patterns and apply them to partitioning models to make them more mechanistically representative of the
process within the plant [15]. One way to address the problem, as described previously, is simply by
scaling or allometry. It has been shown that ratios such as relative growth rate of root and shoot generally
remain constant even as the age and size of a plant increase [16,17]. For many simple growth models,
these allometric relations are directly applied [18] and usually do not include modification by environ-
mental factors, although there are some that do [3].
In addition to growing root and shoot, there are generally other destinations (sinks) for newly pro-
duced photosynthate. Models often use a priority system, assigning priorities to destinations and uses such
as respiration and fruit development as well as structural growth of various plant organs [12,19]. This is
often coupled with the functional equilibrium concept, as it is used to establish the basis for production
of new photosynthate by balancing the aboveground and belowground growth. The concept models
growth of a region as substrate limited and the availability of each substrate, generally Cand N, as a
direct function of the regions above and below ground to supply a substrate [8,20]. The ability to supply
substrate is usually a function of size and the environment. In addition to simply assigned priorities, mul-
tiple sinks are assigned priorities based on proximity. This is simply the assumption that the closest sink
to the source gets first delivery and essentially has the best access. Sinks farther from the source have re-
duced priority as they get what is left over. This is done by representing the plant structure generalized as
multiple sinks, with each sink supplied photosynthate on the basis of a combination of assigned priority
and proximity. Proximity is often modeled in terms of resistance along the pathway from source to sink.
The difference in activity of the source and activity in the sink regions provides a potential gradient for
flow of substrate through assigned resistances throughout the plant. Again, often the very basis of this
model is functional equilibrium, used to balance the supply of available substrates to the source.
Thus, the models that make up a simulation can be described as either mechanistic or empirical. A
mechanistic model uses equations to model what we understand of the actual physiological processes.
Empirical models use previous data to predict future performance. For example, once a response has been
characterized over a range of values, that response can be statistically curve fit using regression tech-
niques, resulting in an equation to model the response. One of the drawbacks to this includes the fact that
the response needs to be previously characterized over the expected range. Furthermore, if the model is
used to predicted responses that are outside the previous range, extrapolation may be required [3,21].
Mechanistic models tend to be more robust, giving a more reliable prediction over a wider range of con-
ditions; however, they can be developed only for processes in which we understand the mechanisms well
enough to apply equations [22].
IV. USES FOR COMPUTER SIMULATIONS
Partitioning new growth is an integral part of any plant growth simulation. Because no mechanism has
been identified to regulate the process, modelers have had to rely on essentially empirical models [23].
These models are often based on the performance of plants experiencing optimum growth such as a plant
would experience with an abundance of everything it needed from the environment. Then the effects of
something limited in the environment are added in to reduce the optimum growth. Often, the result is both
a reduction in overall growth rate and a shift in partitioning. This shift can be difficult to predict but can
ultimately be an important aspect of what is being predicted. Growth partitioned above ground is often
the area of most interest to users of a simulation. For example, more vegetative mass above ground can
translate to more fruit or yield to a farmer [3]. But growth below ground is also important; such is the case
in ecological simulations when making predictions about the organic storage matter in soils [24].
Currently, uses for these simulations generally fall into two categories, ecological applications and
agriculture. Some of the ecological applications include predictions about how future climates such as in-
creases in carbon dioxide and temperature may affect forests [25–28] and grasslands [27,28] or how years
of grazing may affect pasture lands [11]. They are used in agriculture to maximize the effectiveness of
farmer input by using artificial neural networks [29] or other decision-making methods such as COMAX
in the simulation for cotton [30] or the Penn State Apple Orchard Consultant (PSAOC) expert system used
in apple orchards [31]. They are also used to aid in managing tree crops for activities such as fruit thin-
ning and canopy management [32]. Farmers can determine such things as optimum N applications [33],
irrigation plans [34], and pesticide applications based on how they affect the final yield [21].
COMPUTER SIMULATION OF ALLOCATION PROCESSES 911