Homework Answers
Species 1 growth rate is negative
These graphs represent the zero isoclines on the bottom left there is growth as the abundance of both species are with in the carrying capacity above that line (zero isoclines) is above the carrying capacity and the population diminish
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The figure below shows the Lotka-Volterra model of competition between two species. What is happening at...
Module 5: Lotka-Volterra competition equations and predictions number of individuals they would b...
Module 5: Lotka-Volterra competition equations and predictions number of individuals they would be in species 1 terms, when considering their effect on species 1's growth. 1. For each of the two equations below for the population growth of Species 1 and 2, solve for .How many different ways can you get population growth rate 0? Just to get you started, "N 0 ifr O. dt Species 1 Species 2 K, dr K, Equilibrium solutions for species 1 (in the presence...
From an ecological perspective, either explain or define the following: 1) Lotka and Volterra model and...
From an ecological perspective, either explain or define the following: 1) Lotka and Volterra model and four outcomes of competition between two species 2) Tilman’s model 3) Gause’s hypothesis 4) r-selection and K-selection theory 5) Grime’s theory of plant strategy
Answer both questions The simplest model for a mutualistic interaction between two species is similar to...
Answer both questions
The simplest model for a mutualistic interaction between two species is similar to the basic Lotka-Volterra model as described in Chapter 14 for two competing species. The crucial difference is that rather than negatively influencing each other's growth rate, the two species have positive interactions. The competition coefficients a and fi arc replaced by positive interaction coefficients. reflecting the per capita effect of an individual of species 1 on species 2 (alpha 12) and the effect of...
• (Problem 2) Consider the second version of the Lotka-Volterra model: F(a – bF – cS)...
• (Problem 2) Consider the second version of the Lotka-Volterra model: F(a – bF – cS) dF dt ds dt S(-k + \F). (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b, c, k, 1. Plot the solutions of...
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds...
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds = S(-k + XF). dt (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b,c,k, X. Plot the solutions of the model and the...
Exercise 3, Section 9.5. Modified Lotka- Volterra Predator-Prey model Consider two species (rabbits and foxes) such that the population R (rabbits) and F (foxrs) obey the system of equations dR d...
Exercise 3, Section 9.5. Modified Lotka- Volterra Predator-Prey model Consider two species (rabbits and foxes) such that the population R (rabbits) and F (foxrs) obey the system of equations dR dt dF dt R2-R)-12RF . What happens to the population of rabbits if the number of foxes is arro? (Use the phase line analysis from Chapter 2) What happens to the population of foxes if the number of rabbits is zero? 3. Using the method of nullclines, draw an approximate...
1. Consider the Lotka-Volterra model for the interaction between a predator population (wolves W(t)) and a...
1. Consider the Lotka-Volterra model for the interaction between a predator population (wolves W(t)) and a prey population (moose M(t)), À = aM - bmw W = -cW+dMW with the four constants all positive. (a) Explain the meaning of the terms. (b) Non-dimensionalize the equations in the form dx/dt = *(1 - y) and dy/dt = xy(x - 1). (c) Find the fixed points, linearize, classify their stability and draw a phase diagram for various initial conditions (again, using a...
have I solved these correctly? (Lotka-Volterra model) Numbered Suppose that porcupines are the only prey and...
have I solved these correctly? (Lotka-Volterra model)
Numbered Suppose that porcupines are the only prey and available food source for fisher, and that the predator-prey interaction follows Lotka-Volterra dynamics. The mortality rate of fisher in the absence of porcupines is 0.2 per week, and the intrinsic growth rate of porcupine is 0.3 per week. The capture efficiency of porcupine by fisher is 0.002, and the efficiency at which porcupine biomass is converted to fisher offspring is 0.1. 3a. If there...
Kila K2 B B Tag K2 Kila i N2 N₂ A 0 K KIB KIB N...
Kila K2 B B Tag K2 Kila i N2 N₂ A 0 K KIB KIB N K N species 1 species 2 (b) (a) Kila K2 B To 7 N₂ ž K2 Kila D E E X с A ܘܠ A 0 Ky K2/B 0 KB K N N (c) (d) In graph (d), in the lower right-hand region (point C), the combined dynamics the equilibrium point and the carrying capacity of species 1. move away from; toward O support;...
3. The graph below has axes to show the population sizes of a predator and its...
3. The graph below has axes to show the population sizes of a predator and its prey. The dashed lines are the predator and prey isoclines. Prey Population Starting at the circle, draw in what will happen to the two populations if they are following the pattern in the Lotka-Volterra model of predation. (Remember that BOTH predator and prey numbers are represented by a point on the graph.) Use a series of arrows to show what happens. 2. Imagine two...
Module 5: Lotka-Volterra competition equations and predictions number of individuals they would be in species 1 terms, when considering their effect on species 1's growth. 1. For each of the two equations below for the population growth of Species 1 and 2, solve for .How many different ways can you get population growth rate 0? Just to get you started, "N 0 ifr O. dt Species 1 Species 2 K, dr K, Equilibrium solutions for species 1 (in the presence...
Answer both questions
The simplest model for a mutualistic interaction between two species is similar to the basic Lotka-Volterra model as described in Chapter 14 for two competing species. The crucial difference is that rather than negatively influencing each other's growth rate, the two species have positive interactions. The competition coefficients a and fi arc replaced by positive interaction coefficients. reflecting the per capita effect of an individual of species 1 on species 2 (alpha 12) and the effect of...
• (Problem 2) Consider the second version of the Lotka-Volterra model: F(a – bF – cS) dF dt ds dt S(-k + \F). (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b, c, k, 1. Plot the solutions of...
Consider the second version of the Lotka-Volterra model: dF F(a - 6F - cS) dt ds = S(-k + XF). dt (1) Explain the model; i.e. what are the terms in the equation signify? How is this model different from equations (1)? (2) Find the equilibrium point(s). (3) Linearize (2) about the equilibrium point(s). (4) Classify if the equilibrium points are stable or unstable. (5) Pick some values for a, b,c,k, X. Plot the solutions of the model and the...
Exercise 3, Section 9.5. Modified Lotka- Volterra Predator-Prey model Consider two species (rabbits and foxes) such that the population R (rabbits) and F (foxrs) obey the system of equations dR dt dF dt R2-R)-12RF . What happens to the population of rabbits if the number of foxes is arro? (Use the phase line analysis from Chapter 2) What happens to the population of foxes if the number of rabbits is zero? 3. Using the method of nullclines, draw an approximate...
1. Consider the Lotka-Volterra model for the interaction between a predator population (wolves W(t)) and a prey population (moose M(t)), À = aM - bmw W = -cW+dMW with the four constants all positive. (a) Explain the meaning of the terms. (b) Non-dimensionalize the equations in the form dx/dt = *(1 - y) and dy/dt = xy(x - 1). (c) Find the fixed points, linearize, classify their stability and draw a phase diagram for various initial conditions (again, using a...
have I solved these correctly? (Lotka-Volterra model)
Numbered Suppose that porcupines are the only prey and available food source for fisher, and that the predator-prey interaction follows Lotka-Volterra dynamics. The mortality rate of fisher in the absence of porcupines is 0.2 per week, and the intrinsic growth rate of porcupine is 0.3 per week. The capture efficiency of porcupine by fisher is 0.002, and the efficiency at which porcupine biomass is converted to fisher offspring is 0.1. 3a. If there...
Kila K2 B B Tag K2 Kila i N2 N₂ A 0 K KIB KIB N K N species 1 species 2 (b) (a) Kila K2 B To 7 N₂ ž K2 Kila D E E X с A ܘܠ A 0 Ky K2/B 0 KB K N N (c) (d) In graph (d), in the lower right-hand region (point C), the combined dynamics the equilibrium point and the carrying capacity of species 1. move away from; toward O support;...
3. The graph below has axes to show the population sizes of a predator and its prey. The dashed lines are the predator and prey isoclines. Prey Population Starting at the circle, draw in what will happen to the two populations if they are following the pattern in the Lotka-Volterra model of predation. (Remember that BOTH predator and prey numbers are represented by a point on the graph.) Use a series of arrows to show what happens. 2. Imagine two...
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