1. Wednesday After Lunch: Add randomness to the Flowers Model
Temperature is from a uniform distribution [20 to 30] degrees C. A new value is selected every DT.

2. Temperature Results for a 10 year simulation, with DT = 0.25 years
Optimum Temperature is 25 degrees
Intrinsic growth rate (max is 1.2 when 25 degrees)

3. Flowers Results for a Stochastic Simulation over 40 years
Flowered area grows to around 700 acres, lower than before due to wide range of temperatures

4. Selecting the Properties of the Random Inputs
The statistical distribution: Uniform? Normal? Exponential? Poisson? Etc.
The parameters for each distribution
For example there are 4 parameters for the Random Normal Distribution: min, max, mean, standard deviation, and seed
And don’t forget that a new number is selected every DT
Suppose DT were extremely small (for numerical accuracy): Would the “high frequency noise” have a significant impact on the system??
If the random number should be held for a longer interval, do we increase DT??

5. We all have learned DT has no counterpart with the Real World
So we need a separate parameter for how long a random number is held before a new value is selected
Figure 14.8 on page 175, shows
an example of “sampled noise” that is held for a user specified
Interval. Then it is removed to make room for the selection of a new value. The length of time to hold each value is the “noise interval” shown in green.

6. Example of random numbers (uniformly distributed from 20 to 30) selected every 0.25 years and held for 1 year.

7. Can Randomness change the fundamental pattern of behavior?
The Nonlinear function (in green) for predation is often discussed by wildlife experts (for good reason). The graph shows a predation function similar to Type I and Type II functions used in predation studies.

8. Predator-Prey Dynamics from 1st Model
But predators in the wild do not annihilate their prey!! So what should we change in this model??

9. A type III predation function avoids annihilation
This is more realistic behavior, as oscillations will continue in the wild over the centuries. But the oscillations do not dampen out over time.
So how should we change
This model?

10. Yes, Randomness can change the fundamental pattern of behavior