Reintroduction of Wolves into Yellowstone National Park, Wyoming. The reintroduction of wolves to Yellowstone National Park is a fascinating case study in ecosys- tem management and conservation biology. Here's a brief overview of key aspects of this case: In 1995, wolves were reintroduced to Yellowstone National Park after being eliminated in the 1920s. The primary goal was to restore a vital part of the park's ecosystem that had been missing for nearly 70 years. The initial reintroduction involved 31 wolves from Canada. These wolves were released in sev- eral groups, and their populations grew steadily, benefiting from the abundant prey and lack of human interference. The reintroduction of wolves had profound effects on the Yellowstone ecosystem which are nicely summarized in this interesting (and somewhat controversial) video How Wolves Change Rivers While the Lotka-Volterra model simplifies complex ecological interactions, it provides a useful framework for understanding predator-prey relationships in nature. It's important to note that ecological data can be complex and context-dependent. The interaction between wolves and elk in Yellowstone is influenced by many factors beyond just simple population counts, including environmental changes, human activities, and the presence of other predators and prey species and many modified models have been applied to this case. Expanding the Model One modification of the predator-prey model would be to assume that, in the absence of predators, the prey population obeys a logistic rather than an exponential growth model. One such model is provided by the system of differential equations given by dx dt = 2.4x (1-1/2) 2/2) - 1.2.xy dy dt = -y+0.9xy 6. Find the equilibrium points for the system shown above. Explain the significance of these points in terms of the predator and prey populations. 7. How would you modify the above equations to include the effect of hunting on the prey at a constant rate of a units per unit of time (matching the units in the above equation, whatever they are chosen to be). In the case of elk and wolf example, the elk are hunted in addition to being prey for the wolves. 8. How would you modify the above equations to include the effect of hunting on the predators at a rate proportional to the number of predators? 9. Suppose the predators discover a second, unlimited food source but they still prefer to eat prey when they can catch them. How would you modify the above equations to include this assumption.

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Reintroduction of Wolves into Yellowstone National Park, Wyoming.
The reintroduction of wolves to Yellowstone National Park is a fascinating case study in ecosys-
tem management and conservation biology. Here's a brief overview of key aspects of this case:
In 1995, wolves were reintroduced to Yellowstone National Park after being eliminated in the
1920s. The primary goal was to restore a vital part of the park's ecosystem that had been
missing for nearly 70 years.
The initial reintroduction involved 31 wolves from Canada. These wolves were released in sev-
eral groups, and their populations grew steadily, benefiting from the abundant prey and lack
of human interference. The reintroduction of wolves had profound effects on the Yellowstone
ecosystem which are nicely summarized in this interesting (and somewhat controversial) video
How Wolves Change Rivers
While the Lotka-Volterra model simplifies complex ecological interactions, it provides a useful
framework for understanding predator-prey relationships in nature. It's important to note
that ecological data can be complex and context-dependent. The interaction between wolves
and elk in Yellowstone is influenced by many factors beyond just simple population counts,
including environmental changes, human activities, and the presence of other predators and
prey species and many modified models have been applied to this case.
Expanding the Model
One modification of the predator-prey model would be to assume that, in the absence of
predators, the prey population obeys a logistic rather than an exponential growth model. One
such model is provided by the system of differential equations given by
dx
dt
= 2.4x (1-1/2)
2/2) - 1.2.xy
dy
dt
=
-y+0.9xy
6. Find the equilibrium points for the system shown above. Explain the significance of these
points in terms of the predator and prey populations.
7. How would you modify the above equations to include the effect of hunting on the prey at a
constant rate of a units per unit of time (matching the units in the above equation, whatever
they are chosen to be). In the case of elk and wolf example, the elk are hunted in addition to
being prey for the wolves.
8. How would you modify the above equations to include the effect of hunting on the predators
at a rate proportional to the number of predators?
9. Suppose the predators discover a second, unlimited food source but they still prefer to eat
prey when they can catch them. How would you modify the above equations to include this
assumption.
Transcribed Image Text:Reintroduction of Wolves into Yellowstone National Park, Wyoming. The reintroduction of wolves to Yellowstone National Park is a fascinating case study in ecosys- tem management and conservation biology. Here's a brief overview of key aspects of this case: In 1995, wolves were reintroduced to Yellowstone National Park after being eliminated in the 1920s. The primary goal was to restore a vital part of the park's ecosystem that had been missing for nearly 70 years. The initial reintroduction involved 31 wolves from Canada. These wolves were released in sev- eral groups, and their populations grew steadily, benefiting from the abundant prey and lack of human interference. The reintroduction of wolves had profound effects on the Yellowstone ecosystem which are nicely summarized in this interesting (and somewhat controversial) video How Wolves Change Rivers While the Lotka-Volterra model simplifies complex ecological interactions, it provides a useful framework for understanding predator-prey relationships in nature. It's important to note that ecological data can be complex and context-dependent. The interaction between wolves and elk in Yellowstone is influenced by many factors beyond just simple population counts, including environmental changes, human activities, and the presence of other predators and prey species and many modified models have been applied to this case. Expanding the Model One modification of the predator-prey model would be to assume that, in the absence of predators, the prey population obeys a logistic rather than an exponential growth model. One such model is provided by the system of differential equations given by dx dt = 2.4x (1-1/2) 2/2) - 1.2.xy dy dt = -y+0.9xy 6. Find the equilibrium points for the system shown above. Explain the significance of these points in terms of the predator and prey populations. 7. How would you modify the above equations to include the effect of hunting on the prey at a constant rate of a units per unit of time (matching the units in the above equation, whatever they are chosen to be). In the case of elk and wolf example, the elk are hunted in addition to being prey for the wolves. 8. How would you modify the above equations to include the effect of hunting on the predators at a rate proportional to the number of predators? 9. Suppose the predators discover a second, unlimited food source but they still prefer to eat prey when they can catch them. How would you modify the above equations to include this assumption.
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