Thermodynamics in landscape ecology: the importance of integrating measurement and modeling of landscape entropy
Samuel A. Cushman
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S. A. Cushman (&) USDA Forest Service, Rocky Mountain Research Station
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2500 S Pine Knoll Dr., Flagstaff, AZ 86001
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USA
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Entropy and the second law of thermodynamics are the
central organizing principles of nature. Or perhaps
more accurately, the second law is the central
disorganizing principle. Hot things cool down. Cold things
warm up. You cannot get something for nothing. You
always pay more than you get. Things fall apart. You
cannot repeat the past. We grow old and die. It is all
downhill from here to the heat death of the universe.
While at first these seem like grim and pessimistic
ideas, a deeper understanding reveals that the
disequilibrial processes of increasing entropy are what
enables all organizing actions, such as the formation
of a molecule, building of a cell, birth of a child,
organization of an ecosystem. Yet strangely, the ideas
and implications of the second law are poorly
developed in the landscape ecology literature. This is
particularly strange given the focus of landscape
ecology on understanding pattern-process
relationships across scales in space and time. Every
interaction between entities leads to irreversible change
which increases the entropy and decreases the free
energy of the closed system in which they reside. This
is the essence of the entropy principle. Descriptions of
landscape patterns, processes of landscape change,
propagation of pattern-process relationships across
space and through time are all governed, constrained,
and in large part directed by thermodynamics. This
direct linkage to thermodynamics and entropy was
noted in several of the pioneering works in the field of
landscape ecology (e.g. Forman and Godron 1986;
ONeill et al. 1986; Naveh 1987; Oneill et al. 1989).
Yet in the subsequent decades our field has largely
failed to embrace and utilize these relationships and
constraints, with a few exceptions (see Wu and Loucks
1995; Zhang and Wu 2002; Zurlini et al. 2013).
Landscape ecology sometimes has been criticized
as a descriptive science focused on patterns without
linkage to central organizing theories or principles. In
recent decades this has been reversed in part with
strong landscape ecology research focused directly on
pattern-process relationships, drivers and responses
across scales in space and time. Landscape ecology is
the science of understanding the interactions of
patterns and processes across scales. The second law
of thermodynamics and the entropy principle provide
a theoretical context which could help clarify and
unify a large portion of landscape ecology research,
and connect it to fundamental principles.
In a review paper published in this issue Vranken
et al. (2014) present an overview of the use of entropy
in landscape ecology. They identified three main uses
of the entropy concept in past landscape ecology
research, including: spatial heterogeneity,
unpredictability of pattern dynamics, and pattern dependence on
scale. They conclude from their review that
thermodynamic interpretations of spatial heterogeneity in the
literature are not relevant, that thermodynamic
interpretations related to scale dependence are highly
questionable, and that of all applications of entropy in
landscape ecology only unpredictability could be
thermodynamically relevant if appropriate
measurements were performed to test it. They note that while
entropy is frequently mentioned in landscape ecology
literature, it is rarely formally addressed and usually
only applied in imprecise and descriptive terms. They
note frequent contradictions in the interpretation of
entropy in landscape ecology literature.
The Vranken et al. (2014) review, in my opinion,
shows how poorly the universally important topics of
the second law of thermodynamics and the entropy
principle have penetrated landscape ecology. There
are many examples in the literature of informal
linkage to the entropy concept, but virtually no formal,
quantitative efforts to develop explicit theory derived
from the second law. The review shows very few
examples of the concepts even being mentioned (as a
proportion of the literature) and virtually no formal,
quantitative, theoretically justifiable application of
thermodynamic ideas. They note that most authors
addressing linkages between entropy and landscape
patterns generally use the entropy principle
metaphorically, referring to the linkage between entropy and
landscape disorder, but not formally calculating it.
Further they note contradictory interpretations of the
conceptual linkage between entropy and landscape
pattern. They note that no formal proposal for
calculating the thermodynamic entropy of landscapes
has been published and as a result conclude that any
link between spatial heterogeneity and
thermodynamic entropy should be treated with caution. This
seems astounding for a field that has been so obsessed
with measuring and interpreting landscape patterns
has entirely neglected the fundamentally important
and interesting (...truncated)