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, [OMEGA](r(A,C);A).

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.