Environmental Engineering Reference
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independent dynamics. Simulations of non-interacting species under density-dependent
regulation therefore embody an extreme version of niche theory whereby each species
occupies a unique niche, somehow completely differentiated by resource preferences
rather than partially by trade-offs in vital rates. These models fi t well to species abun-
dance distributions in rainforests and coral reefs [13-16], though without providing
any explanation for what attributes would allow each species to be invisible to all
others (in contrast to the trade-off models). Indeed the condition is unrealistic at least
for mature trees that partition a homogeneous environment by each making their own
canopy. This so-called neutral scenario ([13, 16], more appositely a neutral-niche sce-
nario) has no steady state outcomes in the analyses and simulations described here,
because setting all α ij = 0 ( i j ) allows indefi nite expansion of S and hence also of N .
A slightly less extreme neutral-niche community is modeled by setting all interspecifi c
impacts to a common low value. Simulations at α ij = 0.1 for all i j give a zero-sum
relation N = 4.026 K , which has >4-fold steeper gradient than that for the Lotka-Volt-
erra scenario (Figure 4) refl ecting its >4-fold reduction in α and consistent with its
representation of a highly niched scenario.
Figure 5. Simulated steady-state relationships of species to individuals. Each point shows the mean
± s.e. of the three replicate communities in Figure 4, and regression lines on the means are the
power functions for intrinsically neutral (top) Lotka-Volterra (middle) and dominant-fugitive (lower)
scenarios.
DISCUSSION
Although intrinsic identity is clearly not a necessary condition of ecological equiva-
lence or of zero-sum abundances at dynamic equilibrium, only neutral models sustain
 
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