Agent-based models

We constructed and analyzed a series of agent-based models of mating markets underpinned by different mate preference integration algorithms. All models generated populations of 200 agents at the start of all model runs. Each agent possessed a set of 20 traits and between 20 and 80 preferences corresponding to these traits. Traits were drawn from random uniform distributions with initial values drawn between 1 and 7 in order to be comparable to Likert scales. Preferences were drawn from random uniform distributions with values between −10 and 10. This wider range for preferences relative to traits was chosen to be equally uninformative to all preference integration algorithms: restraining the starting values for preferences to 1 and 7 as for traits would provide an unfair advantage to the Euclidean model as its preferences would be relatively close to optimum by default. This would also unfairly disadvantage models that treat preferences as slopes as these models would not be capable of producing attraction to lower trait values at model start. The wider starting range for preferences helps guarantee all models have relatively equivalently poor starting conditions.

Agents were additionally assigned an energy value based on their traits; at the start of each model run, the model randomly selected a trait value as “optimal” for each trait dimension by drawing from a random uniform distribution for each trait dimension. Agents earned energy inversely proportional to their deviation from this optimal value on each trait; agents reproduced in proportion to their energy values, introducing a selection pressure in favor of trait values closer to optimum and preferences for these trait values. Finally, all agents were randomly assigned to be either male or female in equal proportion. After initialization, agents followed a life cycle in which they computed how attracted they were to one another, selected each other as mates based on these attractions, reproduced with their chosen partner, and then died. This life cycle repeated for 200 generations of simulated evolution. All models were run for 50 iterations per parameter setting, yielding 450 runs per model and 3,600 model runs in total.

Attraction

In the first phase of each life cycle, agents calculated how attracted they were to all opposite-sex agents using their traits, preferences, and preference integration algorithms. We simulated a total of six preference integration algorithms that combined traits and preferences into attraction values in different ways. Agents in the aspiration models had two preferences per trait; these preferences identified an ideal trait range for each dimension. To calculate attraction to a potential mate, aspiration agents determined how many of a potential mate’s traits fell within the agent’s ideal trait range. Cosine agents possessed one ideal preference per trait and calculated attraction as proportional to the cosine similarity between their own preference vector and each potential mate’s trait vector, where cosine similarity is the cosine of the angle formed by the agent’s preference vector, the potential mate’s trait vector, and the origin. Curvilinear agents had two preferences per trait, which acted as slopes in a sinusoidal function. These slopes manipulated the phase and frequency of a sine wave relating potential mate trait values to attraction values. Euclidean agents had one preference per trait and calculated attraction as the Euclidean distance between their own preference vector and each potential mate’s trait vector; shorter distances indicated greater attraction. Linear agents had two preferences per trait and calculated attraction as a linear combination of the potential mate’s trait values, with one preference acting as a slope and the other as an intercept for each trait. Finally, polynomial agents had four preferences per trait, three of which served as slopes and one of which served as an intercept in a cubic polynomial function calculating attraction from potential mate trait values.

Mate selection

The attraction phase in each model produced two matrices: a matrix that indicated how attractive each female agent found each male agent and a second matrix that indicated how attractive each male agent found each female agent. In six of the models, these two matrices were next multiplied elementwise to produce the mutual attraction matrix. Each cell in this matrix represented how mutually attracted all possible agent couples would be. The model next paired agents by identifying the most mutually attracted possible couple, pairing these agents, and removing them from the mutual attraction matrix. This process was iterated until all possible agent couples were formed.

We additionally ran two separate manipulations of the mate selection process. In the random models, agents calculated attraction as a Euclidean distance just as in the Euclidean model. However, rather than pairing based on these attraction values, agents were paired randomly. Finally, in the preference updating models, agents also calculated attraction as a Euclidean distance and also selected mates randomly with respect to these attraction values. However, after mate selection, these agents updated their preferences to be 90% closer to the traits of the mate they had already chosen.

Reproduction

Agents next produced offspring with their chosen mates. We employed roulette wheel selection to determine how many offspring each couple produced. To accomplish this, the model sampled with replacement from the population of agent couples; the size of this sample was equivalent to the initial population size. The probability that a given agent couple was sampled for each reproduction attempt was proportional to the couple’s pooled energy values. This probability was itself scaled by a selection strength parameter, which fixed the likelihood of sampling the highest energy couple relative to the lowest energy couple. We ran all models under three selection strength values: 0.10, 0.15, and 0.20, reflecting a 10%, 15%, and 20% reproductive advantage for the highest energy couple relative to the lowest energy couple respectively.

Agent couples produced one offspring each time they were sampled by this roulette wheel procedure. Offspring agents inherited each of their trait values randomly from either parent. We additionally added a small amount of random normal noise to trait values to simulate mutation. This mutation procedure is intended to simulate the effects of many, small impact mutations on trait values37. The amount of noise was controlled by a mutation rate parameter, which set the standard deviation of this random normal noise; we ran all models under three mutation rates: 0.06, 0.15, and 0.30, representing 1%, 2.5%, and 5% of the maximum trait range respectively. Levels of mutation rate were fully crossed with the selection strength parameter settings, yielding a total of nine parameter settings for all models. Offspring were randomly assigned to be either male or female.

Death

In each generation, all parent agents were erased after reproducing. Offspring agents then started the life cycle anew in the next generation, beginning with the attraction phase. All models were run for 200 generations of simulated evolution in total. The end result of each model was a population of n = 200 agents that represented the results of evolution under mate choice driven by varying mate preference integration algorithms.

Cross-cultural sample

Participants

The cross-cultural sample consisted of n = 14,487 participants (7,961 female) from 45 countries representing all inhabited continents around the world. Participants from each study site were recruited from two sources: half of all participants were supposed to be recruited from university populations and half from community samples. Not all study sites kept records of participant source; we have source records for 45.83% of participants representing 22 out of the 45 countries. From study sites that kept records of participant source, 47.14% of participants did come from community samples. All participant data was collected in person using pen-and-paper surveys because internet samples tend to be unrepresentative, particularly in developing countries38.

Participants were M = 28.79 years old on average and ranged from 18 to 91 years old. Most participants (63.75%) were in a committed romantic relationship; among these, most participants were dating (49.26%), but others were also engaged (12.59%) or married (38.14%). The global cross-cultural study protocol was approved by the Ethics Committee of the Institute of Psychology, University of Wroclaw; many study sites were able to rely on this protocol for ethics approval. Sites that were not submitted additional ethics approvals to local authorities where necessary. A list of the institutional review boards and ethics committees that approved this study is available in the supplementary information. All methods were carried out in accordance with relevant guidelines and regulations; informed consent was obtained from all participants.

Measures

All participants reported their mate preferences in an ideal long-term mate, described as a committed, romantic partner, using a 5-item mate preference instrument. This instrument contained five 7-point bipolar adjective scales on which participants rated their ideal partner’s standing on five separate traits: intelligence, kindness, health, physical attractiveness, and financial prospects. Each trait was rated between two extremes, for instance, from 1 representing “very unkind” to 7 representing “very kind.” Participants additionally used the same rating scales to describe their own standing on each of these five traits and to rate their actual long-term partner, if they had one. This mate preference instrument was translated into local languages and back-translated by researchers at each study site.

Data analysis

Data analysis proceeded in parallel stages for both the cross-cultural sample and the agent-based models.

Data processing

The first stage of analysis was processing the data in order to calculate mate preference fulfillment and Euclidean mate values. We first calculated mate preference fulfillment for both agents and human participants, where applicable, as the Euclidean distance between each individual’s preference vector and their actual chosen mate’s trait vector. These distances were transformed and scaled such that a value of 10 meant the preference and trait vectors were identical and a value of 0 meant the preference and trait vectors were as dissimilar as they could be. For agents whose preferences did not represent a trait value (aspiration, curvilinear, linear, and polynomial) their preference vector was calculated as either the center of the agent’s ideal trait range (for aspiration agents) or the trait value the agent found most attractive (for all other agents).

To calculate mate values, we first calculated the average preferences of all males and all females within country or within model run. We next calculated the overall Euclidean mate value of each agent or each participant as the Euclidean distance between each individual’s trait vector and the opposite sex’s average preference vector. We additionally calculated the mate value of each agent or participant’s mate as the distance between their mate’s trait vector and the average preference vector of the mate’s opposite sex. Finally, as a measure of choosiness, we calculated the mate value of each agent or participant’s ideal partner as the Euclidean distance between the individual’s own preference vector and the average preference vector of that individual’s sex. All mate value distances were scaled in the same manner as preference fulfillment such that a value of 10 indicated maximum possible mate value and a value of 0 indicated minimum possible mate value.

Model fitting

Next, data analysis proceeded in two steps. First, we calculated for all agent-based models and the cross-cultural sample the average degree of mate preference fulfillment and 3 correlations reflecting the degree to which high mate value individuals experienced higher power of choice on the mating market12. Average mate preference fulfillment was calculated within model run and within country. Power of choice on the mating market was quantified using either multilevel models predicting mate preference fulfillment, ideal mate value, and partner mate value from own mate value, with agents nested within model runs or participants nested within countries, or by calculating correlation coefficients between these variables within model runs.

To compare the similarity of the agent-based models to the cross-cultural sample, we used a model training and testing procedure. To accomplish this, we first trained multilevel models on each of the 72 model and parameter setting combinations. Within model runs, these models predicted agent preference fulfillment, ideal mate value, and partner mate value from the interaction of agent mate value and outcome variable type, with observations nested within agent or participant. This resulted in 50 regression models for each agent-based model (ABM) and 3,600 regression models overall. We then applied these models to predict the same values sight-unseen in the cross-cultural sample based on the participant’s actual mate value. We then quantified prediction accuracy with two metrics: (1) the root mean squared error (RMSE) between observed participant values and predicted values from the ABM-trained multilevel models and (2) the correlation between observed participant values and the predicted values from the ABM-trained multilevel models. This yielded two objective values that each reflected the degree to which each simulated mating market could account for human mate choice data across cultures. All data, model code, and analysis script is available on the Open Science Framework: https://osf.io/bz84c/?view_only=43711fed002e41e1876aecf1f3f0aa6e.