Biology Reference
In-Depth Information
There is something fascinating about science. One gets such whole-
sale returns of conjecture out of such a trifling investment of fact.
Mark Twain (1835-1910)
In the first chapter, we modeled the behavior of several
single-population biological systems. Few populations
exist in isolation, however, so we now want to expand the
range of biological phenomena we can investigate by
modeling the interactions of systems with multiple
groups. Our basic questions remain the same: What is the
long-term behavior of the system, are there equilibrium
states, and how do we classify them? Although our
models will be necessarily more complex, in every
example a single differential equation determines the
evolution of each element of the system.
Chapter 2
COMPLEX DYNAMICS
EMERGING FROM
INTERACTING
DYNAMICAL SYSTEMS
When two or more groups of organisms interact, a variety
of relationships and outcomes are possible. Let us begin
by exploring some of the possibilities.
When two or more groups of individuals of different
species live in the same area, we describe the members of
each species as belonging to a population and the group
of populations as belonging to a community. Interactions
among community members may take many forms. One
population may feed upon another, or two may compete
with each other to feed upon a third. Competition
between populations, in fact, may occur over any
valuable aspect of the habitat, including nesting sites or
hiding places. Such competitions may be classified as
exploitative or resource competition, where the two species
use the same resources, or as interference competition,
where the two species cause harm to each other.
Introduction to Infectious Disease
The Spread of an Epidemic
Phase Plane Analysis
Stability of Equilibrium Points
Epidemic Models with Delay and Models
with Intermediate Groups
Predator-Prey Interactions
A Model of Competitive Interaction
Appendix: Validation of a
Mathematical Claim
Interactions between species need not always be harmful.
Mutualism, which is also sometimes called symbiosis,
occurs when two species benefit from living in close
association with each other. A good example of
mutualism occurs when an alga and a fungus combine to
form a lichen and together wrest a living from extremely
inhospitable environments, such as bare rock faces. Two
related associations are commensalism, where one species
benefits and the other is unharmed, and amensalism,
where one species suffers but the other is unaffected.
Predations are interactions in which one species benefits
while the other is harmed. In addition to the well-known
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