FROM ORDER TO CAUSES A personal view concerning the principles of Syndynamics
FROM ORDER TO CAUSES A personal view concerning the principles of Syndynamics
László Orlóci
SCADA PUBLISHING London, Canada
Title ID: ISBN-13: ISBN-10: First edition 2000 Second edition 2014
Find further information at URL https://sites.google.com/site/statisticalecology/ FROM ORDER TO CAUSES All rights reserved © 2014 by L. Orlóci & M. Orlóci
[email protected]
“… in nature there is no ending and no standing still, but only an ever coming and ever going.” Anton Kerner von Marilaun 1863
This is a rewrite of an earlier essay from way back in the 1990s under similar title. Generally speaking science’s approach to finding governing principles is remarkably uniform: - order observed, - precisely described, and - causes sought. Newton’s deterministic laws of motion1 have come about this way, and so have the Darwin-Wallace theory2 of species evolution, Mendel’s rule of particle-based inheritance3, Kerner’s doctrine4, of community development, and Dokuchaev’s theory5 of pedogenesis. The question to be put in this essay is not about the validity of the order-to-causes approach. It worked before, it is working now, and there is no reason to assume that it will not lead to success in future scientific studies. As I see it, the central question is how to use the approach to its full advantage when we seek to identify process characteristics from which a general theory of syndynamics can emerge. A practical first approximation begins with the most general expressions of the process at the community level by the process trajectory’s parameter oscillations. What 1
Sir Isaac Newton (1642-1727).
2
Alfraid Russell Wallace (1823-1913), Charles Robert Darwin (1809-1882.The mechanisms in the broadest sense are random mutation and natural selection 3
Gregor Johann Mendel (1822-1884). His rule is statistical consistent with expectations for large numbers. 4
Anton Kerner von Marilaun (1831-1898). Kerner observed the tendency of populations already present in the community to make the site increasingly less favourable for their community and more favourable for others from outside. The modern term for this tendency is "facilitation" or "action-reaction feedback". 5
Dokuchaev (1883), a keen observer of nature, came to the conclusion that soils are specific to the natural vegetation under which they are found. He also observed that soils vary the parent material, climate, and topography. He knew all five undergo change in time. He added time to his equation and came up with the idea of soil development (pedogenesis), a process mediated by the ongoing physicochemical processes in the profile.
6 are these? Technically speaking, the trajectory is the imaginary turning and twisting line that compositional and functional transitions generate as the plant community undergoes change in time. Can the trajectory be made to appear as a mapping within a reference system of the ecologist’s choosing? It can be. In actual fact without a choice, the trajectory remains undefined. The choice of variables to be used as trajectory co-ordinate axes determine the nature of the trajectory. We refer to a reference system of such axes as our phase space6. The flexibility in choice allows to create a multiscale reference system in time and space, which I turn allow to determine the intensity of response specific to selected forcing factors, and to measure the extreme values of the effects at different scales. This makes the analysis multiscale and also hierarchical. A very simple example is Greig-Smith’s (1952) use of multiscaling to determine the scale (such as varying quadrat size within the same transect of contiguously laid quadrats on the ground) at which species’ response is most intensive with regard to a specific forcing variable (a soil condition). When random variation is considered and isolated, the analysis becomes statistical multiscaling. When the scale cuts through different levels of a hierarchy, the analysis is hierarchical. The tools which create the phase space mapping of the trajectory and allow to make statistical generalisations about its parameters are the tools of trajectory analysis (Orlóci 2014a and references therein). The phase space for this requires real data for response (for example a chronosere of density transitions in an assemblage of palynomorph taxa7 in sediments) and real data for intensity of forcing (for example a chronosere of global temperature oscillations). There are indirect ways to estimate transitions when a chronosere is not directly accessible. The most noted among these substitutes a surrogate developmental series (proxy series) for a natural series. The idealised Kerner (1863) vegetation chronosere is this type. Ecologists call such a construct a “space for time substitution” (Wildi and Schüts 2000).
Arguments in favour of the trajectory approach always mention that trajectory mappings allow the quantification of complex process characteristics by simple synthetic parameters8. These can identify process regularities, and ultimately, the critical scales of forcing. Deciphering process regularities in a foregoing sense is the central theme of the present Essay. 6
In trajectory analysis the phase space has an extra dimension, time or spatial contiguity.
7
Taxa identified by types of pollen grain or other plant tissues extracted from sedimentary materials.
8
These include: determinism (for which another term is directedness, the manner in which the process could be running its course if the attractor, the set of conditions that define process direction, has not been affected by random influences); phase structure (the segmentation of a process into significantly distinct intervals); periodicity (the tendency for certain process variables to revisit past states with regularity; complexity); fractal dimension (related to trajectory or process shape); parallelism (the tendency of the process to run its course in a manner of co-ordination with itself during different periods of time or with other trajectories of sites near or far).
The approach to finding governing principles in the manner of “regularity observed in nature, precise description made, causes identified” is one branch in a trichotomous approach. The second is pure reasoning from basic principles, and thirds, a combination of the two, such as what we see often practiced in mathematical ecology, etc. The first and the second are fundamentally different approaches. To see this point we should remember that under the “regularity observed in nature, precise description made, causes identified” approach we find the functional responses empirically then the integral function is functions for properties, such as the extreme points in te manner of differential equations. In the other extreme, we start with rates (not differential equations) then the integral functions are found. This is why the exponential function so often the conclusion. What about principles that interest us at the most? In mathematics a principle is the absolute truth independent of space or time. It is the same anywhere and anytime. A principle cannot perish since it has no currier. It is a generalization in the abstract. A mathematical principle can be discovered but it cannot be created. It always existed on its own independently from anything else - as an abstraction.9 I use Euclid’s equation a2=b2+c2 for my example. How do we know that it is has always existed? We know, because right angled triangles always existed.
In the world of empiricism, such as Ecology, a principle usually has context. When the context change, the principle will change. This is the reason why in ecology a statement hardly ever a Yes/No proposition. Taking this a step further we may say true or false is measured on a probability scale in statistics. This mandates the ecological approach to be a successive approximation. In this regard Poore’s 1962 essay is highly relevant.
9
Platonic realism is highly relevant here (http://en.wikipedia.org/wiki/Platonic_realism). So is a discussion by Brown, J.R. 1999.Phylosophy of mathematics. Routledge, New York.
8
1.1 Some readers will find it strange when they discover my decision to expel the term succession as a technical term from my Essay’s vocabulary. I see no reason to attach to it significance beyond its colloquial meaning: the act or an instance of one person or thing following another.10 What motivates me to do this is the worn out context. Consider for example the version as it is defined in Webster’s New World Dictionary & Thesaurus (Macmillan 1977): “[Succession is] the slow, regular sequence of changes in the regional development of communities of plants and associated animals, culminating in a climax characteristic of a specific geographical environment.” 1.2 The set of characteristics italicised by me will be seen extremely limiting when considered juxtaposed with the set of process properties I see as minimum requirement to capture the essence of the community assembly/disassembly process. What are these? (i) Temporal seriation of process stability and instability levels in terms of oscillating compositional transition velocity and acceleration and even potential energy. (ii) Structural dynamics by way of alternating linear to dominantly nonlinear process phases, (iii) Oscillating attractor which sets the momentary process directions, (iv) Cyclic change of process shape complexity seen as the fractal dimension oscillations. (v) Process parallelism, divergence, and convergence. I discuss these in a series of essays. “Statistical Ecology (2014) and “Quantum Ecology” (2013) have much on the topic. 1.3 What is my idea for a relevant definition? 10
Anderson (1986) and Fekete (1985) give comprehensive reviews of term and concepts.
It must be broad in scope able to be applied to any process speed, any type of regularity/irregularity condition, any level of process stability/instability, and any level parallelism or the lack of it within any realistic time frame and geographic extent. Further, an acceptable definition must make provision for real scale dependence of process and observation (Orlóci 2012). Without these perception becomes unreliable and the handling of convoluted random and non-random oscillations, in all phases and in all manifested characteristics of the process, impossible. 1.4 The use of “culmination” is ambiguous. It may even mislead by conjuring a process capable of reaching the state of standing still that Anton Kerner von Marilaun (1863) already rejected: “… in nature there is no ending and no standing still, but only an ever coming and ever going.” The stochastic attractor concept covers the idea well in the natural biological community process idea of a directed process well in which compositional transitions acceleration and deceleration in continuity. Trajectory analysis can trace such a process sensitively in comparable terms. 1.5 ‘Regularity’ in the Essay’s title implies reoccurrence of a state or condition as logic dictates. ‘Regularity’ is firm habit or behaviour. 1.6 When a specific regularity is observed, an intrinsic property is revealed. Consider three plant taxa: Douglas fir, Broadleaf maple, and the epiphyte liverwort Neckera menziesii. Examination of the tree specificity of Neckera in the Coastal Western Hemlock Zone (Krajina 1964) of the Pacific Northwest reconfirms a clear regularity: masses of Neckera inhabit the bark of maple but avoid the bark of Douglas fir. What attracts or repels Neckera? The run off on maple bark is basic (pH >>7), but on Douglas fir very acid (pH
