PE EIE[R-Rg RESEARCH ON - HJ Andrews Experimental Forest

which may be of importance in model selection
or approach . Some nonlinear systems of
differential equations are extremely difficult
to solve and their solution may consume a
great deal of computer time . Parameter estimation
is often a significant problem in man y
models. Some models require highly precis e
measurement of input variables, reducin g
their practical applications, but their theoretical
contributions may be important . On the
other hand, we sometimes settle for use of a
linear regression model when the system is
poorly understood and it is much easier t o
measure the variables than to determine their
exact interrelations . Such models are useful in
science, but have some built-in dangers, e .g . ,
the hazard of extrapolation of linear regression
models .
One danger of reliance upon regressio n
models is that the confidence in the model i s
greatest at the mean and diminishes at th e
extremes. In fact, it is possible to fit a curvilinear
function to data of a given range, only
to have the model become totally inadequate
at the extremes .
For example, net photosynthesis as a function
of temperature can be described as a
symmetrical quadratic (Pisek and Winkle r
1958, Webb 1972) (fig. 3) .
values. Thus equation 6 is valid only in th e
range of temperature within which the
parameters were estimated .
The failure of a model to predict syste m
behavior at extremes is not necessarily fatal ;
such models are common in physics, e .g., the
ideal gas law and Newtonian physics . It i s
necessary to understand the limitations of
one 's models to know when the system deviates
from the model .
In choosing a model, it is important t o
understand the assumptions and limitations of
the model . For example, it is questionable to
describe a biological system with a model tha t
assumes a closed reversible system . Th e
assumptions implicit in the model should be
compatible with present knowledge of th e
system of interest .
This is not to say that models of different
systems cannot be used to model another
system. The idea of isomorphism of system s
models is central to general systems theory
(von Bertalanffy 1969) . Thus thermodynami c
models, for example, may be of great utility
in certain biological systems models . It re -
mains for the researcher to be sure that the
systems are isomorphic so that such model s
are applicable .
Pn = X30 + R1 T - 32 T2 ( 6)
But extrapolation of the curve in either direction
will lead to progressively more negativ e
G(T)
Examination of
Some Models
of Photosynthesis
The discussion above dealt with criteria fo r
selection of models . It would be useful to discuss
some models described in the literature .
Leaf Environment Mode l
a
Figure 3 . Net photosynthesis, G(T), as a quadrati c
function of temperature .
T
Botkin (1969) simulated photosynthesis in
an open oak-pine forest near Brookhave n
National Laboratory . He developed a linea r
model of net photosynthesis :
Pn=c 0 + 01 T+ (3 2 ln S
+ Q3 (ln s) 2 + Q4 T2 + (3 5 T 1n S (7)
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