Playing Evolution Games in the Classroom

Colin GarveyGK-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 = - 100 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 GAMEMy Play Opponent Outcome Total

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 = 40Loser = -10

Hawk vs Hawk –

Loser is seriously injured

Winner = 50Loser = -100

Hawk vs Dove

Dove quits immediately; Hawk wins

Winner = 50Loser = 0

Dove vs Hawk

Dove quits immediately; Hawk wins

Winner = 50Loser = 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)