tendency for larger areas or more samples of unit i to have increasing pedodiversity independent of environmental heterogeneity related to SFF.
where k i is the number of soil types in unit i already encountered in other units and m an adjustment factor for taxa (e.g., series) counted in multiple elementary units (m = S/ΣS i ≤ 1). Therefore,
with the overbars indicating mean values.
therefore indicates the relative importance of between-unit (extrinsic) sources of variability and within-unit (intrinsic) variability. In many cases, the number of samples N, N i can be substituted for A, A i in any of the equations above. For an agricultural soil landscape, Phillips (2001b) found a b i /b ratio of 1.145, indicating a greater importance for chaotic, intrinsic, within-unit variation. Phillips and Marion (2007) also found b i /b > 1 for soils in a subtropical forest setting. Other pedological applications of this type of richness-area analysis include Svoray and Shoshany (2004) and Petersen et al. (2010)), which both found evidence of divergent evolution. The approach is analogous to the species-area relationships commonly used in biogeography since the 1960s. Ibáñez et al. (1995; 2005; 2009) have applied richness-area analysis in a similar way to analyze scale relationships and geographical patterns of pedodiversity.
Graphs and Networks
Graph theory and network-based approaches to pedology, geomorphology, and ecology have developed rapidly in recent years. Some of these are directly relevant to assessing divergent pedogenesis. Heckmann et al. (2015) and Phillips et al. (2015) distinguish between spatially explicit applications of graph theory in Earth and environmental sciences and structural graphs. Spatially explicit graphs have locations or spatially-discrete entities as their nodes (for instance, the starting and end points of landslides in Heckmann and Schwanghardt, 2013). Like spatial analytic methods in general, graph-based methods of assessing variability and complexity can be used to assess convergence or divergence when applied at two or more periods or iterations of system evolution.
Structural graph models are network representations of the structure of soil systems. These may be empirically derived state-and-transition models, correlation structures, theoretically derived networks based on fundamental equations, or system models. Applications of graph theory to structural models of Earth surface systems typically seek to identify or measure the complexity or synchronization properties of environmental state transitions or to deduce geosystem properties from network structures. This can include indications of possible divergence.
Soil spatial adjacency graphs (SAGs) are a hybrid where the nodes (soil types) are not spatially explicit, but links are based on whether or not the soil types are spatially contiguous in the landscape. Phillips (2013b) developed methods for analyzing SAG and associated soil factor sequences that allow assessment of how much complexity in the spatial pattern is associated with gradients or sequences of SFF. Complexity not explained by SFF implies either unidentified state factors or dynamical instability and divergent pedogenesis. One of the two coastal plain agricultural soil landscapes analyzed by Phillips (2013b) showed evidence of divergence. These methods were extended by Phillips (2016a) and applied to a soil system in karst terrain, where only minor evidence of complexity not associated with SFF was found.
Daněk et al. (2016) analyzed the SAG for the soil landscape of an old-growth forest using a sequentiality index that indicates the extent to which soils have gradual versus abrupt variations in underlying soil factors. They found that geomorphology is the primary control over a very locally complex soil pattern, but microtopography and local disturbances, mostly related to the effects of individual trees, are also critical. Spatial complexity greater than that of the local SFF implies divergent pedogenesis (Daněk et al., 2016).
Evolutionary and Historical Approaches
Pedogenesis cannot be directly observed over periods of more than a few decades, and in most cases, original conditions are unknown, although an increasing number of multi-decadal field observations are, or will become, available. Furthermore, although paleosols and fossils within soils and paleosols are keys for paleoenvironmental reconstruction, fossil records of modern soils are rare. This makes it difficult to evaluate convergent or divergent trends.
Of major importance to initial conditions are the many situations where anthropic activities or major disturbances create new environments for soil formation or reset the pedogenetic clock. For instance, Montagne et al. (2013) documented chaotic development and divergence in Albeluvisols triggered by artificial drainage. In this example, positive feedbacks associated with moisture flux, translocation, and resulting morphological modifications drove the chaotic divergence. Field evidence suggests that such local divergence due to similar feedbacks may be common (Fig. 2).
Another example is where rapid or recent geomorphic changes create new surfaces for pedogenesis. For instance, Roland et al. (2016) examined a vegetation/soil chronosequence across a set of different-aged terraces exposed by melting ice over a 54-year period. They linked the spatial pattern of vegetation expansion (mainly balsam poplar) to changes in the soil. Sparsely vegetated sites allow for rapid invasion or expansion of plants such as mosses that insulate and paludify the soil. Roland et al. (2016) indicated established vegetation communities have cold and/or acidic soil profiles that impede establishment of balsam poplar. However, early successional species such as balsam poplar, with traits that allow it to persist and fundamentally alter the vegetation mosaic, may serve as a vanguard of a profound landscape change. The spatial mosaic of the transformative species thus influences, and is influenced by, changing or evolving soil properties. The result is divergent pedogenesis. There is significant potential to advance this type of research. For example, in some of my own work on effects of vegetation in early stages of soil formation on newly exposed bedrock, the association of biotic weathering with local geological structural features implies divergent regolith development, at least initially (Phillips et al., 2008). However, although work elsewhere in the region suggests this is likely the case (Phillips and Marion, 2005; 2007), we did not explore this sufficiently to go beyond mere suggestion.
Chronosequences are the classic method for evaluating pedogenetic trends, although establishment of a good chronosequence is difficult and interpretation is not always straightforward (e.g., Huggett, 1998 ; Sauer, 2010; 2015). Chronosequence studies have mostly used single or mean characterizations of the soil at each time increment. However, as chronosequences have spatial and temporal dimensions, several different soil types may exist during the same stage. Some soil chronosequence studies address, or at least acknowledge, variations within periods and changes in variability or diversity over time (Sondheim and Standish, 1983 ; Thompson, 1983, 1992 ; Barrett and Schaetzl, 1993 ; Phillips, 1993a, 2001c ; Eppes and Harrison, 1999 ; Barrett, 2001 ; Richter and Markewitz, 2001 ; Saldaña and Ibàñez, 2004 ; Toomanian et al., 2006 ; Caldwell et al., 2012). Mostly, these studies show an increase in soil richness over time, indicating divergence; however, some show convergence or are ambiguous in this regard. (e.g., Howard et al., 1993), and in some cases, both convergent and divergent trends could be observed between different stages in the same chronosequence (e.g., Zilioli et al. 2011 ; Botha and Porat 2007 ; Gracheva, 2011).
A typical objective in chronosequence research is to identify rates and trends of soil development or of changes in soil properties over time. Indeed, the assumption in a chronosequence is that all SFF other than time or age are constant (although this is rarely, if ever, strictly true). If the chronosequence assumption is valid, observed changes unrelated to time imply either unknown SFF, transient effects of disturbances, or dynamical instability and potential divergence. A review of pedogenesis in old landscapes of tropical Africa (Da Costa et al., 2015) identified a need to distinguish among soil parameters that are, or are not, closely related to soil age, which could assist in making the distinction above between unknown SFF, transient effects, and divergence. Da Costa et al. (2015) also underscored the role of geological rejuvenation of landscapes and geomorphic reworking by water and wind erosion in complicating paleopedological reconstructions—although, as mentioned previously, in some cases, these may provide opportunities for shorter time frame observations of pedogenesis. In the quite different environmental setting of postglacial pedogenesis in formerly ice-covered landscapes, Johnson et al. (2015) made similar points in their study of soils formed on a temporal sequence of relatively young, post-glacial landforms with varying parent materials and climate histories.
The temporal patterns of changes revealed in chronosequences or other historical sequences can be represented as a graph or network, and Phillips (2015; 2016b) has developed methods specifically for analyzing their complexity. Path stability is a measure of chronosequence robustness; that is, the degree to which developmental trajectories are sensitive to disturbances or change (Phillips, 2015). Several generic chronosequence structures indicate five general cases: (1) path-stable reversible progressions, (2) neutrally path-stable irreversible progressions, (3) path unstable with very low divergence, (4) path unstable with low divergence, and (5) highly divergent complex multiple pathways (Phillips, 2015). Path stability is probably rare in soil chronosequences because of the directionality inherent in most of them. A complex soil chronosequence on the lower coastal plain of North Carolina was analyzed as described previously, indicating very low divergence. This outcome is consistent with field evidence, 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 (Fig. 3; Phillips, 2015).
Phillips (2016b) studied the complexity of network representations of evolutionary sequences more generally, with a pedological case study. He found that converging and diverging graphs with the same topology did not differ with respect to graph complexity measures so that change in complexity over time depends on increasing or decreasing richness. Results also showed that identification of additional changes in the historical record (e.g., soil shifts in paleosol sequences) produces more structurally complex but less historically contingent representations (Phillips, 2016b).
Soil morphology provides indicators of past or ongoing change, such that the trajectory of change can be discerned from careful profile description and analysis. Standard soil stratigraphic and morphological indicators included in typical profile descriptions sometimes indicate the direction of pedological changes and, combined with a suitable metric such as Kolmogorov entropy, can be used to detect signatures of divergence (or convergence) in weathering profiles and soils. In a study of subtropical ultisols, Phillips (2000) found evidence of both convergence and divergence, linked to relative rates of processes associated with horizon differentiation in surficial horizons by the formation of transitional AE or A&E horizons because of secondary podzolization, thickening of the solum at the weathering front, and surface erosion.
Soil stratigraphic variation can, in some cases, be analyzed with techniques that allow determination of whether variability is inherited from parent material or acquired during pedogenesis. Where the latter is dominant (as in the east Texas weathering profiles studied by Phillips, 2001a), this indicates divergence, whereby parent material anisotropy is magnified and overprinted by pedogenesis. Inherited versus acquired properties were also assessed by Peh et al. (2010), who analyzed soil geochemical data from Croatia with a trimming procedure, in which the outliers were removed and attributed to nonlinear causes precluding simple cause-and-effect relationships (the necessary condition of a Gaussian distribution). The geochemical background (equivalent to the inherited portion) was then defined as the normal range of data of the remaining (trimmed) data.
In addition to large landscape scale disturbances resetting the clock for pedogenesis, the effects of relatively small local disturbances can give insight into trends in complexity over time. If a local disturbance has impacts on soil morphology, convergent pedogenesis will cause these effects to be reduced or smoothed out over time, returning toward its original self. Divergence will be characterized by persistence of the local pedological effects well beyond the duration of the disturbance and includes their possible amplification. This has been most explicitly studied with respect to effects of individual trees on soil morphology. Such effects are associated with uprooting, locally accelerated weathering, stemflow and concentrated hydrological fluxes, root penetration of subsoils and parent materials, mass displacement by tree growth, and other processes.
Vasenev and Targulian (1995), for instance, developed a model for development of forest podzols by uprooting, based on Russian field experience, involving eventual convergence to the background soil. However, other studies show divergent soil development associated with persistence of pedologic impacts of uprooting (e.g., Šamonil et al., 2014; 2015; 2016). Overall, both convergent return to background soils and divergent persistence and growth of uprooting effects may occur (see reviews by Ulanova, 2000 ; Šamonil et al., 2010 ; Pawlik, 2013).
Biomechanical effects of individual trees, along with facilitation of chemical weathering and hydrological effects, can result in local deepening of soils beneath trees, which has feedback effects that promote future tree establishment at the same microsites. This produces the hypothesis that divergent evolution of soil thickness occurs, with increasingly thicker soils at tree-occupied sites. This has been tested and confirmed in several studies (Phillips, 2008 ; Shouse and Phillips, 2016). However, this phenomenon may only be applicable where soil thickness is less than coarse rooting depth of trees.
The idea of chronosequence, lithosequence, biosequence, toposequence, and climosequences is to assess the effect of a single SFF by sampling where all factors other than the one of interest are considered to be constant (only minimal variability, not true constancy, can realistically be obtained). These are generally carried out where significant qualitative differences or a strong quantitative gradient in the SFF of interest exists.
Where the concern is primarily with soil heterogeneity or convergence/divergence, however, a comparative analysis between variation in soils or their properties and that of a key SFF need not involve the kinds of differences typically reflected in SFF sequence studies. For example, in the study of microtopographic effects on soil morphology by Miller et al. (1994), they used sites where all factors except microtopography were constant. As the observed morphological effects (driven by local moisture fluxes) were disproportionately large compared with the microtopographic variability (Miller et al., 1994), this indicates divergent pedogenesis. To distinguish this type of work from typical broader-scale toposequences, and so on, I refer to them as monosequences. Other examples include Price (1994) , Phillips et al. (1996) , Dubroeucq and Volkoff (1998)), Borujeni et al. (2010), and Šamonil et al. (2011).
One issue in monosequence studies is measurement techniques and the level of detail in the SFF and soil characterizations. In central Kentucky, for example, geological mapping at the same 1:24,000 spatial scale as soil maps has identified more surficial formations than there are soil series (Phillips, 2013a). This implies convergent evolution—but the soil and geological mapping were conducted at different times by different individuals and organizations and for different purposes. A local-scale analysis in the same region found multiple soil types in identical parent materials with other SFF constant, implying divergence (Phillips, 2013a).
PATHWAYS TO CHANGING SOIL COMPLEXITY
Three sets of pathways to changes in soil complexity can now be identified. These pathways are likely not exhaustive, nor are they mutually exclusive, as increasing complexity and decreasing complexity pathways could operate contemporaneously in the same soilscape, with the net effects depending on relative rates and intensities.
The first set of pathways is associated with changes in the environmental controls and influences on pedogenesis—the SFF (Fig. 4). As topography, hydrology, biota, and other factors change, related changes in soil can occur. Changes in SFF themselves can involve convergence (for instance, when biota are homogenized by monoculture cropping or a highly successful invasive species) or divergence (e.g., topographic divergence during fluvial landscape dissection). Convergent development of an SFF would promote convergent development and decreasing complexity of soil, other things being equal (Fig. 5). In the Cumberland Plateau region of the United States, for example, valley side slopes expose various types and combinations of sandstones, conglomerates, shales, and siltstones (as well as coal and limestone in some areas). Each parent rock has distinct sets of soils associated with it. However, development of a colluvial cover on many slopes effectively reduces parent material variability, resulting in a reduction in soil richness to a few soil series formed in colluvium, independent of the underlying bedrock (see, e.g., Kelley, 1990).
Soil-forming factor divergence will promote soil divergence, but the latter may be greater or less than the differentiation of the SFF. Soil divergence greater than or equal to that of the SFF leads to increasing complexity. This is the case, for example, in the coevolution of soils and landforms associated with fluvial dissection in the Iberian Peninsula (Ibáñez et al., 1990), where increasing pedological complexity was documented. However, if the rate of pedological divergence is disproportionately small compared with the SFF, decreasing complexity may occur—if not absolutely, at least with respect to soil-SFF relationships. This appears to be the case at the regional (but not necessarily local) scale in the Inner Bluegrass physiographic region of Kentucky, where the richness of geological parent materials exposed by Quaternary incision is greater than the number of recognized soil series (Phillips, 2013a).
A second set of pathways is related to sublandscape scale, local disturbances (Fig. 6). Disturbances that modify soils create, at least temporarily, increasing differentiation of the soil cover. If the frequency of such disturbances is greater than the relaxation time for pedological recovery (i.e., the disturbances reoccur before recovery is complete), increases in soil complexity persist. Several examples exist related to faunalturbation, where patchy habitats concentrate repeated animal foraging and nesting, which can enrich soil complexity by evolving to distinct soil “islands” within the soilscape (Wilkinson et al., 2009). Even if disturbance frequency is less than relaxation time, divergent pedogenesis can result when dynamical instabilities associated with net positive feedbacks are present. This is the case, for instance, with interactions among runoff, soil erosion, vegetation, and soils that promote divergence with respect to an increasingly complex spatial mosaic in semiarid environments (Puigdefabregas et al., 1999). Another example is local vegetation disturbance in sand dunes, which creates blowouts that grow unstably and persist, with attendant effects on dune soils (Gares and Nordstrom, 1995).
Decreasing complexity and convergent evolution can occur, however, in disturbed soil systems dominated by dynamical stability and net negative feedbacks. This occurs, for example, when soils disturbed by tree uprooting recover to the background soil (Vasenev and Targulian, 1995).
Even without (or independently of) changes in environmental factors or disturbances, changes in soil complexity can occur because of intrinsic factors and feedbacks. These pathways are shown in Figure 7. Because of the prevalence of thresholds, storage effects, lag times, and other factors, soil systems are nonlinear. When these nonlinear dynamics are stable, pedogenesis is convergent, and complexity is reduced. For example, feedbacks between organic matter accumulation and decomposition rates may lead to a steady state in organic matter content or O-horizon thickness. Effects of local variations in litter inputs or decay rates may thus be smoothed, thereby decreasing spatial complexity (e.g., Ryzhova, 1996). Cases where initial variations associated with parent material are reduced as the soil develops toward a climatically controlled zonal soil are another example (Chesworth, 1973 ; Chandran et al., 2005), although parent rock effects may often persist. Complex nonlinear dynamics are often associated with dynamical instability, however, which fosters divergent evolution and increasing complexity independent of external forcings or disturbances. This can occur, for example, with respect to illuvial accumulation and moisture flux in podzolized soils (Phillips et al., 1996) or because of feedbacks among weathering and moisture penetration (Phillips, 2001a).
Soil complexity is directly related to soil spatial and temporal variability, pedodiversity, conceptual models of pedogenesis and soil geography, and appropriate representations of soil information. Evolution of, and changes in, soil complexity are directly related to divergence and convergence in pedogenesis.
Traditional theories and conceptual models of soil formation have focused on stratigraphic differentiation at the pedon scale driven primarily by vertical processes. However, many possibilities exist between the end members of layering entirely inherited from parent material and wholly created by pedological processes, and viewing soil stratigraphy through a particular conceptual lens can lead to quite different interpretations of the same profile. Thus, a recognition that both convergent and divergent evolution are common, and a better understanding of the circumstances under which they occur, will lead to better interpretations of soils, paleosols, and weathering profiles (Johnson et al., 1987; 1990; 2005 ; Johnson and Watson-Stegner, 1987 ; Wilkinson et al., 2009).
Traditional theories and conceptual models of soil formation have focused on convergence of the soil cover at the landscape scale, in the form of progress or maturation toward zonal or mature, climax soils. Recognition that divergent evolution also occurs has had dramatic impacts on soil formation theory, and soil geography and geomorphology (e.g., Richter and Yaalon, 2012 ; Toomanian, 2013 ; Šamonil et al., 2014 ; Schaetzl and Thompson, 2015 ; Temme et al., 2015 ; Ibàñez and Pérez-Gómez, 2016). These expanded views have even greater relevance in the context of increased interest in the coevolution of soils, ecosystems, and landforms; and in the response of these environmental systems to climate and other environmental changes.
Convergence, divergence, and complexity also have recursive importance for chronosequence studies. On one hand, explicit attention to changes in complexity in chronosequences holds great promise for addressing the evolution of complexity in soils. On the other hand, appreciation of various theoretical frameworks that accommodate both convergence and divergence is critical for chronosequence interpretations (Sauer, 2010; 2015).
Convergence, Divergence, and Complexity
Pedogenesis may be convergent or divergent. This review emphasizes evidence of divergent evolution of the soil cover, but this is in counterbalance to many others indicating convergence. Much of the work cited herein indicates both, or either of, convergent and divergent pedogenesis.
Convergence and divergence may vary according to what aspects or properties of soils are considered, as well as the spatial and temporal scale. Certainly progressive, proanisotropic divergence could be dominant at the profile-pedon level, coupled with convergence at the landscape scale—this is the view implied in traditional views of pedogenesis. However, this is only one possibility. One relatively common finding is that divergence at more local scales may be coupled with convergence (or at least strongly constrained divergence) at broader regional scales (e.g., Phillips, 2001c; 2013a ; Phillips and Marion, 2007). The same soil or soil system might be divergent or convergent at different periods and undergo changeovers between the two modes (e.g., Johnson et al., 1987 ; Phillips, 2014 ; Maurer and Gerke, 2016).
Pedology and Complexity Theory
Much of the work on complexity in pedology and related fields is strongly linked to the study of complex nonlinear dynamical systems. Particularly early on, many of the associated methods and concepts were imported from mathematics, systems theory, and physics. Compared with pedology more generally, this work was more abstract and mathematical. However, as has been the case in pedometrics and quantitative soil geography, soil scientists quickly adapted and developed methods and concepts for complex nonlinear dynamics specifically tailored to soils and grounded in pedology. Concurrently, phenomena associated with nonlinear dynamics such as deterministic chaos were more directly linked to divergent pedogenesis and field evidence. This is revealed in the methodological review here. Richness-area analysis, for instance, arose directly from emerging concepts of pedodiversity. A subset of those methods were adapted specifically to separate intrinsic complexity from that controlled by SFF.
Graph theory methods are quite broadly applied across the sciences, and their increased application in environmental sciences was inevitable. Many applications to soils, particularly of spatially explicit approaches, diffused into pedology naturally via pedometrics and landscape ecology. Structural graph methods, based on algebraic and spectral graph theory, still borrow heavily from mathematics and from applications in systems theory and engineering. However, since 2013, several graph and network techniques have been developed that arise directly from pedological problems rather than graph theory (e.g., Phillips, 2013b ; 2015 ; 2016a ; Daněk et al., 2016).
Chronosequences have been an important component of pedology and plant ecology for at least a century, and it was straightforward to deploy them to investigate convergent and divergent trends in pedogenesis. Indeed, some of the earliest pedology-based (rather than grounded in, e.g., chaos theory or fractal geometry) studies of instability and chaos in soils were based directly on chronosequences. Nearly 20 years ago, Huggett's (1998) synthesis of soil chronosequence studies concluded that soils “may progress, stay the same, or retrogress, depending on the environmental circumstances.” Further progress is contingent on attention to spatial variability within time increments in chronosequences.
Pedological indicators have also long been central to soil science, in soil descriptions, taxonomy, and mapping, as well as in paleopedology, soil geomorphology, and soil stratigraphy. The use of indicators to assess convergent and divergent trends is thus a direct link between soil complexity studies and field pedology. Monosequence approaches are also clearly linked to traditional pedology, based on a straightforward notion of the relative variability of soil properties related to variability of environmental controls.
Consideration of the effects of disturbances in pedology parallels thinking in disturbance ecology (Huggett, 1998). In both fields, this led naturally to debates about stability, multiple versus single recovery pathways, and convergence/divergence. Disturbances also provide opportunistic “experiments” to examine pedological recovery trajectories with an eye toward convergent and/or divergent trends.
In the 1980s and 1990s, soil and geoscientists commonly complained—with justification—that notions of environmental complexity associated with emerging ideas in complexity theory were difficult to link to empirical observations and more often derived from abstract complexity theory rather than pedology, ecology, and geosciences. Although studies of soil complexity continue (as they should) to engage with complexity science more broadly, they are now firmly grounded in pedology.
Changes in Complexity
“Complexity” is often conflated with a view of complexity science that focuses on nonlinear dynamics, coupled interactions over a broad range of scales, and emergent or self-organized behavior. However, both complexity concepts and the sources of complexity in soils and other Earth systems are much broader (Phillips, 2016b) than the notions typically associated with contemporary complexity science.
This is reflected in the pathways to increasing or decreasing soil complexity discussed here. Those pathways indeed reflect changes associated primarily with complex soil system dynamics. However, they also include trajectories determined by environmental controls and pathways that reflect a combination of external forcings (disturbances) and intrinsic pedological dynamics.
Complexity may apply to a number of different dimensions, perspectives, and aspects of soils. Here, the attention is mainly on the complexity of soil types within soil landscapes. Soil complexity is intertwined with spatial and temporal variability, pedodiversity, conceptual models of pedogenesis and soil geography, and representations of soil information.
Increases and decreases in soil complexity are directly related to divergent and convergent pedogenesis, which are in turn closely related to dynamical stability and chaos in soil systems. Thus, there is a strong link between contemporary complexity science and nonlinear dynamical systems and the study of soil complexity. However, both the sources and concepts of soil complexity are much broader than the perspectives typically encompassed by the term complexity science.
Traditional theories and conceptual models of soil formation have focused on convergence of the soil cover at the landscape scale in form of progress toward zonal or mature climax soils. Although soil scientists long recognized that divergent evolution also occurs, a view of divergence as a common occurrence, rather than an occasional, atypical aberration, is more recent. It is now clear that soil complexity may decrease, increase, or remain roughly constant over time and that none of these is necessarily “normal” or abnormal. The answer to the question of whether pedogenesis is convergent or divergent is either, neither, or both.
Measurement and analysis of (changes in) soil complexity—even from nonlinear dynamical or complexity science perspectives—is now firmly linked to empirical field pedology. In addition to strong methodological links to pedometrics and soil geography, standard tools for assessing complexity include chronosequences and other historical approaches, relationships between soil properties and soil forming factors, and use of pedological indicators.
A typology of eight generic pathways to changes in soil complexity can be identified. Three are based on changes in environmental controls (soil forming factors) that may affect soil complexity. These may result in increasing or declining complexity, depending on whether the SFF themselves are converging or diverging, and the relative magnitudes of soil and state factor divergence. Three additional pathways are linked to local soil disturbances. If these occur less frequently than the relaxation time for soil responses, and if internal pedological dynamics are stable, then the disturbance-induced complexity is reduced over time. Otherwise, divergence and increasing complexity occurs. Two additional pathways are directly related to dynamical stability of intrinsic pedological processes, which may result in decreasing (in the case of stability) or increasing complexity, either in concert with or independently of environmental controls or disturbances.
The author thanks Daniel Gimenez for suggesting the review and Dan Richter, Juanjo Ibàñez, and an anonymous reviewer for the constructive comments.
Bárány-Kevei I. 1998. Geoecological system of karst. Acta. Carsologica. 27:13–25.
Barrett L. R. 2001. A strand plain soil development sequence in northern Michigan, USA. Catena. 44:163–186.
Barrett L. R., Schaetzl R. J.. 1993. Soil development and spatial variability on geomorphic surfaces of different age. Phys. Geog. 14:39–55.
Biber P., Seifert S. M., Zaplata W., Schaaf H., Pretzsch H., Fischer A.. 2013. Relationships between substrate, surface characteristics, and vegetation in an initial ecosystem. Biogeoscience. 10:8283–8303.
Borujeni I. E., Mohammadi J., Salehi M. H., Toomanian N., Poch R. M.. 2010. Assessing geopedological soil mapping approach by statistical and geostatistical methods: a case study in the Borujen region, central Iran. Catena. 82:1–14.
Botha G., Porat N.. 2007. Soil chronosequence development in dunes on the southeast African coastal plain, Maputaland, South Africa. Quat. Internat. 162–163:111–132.
Caldwell T. G., Young M. H., McDonald E. V., Zhu J.. 2012. Soil heterogeneity in Mojave desert shrublands: biotic and abiotic processes. Water Resour. Res. 48:W09551. doi: 10.1029/2012WR011963.
Caruso T., Rillig M. C.. 2011. Direct, positive feedbacks produce instability in models of interrelationships among soil structure, plants, and arbuscular mycorrhizal fungi. Soil Biol. Biochem. 43:1198–1206.
Chandran P., Ray S. K., Bhattacharya T., Srivastava P., Krishnan P., Pal D. K.. 2005. Lateritic soils of Kerala, India: their mineralogy, genesis, and taxonomy. Austral. J. Soil Res. 43:839–852.
Chesworth W. 1973. The parent rock effect in genesis of soil. Geoderma. 10:215–225.
Crowther J. 1987. Ecological observations in tropical karst terrain. West Malaysia. III. Dynamics of the vegetation-soil-bedrock system. J. Biogeog. 14:157–164.
Da Costa P. Y., Nguetnkam J. P., Mvoubou C. M., Togbe K. A., Ettien J. B., Yao-Kouame A.. 2015. Old landscapes, pre-weathered materials, and pedogenesis
in tropical Africa: how can the time factor of soil formation be assessed in these regions? Quat. Int. 736:47–74.
Daněk P., Šamonil P., Phillips J. D.. 2016. Geomorphic controls of soil spatial complexity in a primeval mountain forest in the Czech Republic. Geomorphology. 273:280–291.
Daryanto S., Eldridge D. J., Wang L. X.. 2013. Spatial patterns of infiltration vary with disturbance in a shrub-encroached woodland. Geomorphology. 194:57–64.
D'Odorico P. 2000. A possible bistable evolution of soil thickness. J. Geophys. Res. 105B:25927–25935.
Dubroeucq D., Volkoff B.. 1998. From Oxisols to Spodosols and Histosols: evolution of soil mantles in the Rio Negro basin (Amazonia). Catena. 32:245–280.
Eppes M. C., Harrison J. B.. 1999. Spatial variability of soils developing on basalt flows in the Potrillo volcanic field, southern New Mexico: prelude to a chronosequence study. Earth Surf. Proc. Land. 24:1009–1024.
Estrada-Medina H., Graham R. C., Allen M. F., Jiménez-Osornio J. J., Robles-Casoico S.. 2013. The importance of limestone bedrock and dissolution karst features on tree root distribution in northern Yucatán, México. Plant & Soil. 362:37–50.
Fridland V. M. 1976. The Pattern of the Soil Cover. Israel Program for Scientific Translations, Jerusalem.
Furbish D. J., Fagherazzi S.. 2001. Stability of creeping soil and implications for hillslope evolution. Water Resour. Res. 37:2607–2618.
Gares P. A., Nordstrom K. F.. 1995. A cyclic model of foredune blowout evolution for a leeward coast: Island Beach, New Jersey. Ann. Assoc. Am. Geogr. 85:1–20.
Gracheva R. 2011. Formation of soil diversity in the mountainous tropics and subtropics: rocks, time, and erosion. Geomorphology. 135:224–231.
Hackney C. T., Brady S., Stemmy L., Boris M., Dennis C., Hancock T., O’Byron M., Tilton C., Barbee E. 1996. Does intertidal vegetation indicate specific soil and hydrologic conditions? Wetlands. 16:89–94.
Heckmann T., Schwanghardt W.. 2013. Geomorphic coupling and sediment connectivity in an alpine catchment—exploring sediment cascades using graph theory. Geomorphology. 182:89–103.
Heckmann T., Schwanghart W., Phillips J. D.. 2015. Graph theory—recent developments and its application in geomorphology. Geomorphology. 243:130–146.
Hole F. D., Campbell J. B.. 1985. Soil Landscape Analysis. Rowman and Allanheld, Totowa, NJ.
Howard J. L., Amos D. F., Daniels W. L.. 1993. Alluvial soil chronosequence in the inner coastal plain, central Virginia. Quat. Res. 39:201–213.
Huggett R. J. 1998. Soil chronosequences, soil development and soil evolution: a critical review. Catena. 32:155–172.
Ibáñez J. J., Ballesta R. J., Álvarez A. G.. 1990. Soil landscapes and drainage basins in Mediterranean mountain areas. Catena. 17:573–583.
Ibàñez J. J., Caniego J., San Jose F., Carerra C.. 2005. Pedodiversity-area relationships for islands. Ecol. Mod. 182:257–269.
Ibáñez J. J., De-Alba S., Bermúdez F. F., García-Álvarez A.. 1995. Pedodiversity: Concepts and Tools. Catena. 24:215–232.
Ibàñez J. J., Pérez-Gómez R.. 2016. Diversity of soil-landscape relationships: state of the art and future challenges. In: Zinck J. A., Metternicht G., Bocco G., Del Valle H. F. (eds.) Geopedology. An Integration of Geomorphology and Pedology for Soil and Landscape Studies. Springer, Berlin, pp. 183–191.
Ibáñez J. J., Pérez-Gómez R., San José Martínez F. 2009. The spatial distribution of soils across Europe: a fractal approach. Ecological Complexity. 6:294–301.
Ibàñez J. J., Pérez -Gonzalez A., Jimenez-Ballesta R., Saldaña A., Gallardo-Díaz J.. 1994. Evolution of fluvial dissection landscapes in Mediterranean environments. quantitative estimates and geomorphological, pedological, and phytocenotic repercussions. Z. Geomorph. 38:105–109.
Ibàñez J. J., Vargas R. J., Vázquez-Hoehne A.. 2013. Pedodiversity state of the art and future challenges. In: Ibàñez J. J., Bockheim J. G. (eds.) Pedodiversity. CRC Press, New York, pp. 1–28.
Johnson B. G., Layzell A. L., Eppes M. C.. 2015. Chronosequence development and soil variability from a variety of sub-alpine, post-glacial landforms and deposits in the southeastern San Juan Mountains of Colorado. Catena. 127:222–239.
Johnson D. L., Domier J. E., Johnson D. N.. 2005. Animating the biodynamics of soil thickness using process vector analysis: a dynamic denudation approach to soil formation. Geomorphology. 67:23–46.
Johnson D. L., Keller E. A., Rockwell T. K.. 1990. Dynamic pedogenesis
: new views on some key soil concepts and a model for interpreting Quaternary soils. Quat. Res. 33:306–319.
Johnson D. L., Watson-Stegner D.. 1987. Evolution model of pedogenesis
. Soil Sci. 143:349–366.
Johnson D. L., Watson-Stegner D., Johnson D. N., Schaetzl R. J.. 1987. Proisotropic and proanisotropic processes and pedoturbation. Soil Sci. 143:278–292.
Kelley J. A. 1990. Soil Survey of Pike County. Kentucky. U.S, Department of Agriculture.
Kooch Y., Hosseini S. M., Scharenbroch B. C., Hojati S. M., Mohammadi J.. 2015. Pedodiversity in the Caspian forests of Iran. Geoderma Reg. 5:4–14.
Maurer T., Gerke H. H.. 2016. Processes and modeling of initial soil and landscape development: a review. Vadose Zone J. 15: doi:10.2136/vzj2016.05.0048.
Miller S. T., Brinn P. J., Fry G. J., Harris D.. 1994. Microtopography and agriculture in semi-arid Botswana. 1. Soil variability. Agric Water Manag. 26:107–132.
Minasny B., McBratney A. B.. 1999. A rudimentary mechanistic model for soil formation and landscape development. Geoderma. 90:3–21.
Minasny B., McBratney A. B.. 2001. A rudimentary mechanistic model for soil formation and landscape development II. A two-dimensional model incorporating chemical weathering. Geoderma. 103:161–179.
Montagne D., Cousin I., Josiere O., Cornu S.. 2013. Agricultural drainage-induced Albeluvisol evolution: a source of deterministic chaos. Geoderma. 193:109–116.
Nahon D. D. 1991. Self-organization in chemical lateritic weathering. Geoderma. 51:5–13.
Orson R. A., Howes B. L.. 1992. Salt marsh development studies at Waquoit Bay Massachusetts: influence of geomorphology on long-term plant community structure. Estuar. Coast. Shelf Sci. 35:453–471.
Nyman J. A., DeLaune R. D., Roberts H. H., Patrick W. H.. 1993. Relationship between vegetation and soil formation in a rapidly submerging coastal marsh. Mar. Ecol. Prog. Series. 96: 264–279.
Osterkamp W. R., Hupp C. R.. 1996. The evolution of geomorphology, ecology, and other composite sciences. In: Rhoads B., Thorn C. (eds.) The Scientific Nature of Geomorphology. John Wiley, New York, pp. 415–442.
Pachepsky Y., Crawford J. W., Rawls W. J.. (eds.) 2000. Fractals in Soil Science. Elsevier, Amsterdam.
Pawlik L. 2013. The role of trees in the geomorphic system of forested hillslopes—a review. Earth-Sci. Rev. 126:250–265.
Petersen A., Gröngöft G., Miehlich G.. 2010. Methods to quantify the pedodiversity of 1 km2
areas–results from African drylands. Geoderma. 155:140–146.
Peh Z., Miko S., Hasan O.. 2010. Geochemical background in soils: a linear process domain? An example from Istria (Croatia). Environ. Earth Sci. 59:1367. doi:10.1007/s12665-009-0125-2.
Phillips J. D. 1993a. Chaotic evolution of some coastal plain soils. Phys. Geogr. 14:566–580.
Phillips J. D. 1993b. Progessive and regressive pedogenesis
and complex soil evolution. Quat. Res. 40:169–176.
Phillips J. D. 1993c. Stability implications of the state factor model of soils as a nonlinear dynamical system. Geoderma. 58:1–15.
Phillips J. D. 1994. Deterministic uncertainty in landscapes. Earth Surf. Proc. Landf. 19:389–401.
Phillips J. D. 1995. Time lags and emergent stability in morphogenic/pedogenic system models. Ecol. Mod. 78:267–276.
Phillips J. D. 1999. Earth Surface Systems. Complexity, Order, and Scale. Basil Blackwell, Oxford, UK.
Phillips J. D. 2000. Signatures of divergence
and self-organization in soils and weathering profiles. J. Geol. 108:91–102.
Phillips J. D. 2001a. Inherited versus acquired complexity in east Texas weathering profiles. Geomorphology. 40:1–14.
Phillips J. D. 2001b. The relative importance of intrinsic and extrinsic factors in pedodiversity. Ann. Assoc. Am. Geogr. 91:609–621.
Phillips J. D. 2001c. Divergent evolution and the spatial structure of soil landscape variability. Catena. 43:101–113.
Phillips J. D. 2004. Divergence
, sensitivity, and nonequilibrium in ecosystems. Geogr. Anal. 36:369–383.
Phillips J. D. 2006. Deterministic chaos and historical geomorphology: a review and look forward. Geomorphology. 76:109–121.
Phillips J. D. 2008. Soil system modeling and generation of field hypotheses. Geoderma. 145:419–425.
Phillips J. D. 2013a. Nonlinear dynamics, divergent evolution, and pedodiversity. In: Ibàñez J. J., Bockheim J. (eds.). Pedodiversity. CRC Press, Boca Raton, FL, pp. 59–82.
Phillips J. D. 2013b. Sources of spatial complexity in two coastal plain soil landscapes. Catena. 111:98–103.
Phillips J. D. 2014. Thresholds, mode-switching and emergent equilibrium in geomorphic systems. Earth Surf. Proc. Landf. 39:71–79.
Phillips J. D. 2015. The robustness of chronosequences. Ecol. Mod. 298:16–23.
Phillips J. D. 2016a. Identifying sources of soil landscape complexity with spatial adjacency graphs. Geoderma. 267:58–64.
Phillips J. D. 2016b. Complexity of Earth surface system evolutionary pathways. Math. Geosci. 48:743–765.
Phillips J. D., Marion D. A.. 2004. Pedological memory in forest soil development. For. Ecol. Manage. 188:363–380.
Phillips J. D., Marion D. A.. 2005. Biomechanical effects, lithological variations, and local pedodiversity in some forest soils of Arkansas. Geoderma. 124:73–89.
Phillips J. D., Marion D. A.. 2007. Soil geomorphic classification, soil taxonomy, and effects on soil richness assessments. Geoderma. 141:89–97.
Phillips J. D., Perry D., Carey K., Garbee A. R., Stein D., Morde M. B., Sheehy J.. 1996. Deterministic uncertainty and complex pedogenesis
in some Pleistocene dune soils. Geoderma. 73:147–164.
Phillips J. D., Schwanghart W., Heckmann T.. 2015. Graph theory in the geosciences. Earth-Sci. Rev. 143:147–160.
Phillips J. D., Turkington A. V., Marion D. A.. 2008. Weathering and vegetation effects in early stages of soil formation. Catena. 72:21–28.
Podwojewski P., S. Grellier S., Mthimkhulu S., Titshall L.. 2014. How tree encroachment and soil properties affect soil aggregate stability in an eroded grassland in South Africa. Soil Sci. Soc. Am. J. 78:1753–1764.
Price A. G. 1994. Measurement and variability of physical properties and soil water distribution in a forest podzol. J. Hydrol. 161:347–364.
Puigdefabregas J., Sole A., Gutierrez L., del Barrio G., Boer M.. 1999. Scales and processes of water and sediment re-distribution in drylands: results from the Rambla Honda field site in southeast Spain. Earth-Sci. Rev. 48:39–70.
Raab T., Krummelbein J., Schneider A., Gerwin W., Maurer T., Naeth M. A.. 2012. Initial ecosystem processes as key factors of landscape development—a review. Phys. Geogr. 33:305–343.
Richter D. D., Babbar L. I.. 1991. Soil diversity in the tropics. Adv. Ecol. Res. 21:315–389.
Richter D. D., Markewitz D.. 2001. Understanding Soil Change. Cambridge University Press.
Richter D. D., Yaalon D. H.. 2012. The “Changing Model of Soil” revisited. Soil Sci. Soc. Am. J. 73:766–778.
Roland C. A., Stehn S. E., Schmidt J., Houseman B.. 2016. Proliferating poplars: the leading edge of landscape change in an Alaskan subalpine chronosequence. Ecosphere 7:article no. e01398, DOI: 10.1002/ecs2.1398.
Rosenstein M. T., Collins J. J., DeLuca C. J.. 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D. 65:117–134.
Ryzhova I. M. 1996. Analysis of the feedback effects of ecosystems produced by changes in carbon-cycling parameters using mathematical models. Eur. Soil Sci. 28:44–52.
Saldaña A., Ibàñez J. J.. 2004. Pedodiversity analysis at large scales: an example of three fluvial terraces of the Henares River (central Spain). Geomorphology. 62:123–138.
Šamonil P., Daněk P., Schaetzl R. J., Vasickova I., M. Valtera M.. 2015. Soil mixing and genesis as affected by tree uprooting in three temperate forests. Eur. J. Soil Sci. 66:589–603.
Šamonil P., Král K., Douda J., Šebková B.. 2008. Variability in forest floor at different spatial scales in a natural forest in the Carpathians: effect of windthrows and mesorelief. Can. J. For. Res. 38:2596–2606.
Šamonil P., Král K., Hort L.. 2010. The role of tree uprooting in soil formation: a critical literature review. Geoderma. 157:65–79.
Šamonil P., Valtera M., Bek S., Šebková B., Vrška T., Houška J.. 2011. Soil variability through spatial scales in a permanently disturbed natural spruce-fir-beech forest. Eur. J. For. Res. 130:1075–1091.
Šamonil P., Valtera M., Schaetzl R. J., Adam D., Vašíčková I., Daněk P., Janík D., Tejnecký V.. 2016. Impacts of old, comparatively stable, treethrow microtopography on soils and forest dynamics in the northern hardwoods of Michigan, USA. Catena. 140:55–65.
Šamonil P., Vasickova I., Daněk P., Janik D., Adam D.. 2014. Disturbances can control fine-scale pedodiversity in old-growth forests: is the soil evolution theory disturbed as well? Biogeosci. 11:5889–5905.
Sauer D. 2010. Approaches to quantify progressive soil development with time in Mediterranean climate—I. Use of field criteria. J. Plant Nut. Soil Sci. 173:822–842.
Sauer D. 2015. Pedological concepts to be considered in soil chronosequence studies. Soil Res. 53:577–591.
Schaetzl R. J., Thompson M. L.. 2015. Soils—Genesis and Geomorphology. (2nd ed.) Cambridge University Press.
Shankey J. B., Ravi S., Wallace C. S., Webb R. H., Huxman T. E.. 2012. Quantifying soil surface change in degraded drylands: shrub encroachment and effects of fire and vegetation removal in a desert grassland. J. Geophys. Res–Biogeosci. 117:G02025. DOI: 10.1029/2012JG002002.
Shouse M. L., Phillips J. D.. 2016. Soil deepening by trees and the effects of parent material. Geomorphology. 269:1–7.
Sivakumar B. 2009. Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward. Stochastic Environ. Res. Risk Assess. 23:1027–1036.
Sivakumar B. 2017. Chaos in Hydrology. Springer, Berlin.
Sondheim M. W., Standish J. T.. 1983. Numerical analysis of a chronosequence including an assessment of variability. Can. J. Soil Sci. 63:501–517.
Svoray T., Shoshany S.. 2004. Multi-scale analysis of intrinsic soil factors from SAR-based mapping of drying rates. Remote Sens. Environ. 92:233–246.
Targulian V. O., Goryachkin S. V. (eds.) 2008. Soil Memory. Russian Academy of Sciences, Moscow: (in Russian with English summary).
Temme A. J., Lange K., Schwering M. F.. 2015. Time development of soils in mountain landscapes—divergence
of properties with age. J. Soils Sed. 15:1373–1382.
Thompson C. H. 1983. Development and weathering of large parabolic dune systems along the subtropical coast of eastern Australia. Z. Geomorph. suppl. 45:205–225.
Thompson C. H. 1992. Genesis of podzols on coastal dunes in southern Queensland. 1. Field relationships and profile morphology. Austral. J Soil Res. 30:593–613.
Toomanian N., Jalalian A., Khademi H., Eghbal M. K., Papritz A.. 2006. Pedodiversity and pedogenesis
in Zayendeh-rud Valley, Central Iran. Geomorphology. 81:376–393.
Toomanian N. 2013. Pedodiversity and landforms. In: Pedodiversity. Ibanez J. J., Bockheim J. (eds.). CRC Press, Boca Raton, FL, pp. 133–152.
Turcotte D. L. 2012. Fractals and Chaos in Geology and Geophysics. (2nd ed.) Cambridge University Press, New York.
Twidale C. R. 1991. A model of landscape evolution involving increased and increasing relief amplitude. Z. Geomorph. 35:85–109.
Twidale C. R. 1993. The research frontier and beyond: granitic terrains. Geomorphology. 7:187–223.
Ulanova N. G. 2000. The effects of windthrow on forests at different spatial scales: a review. For. Ecol. Manage. 135:155–167.
Vasenev I. I., Targulian V. O.. 1995. A model for the development of sod-podzolic soils by windthrow. Eur. Soil Sci. 27: 1–16.
Verboom W. H., Pate J. S.. 2013. Exploring the biological dimensions to pedogenesis
with emphasis on the ecosystems, soils, and landscapes of southwestern Australia. Geoderma. 211–212:154–183.
Wilkinson M. T., Richards P. J., Humphreys G. S.. 2009. Breaking ground: pedological, geological, and ecological implications of soil bioturbutation. Earth-Sci. Rev. 97:257–272.
Zilioli D. M., Bini C., Wahsha M., Ciotoli G.. 2011. The pedological heritage of the Dolomites (northern Italy): features, distribution, and evolution of the soils, with some implications for land management. Geomorphology. 135:232–247.
Keywords:Copyright © 2017 Wolters Kluwer Health, Inc. All rights reserved.
Soil complexity; pedogenesis; divergence; convergence