When we (scientists) talk and write about complexity in recent years, the focus is on complex nonlinear dynamics, and related phenomena such as deterministic chaos, dynamical instability, some forms of self-organization, fractal geometry, etc.  These are forms or sources of complexity that are intrinsic to the structure of dynamical systems, but these are hardly the only things that make systems complex. So, to make sure we don’t forget the elements of complexity that transcend so-called “complexity science,” I present the Top 10 Forms of Complexity in Earth Surface Systems (ESS). ESS is a blanket term that includes geomorphic systems, landscapes, ecosystems, soil systems, etc.  Even though the items are numbered, they are actually in no particular order. Many ESS may exhibit only a few of these forms, and still be quite complex!

The list I was gonna do has already been done (http://grogsmovieblogs.com/). 

Forms of Complexity in Earth Surface Systems

In many of my writings I advocate an alternative to reductionist approaches to science. By alternative, I mean a complementary, different way of doing things, not a replacement for reductionism. Many excellent reviews of scientific approaches, viewpoints, and methodological stances exist by historians, philosophers and sociologists of science, and by scientists themselves. I do not intend to review or critique these various approaches here. Further, I have no intent to deny the value or necessity of reductionist science. The crux of my argument is that a reductionist approach, by itself, is inadequate or incomplete for understanding Earth.

The American Heritage Dictionary defines reductionism as an attempt or tendency to explain a complex set of facts, entities, phenomena, or structures by another, simpler set, and provides a quote from John Holland:

For the last 400 years science has advanced by reductionism ... The idea is that you could understand the world, all of nature, by examining smaller and smaller pieces of it. When assembled, the small pieces would explain the whole.

For the past five years or so, I have been working on adaptations of algebraic or spectral graph theory to study geomorphic, pedological, and ecological systems. My most recent development (unpublished, for reasons that will become clear in a moment) is some methods for measuring the complexity of historical sequences in Earth surface systems.

The idea is that a historical sequence represents a series of different states or stages—for example, vegetation communities along a successional trajectory; river channel morphological states; different soils in a paleosol sequence; depositional environments in a stratigraphic sequence, nodes of phylogenetic trees in biological evolution, etc.  These are treated as directed graphs. The states or stages are the graph nodes or vertices, and the historical transitions are the edges or links between the nodes.

Some comments from a reviewer on a recent manuscript of mine dealing with responses to disturbance in geomorphology got me to thinking about the concept of disturbance in the environmental sciences. Though the paper is a geomorphology paper (hopefully to be) in a geomorphology journal, the referee insisted that I should be citing some of the “foundational” ecological papers on disturbance. These, according to the referee, turned out to be papers from the 1980s and 1990s that are widely cited in the aquatic ecology and stream restoration literature, but are hardly foundational in general.

Consideration of the role of disturbance goes back to the earliest days of ecology, and is a major theme in the classic papers of, e.g., Warming, Cowles, and Clements in the late 19^th and early 20^th centuries. A general reconsideration (“reimagining” is the term many would use, but I’ve grown to hate that overused word) of the role of disturbance in ecological systems was well underway by the 1970s, and the last five years or so have seem some very interesting syntheses of these emerging ideas (two I especially like are Mori, 2011 and Pulsford et al., 2014).

One of the classic principles/relationships in biogeography is called the species-area curve, relating the number of different species found (usually of some particular taxonomic group; e.g., birds or plants) to the area sampled. These curves are usually well fit by an exponential relationship:

S = c A ^b

where S is the number of species, A is area, c is a constant representing the number of species in the smallest area sampled, and b represents the rate of increase of species with area. While b could be greater than 1 if major biogeographical boundaries are transgressed (so that whole new sets of species are encountered), otherwise b < 1, and usually much less; 0.25 is a fairly common value.

Juanjo Ibanez and I (in separate studies) found that similar trends apply to soil diversity, with S in this case indicating number of different soil types (e.g., soil series). In his very broad scale analyses, Juanjo also found b » 0.25, while in my landscape-scale studies b was in the range of 0.6.  Syntheses of this work are found in the book Pedodiversity (CRC Press, 2013) edited by Ibanez and James Bockheim.

The online version of my new article exploring biogeomorphology from the perspective of niche construction and extended phenotypes is now out. The abstract is below. I appreciate my colleague Daehyun Kim encouraging me to stick with some of the more speculative and provocative ideas here. I was about to back off from them at one point, but he encouraged me to go for it.

Reference: Phillips, J.D. 2015. Landforms as extended compositive phenotypes. Earth Surface Processes and Landforms DOI: 10.1002/esp.3764.

I recently submitted a manuscript to Catena, entitled Hillslope Degradation by Trees in Central Kentucky. The reviews came back generally positive, and requesting minor to moderate revisions. I took care of those revisions, and resubmitted. The paper was then sent to a third referee, who pretty thoroughly trashed it. Catena's editor then rejected it (with option to resubmit). However, I am at an age & stage where I have to pick my battles, and this is not one I choose to fight. But I still think the paper has some worthwhile stuff in it, so I have posted it online. You can get it here. 

The abstract is below, but be forwarned that the third reviewer deemed it "quite poorly written", "hard to follow," and a "mishmash of various statements." I don't think it's that bad . . . .      

What is the relationship between the diversity of resources (e.g., space, sunlight, water, nutrients) and biodiversity? In most cases it is direct and positive—that is, the greater the diversity of resources the greater the biodiversity.  The relationship is also often mutually reinforcing—that is, byproducts, detritus, and the organisms themselves increase the diversity of the resource base. Of course, ultimately both resource and biodiversity are limited by both abiotic and biotic controls. The relationships look something like this: