What is ecological Isoclines?

isocline A line joining points on a graph at which combinations of resource levels or population densities produce a similar rate of population growth for a particular species. A Dictionary of Ecology.

1. What are Isoclines used for?
2. How do you calculate Isoclines?
3. What do zero growth Isoclines represent?
4. Can isoclines intersect?
5. Can Isoclines be curved?
6. What is the Lotka-Volterra competition model?
7. What is an isocline map?
8. What direction do trajectories have when they begin on Isoclines?
9. What is the predator isocline?
10. How does competition limit population size?
11. What are competition coefficients?

What are Isoclines used for?

Isoclines can be used as a graphical method of solving an ordinary differential equation. The term is also used to refer to points on maps of the world having identical magnetic inclinations.

How do you calculate Isoclines?

An isocline is a set of points in the direction field for which there is a constant c with dy dx = c at these points. Geometrically, the direction field arrows at the points of the isocline all have the same slope. Algebraically, we find the isocline for a constant c by solving f(x, y) = c.

What do zero growth Isoclines represent?

The zero-growth isocline describes expected equilibrium population sizes of one species if abundance of the second species is held constant, and vice versa.

Can isoclines intersect?

If the isoclines are linear and they cross above the K-connector, then yes, we have the stable equilibrium case. BUT, the isoclines can cross below the K-connector, and coexistence can still be stable, IF the isoclines are curved, as in the graph below.

Can Isoclines be curved?

Generally, an isocline will itself have the shape of a curve or the union of a small number of curves. Isoclines are often used as a graphical method of solving ordinary differential equations.

What is the Lotka-Volterra competition model?

The Lotka-Volterra competition model describes the outcome of competition between two species over ecological time. Because one species can competitively exclude another species (Figure 1) in ecological time, the competitively-inferior species may increase the range of food types that it eats in order to survive.

What is an isocline map?

isoclinenoun. A line on a map linking places with the same magnetic dip.

What direction do trajectories have when they begin on Isoclines?

In this case, however, when the populations of the two species are between the isoclines their joint trajectories always head toward the intersection of the isoclines. Rather than outcompeting one another, the two species are able to coexist at this stable equilibrium point (open circle).

What is the predator isocline?

The predator's isocline is the green vertical line, labeled V-hat -- when prey are more abundant than d/ ( ab) the predator increases (upward dashed arrows). When the prey are below d/ ( ab) the predator declines (downward dashed arrows). ... When predators are below r/a, the prey increase (rightward dashed arrows).

How does competition limit population size?

Competition for resources like food and space cause the growth rate to stop increasing, so the population levels off. This flat upper line on a growth curve is the carrying capacity. The carrying capacity (K) is the maximum population size that can be supported in a particular area without destroying the habitat.

What are competition coefficients?

The most general definition of competition coefficient is a number giving. the degree to which an individual of one species affects through competition. the growth or equilibrium level of a second species' population, relative to. the effect of an individual of the second species.