Biomedical Engineering Reference
In-Depth Information
microenvironment. The latter is known to exist in tumors, and the Gatenby-
Gawlinsky model analyzed the effects of tumor-induced acidity in the tissue
microenvironment. The model not only contributed to an understanding of tu-
mor progression but also generated testable clinical predictions.
The spatially extended competition model can be simulated on a given spa-
tial domain using appropriate boundary conditions. A standard procedure begins
with an initial condition where the two populations start displaying the same
local population plus a small noise term. In other words, we start with an almost
homogeneous system very close to the coexistence point. The outcome is illus-
trated in Figure 3. Here two populations start growing and eventually exclude
each other. The exclusion strongly depends on the initial local conditions; small
initial advantages are rapidly enhanced and at a local scale competitive exclu-
sion is completed. Together with competition there is diffusion: locally advan-
taged populations might disperse toward adjacent areas vacated by dying cells
and create patches of homogeneous populations. Since both clones follow iden-
tical rules, the resulting situation is a set of patches that at the global scale
achieve effective coexistence.
One possible limitation of the previous scenario is the initial condition
where both populations are scattered over the surface. This circumstance could
fit an experimental setup based on seeding a cell culture with a suspension of
cells composed of two well-mixed populations but does not seem to apply to in-
vivo adult tissues where small clones occupy a defined space compartment.
When we simulate tumor growth starting from a spatially nonhomogeneous ini-
tial condition, the resulting "tumor" is highly heterogeneous and the two popula-
tions coexist on a global basis despite local exclusion.
These simple models explain how the local character of interactions im-
posed by tissue architecture constrain competitive interactions. Thus, we may be
confronted by a situation common to other communities that largely evolve
through competition such as plants. As stated by Tilman (17),
Plants compete only with individuals living sufficiently nearby but each
could cast shade on or have roots that overlap with the other. Because of
poor dispersal ability, low local abundance, or chance events, however,
many plant species may be absent from such a neighborhood and have
their abundance be recruitment limited. Like a team that fails to appear
at a sporting event, a species that is locally absent has forfeited any
chance of competitive victory at the site. This can allow inferior compe-
tition to win by default. If there is recruitment limitation, the winners of
local competition are not necessarily the best competitors that exist in
the region, but the best competitors that happened to colonize a particu-
lar site. This can lead to essentially unlimited diversity.
