11.5: No differentiation

Last updated
Save as PDF

Page ID: 46671

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Before we run the simulation, we have to specify the behavior of choose_dead and choose_replacements. We’ll start with simple versions of these functions that don’t depend on fitness:

# class Simulation 
    
    def choose_dead(self, fits): 
        n = len(self.agents) 
        is_dead = np.random.random(n) < 0.1 
        index_dead = np.nonzero(is_dead)[0] 
        return index_dead

In choose_dead, n is the number of agents and is_dead is a boolean array that contains True for the agents who die during this time step. In this version, every agent has the same probability of dying: 0.1. choose_dead uses np.nonzero to find the indices of the non-zero elements of is_dead (True is considered non-zero).

# class Simulation 

    def choose_replacements(self, n, fits): 
        agents = np.random.choice(self.agents, size=n, replace=True) 
        replacements = [agent.copy() for agent in agents] 
        return replacements

In choose_replacements, n is the number of agents who reproduce during this time step. It uses np.random.choice to choose n agents with replacement. Then it invokes copy on each one and returns a list of new Agent objects.

These methods don’t depend on fitness, so this simulation does not have differential survival or reproduction. As a result, we should not expect to see evolution. But how can we tell?