Evolution is Not Optimal Solution?

While reading about Evolutionarily Stable Strategies (ESS), I came across an example... and then I got to thinking...

Background:  One species with 2 members, with differing traits
(Points corresponding to action performed in parenthesis)

1. Hawks - behave aggressively
• If opponent runs, eat food (+50)
• If opponent fights back, they will fight to near-death
• 1 always wins (+50), 1 always loses (-100)
2. Doves - behave submissively
• If attacked, will run away (+0)
• If not attacked, will make threatening display
• 1 always wins (+40), 1 always loses (-10)

Scenario 1 - Doves Only

• Average of 15 points per confrontation to each member
• However, susceptible to Hawk mutation
• One Hawk will receive 50 points per encounter
• More food will result in increased Hawk population

Scenario 2 - Hawks Only

• What if Hawks take over?
• Average of -25 points per confrontation to each member (DISASTER)
• Population would go extinct (Fighting is costlier than the food)

Scenario 3 - Equilibrium

• 5:7 Dove to Hawk ratio
• Stable population balance
• Average of 6.25 points per confrontation to each member

Why is this so interesting?

The real world is probably closer to Scenario 3 than Scenario 1.  However, Scenario 1 is BY FAR, the better world to live in (15 points vs 6.25 points).  Evolution led us to where we are, but quite likely there are better ways to improve life in our communities through concerted efforts to 1) cooperate, and 2) resist the urge to act in our own self-interest at the expense of others - Love Thy Neighbor

Note:  if the doves decide to make no threatening display, the expected value (per member, per encounter) would increase from 15 to 20 - Ninth Commandment (You shall not bear false witness against your neighbor)

Statistical Mechanics - Entropy is Not Certainty

Statistical Mechanics

Model - Closed box full of gas particles
Hypothesis - Gases will eventually distribute themselves in more or less even concentrations across the volume of the box
Puzzle - Newtonian laws of mechanics do not forbid the gases from moving into one half of the box, or alternative otherwise uneven concentrations

Then Why?- to answer this, its helpful to look at the scenarios below

2 Particle Scenario

• Imagine a box with 2 particles inside
• Particles are moving, constantly bouncing off walls, or each other (Newton's 2nd Law)
• Possible Arrangements (at any given time)
• 0 particles on left side, 2 particles on right side (25%)
• xx-AB
• 1 particle on left side, 1 particle on right side (50%)
• Ax-Bx
• Bx-Ax
• 2 particles on left side, 0 particles on right side (25%)
• AB-xx

4 Particle Scenario

• Imagine a box with 4 particles inside
• Particles are moving, constantly bouncing off walls, or each other (Newton's 2nd Law)
• Possible Arrangements (at any given time)
• 0 particles on left, 4 on right (6.3%)
• xxxx-ABCD
• 1 particle on left, 3 on right (25%)
• Axxx-BCDx
• Bxxx-ACDx
• Cxxx-ABDx
• Dxxx-ABCx
• 2 particles on left, 2 on right (37.5%)
• ABxx-CDxx
• ACxx-BDxx
• ADxx-BCxx
• BCxx-ADxx
• BDxx-ACxx
• CDxx-ABxx
• 3 particles on left, 1 on right (25%)
  
• ABCx-Dxxx
• ABDx-Cxxx
• ACDx-Bxxx
• BCDx-Axxx
• 4 particles on left, 0 on right (6.3%)
• ABCD-xxxx

As you can see from the above scenarios, at N=2 and N=4, the most likely outcomes are the ones where the particles are arranged evenly into the two sides of the box.  The shape that is revealed is what in statistics is referred to as the bell-shaped curve (x representing the distinct outcome and y representing the corresponding probability).

The most common outcomes are the ones that lie near the peak of the curve.  So, in statistical mechanics, we find that outcomes were the particles are more evenly distributed are probabilistically speaking more likely to occur.

This characteristic would hold true for progressively larger numbers of particles (as N approaches infinite).  Therefore, in the words of Gribbin, Boltzmann's gases spread out to fill the box because that is the more likely outcome, while gases huddling close together in one corner, while far from impossible, is very unlikely.