OPTIMALITY IN EARTH SURFACE SYSTEMS

 

A number of theories in geomorphology, ecology, hydrology, etc. are based on the idea that Earth surface systems (ESS) develop according to some optimal principle or goal function. That is, the ESS develops so as to maximize, minimize, equalize, or optimize some quantity—energy, exergy, entropy, work, mass flux, etc.  Some of these notions have some explanatory power and have resulted in some important insights. However, they have always bothered me--no one has ever been able to convince me that there is any inherent, a priori, rule, law, or reason that, e.g., a hillslope or a stream channel or a soil would operate so as to optimize anything. The conservation laws for mass, energy, and momentum are the only laws of nature that absolutely must hold everywhere and always.

So how does one explain the apparent success of some optimality principles in describing, and even predicting, real ESS behavior?

Suppose we use P to represent possible developmental pathways for an ESS. An optimality principle is essentially arguing that a particular P among all those possible is the most likely1. But the sufficient conditions for a particular path need not invoke any extremal or optimal goal functions.

Sufficient conditions for preferential development along trend or pathway Po, PoÍ Pi, i = 1, 2, . . . , n potential pathways are threefold:

1. Pois associated with processes or behaviors that confer advantages or higher probability of persistence or replication relative to other Pi. For instance, with respect to hydrological flow paths, concentrated pathways are favored over diffuse ones; and steeper and hydraulically more efficient routes over gentler and less efficient ones. With respect to hillslope gradients, angles less than the angle of repose persist, while those greater fail. In ecosystem or community composition, for example, more rapid or efficient resource use and cycling may confer competitive or selective advantages.

2. The ESS is at or approaching saturation (i.e., given enough time without change in boundary conditions or disturbance, it will become increasingly saturated). The “saturated” condition is associated with biological saturation (i.e., all available niches are filled) in ecology; with fully developed drainage systems in hydrology; and with relaxation time equilibrium in geomorphology. Condition 2 does not require the ESS to have reached saturation; only that if it has not, then (e.g.) niches will continue to be filled, drainage systems will continue develop, and geomorphic responses will continue until saturation is achieved.

3. There are no significant changes in boundary conditions, or clock-resetting disturbances.

In the absence of environmental change (no. 3 above), two conditions (1, 2 above) are sufficient.

Hypothesized “optimal” development does typically correspond or overlap with pathways that are advantageous in the sense of condition 1 above. Thus observations of supposedly optimal evolution are better explained as emergent outcomes of the simple selection principle indicated in item 1 above, subject to items 2 and 3.

I prefer the emergent explanation based on selection to the optimization hypotheses because it is simpler, it works at least as well2, and it requires no suppositions of goal functions for ESS.

 

 -----------------------------

1Though in some cases it has been shown that there are many ways an ESS might be configured to achieve a particular optimum.

2”Works as well” refers to explanation and interpretation. For modeling, assuming a particular optimal condition often simplifies things immensely. However, in those cases the optimality principle should indeed be viewed as a simplifying assumption rather than a truth statement about ESS. 

X
Enter your linkblue username.
Enter your linkblue password.
Secure Login

This login is SSL protected

Loading