Playing Evolution Games in the Classroom Colin Garvey GK-12 Fellow

Why don’t lions eat lions? Lions compete with other animals for space on the savanna, but they surely compete most with other lions – overlap of needs is highest. If individual selfishness is the overriding strategy, why don’t conspecifics overwhelmingly target one another for destruction? Cannibalism does happen but why isn’t it the norm?

The central problem of evolution Individual organisms’ needs overlap most with others of their own species How does cooperation evolve in a cut-throat environment of selfish individuals? Altruism is the “central problem” for modern evolutionary theory – It is locally disadvantageous, so how can it evolve in a system wherein each system change must be more fit (adaptive) than before

Modeling the real world How can selfish gene theory explain the altruistic “gloved fist of nature”? – Economic cost/benefit analysis in terms of individual energy expenditure (over time) – Turns out that for A to kill B actually helps their mutual enemy C, who benefits by losing a potential threat free of energetic cost – The conditions of social life amongst selfish individuals can still lead to the evolution of altruistic behavior and the formation of groups

Strategies for living in the real world Consider an idealized account of an interaction between two organisms of the same species, X – They are in competition for some resource, R – In their encounter, they have behavioral options: Fight or Flight reactions are modeled as – Hawk & Dove strategies The dynamics of these two idealized strategies can tell us something about the evolution of behavior

Get that paper, son

Hawk

Hawk vs Hawk Brutal battle leaves one hawk triumphant, and one poor hawk gravely injured – Winner = 50 points – Loser = points

Dove

Dove vs Dove Lots of posturing, feinting, stare-downs Eventually, single winner emerges with 50 pts Loss of time, but no one physically hurt Thus both players lose 10 points – Winner = (50 – 10) = 40 – Loser = -10

Hawk vs Dove / Dove vs Hawk Hawks always win because Doves quit immediately, avoiding injury and loss of time – Winner = Hawk = 50 points – Loser = Dove = 0 points

HOW TO PLAY THE GAME My PlayOpponentOutcomeTotal

Fight! Let’s

Average Payoff The average payoff for any player depends on the strategies of other players What is the average payoff for a population of – All hawks? – All doves? – 50/50 mix?

The Payoff Matrix Dove vs Dove Lots of posturing, but no one hurt Winner: 50 – 10 = 40 Loser = -10 Hawk vs Hawk – Loser is seriously injured Winner = 50 Loser = -100 Hawk vs Dove Dove quits immediately; Hawk wins Winner = 50 Loser = 0 Dove vs Hawk Dove quits immediately; Hawk wins Winner = 50 Loser = 0

Evolutionary Stable Strategies Imagine if cach individual can play either Hawk or Dove each time – Simple pattern-based strategies will be outwitted An important question is then if one can do better than random by playing some optimal combination of Hawk and Dove strategies – The optimal ratio of hawk/dove-ishness depends on the payoff and thus on (environmental) initial conditions

Fight!

Conclusions Evolution in Action Cost/benefit Analysis Optimization of Goal Oriented Behavior (GOB) Future Directions Computer Simulations Incorporate an Understanding of Heredity Family Trees Exploring “Relatedness” (in a broader context)