As is intuitive, locations with characteristics that contribute to high productivity or amenities have a larger equilibrium population
(Rappaport 2008a, 2008b, 2016).
The total equilibrium population
[x.sup.*] is given as
However, a second result of increased shrimp harvesting rate is that the equilibrium population
of adult shrimp is lower.
In order to quantify the effect of the disease in the equilibrium population
, we set [b.sup.1] = [b.sup.1.sub.S], [b.sup.1.sub.I] = [lambda][b.sup.1], where [alpha] > 0 is a measure of the effect of the disease on the reproductive capability of infected individuals in species 1.
where [I.sup.*.sub.i]([x.sub.1], [x.sub.2]) (i = 1,2) is the equilibrium population
density of the resident infected [I.sub.i](i = 1,2); (1/2)[[delta].sub.i][[rho].sup.2.sub.i] (i = 1,2) is mutational rate of the infected [I.sub.i](i = 1,2).
Having equilibrium rents defined allows us to determine equilibrium wages, w(r(A,C);A), and equilibrium population
This implies the fast depletion of fish stock in the fishing zone does not affect the equilibrium population
level of fish stocks in the reserve area.
This equilibrium population
or niche is a function of the populations of all the other species in the system with which a particular species interacts, either cooperatively or competitively or through predation.
If X(t) > 0 and Y(t)>0 then [X.sub.e] > 0 and [Y.sub.e]>0 represent the equilibrium population
of the prey and the predator respectively, and this equilibrium can be obtained by solving the right hand sides of equation (1.1):
Any increase in the ratio of (gross) wages to land rents will lead to decreases in equilibrium population
; thus, when firms receive benefits from the public goods provision leads to declining city (and metro) population (as firms and employment move to other locations with lower wage to land rent ratios).
Assume that for any x [EPSILON] [0, 1], g(x) has a convergent Taylor series near x and let ([x.sub.1], [x.sub.2], [x.sub.3]) be an equilibrium population
. Then, we can express g([x.sub.1]) as:
Computer algorithm for obtaining a random set of allele frequencies for a locus in an equilibrium population
. Genetics 86:482-483.