Question

Given the phase-plane output below: The zero-growth isocline of species 1 (red) crosses the vertical axis at 273.33 and the horizontal axis at 410, and the zero-growth isocline of species 2 (blue) crosses the vertical axis at 410 and the horizontal axis at 273.33. Lotka-Volterra Competition: Phase Plane a) What is the main characteristic of an isocline (i.e. give its definition) (4 pts) b) Calculate ? and ?. Provide a detailed answer. Include the meaning (in mathematical terms) of the intersection between the isoclines, as well as the meaning of their slopes (10 pts) c) Draw on the graph the arrows representing the direction of population growth within and outside the area under both isoclines (Hint: think back to the diagrams shown in Tutorial 7) (4 pts) d) Based on these arrow, this corresponds to which of the Lotka-Volterra competition outcomes (I, II, III, or IV) ? Explain (4 pts) e) Assuming that the intrinsic population growth of each species is identical (r1=r2), what happens if one increases the initial population size of species 1? (3 pts)

          Given the phase-plane output below:
The zero-growth isocline of species 1 (red) crosses the vertical axis at 273.33 and the horizontal axis at 410, and the zero-growth isocline of species 2 (blue) crosses the vertical axis at 410 and the horizontal axis at 273.33.
Lotka-Volterra Competition: Phase Plane
a) What is the main characteristic of an isocline (i.e. give its definition) (4 pts)
b) Calculate ? and ?. Provide a detailed answer. Include the meaning (in mathematical terms) of the intersection between the isoclines, as well as the meaning of their slopes (10 pts)
c) Draw on the graph the arrows representing the direction of population growth within and outside the area under both isoclines (Hint: think back to the diagrams shown in Tutorial 7) (4 pts)
d) Based on these arrow, this corresponds to which of the Lotka-Volterra competition outcomes (I, II, III, or IV) ? Explain (4 pts)
e) Assuming that the intrinsic population growth of each species is identical (r1=r2), what happens if one increases the initial population size of species 1? (3 pts)

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Given the phase-plane output below:
The zero-growth isocline of species 1 (red) crosses the vertical axis at 273.33 and the horizontal axis at 410, and the zero-growth isocline of species 2 (blue) crosses the vertical axis at 410 and the horizontal axis at 273.33.
Lotka-Volterra Competition: Phase Plane
a) What is the main characteristic of an isocline (i.e. give its definition) (4 pts)
b) Calculate ? and ?. Provide a detailed answer. Include the meaning (in mathematical terms) of the intersection between the isoclines, as well as the meaning of their slopes (10 pts)
c) Draw on the graph the arrows representing the direction of population growth within and outside the area under both isoclines (Hint: think back to the diagrams shown in Tutorial 7) (4 pts)
d) Based on these arrow, this corresponds to which of the Lotka-Volterra competition outcomes (I, II, III, or IV) ? Explain (4 pts)
e) Assuming that the intrinsic population growth of each species is identical (r1=r2), what happens if one increases the initial population size of species 1? (3 pts)

Added by Andrew B.

Biology for AP Courses

Julianne Zedalis, John Eggebrecht

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Solved by Expert Suman K

03/29/2022

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**Step 2: Intersection between Isoclines and Meaning of Slopes** The intersection point between the isoclines represents two situations: Show more…

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Given the phase-plane output below: The zero-growth isocline of species 1 (red) crosses the vertical axis at 273.33 and the horizontal axis at 410, and the zero-growth isocline of species 2 (blue) crosses the vertical axis at 410 and the horizontal axis at 273.33. a) What is the main characteristic of an isocline (i.e. give its definition) (4 pts) b) Calculate ̑ and ̒. Provide a detailed answer. Include the meaning (in mathematical terms) of the intersection between the isoclines, as well as the meaning of their slopes (10 pts) c) Draw on the graph the arrows representing the direction of population growth within and outside the area under both isoclines (Hint: think back to the diagrams shown in Tutorial 7) (4 pts) d) Based on these arrow, this corresponds to which of the Lotka-Volterra competition outcomes (I, II, III, or IV) ? Explain (4 pts) e) Assuming that the intrinsic population growth of each species is identical (r1=r2), what happens if one increases the initial population size of species 1? (3 pts)

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00:01 In this question we are provided with the isocline lines of two species in case of lotka -v -waltera model which is also written as lv model.

00:12 One species is represented by red isocline line whereas the isocline line for other species is represented by the purple line.

00:22 Also in between these two isocline lines, they are present an intersection point which is represented by the green circuit.

00:30 The first question is asking to define isocline.

00:38 Isocline is also called as zero growth isocline.

00:47 It is an equilibrium line and this isocline line tells about the status of a specific species when the abundance of other species is kept constant.

00:58 The second question is asking to define alpha and beta in the lotka -waltera model.

01:05 Alpha is also written as alpha 1 -2 and it is the impact of species 2 on species 1.

01:11 Or it is the competition effect of species 2 on species 1.

01:17 Beta is also written as alpha 21 and it is the impact of species 1 on the species 2 or it is the competition effect of species 1 on species 2.

01:28 In the lotka -waltera model which is also written as the lv model, on the x -axis of the graph there present the population size of species 1, that is the n1.

01:40 Also along with n1 on the x -axis k1 upon alpha 1 2 is also.

01:45 Also written, where k1 represents the carrying capacity of species 1.

01:57 And on the y -axis of the lv model, the population size of species 2, that is, n2 is represented.

02:04 Along with n2, k2 upon alpha 2 is also represented and here k2 represents the carrying capacity of species 2.

02:13 Now comes the concept of intersection between the two isocline lines.

02:19 And these intersection between the two isoclines may represent two situations.

02:22 First one is stable coexistence of the two species.

02:33 In this case, the two species approach towards each other.

02:37 The second case is unstable coexistence of the two species...

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