Telecom Paris Dep. Informatique & Réseaux J-L. Dessalles ← Home page October 2025

Module Athens TP-09

    Emergence in Complex Systems

Lecturers:

Ada Diaconescu - Associate professor at Telecom-Paris

Jean-Louis Dessalles - Associate professor at Telecom-Paris

Samuel Reyd - PhD student at Telecom-Paris

                            ➜    other AI courses

Please answer in English!
Load the configuration Favourable.evo in the Configuration Editor (Starter). In this application, implemented in Scenarii/S_Favourable.py, individuals are rewarded depending on the value of the gene named favourable. The other gene, named neutral, has no effect. Choose a positive value for parameter IndividualBenefit (in the section Scenarios/BehaviouralEcology/Favourable in the Configuration Editor). Run Evolife (button [Run]). As predicted by basic Darwinian principles, the average value of the first gene should rise to maximum, whereas the neutral gene average value oscillates around 50 (the amplitude of the deviation depends on the size of the population).

➜    You might restore GeneCoding to Weighted.

➜    Restore a positive value for IndividualBenefit.

➜    You may load Favourable_collective.evo from starter.
Individuals may contribute to public welfare. This is controlled by parameter CollectiveBenefit (in the section Scenarios/BehaviouralEcology/Favourable in the Configuration Editor). The value of the gene favourable, cumulated over all individuals in the group, provides a public good that will be redistributed to all members in the group (see S_Favourable.py). Intuitively, we would expect the gene to remain stable at high values, as the whole group benefits from the contribution of all its members.

Set CollectiveBenefit to a high value such as 100, and IndividualBenefit to a smaller negative value, such as -10. The net profit for each member of the group may be significant, with a maximum of 90 if everyone contributes 100% to the public good. We may thus intuitively expect the value of the gene to rise.

To understand the limits of the so-called "group-selection", you may read Group Competition, by Samuel Bowles.

Let’s suppose that all individuals have the same gene value m, except for a proportion p of them (mutants) whose gene value is M. Let’s call:

• N the size of the group
• p the proportion of mutants
• CB the CollectiveBenefit factor (/100)
• IB the IndividualBenefit factor (/100)
• m the value of the non-mutant gene
• A a mutant individual with gene value M.
• M the value of the mutant’s gene
• B an average individual of the same group with gene value m.
• C an average individual in another group with gene value m.

C’s benefit is: CB * (N*m/N) + IB * m = (CB+IB)*m

    
This small experiment was popularized by Richard Dawkins in his book The selfish gene. It shows how some interesting coupling between genes may emerge in a population.

Suppose a given gene has two effects on its carriers:

• (1) they get a conspicuous characteristic, like a green beard.
• (2) they tend to behave altruistically toward green-bearded individuals.

Load the configuration GreenBeard.evo in the Configuration Editor. The scenario offers two parameters: GB_Gift and GB_Cost that you may use to control individuals’ altruistic behaviour.

Open the file S_GreenBeard.py (in the Scenarii directory) and implement the function interaction so that green bearded individuals (those whose gene named GreenBeard has value 1) behave altruistically toward their green-bearded fellows by helping them: they give them life points (through the score function) at their own expense (they lose points, but possibly less, as controlled by the GB_Cost coefficient). To do so, you need to use functions such as:

• indiv.score(bonus) (defined in Individual.py; if score is omitted, merely reads the individual’s current score). bonus may be positive or negative.
• indiv.gene_value(GreenBeard) (defined in Genome.py; returns the gene’s value).

The values of parameters may be accessed from the scenario through:

    self.Parameter('GB_Gift')
    self.Parameter('GB_Cost')

Observe that the GreenBeard gene invades the population. To understand the phenomenon, one must look at genes rather than at individuals. On average, the payoff of the GB+ allele is:

\(p * (GB_{Gift} - GB_{Cost})\)

where $p$ is the probability of GB-GB encounter. The average payoff of the GB- allele is 0.

The GreenBeard gene happens to have two coupled effects:

• appearance (green beard) and
• altruism (toward other green-bearded individuals).

If you made appropriate changes, appearance is now controlled by GreenBeard, whereas the altruistic behaviour is controlled by Altruist. So whenever a green beard agent meets one of its fellows, it checks for the value of its own Altruist gene before helping at its own cost.

You may play with the idea.

• For instance, in the initial situation where the GreenBeard gene has the two effects, you may use a second gene (name it Nasty instead of Altruist) that prompts its carriers to attack green bearded individuals at their own expense (i.e. both lose points). It becomes good and bad to carry a green beard. The new gene may check (or not) that its carrier has a green beard or not.
• Keep the idea that ‘green beards’ help each other only if they are ‘altruists’. Now mimic a brotherhood effect by implementing a collective benefit: ‘altruists’ get a bonus divided among their kind. For certain values of the parameters, oscillation may emerge.

    
Sex ratio is one the most famous problems in evolutionary theory. It is also one of the most impressive achievements of the game theoretic approach to evolution.
In our species, the sex ratio is roughly 1:1 (it is actually 1.05:1 in favour of boys; note that the ratio is currently 1:1.2 in some developing countries (see diagram) for non-biological reasons that you can figure out!!). From a "Public Goods" perspective, a 1:1 ratio is absurd. Only females contribute energetically to the reproduction of the population; tolerating 50% of males seems underproductive, since 1% would suffice for siring all the children.

What’s wrong in this reasoning?

As it turns out, the welfare of the population is not what is maximized through the mechanics of natural selection. If one adopts the perspective of gene (or schema) replication, then the game theoretic optimum is predicted to be reached, in most species, for a 1:1 ratio between sexes.

Run Evolife with the SexRatio configuration (button [Run]). Observe that both the average value of the gene and the sex ratio itself remain stable around 50% .

Open the S_SexRatio.py file. In this scenario, individuals can be male or female (interestingly, we chose to implement the distinction as a phenotypic character, as it is not inherited). Individuals have a gene, called sexControl. When expressed in females, this gene is supposed to control the sex ratio of children. This is performed in the new_agent function.
Have a look at the implementation in S_SexRatio.py. Locate the lines in the new_agent function where the child’s sex is determined. Replace the line:

if random.randint(0,100) >= mother.gene_relative_value('sexControl'):

by either of the following lines:

if random.randint( 0, 60) >= mother.gene_relative_value('sexControl'):
if random.randint( 0, 60) <= mother.gene_relative_value('sexControl'):
if random.randint(40,100) >= mother.gene_relative_value('sexControl'):
if random.randint(40,100) <= mother.gene_relative_value('sexControl'):

These lines introduce a sex bias in favour of one of the two sexes.

To explain what we see, let’s consider three alleles of 'sexControl':

• SC1 = 0.1 (0.1 means that the child is ten times more likely to be female)
• SC5 = 0.5 and
• SC9 = 0.9

Let’s suppose that we are in a situation in which the actual sex ratio in the population is 1:9 (there are nine times more females).

➜    Restore the code line as it was.

Hymenoptera (which include ants, wasps, bees) are known to have sometimes a sex ratio close to 3:1 in favour of females. This is explained by the imbalance of relatedness: In these species, female workers are related 0.75 to their sisters (one inherited mutation has 75% chance to be present in a sister), whereas they are related 0.25 with their brothers. The female workers are observed to bring the sex ratio from 1:1 among eggs to 3:1 (3 females for 1 male) by killing a certain amount of male larvae. This phenomenon provides one of the most striking evidence that evolution is governed by strict (and computable) laws.

Let’s compute the probability of transmission of a mutation from worker to niece or nephew. Let p be the proportion of females in the population, and b the worker’s bias in favour of sisters. The transmission w --> f --> f involves bias b times prob. 0.75 that the mutation be present in the sister, times prob. 1/(Np) that the sister be selected for reproduction (N = size of the local population), times prob. 0.5 that the child born is female, times prob. 0.5 that the mutation is passed on to the niece.

w --> f --> f:    b * 0.75 * 1/(Np) * 0.50 * 0.50

Similarly:

w --> f --> m:    b * 0.75 * 1/(Np) * 0.50 * 0.50
w --> m --> f:    (1-b) * 0.25 * 1/(N(1-p)) * 0.50 * 1
w --> m --> m:    (1-b) * 0.25 * 1/(N(1-p)) * 0.50 * 0

If we sum the four probabilities, take the first derivative in b and make it zero, then make p=b (equilibrium), we get b = p = 3/4, which means a 3:1 ratio in favour of females.

To represent the phenomenon (in a somewhat crude way) in our scenario, we suppose that the mother (not the worker) still controls the sex ratio, but that the daughter’s DNA is re-crossed with the mother’s genome a second time (see S_SexRatio.py). As a consequence, the mother-daughter relatedness is 0.75 (Note that this situation resembles the hymenoptera case, but only vaguely).

Run the simulation (button [Run]) after having set parameter Hymenoptera to 1. Observe the resulting sex ratio.

To explain it, we will compute the probability that a given mutation expressed in the female propagates to her grandchildren (distinguishing the four possibilities).
Let p be the proportion of females in the population, and b the mother’s bias in favour of daughters.
The transmission f --> f --> f involves:

• probability b that the first child be a daughter (= 2^nd f) ,
• times prob. 0.75 that the mutation be present in the daughter,
• times prob. 1/(Np) that the daughter be selected for reproduction (N = size of the group),
• times prob. b that the grandchild is female,
• times prob. 0.75 that the mutation is passed on to the granddaughter:

f --> f --> f:    b * 0.75 * 1/(Np) * b * 0.75

• You may stick closer to the hymenoptera case. The SexControl gene may be expressed in daughters (representing workers). You can modify the new_agent function to that the first child, representing the worker, controls the sex of the ‘real’ child to which it is closely related. Only the latter is introduced in the population.
• Study the case in which the sex ratio in the ant colony is controlled by the queen, as is the case when workers are imported slaves from other species.
• Study the case in which several males father the beehive (the queen stores their contribution in her spermatheca).
• Study the case in which there are several queens in a wasp colony.
• In mammals, study the case in which males must adopt high risk behaviour (with high mortality) to have a chance to breed. Does it have an effect on sex ratio?
• In mammals, suppose that males can physiologically take their relative success in the male competition into account to determine the sex ratio of their progeny. Suppose that this success depends on some general strength that is heritable. Show that it may affect the sex ratio of winners and losers.
  To avoid the strength gene to reach a maximum, one may suppose that there is a trade-off between strength and the ability to survive when food is scarce.
• The parthenogenetic bomb. Study a situation in which a mutation allows females to make copies of themselves, instead of incorporating the male’s genome through crossover. The child is female. This situation increases the number of females and eventually leads to a clone (only females, all identical). You may have to change the parent procedure. You may study the poor adapatability of the clone in the presence of fast evolving parasites.

    
Runaway selection has been imagined by Ron Fischer to explain extravagant features in animals (such as the peacock tail) as resulting from sexual selection. The scenario presented here is somewhat simpler than Fischer’s. However, it presupposes a direct advantage for females making the right choice.

We suppose that it is crucial for females to mate with males that are in good health. The reason for this might be to avoid being infected by a contagious male during contact (see: Hamilton, W. D. & Zuk, M. (1982). Heritable true fitness and bright birds: a role for parasites? Science, 218 (4570), 384-387).

• Males may show that they are healthy by displaying costly attributes that unhealthy individuals cannot afford developping.
• Females may be choosy about partners, by comparing more males.

If the risk for females is significant, we observe that

• Females increase their demand by comparing more males, even if their patience is costly (e.g. waste of time).
• Males evolve to display costly signals.

Open the file S_Runaway.py (in the Scenarii directory). Locate the start_game function. Observe that both sexes pay a cost.
Open Starter    from the Evolife directory and load the Runaway scenario. Run it and observe that males evolve to invest massively in costly signals. The phenomenon is slightly richer than that. The two genes 'FemaleDemand' and 'MaleInvestment' co-evolve: females compare more males and males compete to please them. The crucial point here is that females have no absolute reference. They just compare males with one another.

In the current implementation, females get a proportional penalty for mating with an unhealthy male. To get closer to the infection metaphor, we want to make penalty binary (the male is infected or he is not).

You should observe that the runaway mechanism still works, though for different values of LowQualityCost.

• You may play with parameters. For instance, you may try different values for ParasiteProbability, including 0 and 100%.
• Consider that parasites or infection may be transmitted to offspring rather than to the mother (e.g. if the male contributes to raising the young).