A point originating in (iii) or (iv) oscillates between (iii) and (iv) until convergence at the

isocline.

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.

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

isocline shifts down since [Mathematical Expression Omitted], but the [Mathematical Expression Omitted]

isocline is unaffected because [Mathematical Expression Omitted].

The first condition is no local coexistence, which requires that isodine 2 has a lower slope than

isocline 1 (Roughgarden 1979).

5a), and that the producer

isocline is then much less likely to have a significant "hump" (Fig.

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.

This way, the self-thinning line for a set area in Petraitis' model becomes an

isocline for zero patch areal change [I.

This means a shift downwards or to the left in the prey null

isocline (if the prey suppresses), or a shift downwards or to the right in the predator

isocline (if the predator suppresses).

This situation arises when the herbivore

isocline is a "humped"

isocline, and the predator

isocline is sigmoidal in shape, which potentially results from a variety of ecological sources (type III functional response, predator switching behavior, or a tendency of predators to congregate where there are congregations of prey).

Instead, populations will evolve to the highest fitness

isocline that is energetically and physiologically attainable ([ILLUSTRATION FOR FIGURE 5 OMITTED], filled dots).

Regardless of model, the prey zero

isocline is a hump-shaped curve in the predator-prey phase plane [ILLUSTRATION FOR FIGURE 8 OMITTED].

The rising portion of the algal

isocline reflects saturation of zooplankton feeding response (once individual grazer functional response is saturated, it takes more zooplankton biomass to match a given rate of algal growth), and its intersection with the x-axis reflects the constraint of total P in the system (algal P:C has a minimal value due to physiological constraints; thus, a given amount of P can produce [algal biomass] [less than or equal to] [total P]/[minimal algal P:C]).

For example, the addition of predator carrying capacity or density-dependent predator mortality to classic models results in the predator

isocline being tilted or bent to the right, thus stabilizing dynamics and preventing the paradox of enrichment (Gilpin 1975).

Initially, this trade-off in resource acquisition is described by a linear resource acquisition

isocline representing the maximum annual amount of the two resources each species can acquire in isolation ([ILLUSTRATION FOR FIGURE 1A, B OMITTED], solid lines).