Money, Sex and Evolution (v3)

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Money, Sex and Evolu0on Agent-‐based modeling with Ruby Sau Sheong Chang PayPal Oct 2014

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About me

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Common Starling (Sturnus vulgaris)

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•  Boids by Craig Reynolds •  Models animal mo0ons through 3 simple rules, resul0ng in ﬂocking behavior •  Emergence – complex behavior arises from simple rules •  Eventual basis for some impressive cinema anima0on – Lord of the Rings, Batman Returns, Lion King etc

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Agent-‐based modeling •  Autonomous agents interac0ng with each other and the environment •  Used in analysing supply chain op0miza0on, traffic paSerns, economic models, spread of epidemics •  Influenced by John Conway’s Game of Life •  Heavily influenced by Epstein and Axtell’s Sugarscape simula0ons

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Utopia •  Ar0ﬁcial world called Utopia •  Populated by roids (implementa0on of boids in Ruby) •  Free to wander through an inﬁnite landscape •  Simula0ons are created with Ruby and the Gosu library

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Base simula0on

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Why does income inequality exist?

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Change behavior in base simula0on •  Roids now have an energy level (randomly assigned, max 100) •  At every 0ck, roids lose 1 energy •  If energy level reaches 0, it will die •  To prevent this, it will ac0vely seek out food and consume it •  Consuming food replenishes energy level •  (But roids are s0ll immortal)

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Data collec0on •  At every 0ck record the energy level of each roid •  Do this un0l the end of the world (simula0on completes)

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First simula0on

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Energy level analysis

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On the day of reckoning Most roids are dead A few roids have a lot of energy

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Gini coefficient and Lorenz curve •  The Gini coefficient is a measure of the inequality of a distribu0on, 0 is perfect equality and 1 is perfect inequality •  Defined mathema0cally based on the Lorenz curve Area is the amount of inequality

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Lorenz curve on inequality Not much inequality A lot of inequality!

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Observa0on •  Over a period of 0me, a small percentage of the popula0on gets a large propor0on of the energy •  What is the cause of this?

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Why the inequality? •  Hard work and inherent talent/ability? – All roids are the SAME •  Some roids luckier than others i.e. random distribu0on? – If it’s random then it should follow a normal distribu0on

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The rich get richer, the poor get poorer •  Back to where we started – emergence •  Small changes ripple down to large eﬀects over a period of 0me •  Simple local rules brings complex global changes

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Spicing things up with sex •  Roids have gender now – male and female •  Males are blue, females are red, underaged are •  If female is within childbearing age (25 to 50 0cks) and if it has enough energy, it will look for a nearby male •  If the male it encounters is also within childbearing age and have enough energy, they will procreate and produce a baby roid •  Both male and female loses energy each 0me they procreate

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Grim reaper arrives •  With birth we introduce death •  Each roid has a randomly assigned lifespan •  Each 0ck increases the age of the roid •  Roid dies when it reaches its lifespan (no maSer how much energy it has)

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Data collec0on •  We want to inves0gate how the popula0on changes once we introduce sex and death •  At every 0ck we collect the popula0on of the en0re world, as well as popula0on of males and females

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Second simula0on

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Data analysis Popula0on ﬂuctuates

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With a minor change What happens here?

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What just happened? •  I changed a parameter -‐ the childbearing age •  Original – CHILDBEARING_AGE = 25..50 •  Changed – CHILDBEARING_AGE = 30..50 •  Does it happen all the 0me? NO -‐ 4 out of 5 0mes

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Looks familiar? •  Financial crashes, social unrest (Arab Spring?), animal ex0nc0ons, climate change? •  Simula0on suggests small internal factors can be enough to trigger crises that cannot be recovered •  Not necessarily need large external triggers

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Things are NOT as stable or as unrelated as we like to think it is

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Natural selec0on •  A central concept in evolu0on •  “Survival of the ﬁSest” •  Organisms with more suitable aSributes are more likely to reproduce and pass these aSributes to the next genera0on •  Over 0me these aSributes become more prominent

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Natural selec0on in Utopia •  Previously all roids have the same aSributes, only diﬀerence is maximum lifespan and energy level •  In this simula0on, we add 2 new aSributes –  Metabolism How well the roid converts the food it eats into energy (higher number beSer) –  Vision range How far away it can see food (higher number beSer) •  Roid babies inherit these 2 aSributes from their parents

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Crossover of gene0c aSributes •  We follow very simple Mendelian rules for crossover •  Assume the father has the genotype (m,v) and the mother has genotype (M,V) •  Possible genotypes of baby are (m,v), (m,V), (M,v) and (M,V) •  We randomly chose 1 of these 4 possibili0es

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Data collec0on •  We want to ﬁnd out how the metabolism and vision range aSributes of the popula0on changes over 0me •  At every 0ck, we calculate the average metabolism and vision range of all roids that are alive

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Third simula0on

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Natural selec0on in ac0on! Metabolism improves over 0me Vision range improves over 0me Natural selec0on is not a straight line

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What did we just see? •  Natural selec0on -‐ the roids with the beSer aSributes are able to survive longer and reproduce with similar aSributes •  Natural selec0on is not necessarily a straight line (vision range meanders for a while)

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One more thing …

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Is inheritance any good? •  In our simula0ons, when a roid dies of old age, his collected energy dissipates •  What happens if the collected energy of a roid is passed on to his children instead? •  This simulates wealth gathered by the parents being inherited by the children

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Fourth simula0on •  Simula0on the same as the evolu0on simula0on except that when a roid dies, the energy he collects over his life0me is distributed to his children •  Compare the evolu0on simula0on with the inheritance simula0on

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One more 0me, with inheritance With inheritance, natural selec0on gets there but takes a longer 0me

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Eﬀects of inheritance •  From the simula0on, inheritance seem stunt evolu0onary advances, causing natural selec0on to take a longer 0me

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Base Money Sex Evolu0on Inheritance Recap

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Wrapup •  Simula0ons ≠ real life, but is good to isolate factors for inves0ga0on •  Conclusions open for interpreta0on (Lies, damn lies and simula0ons) •  Programming as tools to discover the world around us

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Miscellaneous stuﬀ •  Simula0on – Ruby, Gosu •  Analysis – Ruby, Gruﬀ •  hSps://github.com/sausheong/utopia •  [email protected] -‐ personal •  [email protected] -‐ work •  @sausheong -‐ TwiSer