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WHAT IS IT?

This model explores the evolution of aggresion in a system consisting of animals fighting for a resource necessary for reproduction. Three different strategies are considered: doves, hawks and retaliators.

1. Doves are not aggresive, they start displaying and retreat at once if their opponent is aggresive. When both opponents display one of them eventually gives up the reward to the other one but both pay a cost for wasting time.

2. Hawks are aggresive and fight with opponents that do not retreat until one of them is seriously injured and the other one gets the reward.

3. Retaliators start displaying but become aggresive when their opponents are aggresive. They behave as doves when confronted with a dove or another retaliator and as a hawk when they fight a hawk.

This project explores if any of the three strategies is an ESS (Evolutionary Stable Strategy), a strategy that when adopted by most of the individuals in the population cannot be invaded by another strategy.

HOW TO USE IT

1. Set the SHOW-FITNESS? switch On to display the fitness associted with each individual or Off otherwise.
2. Adjust the slider parameters (see below), or use the default settings.
3. Press the SETUP button.
4. Press the GO button to begin the simulation.
5. Look at the POPULATIONS, FITNESS and RATIO plots to watch the population sizes, their fitness and the ratio of each individual type in the population fluctuate over time.
6. Look at the monitors to see the current subpopulation sizes, their fitness and ratio.

Parameters:
SHOW-FITNESS?: Whether or not to show the fitness associate with each individual
TIME-TO-REPRODUCE: Expected time to elpase before an individual reproduces
INITIAL-NUMBER-DOVES: The initial size of the dove population
INITIAL-NUMBER-HAWKS: The initial size of the hawk population
INITIAL-NUMBER-RETALIATORS: The initial size of the retaliator population
INITIAL-FITNESS: The initial fitness associated with each individual
REWARD: Value added to an individual fitness after winning a fight
COST-INJURE: Value substracted from an individual fitness after being injured during a fight
COST-WASTED-TIME: Value substracted from an individual fitness after dove or retaliator fitness

THINGS TO NOTICE

None of these strategy is an ESS with the default settings.

Note that a population of hawks can be invaded by a population of doves and viceversa.

Note that a population of retaliators cannot be invaded by a population of hawks but tolerates a subpopulation of doves.

Note that a population of retaliators is driven extinct when both doves and hawks are introduced.

THINGS TO TRY

Try adjusting the parameters under various settings. Can you find any parameters that make one of these strategy an ESS?

REFERENCES

Smith, J.M. (1982). Evolution and the Theory of Games. Cambridge University Press

COPYRIGHT NOTICE

Copyright 2011 Francisco J. Romero-Campero. All rights reserved.

Permission to use, modify or redistribute this model is hereby granted, provided that both of the following requirements are followed:
a) this copyright notice is included.
b) this model will not be redistributed for profit without permission from Francisco J. Romero-Campero.

This model was created as part of the projects: COMPUTATIONAL MODELLING AND SIMULATION IN SYSTEMS BIOLOGY (grant number P08-TIC-04200) and CELLULAR COMPUTING; APPLICATIONS TO SYSTEMS AND SYNTHETIC BIOLOGY (grant number TIN2009-13192).These projects gratefully acknowledge the support of the Spanish Ministry of Science and Innovation and the Andalusian Agency for Economy, Innovation and Science.