Biology Reference
In-Depth Information
(owl) exerts control over the population of the prey (vole), and vice
versa. In our work with this model, the thresholds were manifested as
critical lines (the null clines) determined by the rate of change of the
variables being equal to zero.
If a system involves more than one variable and the variables interact
with one another, it is possible that one of them inhibits the growth of
the other, which in turn stimulates the first one. This is, for example, the
case in the Lotka-Volterra models. Such interaction is in essence a
(negative) feedback and is often a factor that creates oscillations. When a
single variable is considered, a self-inhibitory feedback is sometimes
possible—in this case, we talk about autofeedback (see
Example 10-1).
Whether a delay and/or a feedback will generate oscillatory behavior
depends on the specific context of the problem and on the particular
values of the system parameters. In this light, the presence of delays
and/or feedbacks should be considered a factor that is likely to cause
oscillations and should not be understood as a sufficient condition for
oscillatory behavior in biological systems.
II. SYMBOLIC SCHEME REPRESENTATIONS OF
THEORETICAL MODELS AND MODELING GOALS
Schematic diagrams are often used to show the most important
components of a biological system and the connections between them.
Standard symbols have been adopted to facilitate the display of
information:
1. Rectangles (A, B, etc.) denote system variables (also referred to as
nodes);
2. Lines (arrows) indicate specific relationships (also referred to as
conduits) and are additionally marked with one of the symbols
(
) indicates an excitatory action on the variable at
which the line terminates, whereas a (
þ
)or(
): a (
þ
) denotes an inhibitory
action; and
3. Triangles (D) on one or more of the lines indicate that a delay
occurs from the change in the variable from which the line initiates
until the corresponding effect is actually exerted.
(
+
)
D
A
B
(
−
)
For example, Figure 10-2 presents a schematic diagram of a network
representing the interaction between two variables A and B. The line
from A to B is marked with a (
FIGURE 10-2.
Schematic diagram of a two-node network with
feedbacks and delay.
), indicating an excitatory input. The
line from B to A is marked with a (
þ
) to indicate that B inhibits the
