Base model: Does a larger prey population growth rate (R) increase or decrease the stability of the predator-prey interaction? What about a smaller R?
Both a larger and smaller R value destabilize the predator-prey dynamics, but in different ways.
Larger R value: cycles become increasingly steep, with prey population crashing and predator populations dropping to low values.
Smaller R value: cause fewer
Base model: What happens if the predators starve more quickly? Less quickly? (Predator starvation same as predator mortality rate "d" in Lotka-Volterra model)
More quickly: fluctuations become more violent and extreme; predator population drops to low values and prey population increases; number of cycles remain the same
Less quickly: number of cycles decrease; prey cycles more violently to lower numbers; preda
Base model: What happens if the predator is more efficient at converting prey into offspring? Less efficient?
More efficient: dramatically de-stabilizes; predator at higher levels with subsequent cycles and vise versa for prey
Less efficient: also destabilize the system
Base model: Is the behavior of the model sensitive to starting populations?
Very sensitive. The apparent stability of the populations with default parameters is not even neutral stability, it is even less than neutral stability, because any infinitely small deviation away from those values causes the system to fluctuate wildly wi
Base model: What is the ultimate outcome of this predator-prey modeled interaction, regardless of parameter values?
For all values of the parameters the model is unstable and populations spiral outwards with increasing amplitude of both populations over time. Eventually both populations go to zero.
Base model: How does this compare to real predator and prey populations? What factors not included in this model may help explain the differences between model predictions and reality?
This model does not create a realistic approximation of nature.
Factors that could improve reality: (1) no individual differences among either predator or prey, (2) no sex differences, (3) no carrying capacity for either predator or prey, (4) no prey refu
Prey refuge model: . Does a larger prey population growth rate (R) increase or decrease the stability of the predator-prey interaction? Does a decreased R increase or decrease the stability? How many qualitatively different system behaviors can you discov
Increasing R: increasing magnitude of system fluctuations, which is unstable.
Decreasing R: causes slower changes, fewer cycles per time unit and low predator population sizes or crash.
Overall, interaction remains stable over wider range of R values than
Prey refuge model: What happens (to the stability of this model system) if the predators starve more quickly? Less quickly? How many qualitatively different system behaviors can you discover, and how do you explain them?
Higher predator starvation: prey population increases, then followed by predator population and therefore increased magnitude of fluctuations and number of fluctuations - unstable (not as much as base model due to presence of refuge); extreme values cause
Prey refuge model: What happens (to the stability of this model system) if the predator is more efficient at converting prey into offspring? Less efficient? How many qualitatively different system behaviors can you discover, and how do you explain them?
Increased predator efficiency: predator population grows, prey is forced to refuge; fewer cycles; system destabilized (still more stable than base model)
Decreased predator efficiency: destabilizes model by allowing prey to reach high levels and predators
Prey refuge model: What is the ultimate outcome of the predator-prey interaction, in general, over a wide range of parameter values? How would you describe the behavior of this system (be thorough, and as concise as possible)? What generalization(s) can y
System tends to fluctuate with increasing amplitude but only up until the point that the prey reaches their refuge size, at which point the system cycles regularly. The refuge tends to stabilize the population compared to the base model.
The system can be
Prey K model: Does a larger prey population growth rate (R) increase or decrease the stability of the predator-prey interaction? What about a smaller prey population growth rate? How many qualitatively different system behaviors can you discover, and how
Increased R: initially, increasing R stabilizes the system and more predators are necessary to maintain prey population; however, with greatly increased values of R the prey population experiences an overshoot and a resulting population crash due to densi
Prey K model: What happens (to the stability of the system) if the predators starve more quickly? Less quickly? How many qualitatively different system behaviors can you discover, and how do you explain them?
Starve more quickly: destabilizes system because predators decline, eventually reaching zero, and prey reach carrying capacity
Starve less quickly: destabilizes the system by creating fluctuations, causing system to take longer to reach equilibrium for bo
Prey K model: What happens (to the stability of the system) if the predator is more efficient at converting prey into offspring? Less efficient? How many qualitatively different system behaviors can you discover, and how do you explain them?
Increased predator efficiency: destabilizes system; fluctuations are immediate; if too high, predators population goes below 1 individual and the system crashes
Decreased predator efficiency: prey approach a greater abundance asymptotically and predator r
Prey K model: What is the ultimate outcome of the predator-prey interaction, in general, over a wide variety of parameter values? Describe how this system behaves as thoroughly and concisely as you can. How does the behavior of this system compare to real
Existence of carrying capacity greater stabilizes the system over a wide array of circumstances, but this is not enough to keep the system from crashing under certain extreme conditions.
What assumptions do all three of these models (i.e., base, refuge, prey-K) make about how predators and prey interact? List at least four distinctive assumptions of these models, and discuss briefly how realistic is each assumption.
(1) constant environment (i.e., constant growth rates, carrying capacities, etc.)
(2) individuals within a population are all identical (no difference due to sex, age, genetics, etc.)
(3) prey population's interaction with its own resources and possible p