THE GREAT LAKES

The numerical difference between a region's maximum
number of species and the actual number present scales the
region's attraction of new species and is called its
species potential. This definition has two major
implications:
1) Species potential does not presume the mechanism for
species colonization and resource exploitation.
2) Species potential can confer integrity to an ecosystem
by assuring that the number of species in biotic
communities and ecosystems cannot be made arbitrarily
large. Combined with cooperativity, this notion
suggests that species are forced to interact to achieve
ecosystem structure and cannot behave independently at
all levels of population density and species number.
MacArthur and Wilson
(1967), in developing the
stochastic version of a model of species colonization of
islands, studied species-area curves and carrying capacity
of habitats in great detail. Their excellent model ignored
edge effects (the special problems of certain classes of
models when parameters approach maximum permissible
values) . Hill ' s (1968) small thermodynamic lattice models
offer a more comprehensive approach and already have the
appropriate chemical-reaction analog form. Species
potential expresses the thermodynamic affinity for the
colonization process and is a possible candidate for the
ecological chemical-potential counterpart of embodied
energy.
In Hill's and in MacArthur and Wilson's models, the
rates of species colonization are linear functions of the
species potential, and the rates of species loss are linear
functions of the number of species already in the region.
These simple density-dependent rate laws yield a unique
steady-state number of species that is less than the
maximum and is determined by the rate coefficients of the
colonization and loss processes. Rate coefficients do not
depend on the number of species present but may depend on
species identity, habitat type, and climate.
Hill's models have interesting evolutionary
trajectories. A region treated as a one-sided lattice has
only one possible steady state: thermodynamic equilibrium.
The evolutionary trajectory, a simple decreasing
exponential function, is MacArthur and Wilson's initial
case. A region treated as a two-sided lattice also has as
its evolutionary trajectory a simple decreasing exponential
function. The trajectory passes through a series of
predictable steady states, the end one being thermodynamic
equilibrium. Evolution is a transition between adjacent