Ecological Equivalence: Niche Theory as a Testable Alternative to Neutral Theory - Recent Advances and Issues in Environmental Science - page 8

of total population density, N . This can be expressed as the Arrhenius relationship: S =
cK z (Figure 4 right-hand column) by virtue of the zero-sum relation of N to K (Figure
4 left-hand column). Further simulations show that reduced dispersal limitation raises
c and reduces z , and a higher rate of new-species invasions raises c (though not z , in
contrast to predictions from spatially explicit neutral models [29]).
The closely aligned proportionality of total individuals to habitable area for all
communities illustrates emergent zero-sum dynamics for neutral and non-neutral sce-
narios (Figure. 4 left-hand column). Despite sharing this type of pattern, and rather
similar densities of species (Figure 4 right-hand column), the non-neutral communities
sustain more than double the total individuals. This difference is caused by a more than
halving of their competition coeffi cients on average (all α ij = 1 for neutral, mean α ij ( i ≠
j ) = 0.45 for Lotka-Volterra, mean ratio of 0:1 values = 58:42 for dominant-fugitive).
The zero-sum gradient of N against K is simply the equilibrium fraction of occupied
habitat, which is 1-1/ R for a closed neutral scenario, where R is per capita lifetime
reproduction before density regulation ( b/d in Materials and Methods Equation 1 [23,
24]). The closed dominant-fugitive scenario modeled in Figure 1 has a slope of k F / K =
(1-1/ R )/α, where R and α are system averages. Further simulation trials show the slope
increasing with immigration, for example by a factor of 1.9 between closed and fully
open (dispersal unlimited) Lotka-Volterra communities. Dispersal limitation therefore
counterbalances effects of the net competitive release obtained in niche scenarios from
α ij < 1 (as also seen in models of heterogeneous environments [19]).
The less crowded neutral scenario sustains a somewhat higher density of species
than non-neutral scenarios (comparing Figure 4 z -values for right-hand graphs), and
consequently it maximizes species packing as expressed by the power function pre-
dicting S from N in Figure 5. With no species intrinsically advantaged in the neu-
tral scenario, its coeffi cient of power is higher than for pooled non-neutral scenarios
(0.594 and 0.384 respectively, loglog covariate contrasts: F 1,42 = 122.72, P < 0.001).
The lower coeffi cients of Lotka-Volterra and dominant-fugitive scenarios are further
differentiated by competitive asymmetry (0.412 and 0.355 respectively, F 1,42 = 7.24, P
< 0.01). In effect, the neutral scenario has the lowest average abundance of individuals
per species, n , for a community of size K with given average R , which is also refl ected
in the modal values in Figure 3 histograms for K = 1,000 patches.
The lower N and n predicted for the intrinsically neutral scenario point to a de-
tectable signal of steady-state intrinsically neutral dynamics: α = 1 for all, because
intrinsically identical species cannot experience competitive release in each others'
presence (cf. α ij < 1 in niche models). These interactions may be measurable directly
from fi eld data as inter-specifi c impacts of equal magnitude to intra-specifi c impacts;
alternatively, Lotka-Volterra models of the sort described here can estimate average
competition coeffi cients at an observed equilibrium N , given an average R (a big pro-
viso, as fi eld data generally measure realized rather than intrinsic vital rates). This
distinction of intrinsically neutral from non-neutral dynamics has been masked in pre-
vious theory by the convention for neutral models either to fi x N [1, 11, 12] or to set
zero interspecifi c impacts [13, 16]. By defi nition, identical species cannot be invisible
to each other unless they are invisible to themselves, which would require density