The figure shows the loci and depicts the nonnegative orthant where the

isoclines in equations and compose four isosectors labeled (i) - (iv).

Necessary and sufficient conditions for the intersection with the vertical

isocline and applications, Funkcial.

This path must always be the right of k*, because from (16) m'([k.sub.1]) = [rho] + [omega], whereas from (22) the [dot.q] = 0

isocline is always defined at m'(k*) = [rho] + [omega] + [theta].

Since the intraspecific response to density was shown above to be linear, the expected mean and variance of the

isocline at the 50:50 mixture point was determined from a sample obtained by dividing yield or papillae density of each replicate in the 100% treatment by two.

From the Implicit Function Theorem and equation (7), the [Mathematical Expression Omitted]

isocline shifts down because [Mathematical Expression Omitted], as does the [Mathematical Expression Omitted]

isocline since [Mathematical Expression Omitted].

The

isocline [L.sub.2] : [C.sub.2] ([v.sub.1], [v.sub.2]) = b + [[sigma].sub.12] ([alpha]/[V.sub.1]) -[v.sub.2]/[V.sub.2] - [[sigma].sub.12]([absolute value of [v.sub.1] - [alpha]]*/[V.sub.1] = 0 is smooth as shown in Figure 1.

In the nonspatial system (i.e., system (2a), (2b) without spatial derivatives), according to f(x, y) = 0 and g(x,y) = 0, vertical

isocline and horizontal

isocline(4.) In the special case of an infinitely elastic demand, price is unaffected by harvest levels, and in Figure 1 the [E.sub.t+1] = [E.sub.t] = E =

isocline defined by zero equilibrium rents will be vertical in X - E space.

For fixed x, the

isoclines are linear; x determines where the

isoclines intersect the [u.sub.2] axis: as x increases, isodine 1 moves down while

isocline 2 moves up (Fig.

3, and it is necessary to consider zero

isoclines. The previous assumption of grazer emigration being independent of producer biomass yields a grazer

isocline parallel to the producer axis.

From the general setting of Section 3.1, the

isocline [[GAMMA].sub.1] now degenerates into a straight line.

Besides, we suppose the vertical

isocline dx/dt = 0 intersects the impulse set and the phase set at point C and point D, respectively.

The predator zero

isocline, with the slope ([[alpha].sub.1] - [beta])/[beta], is a straight line passing through the origin, and it lies in the first quadrant if the following restriction holds

The data are presented as

isocline and interpolated surface plots using ArcView GIS software.

More generally, prey evolution is thought to move the predator

isocline to the right (i.e., toward greater prey densities; Rosenzweig 1973), which is also often stabilizing.