On Group Selection

This post is an attempted response to Steven Pinker's 
                                 "THE FALSE ALLURE OF GROUP SELECTION"

Introduction

Can natural selection allow for reproductive individuals in a group to exhibit altruistic behaviors?
In his lengthy article, Steve Pinker suggest that it cannot:

"A new mutation with this effect would not come to predominate in the population, and even if it did, it would be driven out by any immigrant or mutant that favored itself at the expense of the group." 

Again, to flip this around a bit. Steve Pinker is suggesting that natural selection has no solution to environmental pressures based on altruism.

In contrast, our simulations indicate that, if species is organized into groups, that the group order selection mechanism provides the solution to the problem of altruism. I would call this type of selection "Anthropic Selection" as selection is based on the ongoing non existence of the low altruistic groups.

Let us first clearly define our terms:
group - a sub species that is only sexually reproductive with its own members.
altruism- a choice by an individual that is harmful to that individual but beneficial to the group.
reproductive individual - individuals that produce offspring with a mate where the offspring are formed through the (random) combination of parental traits and (possibly) mutation
altruism trait - genetically inherited tendency to participate in altruism behaviors

dominating trait - significant representation of a trait (above mutation rate)

Simulation

"What's satisfying about the theory [of natural selection] is that it is so mechanistic. " - Pinker

The simulation to find the contradictory case to the arguments made by Pinker were designed to be as simple as possible but still legitimately express the intended mechanism.

The simulation is composed of temporal collection of groups which are composed of individuals. Each individual belongs to only one group and contains within them a single boolean representing the prevalence of the altruistic expression. Every update tick each group breeds fully. This means all individuals in a group are randomly paired with another intra group member and three offspring are produced. To simulate individual longevity only the offspring remain in the group. The parents can be viewed to completely expire (having successfully bred)

The act of heritable breeding is simulated in the following way. It should be noted that in the actual simulation we can introduce a small mutation probability for each child that will randomly flip the mutation trait.

The expected growth rate for each group is 50% per update. Instead of capping this growth we simply split the groups once they exceed a certain group size.The fission of a group into two groups always results in two new equal sized groups but its members are randomly distributed.

As so far described the number of groups would simply grow without end and the altruistic trait, experiencing no selection pressure, would normalize in the population.  Our final critria is to add the altruistic selection phase.


Once the number of groups get to a specific maximum a culling altruistic test is performed on each group independently. A single random individual is pulled from a specific group. If this individual is altruistic then that individual is destroyed but the rest of the group passes the test. If this individual is not altruistic then this entire group is destroyed with probability Pcritical. 

It should be noted that if the individual that is chosen is altruistic they will not produce any offspring. This is in contrast to a non altruistic individual which still has the probability of Pcritical of surviving to breed.

Hypothesis:

• Altruistic trait will eventually dominate all groups for values of Pcritical sub threshold.
• The introduction of low mutation rates will not significantly effect the domination outcome.

Setup:

Simulation basic parameters were configurable but set to values to reduce mechanism noise for all runs.

Default conditions:
Mutation probability = 0.1%
Max number of groups before cull phase = 10000
Init Altruism trait = 50.0%    (effectively achiving centered normal distribution)

Results:

Many various simulations were run that all indicate the domination of the altruism trait over the course of time. (see below)

Max pop 100, default conditions.

Max pop 500, default conditions

Max pop 1000, default conditions

As expected it is also possible to change Pcritical to a value where altruism is no longer favored. (see below)

Max pop 200, Pcrit = 1.0, default conditions

Domination table:

Domination of the altruism trait was not only dependent on Pcritical but also dependent on group size. These values were experimentally determined via simulation runs.

Group Size:  <Pcrit - altruism dominates:   
20                  0.92
100                0.94
500                0.95
1000              0.96

Mutation effect:

Mutation rates increase the normalization of the simulation (expected) but do not directly effect the domination outcome. This movement to normalized is likely purely based on individual mutation effect being normalized. The graphs below contrast very low mutation rate with very high mutation rate.

Max pop 1000, mutation rate 0.01%, Pcrit 50%

Max population 1000, mutation rate 1%, Pcrit 50%

Algebraic Example:

Concerns about correctness of simulation motivates us to seek a simpler way to mathematically grasp its conclusions. A tractable example is enough to give us an intuitive feel for the mechanism at work.

Supposedly we have just 2 groups
group A:75 altruistic individuals out of 100 total
group B:25 altruistic individuals out of 100 total

Total average altruism rate is 50% of we simply combine the two groups (A + B)
However if we do a per group culling phase.

Case probabilities:
Case 0: 0.75 * 0.25 = 0.1875  - A pass, B pass
Case 1: 0.75 * 0.75 = 0.5625  - A pass, B fail
Case 2: 0.25 * 0.25 = 0.06.25  - A fail, B pass
Case 3: 0.25 * 0.75 = 0.1875  - A fail, B fail

Case    #Altruist, #Total => normalized by probability of case
Case 0: 74 + 24, 99 + 99  =>                           
                                              18.375, 37.125
Case 1: 74 + 25 * Pcrit, 99 + 100 * Pcrit  =>
                                                                      41.625 + 14.0625 * Pcrit, 55.6875 + 56.25 *Pcrit
Case 2: 75 * Pcrit + 24 , 100 * Pcrit + 99 => 
                                                                         4.6875 * Pcrit + 1.5 , 6.25 *Pcrit + 6.1875
Case 3: 75 * Pcrit + 25 * Pcrit, 100 * Pcrit + 100 * Pcrit =>
                                                                                                18.75 * Pcrit , 37.5 * Pcrit

Sum all normalized cases:
61.5 + 37.5 * Pcrit, 99 + 100 * Pcrit
In this example Pcrit values less than 0.96 altruistic is increased.

Conclusion

It is possible to construct a simulation of natural selection that favors altruism in sexually reproductive individuals so long as these individuals are confined to groups. It is also a hope of this article to lend credence to the idea that implied mechanistic behaviors should be explored mechanically. 

Notes

Relevant Quotes from Paper

"If a person has innate traits that encourage him to contribute to the group's welfare and as a result contribute to his own welfare, group selection is unnecessary;  It's only when humans display traits that are disadvantageous to themselves while benefiting their group that group selection might have something to add."

" Natural selection could legitimately apply to groups if they met certain conditions: the groups made copies of themselves by budding or fissioning, the descendant groups faithfully reproduced traits of the parent group (which cannot be reduced to the traits of their individual members), except for mutations that were blind to their costs and benefits to the group; and groups competed with one another for representation in a meta-population of groups. But everyone agrees that this is not what happens in so-called "group selection." In every case I've seen, the three components that make natural selection so indispensable are absent."

"Modern advocates of group selection don't deny that selection acts on individual organisms; they only wish to add that it acts on higher-level aggregates, particularly groups of organisms, as well. "

"Human beings live in groups, are affected by the fortunes of their groups, and sometimes make sacrifices that benefit their groups. Does this mean that the human brain has been shaped by natural selection to promote the welfare of the group in competition with other groups, even when it damages the welfare of the person and his or her kin? If so, does the theory of natural selection have to be revamped to designate "groups" as units of selection, analogous to the role played in the theory by genes?"

"Is group selection necessary to explain the evolution of psychological traits adapted to group living such as tribalism, bravery, self-sacrifice, xenophobia, religion, empathy, and moralistic emotions? "
   

Ref

https://www.edge.org/conversation/steven_pinker-the-false-allure-of-group-selection

https://eli.thegreenplace.net/2016/drawing-animated-gifs-with-matplotlib/