The Impact of Fitness Landscapes on the Emergence of Culture
Abstract:
Culture is an adaptive mechanism which allows organisms to find and occupy niches in their fitness landscape not immediately available through genetic evolution. Novel learned behaviors propagate through the population in space and time through diffusion. In this project the adoption and diffusion of novel behaviors is modeled under simple one dimensional fitness landscapes. Fitness landscapes favorable to the emergence of culture are identified and previously identified phenomena such as Shielding and the Baldwin Effect are investigated.
Introduction:
Culture is defined by anthropologists as “the customary ways of thinking and behaving of a particular population or society.” [Ember & Ember, 1990] This definition purposefully does not discuss whether culture is adaptive or how culture comes about. The notion of cultural evolution was explicitly rejected for some time due to the cultural and ethnic elitism it fostered. Over the past ten years however anthropologists and psychologists have become more willing to place culture back into a framework of adaptation and to look at Culture in the context of its fitness given a particular environment.
For the purposes of this project Culture is defined mechanistically to be the information shared between individuals through the process of emulation (I treat imitation and emulation to be synonyms here). Emulation is a sufficient mechanism to achieve “customary ways of thinking and behaving.”
Goals:
Question retained from First Crit:
Is Cultural Adaptation functionally any different than the process of natural selection and genetic recombination. If so will shared learning replace the genetic learning? I.e. will it be so successful that it halts genetic learning (shielding). Will there be a switch off at some point with the GA bootstrapping the cultural process?
New Question:
What kinds of fitness landscapes (environments) trigger cultural formation, which don’t?
Old Model:
The initial model presented at the first two crits attempted to model the individual agents in detail and to give them enough intelligence through large hidden layer back-prop neural networks to evolve emulation and culture in their lattice world. The agents did the opposite and seemed to actively repress emulation. In order to understand why this might be happening the fitness landscape the agents were adapting to needed to be very well understood. This was too difficult with the complex first model.
New Model:
Culture is modeled using an Artificial Life program with agents representing biological organisms in a zero-D space. These organisms consist of a genome and a phenotype.
The phenotype contains five real valued loci that can range from 0 to 1.0:
TraitX: This is the trait (or traits) that determine the probability of the agent surviving the current time step. At the beginning of each time step a number is drawn for each agent from a uniform distribution between 0 and 1.0. If the number is greater than the fitness of agent’s TraitX then it dies otherwise the agent lives and can perform an action. The fitness function for TraitX is defined by the experimenter. (See diagram)
Action Loci: Learn_prob, Emulate_prob, Procreate_prob, Control_prob (no-op) each determine the probability of a particular agent performing the associated action during the current time step.
The genotype also contains five real valued numbers which are used to initialize the phenotype values at birth. The genotype values are the average of the parents’ genotypes with some mutation. A separate mutation rate is used to mutate TraitX from that used to mutate the other loci. The mutation rate of TraitX is the basis for several experiments later on and so it needed to be changed independently. The initial value for TraitX in the genotype is set by the experimenter according to the fitness landscape while the other loci have initial random values.
The four possible actions are:
Learn(): The agent performs a single experiment that consists of picking a new TraitX from a uniform distribution less than learning_rate distance from the agent’s current phenotype. If the fitness of the randomly chosen TraitX is greater than the fitness of the agent’s phenotypic TraitX the agent adopts this new TraitX. It has modified its TraitX phenotype through learned behavior. If the experimental phenotype is not better than the one the agent already has the agent keeps the old phenotype and essentially wastes its turn.
Emulate(): The agent examines the TraitX phenotypic fitness of five other agents from the population. The fittest TraitX phenotype replaces the agent’s current TraitX phenotype. The agent has emulated the phenotype of an agent with a fitter TraitX unless it was the fittest in which case the time step was wasted.
Procreate(): The agent examines the TraitX phenotypic fitness of five other agents from the population. The fittest agent of the five is selected as a mate and one offspring is generated. It is possible for the agent to select itself in which case the turn is wasted but this should happen infrequently since the agent population is usually around a thousand individuals.
Control(): This is a no-op used to provide a baseline for examining the other loci. It measures the null-hypothesis that genetic drift alone without selective pressure could explain the probability values.
GUI:
The GUI displays the TraitX fitness function in red with the x axis being the TraitX phenotype and the y axis being the corresponding fitness.
Whenever an action is taken that alters the phenotype of an agent a line is drawn by the GUI from the old phenotype to the new one. A blue line indicated the change was due to novel learning a green line indicates that the phenotype changed because the agent emulated someone else.
Agents born this round are marked red and agents that initiated procreation are marked green.
Experiments:
Experiment 1) Does Culture Matter?
Setup: Observed the probability of a population starting at 250 individuals lasting 1000 time steps when presented with two different fitness landscapes, one flat (landscape 1) and one with well defined fitness peaks (landscape 2). The height of the landscape was increased from 0 to 1.0 over the course of the experiment, the whole landscape for landscape 1 and just the fitness peak on the right in landscape 2 (this is OK because it is genetically inaccessible anyway).
(Figure 1) (Figure 2)
Culture provides a benefit when there are fitness peaks nearby but provides no advantage on a flat landscape. Culture is able to utilize the nearby peak and raise the overall fitness of the population. This allows the population to withstand much lower genetic fitness than is possible in the flat landscape. Here the nearby peak is genetically inaccessible.
Experiment 2) What about genetically accessible peaks? Shielding
Setup: A population is presented with a landscape that has a single well defined and easily accessible peak. Observed how long it takes the genetic fitness (where new agents are born) of the population to reach the summit, also recorded the number of times out of twenty trials that the population died without reaching the summit. Ascension to peak observed from the GUI not statistically.
Emulation and Learning Turned Off (Just genetic natural selection)
Observations:
Population reaches the summit genetically 9 out of 20 times.
Average time taken 75 time steps.
Emulation Turned Off (Genetic natural selection and Learning only)
Observations:
Population reaches summit 1 out of 20 times (!), took 100 time steps
Emulation, Learning and Genetic Natural Selection all turned on.
Observations:
Reached the summit genetically 20 times out of 20 trials
Took an average of 2500 time steps to reach the summit
Emulation with learning clearly reduces the selection pressure being applied to the agents’ genomes. This slowed genetic adaptation considerably. In previous work [Ackley and Littman, 1992] observed Shielding of one genetic trait by another. This experiment seems to show shielding of genetics by learned and emulated behaviour. Notice that the many agents are emulating other agents already at the peak so natural selection gets to act on agents only while relatively young (before they emulate or learn to a higher fitness).
Experiment 3: Research is Risky, School is Safe, and Sex is Essential
Setup: Track agent preferences for Emulation, Procreation and Learning among populations with random initial TraitX genotypes faced with a complex fitness landscape. Ran populations ten times and tracked preferences (learn_prob, emulate_prob, procreate_prob, control_prob) over 3000 time steps.
Observations:
The mutation rate for the action probability loci is a uniform distribution from 0 to 0.05. Given that, learn_prob has gone to the lowest level possible for this model while emulation is still very important to the population, almost as important as procreation. This pattern has been confirmed with several other experiments on different landscapes. With Emulation you only need one agent to find a better phenotype and be emulated for the new idea to propagate exponentially through the population so that almost everyone benefits. But for the individual doing the learning the odds are relatively low that they will benefit themselves (depending on the landscape). Choosing the best of five established phenotypes (emulation) is a far safer bet than looking at “uncharted” phenotypes. Everyone wants an education but very few want to be scientists.
Experiment 4: The
Setup: given the following fitness landscapes and a TraitX start location of 0.3 and 0.5 (the middle peak) respectively how often does the population shift to the higher peak genetically as learning rate and mutation rate are varied together? The model was run for 1125 combinations of TraitX genetic mutation and learning rates in the range observed to be a transition from always seeing the Baldwin Effect and never seeing it. Each combination was run 10 times (spot checked with 100 runs per combination) and the fraction of populations to achieve an average fitness of 0.7 while maintaining a population of more than 500 where classified as having successfully moved from the middle peak to the highest peak genetically as well as culturally. This unfortunately ignores genetic shifts to the lower peak which would also be an instance of the Baldwin Effect.
Experiment 4a) Example of the
1)
2)
3)
4)
Without Learning and Emulation
Experiment 2b) Varying mutation and learning rates
Observations:
A sufficient learning breadth (rate) is needed for culture to reach the higher peak and shield the population (see experiment 2) the population for the Baldwin Effect to take place. This shielding has two important implications 1) The population as a whole is protected and random chance has an increased amount of time to move the population genetically, and 2) selection pressure is reduced so the population’s viable genetic pool is not restricted to the very tip of their peak. This increases the likelihood of agents exploring the region of their peak to the right and consequently the likelihood of the higher peak being discovered. Shielding gives the agents the freedom to explore further genetically and perhaps find the higher peak leading to the Baldwin Effect.
Experiment 5: Culture in the Face of Adversity
Setup: An agent population is presented with a landscape consisting of two adjacent fitness peaks of slightly different height. TraitX starts on the lower peak. Does introducing environmental stress (lowering the peak the agents occupy) trigger culture?
x < 0.5 : y = sin(4*(x+0.1))-0.1;
x >=0.5 : y = sin(4*(x-0.5+0.15))-0.125
peak differential = 0.025;
x < 0.5 : y = sin(4*(x+0.1))-0.1;
x >=0.5 : y = sin(4*(x-0.5+0.15))-0.2
peak differential = 0.1;
Observations: lowering the fitness peak occupied by a population of agents showing only a background rate of emulation and learning triggered the population into adopting a high rate of emulation typical of cultural agent populations. The investment in emulation and learning is not worth the benefit if the peak reached is only marginally better then the genetically accessible one.
Experiment 5b: Population Survival Odds as Culturally available peaks change height
Summery:
Learning in this model benefits the population as a whole through emulation but is counterproductive for the learner who is much better off copying others and procreating. Learning preference is reduced to the lowest levels possible but, fortunately, these low levels of innovation are sufficient to explorer and utilize the simple landscapes presented in this project. The most prevalent impact culture has on genetic evolution is shielding, which allows populations to survive that would otherwise die out and allows genetic mutation to explore the fitness landscape with more freedom (Baldwin Effect). Culture, or cultural shifts, can be triggered through environmental stress and appear to occur very rapidly.
Further Work:
Need to investigate the anomalous result in experiment 2 where Learning doomed all but one of 20 populations in a very easy fitness landscape. The spread of culture has been observed to be rapid but how rapid is it? Is it an exponential in the size of the neighborhood examined by emulate()? How does changing the size of this neighborhood change the results?