Ecological Equivalence: Niche Theory as a Testable Alternative to Neutral Theory - Recent Advances and Issues in Environmental Science - page 4

of recruitment following deaths and extinctions among multiple species of dominants
and fugitives.

Figure 1. Equilibrium co-existence of a fugitive species invaded by a competitive dominant. With
competition coefficients α FD = 1, the fugitive persists provided it has the greater carrying

capacity: k F / k D >1. (A) Lotka-Volterra phase plane with steady-state abundance at the intersection
of the isoclines for the fugitive (dashed line) and the dominant (solid line). (B) Equilibration of
abundances over time given by Runge-Kutta solutions to Equation 1, with a 20% drop in the
dominant's intrinsic death rate, d D , imposed at t = 3 (equivalent to a rightward shift in its isocline) to
illustrate the constancy of N = n F + n D .

α DF = 0,

The same principle of trade-offs in character traits conversely allows a sexually
reproducing species to withstand invasion by highly fecund asexual mutants [25, 26].
A 2-fold advantage to the mutant in growth capacity resulting from its production of
female-only offspring is canceled by even a small competitive edge for the parent
species (Figure 2). Sexual and asexual types coexist as ecological equivalents to the
extent that each invades the other's population to symmetric (zero) net growth for all.
Although the dynamics are not zero-sum if the mutant has some competitive impact on
the parent species, they approach it the higher the impact of parent on mutant and the
faster its growth capacity (albeit half the mutant's). Attributes such as these accommo-
date greater similarity between the types in their carrying capacities and competitive
abilities, which aligns the two isoclines. A consequently reduced stability of the co-
existence equilibrium may result in the sexual parent ousting the asexual mutant over
time, for example if the latter accumulates deleterious mutations [26, 27].
These local-scale dynamics apply equally at the regional scale of biogeography,
reconfi guring individual death as local extinction, and birth as habitat colonization
[24]. Equally for regional as for local scales, rate equations take as many dimensions
as species in the community, with their coupling together defi ning niche overlap [24,
28]. Co-existence of the species that make up a community is facilitated by their dif-
ferent heritable traits, which is a fundamental premise of niche theory. Ecological
equivalence, and hence modeling by neutral theory is nevertheless possible by virtue
of the co-existence equilibrium leveling the playing fi eld to zero net growth for all.