'data.frame': 300 obs. of 6 variables:
$ X.run.number. : int 3 5 2 6 1 7 4 11 8 12 ...
$ carrying.capacity: int 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 ...
$ red.fertility : int 2 2 2 2 2 2 2 2 2 2 ...
$ blue.fertility : num 2.1 2.1 2.1 2.1 2.1 2.1 2.1 2.2 2.1 2.2 ...
$ X.step. : int 116 122 132 127 176 99 228 80 152 67 ...
$ ticks : int 116 122 132 127 176 99 228 80 152 67 ...In Silico Experimentation
April 12, 2023
Learning Objectives for Chapter 8
- Develop an understanding of what makes the results of ABMs more vs. less emergent, by looking at two of NetLogo’s library models (subtle).
- Start using the most important techniques in agent-based science: designing and analyzing simulation experiments to test hypotheses and develop understanding about how an ABM works and how well it reproduces the system it models (concrete).
- Master the use of BehaviorSpace, NetLogo’s extremely useful tool for automatically running simulation experiments and producing output from them (concrete).
- Analyze output produced by NetLogo models by importing results to other software for graphing and statistical analysis (concrete).
Learning Objectives for Chapter 8
- Develop an understanding of what makes the results of ABMs more vs. less emergent, by looking at two of NetLogo’s library models (subtle).
- Start using the most important techniques in agent-based science: designing and analyzing simulation experiments to test hypotheses and develop understanding about how an ABM works and how well it reproduces the system it models (concrete).
- Master the use of BehaviorSpace, NetLogo’s extremely useful tool for automatically running simulation experiments and producing output from them (concrete).
- Analyze output produced by NetLogo models by importing results to other software for graphing and statistical analysis (concrete).
Emergence
From
local agent rules and behavior
to
emergent system-level dynamics
Emergence
Question #1: What dynamics of the system and what model outcomes
emerge - arise in relatively complex and unpredictable ways - from what behaviors of the agents and what characteristics of their environment?
Question #2: What other model dynamics and outcomes are instead
imposed - forced to occur in direct and predictable ways - by the model’s assumptions?
Qualitative Criteria for Emergence
- Emergent phenomenon is not simply the sum of the properties of the model’s individuals (nonlinear),
- Emergent phenomenon is a different type of result than individual-level properties (system-level), and
- Emergent phenomenon cannot easily be predicted from the properties of the individuals (complex).
Discuss: Do the butterfly model’s corridor width results (system-level phenomenon) meet the three criteria for being emergent?
Example: Simple Birth Rates
From Info tab:
“This is a simple model of population genetics. There are two populations, the REDS and the BLUES. Each has settable birth rates. The reds and blues move around and reproduce according to their birth rates. When the carrying capacity of the terrain is exceeded, some agents die (each agent has the same chance of being selected for death) to maintain a relatively constant population. The model allows you to explore how differential birth rates affect the ratio of reds to blues.”
Example: Simple Birth Rates
Example: Simple Birth Rates
In-Silico Experiments
Using BehaviorSpace to run in silico experiments.
Question: Why do we need to run experiments?
Answer: When all parameters are fixed,
stochasticity in the system leads to results that are different each time it is run. Thus, we need to estimate the average results, as well as the variability around those averages.
Experiments allow us to include replicates of several different scenarios, where a scenario is the model with a specific set of parameters, initial conditions, and inputs.
In-Silico Experiments
Two main types of experiments:
- Sensitivity experiment: Vary one parameter over a wide range to see how model response changes (single-factor).
- Contrast scenarios: Look at differences in model response between two or several distinctly different scenarios.
The contrast scenario is most similar to typical experimental designs with a control and treatment.
Example: Simple Birth Rates
Let’s learn BehaviorSpace!
Example: Simple Birth Rates
Example: Simple Birth Rates
We need to replicate this figure:
Example: Simple Birth Rates
First, we need the blue fertility values:
Example: Simple Birth Rates
Second, we need to compute the average ticks until red extinction.
N <- length(bf.vals) # How many bf.vals?
time.to.red.extinction <- rep(0,N) # Initialize
sdev <- rep(0,N)
for (i in 1:N) {
# Subset the data
tmp <- subset(mydata, mydata$blue.fertility == bf.vals[i])
# Compute average over subsetted data
time.to.red.extinction[i] <- mean(tmp$ticks)
# Compute standard deviation over subsetted data
sdev[i] <- sd(tmp$ticks)
}Example: Simple Birth Rates
Let’s plot!
Example: Simple Birth Rates
Intro to Quantitative Biology, Spring 2023