Intransitive networks involving multiple toxins
and multiple resistance factors to those toxins,
along with trade-offs between the ability to produce
or resist toxins and to compete consumptively for
resources, might provide a mechanism to explain
how so many bacterial taxa can coexist in soils
(Cza ́ra ́net al.2002). These authors present a theo-
retical analysis showing that, by including multiple
toxins and multiple toxin resistance genes, a large
number of taxa will persist in a two-dimensional
model grid of interacting bacteria. They find that a
system with a few toxin genes and many resistance
genes can support up to 1000 different strains in a
180 180 spatial grid. This is obviously somewhat
less than the diversity estimates obtained for soils,
but it is of the right order of magnitude.1.2.2 Mechanisms
Intransitive networks of competitive interactions
may explain the high diversity of some systems of
competitors. It appears that high diversity can be
maintained by intransitive competitive networks
only in spatially structured environments, such as
soils or two-dimensional surfaces (Reichenbach
et al.2007). In well-mixed environments without
opportunities for much spatial structuring, such
as aquatic systems, other mechanisms must be in-
voked to explain the coexistence of large networks
of competitors.
What maintains competitor diversity in well-
mixed habitats with only few limiting resources?
One possibility has been suggested by Huisman
and Weissing (1999). Their models show that
large networks of many resource competitors,
when competing for several resources (four to
six), can persist due to chaotic fluctuations in spe-
cies abundances (Fig. 1.4). They suggest that
switches along alternative transitive networks also
seem to play a role. The presence of multiple limit-
ing nutrients in their model prevents the formation
of clear competitive hierarchies. This might pro-
vide an explanation for the coexistence of large
numbers of phytoplankton species in well-mixed
environments such as lakes and oceans, a problem
that has interested ecologists for many years
(Hutchinson 1961). Recently, Huisman and collea-
gues found experimental evidence for similar
chaotic dynamics in a closed experimental multi-
trophic plankton system that was observed for a
large number of generations (Benincaet al.2008).
This seems to be the first well-documented example12a Static platebcFlaskMixed plateGenerationsLog (abundance)Log (abundance)Log (abundance)10
8
6
4
2
0
01020304050607012
10
8
6
4
2
0
0 1020304050607012
10C
S
R8
6
4
2
0
0 10203040506070Figure 1.3Dynamics of an intransitive competitor
network. C is a colicin (toxin producing) bacterial strain,
which excludes S, a colicin-sensitive strain, which excludes
R, a colicin-resistant strain, which in turn competitively
displaces C. All three strains persist in a static two-
dimensional habitat (a), but R eventually predominates in
mixed environments (b and c). Reprinted with permission
from Macmillan Publishers Ltd:Nature,171–4,B.Kerret al.
#2002.
THE TOPOLOGY OF ECOLOGICAL INTERACTION NETWORKS 13