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      where c₁ is the maximum rate of progressive pedogenesis and k₁ a coefficient describing the decrease in P rates as soil develops; c₂ is the maximum rate of regressive pedogenesis and k₂ a coefficient describing the decrease in R rates as soil develops (negligible). Phillips’s analysis revealed that soil development may display deterministic chaos, with soil profile state at any time being unique to the interplay of progressive and retrogressive soil‐forming processes and sensitive to initial conditions, rather than simply the age of the deposit in which the soil is formed. This possibility challenges the classic view of soil developing unidirectionally to an increasingly differentiated state. Rather, it shows that pedogenesis can proceed in different directions due internal dynamics and thresholds, a point first made by Daniel Muhs (1982, 1984; see also Phillips, 1993b, 2001, 2013, 2017; Chadwick & Chorover, 2001).

      1.4.2. Soil Catenas

In 1935, Geoffrey Milne, inspired by an idea of his colleague W. S. Martin (Brown, 2006), put forward the concept of the catena as a unified framework within which to study functional aspects of soils on hilly terrain. Milne was based at the East African Agricultural Research Station, Amani. A problem he faced was to map on a small piece of paper the complex entanglement of soils in a large piece of country. To surmount the problem, he took advantage of the fact that in many parts of East Africa, the topography over large tracts consists of little else but a repetition of crests and hollows, and a transect running from crest to hollow traverses very different soil profiles. Mapping the individual soils along the transect would be impossible in all but the most detailed of surveys. Nor, he reasoned, would it be necessary to do so because “they are not, properly speaking, individual soils at all, but are a compound soil unit of another kind in which a chain of profile‐differences occurs in a regular manner” (Milne 1935a, 192).

      Milne used the term catena (the Latin word for “chain”) to describe the regular repetition of soil profiles on crest–hollow topography. He considered adopting the word suite, as used by Gilbert Wooding Robinson (1936) to describe a range of differing soils related by topography in Wales. Robinson confined his suites to soils formed in the same parent material; he did not deal with such extreme differences in soils on hills and in valleys as Milne did. In summary, Milne proposed the term catena to describe the lateral variation of soils on a hillslope and reasoned that, owing to the agency of geomorphological and pedological processes, all soils occurring along a hillslope are related to one another. He was quite explicit that the topographic relationships of the soils were the prime concern, and that the uniformity of parent material was of subsidiary interest.

      At the time of its inception, the idea of a soil catena had a mixed reception, but it was generally hailed a valuable, if radical, idea. Its radicality stemmed from Milne’s contention that soils of the bottomlands are as important as soils on the ridges and his conclusion, shared by Sergei Neustruev (1915) before him, that soil‐climatic zones comprise zonal complexes rather than zonal soil types. At the time, it was mainly the well‐drained soils of a region that were singled out as characteristic zonal soil types and displayed on maps; the ill‐drained soils in valley bottoms were demoted to intrazonal status (see Gennadiyev & Bockheim, 2006).

      The catena concept was embellished by Thomas M. Bushnell (1942, 1946), who also identified precedents to it, though the term catena was assuredly first adopted by Milne. Bushnell (1942) argued that differences in soil drainage classes along a catena create a hydrological sequence, which suggestion led eventually to the idea of the soil association in USA’s Soil Survey. Some researchers believe that Bushnell narrowed the catena concept to slopes on which all soils have formed in the same parent material; however, that was only the case for his “simple catenas,” in which all soil‐forming factors were the same except for drainage conditions; in his “multiple catenas,” soil‐forming factors, including parent material, could vary. Even so, Bushnell’s emphasis on catenas as hydrological soil sequences did lead to the playing down of the role of slope‐influenced transport and depositional processes that had been held previously as important to the explanation of soil development along slopes (cf. Schaetzl, 2013, 146). Indeed, David Brown (2006, 79) went as far as to say, ‘The U.S. soil survey community distorted and confused Milne’s catena, and only through the work of Robert Ruhe in the 1950s and 1960s,” which re‐energized thinking about connections and interactions between soils and hillslope processes, “was the concept saved from scientific obscurity.”

      Topography was one of Jenny’s state factors of soil formation, and he termed variations in soil properties due to topography a toposequence (a contraction of topographical sequence). Unfortunately, partly owing to Bushnell, confusion surrounds the words toposequence and catena. Technically speaking, a toposequence involves variations of soils and soil properties in relation to topography (a state factor) with all other state factors held constant, which means that parent material should be uniform along the sequence; that would make a toposequence equivalent to Bushnell’s narrower definition of a catena. Jenny (1980, 280) suggested that a catena runs from crest to crest across an intervening valley, with the sequence from crest to valley bottom (what he called a half catena) being a toposequence (on uniform parent material). It seems helpful to use catena as originally defined by Milne and distinguish it from toposequence, where slope properties vary but parent material and all other state factors are constant.

      Back in Africa, a potent development that underscored the connection between hillslope soils and hillslope hydrology came from Cecil Morison (Morison et al., 1948; Morison, 1949), then at the Department of Agriculture, University of Oxford. Morison and his colleagues went on several expeditions to the Anglo‐Egyptian Sudan to investigate the soil–vegetation units. Preliminary work suggested that the catena concept could be usefully adopted as a framework of study in this area. He found it helpful to distinguish three zones (he termed them complexes) along a catena, each associated with a broad topographic site: the eluvial zone, the colluvial zone, and the illuvial zone. The eluvial zone is a high‐level site that loses water and soluble and suspended matter. Material washed from it is used to build up the colluvial and illuvial zones. The colluvial zone occupies slope sites. It receives material from soils in the eluvial zone and loses some of it to the illuvial zone. The illuvial zone occupies low‐level sites. In many cases it has very mixed parentage, consisting of either a simple mosaic or else a mosaic of zoned patterns, depending upon the amount and nature of drainage. It has three distinguishing characteristics: it receives more water than the climatic normal site, it receives much dissolved and suspended matter, and water is lost from it by surface movement, by drainage, or by evaporation.

Interestingly, at around the same time as Milne proposed the soil catena, Boris B. Polynov put forward the notion of geochemical landscapes. Polynov believed in the integrity of the landscape in producing,

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