Modeling Mate Choice in Monogamous Mating Systems with …abcwest/pmwiki/pdf/simao.adaptbehav... · 2016-01-08 · Simão & Todd Mate Choice in Monogamous Systems with Courtship 3

1

Modeling Mate Choice in Monogamous Mating

Systems with Courtship

Jorge Simão1, Peter M. Todd2

1Center for Artificial Intelligence, Computer Science Department, College of Sciences and Technology, New University of Lisbon 2Center for Adaptive Behavior and Cognition, Max Planck Institute for Human Development

We present a conceptual framework for the study of mate choice in monogamous mating systemswith non-negligible courtship time. Within this framework, we develop a mate choice model for thecommon case where individuals have a changing social network of potential partners. The perform-

ance and robustness of different agent strategies is evaluated, emphasizing the important role thatcourtship plays in mate choice. Specifically, the courtship period can be used by individuals to swap tobetter partners when they become available. We found that using courtship as a mechanism for hold-

ing partners before full commitment to mating provides strategic advantages relative to sequentialsearch using aspiration levels. Moreover, simple heuristics that require little computation provide adegree of robustness to environmental (parameter) changes that is unattainable by strategies based

on more extensive information processing. Our model produces realistic patterns of assortative mat-ing (high within-couple mate value correlations) and rates of mating that match empirical data onhuman sexual/romantic relationships much more closely than previous accounts from biology and the

social sciences.

Keywords mate choice · mate search · courtship · human mating · heuristics · agent-based model-

ing · evolutionary functional analysis

1 Introduction

Perhaps the most important set of adaptations thathumans and other animals are endowed with are thoserelated to mating and reproduction (Bateson, 1983;Symons, 1979; Barkow, Cosmides, & Tooby, 1992;Buss, 1994). Although individuals can promote theirgenes indirectly by helping kin (as in social insects), amore direct strategy is to mate with a member of theopposite sex and produce offspring (Alcock, 1997).Therefore, it is expected that evolution would provideindividuals in sexual species with specially designed

psychological mechanisms that allow them to performthese reproductive tasks efficiently. Discerning thestructure of such mechanisms is crucial if we hope tounderstand the behavior and minds of humans andother animals.

Within the set of such mechanisms associatedwith mating and reproduction, the ones related to matechoice are central. Because individuals of the oppositesex tend to vary in their quality as suitable mates (e.g.,due to genetic makeup, social status, or parentalskills), and because mate quality strongly influencesoffspring quality, mate choice decisions are crucial to

Copyright © 2002 International Society for Adaptive Behavior(2002), Vol 10(X): XX–XX.

Correspondence to: J. Simão, Departamento de Informática, FCT/UNL,Quinta da Torre, 2829-516 Caparica, Portugal.E-mail: [email protected]

2 Adaptive Behavior 10(X)

the fitness of offspring (Bateson, 1983). This is espe-cially true when these decisions are performed inhighly competitive settings, as is the case in monoga-mous mating systems where partner sharing is notbeneficial and therefore not easily tolerated by (atleast) one of the sexes. In such cases, both sexes tendto be highly choosy, leading to a process of mutualmate choice where each individual strives to get thebest possible mate for itself.

It is thus not surprising that many computationaland mathematical models have been proposed in thebiological and social science literature that address theissue of mate choice behavior (Kalick & Hamilton,1986; Todd & Miller, 1999; Parker, 1983; McNamara& Collins, 1990; Johnstone, 1997; Bergstrom & Real,2000). These models allow important conclusions tobe drawn about mating behavior of animals andhumans, but very often they rely on assumptions thatfail to hold in realistic mating environments, particu-larly for humans. Typical assumptions of models ofmutual mate choice are that individuals search andencounter mates sequentially (usually without theability to go back to, or “recall,” earlier mates), andthat individuals make their mating choices as a single,irreversible decision whether to mate with an individ-ual or not (Kalick & Hamilton, 1986; Todd & Miller,1999; Parker, 1983; McNamara & Collins, 1990;Johnstone, 1997). This conflicts with the fact thathumans use extensive courtship periods to establishlong-term sexual/romantic relationships, and that thisallows individuals to engage in relationships in tenta-tive ways—possibly switching to better alternatives ifthey become available in the future (Buss, 1994;McKnight & Phillips, 1988; Weisfeld, 1999). As weshow in this article, the existence of a non-negligiblecourtship time and access to potential alternative part-ners has, indeed, significant consequences for the stra-tegic behavior of individuals when choosing mates.

Taking the opposite extreme from sequentialchoice, some earlier models make the unrealisticassumption that the complete set of potential mates inknown instantaneously and is common to all membersof the same sex (Bergstrom & Real, 2000). More gen-erally, these models often assume that individualsseeking mates have complete and accurate informa-tion about the distribution of qualities of potentialpartners, about their own quality, and sometimes evenabout the preferences of other individuals (Parker,1983; McNamara & Collins, 1990; Johnstone, 1997;

Bergstrom & Real, 2000). Given that such informationis typically not available in the real world, it is not sur-prising that most of these models are of limited empir-ical validity.

In this article, we present a conceptual frameworkfor modeling mate choice in the context of long-termrelationships with extended courtship periods, withparticular emphasis on the human case. (The resultscan also be generalized to other animals where similarassumptions hold.) Based on an evolutionary func-tional analysis, we develop an agent-based model thatcaptures key aspects of this adaptive problem. Ourmodel differs from previous computational and math-ematical models of mutual mate choice in that it relieson more realistic assumptions about the specifics ofthe human social environment and the nature ofhuman psychological constraints. In particular, weassume that individuals have dynamic, growing socialnetworks of potential partners, instead of meetingthese partners sequentially or having complete infor-mation about all of them instantaneously. Further-more, our model postulates choice mechanisms(decision rules or heuristics and strategies that com-bine them) that are more psychologically plausiblethan those in previous models. We argue that individu-als can make simple, efficient, and robust mating deci-sions by using heuristics that exploit the specifics ofthe adaptive problem domain rather than attempting toperform complex optimizations, thus constituting anexample of ecological rationality (Todd, Krauss, &Fiddick, 2000). In addition to arguing for this newconceptual framework for understanding mating deci-sions, we demonstrate the empirical power of ourmodel by showing that its predictions about overallrelationship patterns observable at the population levelfit data from the social sciences much better than com-peting models.

This article is organized as follows. In Section 2,we review work in the area of computational andmathematical modeling of mutual mate choice behav-ior in humans and animals. We focus only on modelsof two-sided matching (rather than one-sided search)because these are more relevant to the study of humanbehavior. In Section 3, we establish a conceptualframework for the study and computational modelingof human mate choice. Capitalizing on this frame-work, in Section 4 we present a model of (human)mate choice based on non-negligible courtship peri-ods. Section 5 describes the different decision rules

Simão & Todd Mate Choice in Monogamous Systems with Courtship 3

used by agents, and Section 6 compares their perform-ance. Section 7 presents the model predictions andmakes an analysis of these predictions in the face ofknown empirical evidence. In Section 8, we compareour model results with those of previous models anddiscuss future research directions. Finally, Section 9summarizes our conclusions.

2 Previous Work on Models of Mate Choice

Seminal studies of human mate choice using computersimulations were conducted by Kalick and Hamiltonin the 1980s (Kalick & Hamilton, 1986). Theystarted with the fact that observations of many humanpopulations show that individuals in couples arehighly correlated in attractiveness (correlationsbetween 0.4 and 0.6 in different studies). This find-ing led social scientists in the 1960s to propose the“matching hypothesis” that people actively seek amate matched to them in attractiveness. But thisseemed to contradict experimental data indicating thatpeople in general tend to prefer more physically attrac-tive individuals as prospective partners (i.e., not takingtheir own attractiveness into account). To explain thisapparent contradiction, Kalick and Hamilton set upindividual-based simulations to study the relationshipbetween individual-level preferences and population-level patterns. In their simulations, randomly selectedindividuals with particular attractiveness values arepaired up sequentially in “dates.” Both individuals ina date then use a probabilistic acceptance criterion todecide whether or not they accept each other, and, ifboth agree, they mate and leave the population. A dis-counting factor was introduced to make individualsless choosy with time.

Kalick and Hamilton’s results demonstrated thatuniversal preferences for high attractiveness, asopposed to preferences for similarity in attractiveness(matching), can produce realistic degrees of intracou-ple correlation of attractiveness (.55). This is becausehigher-attractiveness individuals tend to pair (andleave the mating pool) earlier than lower-quality indi-viduals, leaving the lower-quality individuals with nooption other than mating among themselves (Burley,1983). One critique of Kalick and Hamilton’s supportfor preferences for high attractiveness was that anunrealistically high number of dates (evaluations of

members of the opposite sex) was required in themodel for a realistic intracouple attractiveness correla-tion to be obtained and a significant percentage of thepopulation to mate (e.g., it took 40 “dates” for the cor-relation to reach .43 and 86% of the individuals tomate, Aron, 1988).

More recently, Todd and Miller used a similartype of simulation to explore the efficacy of differentindividual rules for searching through a sequence ofencountered potential mates (Todd & Miller, 1999).They were particularly interested in whether individu-als could make reasonably good (satisficing) matechoices without having to check many potential part-ners. In their model, an “adolescence” (learning)period is used by individuals to adjust an aspirationlevel based on the feedback provided by the matingoffers and rejections of potential mates they encoun-ter. After the adolescence period, individuals makemating offers to everyone they meet who exceeds theiraspiration level, and whenever both individuals in apair make mutual offers to each other, they mate andare removed from the population. Todd and Miller’sresults showed that simple learning rules can adjustindividual aspiration levels quickly (e.g., after an ado-lescence comprising 12 dates or partner assessments)to yield mated pairs of highly matched mate value.However, these learning rules typically left an unreal-istically large proportion of the population unmated(e.g., over 50%).

The animal behavior literature is rich in studies ofmate choice, with the book Mate Choice (Bateson,1983) setting the stage for the work done later in thearea. In particular, the chapter by Parker (Parker,1983) made a provisional formal analysis of (optimal)mating decisions when an infinite-horizon rate-maxi-mization of matings is expected, with individualsalternating between searching and “processing” time.His work was further refined by McNamara and Col-lins with a full game-theoretical analysis of the prob-lem (McNamara & Collins, 1990). They described asingle stable strategy (a Nash equilibrium) where eachsex is partitioned into a finite (or countable) sequenceof categories with decreasing-quality intervals suchthat members of each category end up mated withmembers of the corresponding category in the oppo-site sex. In some cases, low-quality members of one ofthe sexes could end up never mating.

The problem of learning the distribution of quali-ties of available mates during sequential search was


tackled by Mazalov and colleagues (Mazalov, Perrin,& Dombrovsky, 1996). Their model of single-sex dis-crimination showed how individuals could learn themean and variance of the mate quality distribution byincremental updating with each new potential mateseen, and how this information could be used at thesame time to set a varying threshold for mate accept-ance. They found that such learning could be advanta-geous compared to using a fixed strategy if there isenough variation in the distributions that can beencountered, and if the learning time is long enough.We also assume that such conditions hold in the mat-ing situations we consider, and hence we includelearning in our strategies; however, we avoid the full-optimization approach and the assumptions of fixedsearch horizons, fixed population distribution, and nosearch costs that Mazalov et al. adopted.

Considering more realistic constraints than themodels just described, Johnstone presented a model ofmutual choice where individuals have a limited timeto mate (i.e., the duration of a breeding season, John-stone, 1997). In his model, individuals encounter eachother in random pairs and must decide whether or notto mate with this one partner for the duration of thebreeding season. There is also a cost associated withdelaying the mating decision, and the distribution ofavailable mates changes over time. Using a numericmethod (iterative best response), Johnstone computedoptimal aspiration levels as a function of both an indi-vidual's quality and the time left in the breeding sea-son. His results showed that as the breeding seasonprogresses, high-quality individuals tend to becomeless choosy, whereas lower-quality individuals ini-tially tend to increase their level of choosiness, butafter a certain period also become less choosy withtime. This initial increase in choosiness of lower-quality individuals arises as a way of exploiting thedecrease in choosiness of high-quality individuals.

The above models, while representing theoreticaladvances, are limited by their reliance on unrealisticassumptions such as full information or constantsearch costs that are unlikely in environments wherethe rate of encounters is not deterministic. Similarkinds of assumptions are also found in other matechoice models presented in the animal behavior litera-ture, when either one or both sexes discriminatebetween partners (Real, 1990; Dombrovsky & Perrin,1994; Johnstone, Reynolds, & Deutsch, 1996). Thisoften has the effect of removing most of the relevant

problem structure and therefore hampering the empiri-cal validity of the models (Pepper & Smuts, 2000;Hammerstein & Riechert, 1988; Hammerstein, 1999;Simão & Todd, 2001). As Todd and Miller’s workargues, these kinds of assumptions are neither psycho-logically or ecologically plausible nor necessary forbuilding useful models (Todd & Miller, 1999; Todd,1996). More generally, it is likely that animals, includ-ing humans, use simple decision mechanisms thatexploit the rich information structure present in theirtask environments, rather than adhering to the norma-tive, optimizing approach typically used in behavioralresearch (Reed, 1996; Gigerenzer, Todd, & ABCResearch Group, 1999).

Similar criticisms can be aimed at models of two-sided matching presented in the economics literature.In a recent article, Bergstrom and Real review some ofthis work and suggest how it can provide insights forthe study of animal behavior (Bergstrom & Real,2000). Yet, they focus only on models where the set ofall potential partners is defined and known beforehand. This has the effect of making researchers con-centrate mainly on issues of global pairing stability.Because real-world scenarios are more likely toinvolve dynamic social networks, global stability isonly temporarily (or never) obtained (Epstein &Axtell, 1996). Therefore, emphasizing full knowledgeand stability only diverts attention from other issues ofgreater empirical relevance.

3 A Framework for Modeling Human Mate Choice

In this section, we summarize some of the key aspectsthat should be considered when modeling human matechoice from an adaptive perspective. This is used asthe rationale for design decisions in the model pre-sented in the next section. (As mentioned earlier, theseconsiderations also apply to other species, particularlythose that have a tendency to mate in monogamouspairs and that aggregate in groups or clusters, such assome species of birds.)

3.1 The Nature of Preferences

A central question to be asked when studying humanmating is the nature of interpersonal attraction. Froman evolutionary perspective, it is expected that humans


(like other animals) have traits that influence theirability to survive, reproduce, and successfully raisetheir offspring. They will also present some degree ofvariation in those features. Thus, it is reasonable toassume that evolution would endow individuals withthe capability to discriminate among potential part-ners, preferring the ones with better traits. We canconceptualize preferences as being based on somecombination of the different relevant features into anoverall mate value or mate quality, as suggested byDonald Symons (Symons, 1979). Thus, as a firstapproximation, we can build useful models by relyingonly on a one-dimensional quality feature (seeSection 8 for discussion of multi-dimensional quali-ties).

3.2 Courtship Processes

Much evidence exists for a universal tendency inhumans to establish long-term sexual/romantic rela-tionships. Although there is also evidence thathumans like sexual variety and when possible willengage in short-term sexual relationships (Buss &Schmitt, 1993; Buss, 1994), several researchers arguethat this is only a complementary strategy and not analternative to the first pattern (Miller & Fishkin, 1997;Zeifman & Hazan, 1997). Once long-term relation-ships are established, both men and women substan-tially invest in the offspring that result from them(Symons, 1979). However, following the general pat-tern among mammals, human females have a muchhigher minimal parental investment than do males(Trivers, 1972). Thus, women are under selectivepressure to be particularly careful to avoid choosing asmates men who would desert them after mating(Dawkins, 1976/1990). One way to be careful is toimpose a costly courtship process on men, duringwhich women can evaluate a man’s commitment andwillingness to invest in the relationship (and off-spring). During the courtship process, men areexpected to provide women with resources and, evenmore importantly, spend “quality” time with them(Buss, 1994; McKnight & Phillips, 1988). Time is anespecially good predictor of commitment, becausealthough a resourceful man can give gifts to severalwomen, he can only be physically in one place at atime.

The issue of tactical assessment of partner will-ingness to commit to a relationship has been widely

studied in game-theoretical models presented in theliterature within the category battle of the sexes—where fast or coy females (i.e., quick or slow to mate)and helpful or nonhelpful males compete against eachother (Dawkins, 1976/1990; Schuster & Sigmund,1981; Mylius, 1999; Wachtmeister & Enquist, 1999).Of particular importance to mate choice research, isthe result that female coyness can evolve and invadea population, provided that two condition are met:first, a combination of helpful and nonhelpful malesmust be present in the population; and second,females must obtain increasing information aboutthe likelihood that a male will desert her after matingas courtship progresses—so that she is trading breed-ing season or reproductive lifetime for information(Wachtmeister & Enquist, 1999; Wachtmeister, 2000).Both of these conditions are typically valid forhumans (Weisfeld, 1999; Buss, 1994). Therefore, inthis article we make the assumption that individualsdelay mating until a courtship period is completed(See Simão & Todd, 2002, for a detailed discussionof this issue.)

An important side effect of the courtship period inmating processes is that it can be used strategically asan opportunity to switch to a better partner if onebecomes available. This is true not only for women,but also for men, because they are also choosy inselecting partners for long-term relationships. Thedecision to switch can be influenced by several fac-tors, including time and investment already made inthe current relationship, how much better the alterna-tive partner is than the current one, and how likely it isthat the alternative partner will not switch later to abetter partner. From all of these considerations, it fol-lows that human mate choice is better modeled as aprocess that takes time to complete, rather than as asingle atomic event. Contrary to all previously pro-posed models of mate choice that we are aware of, themodel that we present in Section 4 is the only one thatincorporates this aspect of courtship within a back-ground of a realistic social ecology.

3.3 Time Pressure to Mate

Everything else being equal, the earlier individualsmate, the better off they will be from an evolutionarypoint of view. This is because an individual’s (repro-ductive) lifetime is limited, so that the earlier theymate, the more offspring they can potentially produce.


Moreover, in an uncertain and risky environment, thepossibility of premature death is always present.Although these arguments may hold less in modernsocieties, human mate search strategies were designedby evolution with these factors firmly in place(Barkow et al., 1992). All sexual animals, not justhumans, have limited time to find a mate and repro-duce, but many arrange their reproduction periods in anoncontinuous way—usually in the form of breedingseasons, when the conditions for mating and repro-duction are most suitable (Johnstone, 1997; Krebs &Davies, 1993). The model of human mate choice thatwe present in Section 4 can be adapted to animalswith a breeding season by equating that time periodwith the limited reproductive lifetime in humans.1

3.4 Interaction Possibilities

Despite the possibility of switching partners during acourtship process (as discussed in Section 3.2), thereare several reasons why an individual might considerdelaying entering into a relationship. When engagedin an ongoing relationship, the possibilities of meetingand interacting with individuals of the opposite sexmight become significantly reduced (e.g., due to mateguarding, and the requirement to invest “quality” timeand other resources in the current relationship). More-over, changing partners might have inherent costs(e.g., retaliation by the current partner). This meansthat individuals should be sensitive to the quality ofthose that they accept as tentative mates, even whenthey can easily switch to another mate later. Thischoosiness can be accomplished either by setting anaspiration level for the minimal quality acceptable fortentative mates (the typical assumption made by themodels discussed in Section 2), or by starting relation-ships with a low level of commitment and increasing itprogressively, or a combination of both. In Section 4we will compare the performance of all three kinds ofstrategies.

3.5 Estimating One’s Own Quality

In addition to needing to evaluate the mate quality ofothers, it may also be useful for individuals to performa (rough) estimation of their own mate value. Thisinformation can be used in deciding whether or not toinitiate a courtship process (e.g., to aim at others witha similar mate value), and how much to invest in that

courtship. This estimation can be based on at least twosources of information: the outcomes of past interac-tions with members of the same sex, and the outcomesof interactions with members of the opposite sex. Thelatter may provide more accurate information becauseit represents a direct window on the preferences of theopposite sex (Todd & Miller, 1999). In species likehumans, where full maturity and maximum reproduc-tive potential is reached after considerable time,namely, at the middle or end of adolescence in thecase of females (Low, 1997), the opportunity is cre-ated for individuals to assess their mate quality (asperceived by others). In humans this takes the form of“flirting” games where individuals probe others forinterest via short-term, low intimacy, contacts withoutengaging in a formal or socially recognized relation-ship (Montemayor, Adams, & Gullotta, 1994; Weis-feld, 1999). Barnacle geese, Branta leucopsis, havealso been reported to engage in trial partnershipswhile they are young, although the adaptive reasonsmight not be the same as in humans (Jeugd & Blaak-meer, 2001). This trial testing can be done with littlecost in terms of lost reproductive lifetime, exactlybecause maturity has not yet been reached during thisperiod. In the model presented in the next section, weincorporate this aspect of human mating by introduc-ing discrete time frames corresponding to juvenile andflirting periods where individuals assess their matequality before engaging in a costly courtship process.

4 A Model of Mate Choice with Courtship

To take into account all of the important aspects of theadaptive problem outlined above, we have developed anew model of human mate choice. By incorporating abroader range of factors than previous models, we laythe foundations for a better understanding of sexualpartnership formation in humans. We have also beenable to account for a wider spread of empirical results,as we show in the next section. Our model is intendedto capture scenarios where individuals have only par-tial knowledge of mating opportunities and are notaware of competitors. This will be the typical case inmedium to large communities where the network ofacquaintances is sparse.

We assume a population of constant size 2 × Pwith a fixed sex ratio of 50% (so P is the number of


males or females). Individuals of both sexes have aone-dimensional quality parameter qi, randomly gen-erated from a normal distribution with mean µ andstandard deviation σ, truncated such that 0 < Qmin ≤ qi ≤Qmax. Individuals are always in one of two states: sin-gle, when they do not have a partner, and courting,when they are engaged in a courtship process. Time ismodeled as a sequence of discrete steps. Pairs ofmales and females meet at a certain stochastic rate: Ineach time step each individual has a probability Y ofmeeting a new individual of the opposite sex.2 Eachindividual maintains a list of the potential matesalready met—the alternatives list. Single individualsare encountered before those already courting—onlywhen no individual in a single state is available willalready-courting ones be met and inserted in others’alternatives lists. This is intended to model in a simpleway the fact that in the real world (everything elsebeing equal), attempts to interact with single individu-als will be more frequent than attempts to interact withindividuals already courting. This is so because singleindividuals are more likely to be actively searching forpartners, and because courting individuals are riskierbets given that they might be potentially too commit-ted to break their current relationship.3

Within the alternatives list, one member can havethe “special status” of being the individual’s currentdate. This happens when both individuals previouslyagreed to court and have not changed partners in themean time (see below). It is also possible for an indi-vidual not to be courting anybody (e.g., in the begin-ning of its “life,” or when it gets “dumped”). Thelength of time that two individuals are courting isregarded as the courtship time ct. If a pair of individu-als remain courting for a period of K (≥ 0) time steps(i.e., when ct > K), they are deemed to mate and areremoved from the population and replaced with twonew individuals of random quality (one of each sex).

The alternatives list has a maximum size of N.This corresponds to the maximum number of oppo-site-sex individuals an agent can maintain in its socialnetwork to make courting proposals. If the social net-work becomes saturated, that is, if the alternatives listis filled, new meetings happen at the expense of for-getting one randomly selected individual already inthe list (other than the current date). Once again, sin-gle individuals take precedence over courting onesand, therefore, will be removed only if there is nocourting individual in the list.

Every individual has a maximum reproductivelifetime of L (> K) time steps. If individuals are unableto mate during this period they are removed from thepopulation (they “die”). This not only creates a pres-sure for individuals to mate, but also solves the techni-cal problem of keeping individuals with very lowquality from clogging the population due to inabilityto mate. To replace the dead individual, a new one iscreated with the same sex.

In each time step, every individual has a certainprobability of interacting with every member of itsalternatives list. This probability is computed by con-sidering a measure that we designate as the individualinteraction capability (ci), which correlates negativelywith the degree of involvement in the current court-ship process (and therefore ct). This is intended tomodel increasing levels of intimacy and exclusivity asa courtship progresses (as discussed in Section 3.2).Specifically, we define , where I is aconstant that defines the shape of the “intimacycurve.” If an individual is single, its interaction capa-bility is 1 (maximum value). The interaction probabil-ity between two individuals in a given time step isthen computed as the minimum of the interactioncapabilities of the two individuals. In particular, thismeans that if both individuals are single they arealways able to interact. We call the set of all membersof the alternatives list that an individual is probabilisti-cally determined (by random roll of the die) to interactwith in a particular time step the interaction list.

After the interaction lists are computed for allindividuals, each one decides what action to performbased on his or her state. If an individual is single, he/she has to decide whether to try to start a relationship(with some member of the interaction list), or postponethat decision to see if a better alternative becomesavailable. If an individual is courting, he/she has todecide whether to continue to court the same partner ortry to court another individual. To make these choices,binary decision functions are used. These functionsoutput 1 if and only if the respective action is to betaken—that is, try to start a relationship or try to switchpartners. They take as input variables several pieces ofinformation such as the qualities of the individualsinvolved, their ages, and the current courtship time ct

(only in partner switching decisions). Specific decisionfunctions are described in the next section.

Although an individual can make requests tocourt several others in each time step, he/she can only

ci 1 ct K⁄( )I–=


court one individual at a particular point in time.Moreover, if an individual decides to switch to anotherpartner, the ct of the current pair is reset to 0, meaningthat if this pair ever ends up courting again in thefuture, they will have to restart the courtship processfrom scratch.

If individual i requests to court individual j andindividual j simultaneously requests to court individ-ual i, they will start courting (i.e., the decision must bemutual). If an individual is accepted by several othersas a date in a particular time step, then he/she willcourt the one with the highest quality. Any abandoned(“dumped”) individual will be left with no partner(unless he/she also successfully tried to court some-body else). If no individual that i requests to courtaccepts him/her, and if the partner of i did not startcourting someone else, then the pair remains courtingand their courtship time ct is incremented by 1. Daterequests of individuals are processed sequentially so

that if an individual was about to court an alternativeand that alternative starts to court someone else, thefirst individual considers the next best alternative.

In Figure 1, we present more formally the match-ing (proposal making) algorithm used in each timestep in pseudocode. For each agent we define a pro-posals list, which is the subset of individuals of theinteraction list he/she decides to propose to (accordingto the decision function in use). This proposal list issorted by decreasing quality of its members to allow asimple instantiation of preferences for higher qualityindividuals. Once all proposals lists are created (notshown in Figure 1), the algorithm starts by markingthat all agents (of both sexes) will first propose to thebest alternative in the proposals list (i.e., the highest-quality individual). Next, for each agent i the algo-rithm finds the best individual j in i’s proposal list thatis proposing to him/her. If j does not correspond to i’scurrent proposal, i now proposes to j (thus reducing

Figure 1 Pseudocode for matching / proposal making algorithm.


his/her ambition level). Since j might also change pro-posals when this procedure is applied to him/her, thealgorithm is repeated until no agent changes propos-als. In particular, since a proposal first made by imight have been rejected (not matched) by some jonly because j was aspiring too high, this allows agentsto go back to better alternatives and retry proposals.This looping is also terminated if necessary after amaximum (large) number of iterations, to avoid possi-ble endless loops when there is no global ordering ofpreferences. Because in our model we are assumingthat preferences are universal and perceptions areerror-free, this is not strictly necessary here. In thiscase, the algorithm has the property that, when termi-nated, each agent will be paired with the highest qual-ity agent that has reciprocated the courting proposal.

To accommodate an adolescence or flirtingperiod in which individuals try to gather informationabout and assess their quality (as discussed inSection 3.5), all individuals go through an initialphase of A time steps when they are introduced intothe population. In this phase, they can make proposalsand accept them or reject them, as described above,but they will not start a courtship process—in otherwords, they still remain single. The outcomes of theseinteractions are used solely for the purpose of allow-ing individuals to estimate their own quality. In thenext section, we will describe a simple rule to performthat estimation in an effective way. Individuals in theadolescent flirting phase will preferentially meet otherindividuals in the same phase because they are theonly ones receptive to courting proposals that do notinvolve exclusivity and increased levels of intimacy(the reverse applies to individuals who have alreadycompleted the flirting phase).

We also want to explore strategic scenarios wherethe adolescent flirting period of individuals does notcompletely coincide with the initial lifestage of lowcurrent reproductive value (see Section 3.5). To allowsuch possibilities in our model, we define a juvenileperiod of J time steps at the beginning of an individ-ual’s lifetime where his/her current reproductive valueis considered negligible. Figure 2 depicts graphicallythe possible life-histories of agents as structured bythe model, and the possible relationships betweentime periods. In the simplest case, A is equal to J (toptimeline), which means that the only kind of behaviorperformed in the juvenile period is flirting, with realcourtship (pair-formation) attempts starting immedi-

ately after. When A is smaller than J (middle time-line), individuals are allowed to start courting beforethe juvenile period ends to save time and try to reapthe advantages of mating earlier (i.e., sooner after thejuvenile period ends). The only constraint to be main-tained is that mating does not occur until the juvenileperiod is completed. This is implemented by simplyenforcing the inequality . Finally, when A isgreater than J (bottom timeline), individuals extendflirting behavior beyond the juvenile period to try toassess more accurately their own quality. In Section 6.2,we will explore the strategic implications of usingthese alternative life-histories, to see whether less ormore information-gathering is useful when balancedagainst more or less time left to reproduce oncemated. As follows from the above, individuals that areunable to mate will die (and be removed from the pop-ulation) when they reach age .

5 Possible Strategies for Choosing and Switching Partners

To evaluate the success of decision rules and strategies,we assign mated individuals a fitness value F(qd, t) =qd × [(J + L) – t]/L, where qd is the quality of the indi-vidual’s partner (date) and t is the individual's age atmating time. Thus we instantiate a payoff for highquality (rather than quality-matching), along with timepressure to mate early (in addition to the limited life-time). The juvenile period constant J is added to thereproductive lifetime constant L, because we assumethat postponing mating during J is costless. A morerealistic version of the fitness function should alsoincorporate a dependency on the age of the partner, in

Figure 2 Possible agent life-histories: (top) juvenileperiod used only for flirting behavior (A = J); (middle)juvenile period used both for flirting and courting (A < J ≤A + K); (bottom) flirting behavior extends beyond thejuvenile period (A > J).

A K J≥+

J L+


such a way that the oldest individual of the couple dic-tates the time available for the production of offspring(Kenrick & Keefe, 1992). To simplify matters, andbecause we will not address here the issue of age dif-ference within couples, we deliberately ignore this.This has the important advantage of keeping prefer-ences unidimensional (as discussed in Section 3.1).

Each mate choice strategy consists of two deci-sion rules, one used when the agent is in the singlestate and the other in the courting or dating state. As anotational convention, all decision rules defined belowfor the single state will be prefixed by S, and for thecourting (dating) state by D. Strategies will be pre-fixed by ��. Thus, a strategy ��a is fully specified by apair (Sb, Dc), where b and c are identifiers (names) forthe two specific decision rules in use, and a is theidentifier for the strategy as a whole.

In the following sections, we introduce severaldecision rules that are combined in different ways tocreate strategies. We start by introducing a naive deci-sion rule for the single state Snaive and a partner switch-ing dating rule Dswap, which are combined to create astrategy named ��swap. The key feature of ��swap is that itdoes not require agents to estimate their own qualityto make mating decisions. Next, we present a heuristicby which individuals can estimate their own quality.This heuristic is combined with two different decisionrules, Srational and Sfrugal, that dynamically set aspirationlevels specifying the minimal quality accepted in apartner. Sfrugal differs in character from Srational, due toits greater simplicity and indirect estimation of envi-ronmental parameters. A dummy decision rule thatnever swaps partners, Dnull, is then combined withthese two decision rules to create two strategies—��ra-

tional and ��frugal, based purely on aspiration levels.Finally, a mixed strategy ��mix, which both uses aspira-tion levels and performs partner switching, is intro-duced. After the presentation of the strategies, we willperform a thorough evaluation of their relative per-formance.

5.1 Switching Partners

A naive decision rule to initiate relationships whensingle can be defined as follows:

(1)

In the above, ta is age of the prospective alternativedate. The decision rule specifies that a single individ-ual will propose to any agent encountered as long asthat agent is not too old to complete courtship.

Next, given the previously defined fitness func-tion F, we can establish the following decision rule forindividuals to (try to) switch partners whenever theyare already involved in a courtship process:

(2)

In the above equation, qa is quality of the alternativepartner considered, qd is the quality of the currentdate, ct the current courtship time, and t, td, ta the agesof the focal individual, its date, and the alternative,respectively. The individual conditions are evaluatedsequentially from top to bottom, and only when a con-dition does not hold will the next one be evaluated.The first and second conditions of the decision ruledeclare that if there is not enough time left to carry outa full courtship period (within one's own lifetime orthat of the alternative), then the switch should not beattempted. The third condition declares that if theexpected fitness of mating with the alternative (calcu-lated using the total required courtship time K) isgreater than the expected fitness of mating with thecurrent date (calculated using the remaining courtshiptime K – ct), then switching should be attempted.Finally, if none of the above conditions hold the cur-rent courtship process should continue undisturbed.

The more complete form of the third conditionabove would take into account the risk of the currentdate or the alternative abandoning the individual, buthere we assume all individuals are insensitive to thisrisk. Specifically, fitness outcomes could be multi-plied by the probability that a courtship process wouldbe successfully completed and could also take intoaccount the expected residual fitness (i.e., the fitness ifthe courtship is aborted). Making the swap decisionwithout trying to compute all these terms goes in linewith a view of agents with bounded rationality that donot bother to attempt to predict many aspects of anuncertain world and instead exploit the specifics of the

Snaive ta( ) 0 if ta K J L+>+

1 otherwise

=

Dswap qa qd ct t ta td, , , , ,( )

=

0 if t K J L+>+0 if ta K J L+>+

1 if F qa t K+,( ) F qd t K ct–+,( )>0 otherwise


problem domain (Todd et al., 2000; Pfeifer & Scheier,1999; Gigerenzer & Selten, 2001). In this case, we arereducing a game-theoretic problem to an individual-decision problem. This reduction might not be tooproblematic because an initial courting acceptancealready implies some degree of certainty that thecourtship will succeed. We do not make the claim thatcomputing the likelihood of future rejection cannot bedone, or that humans do not compute it, but rather thatreasonably good mating decisions can be made with-out this extensive computation.4

Finally, a first strategy can be defined as: ��swap =(Snaive, Dswap). As mentioned above, the distinguishingfeature of this strategy is that it does not require indi-viduals to estimate their own quality. Consequently,agents using ��swap remain idle during the juvenileperiod.

5.2 Flirting to Set Initial Aspiration Levels

We now turn to a second, slightly more sophisticatedclass of strategies. As we discussed in Section 3.4,when there are costs involved in entering and stayingin a relationship, a natural type of strategy is for indi-viduals to set acceptance or aspiration levels to decidewhether or not to begin courting some partner. Poten-tial partners falling below the aspiration level in qual-ity are not sought (proposed to) as dates. Typically,this aspiration level will reflect to some extent theindividual's own quality, with high quality individualsavoiding lower quality ones, and lower quality indi-viduals having realistic aspiration levels tuned to theirunfortunate lower rank. Rationally bounded agentsshould not be assumed to have information about theirown relative quality automatically, because their rankis relative to all other individuals in the population.Instead, we model agents who must estimate theirquality dynamically and use it to perform mating deci-sions as they go along. As mentioned earlier, the flirt-ing period allows agents to make a first estimation oftheir quality and set their aspiration levels to a corre-sponding (here equal) level (Todd & Miller, 1999).

Specifically, an individual i starts out being totallynondiscriminating by setting their self-quality esti-mate to 0. In each time step of the flirting period, iproposes to all individuals j in its interaction list thathave a quality qj greater than or equal to (inde-pendent of whether or not it has proposed to j before,and what the outcome of such a proposal was). If a

proposal is accepted by j (i.e., matched by a corre-sponding proposal), and qj is strictly greater than thecurrent value of , then the following update rule isused:

(3)

In the above, corresponds to the learning rate (weuse the value .2 in our simulations). This updatingprocedure can be interpreted, metaphorically, as indi-viduals trying to climb a ladder of qualities. At the endof the flirting period, (on average) the higher the qual-ity of individuals the higher they have climbed interms of their self-estimate. Thus, due to therequirement of mutual acceptance, the final value for

will tend to approximate the actual individualquality qi, as long as a reasonable number of individu-als are met during the adolescent flirting period. Thisfinal value is then used as an initial aspiration levelafter the flirting period.5 Because of this, we will bor-row the symbol and use it also to designate theaspiration level of an agent i after the flirting period.

Because the expectations of an individual shouldreflect not only its own quality but also the availabilityof partners, aspiration levels should be reduced when-ever waiting for a higher quality partner does not payoff in terms of lost reproductive lifetime. Moreover,since the initial aspiration level might not have beenproperly calibrated, individuals should not be too con-fident about it. This means it might be advisable toattribute failure to mate after the flirting period to aninflated or inadequate value of the aspiration level—which, in turn, should prompt a drop in the value of

. Below, we describe two ways to perform this(downward) update of . The first is based on aprobabilistic estimate, which to some extent endorsesthe typical computation- and information-intenseapproach used in normative theories of decision mak-ing (Plous, 1993). The second employs a simple heu-ristic that dispenses altogether with such computations(Gigerenzer et al., 1999). It is worth noting that thiskind of aspiration-dropping mechanism has been iden-tified in animals other than humans. For example,female cockroaches of the species Nauphoeta cinereahave been found to have an internal biological clockthat makes them less choosy as they get older (Moore& Moore, 2001).

qi*

qi*

qi*

qinew

* qiold

* 1 α–( ) qj α⋅+⋅=

α

qi*

qi*

qi*

qi*

q*

q*

��

�� Areasonable way to regulate the drop in the value of over time is to try to predict the time tw it will take fora partner of the desired quality to be obtained, andcheck if it pays off to wait that period instead of pro-posing to court a lower quality alternative alreadyavailable. This computation of tw can be done by keep-ing track of the (social) environment and continuouslyestimating relevant pieces of information, such as therate at which individuals are met , the fraction ofindividuals met that are single (s), and the mean andstandard deviation of their quality distribution .To compute we simply divide the number of indi-viduals met during an individual’s life so far by its age(thus assuming lifetime uniformity in the meetingrate). To compute s we check the state of individualswhen they are meet. To compute and , we assumethat the set of all individuals ever met (currently in thealternatives list or not) constitutes a representativepopulation sample. We further postulate a range ofqualities that the agent considers desirable, but stillattainable, as , where and is the quality of the best individual everobserved. As a result agents still prefer others withquality of at least , but do not take into accountwhether or not individuals are likely to reciprocatetheir proposals.

If agents make the assumption that qualities arenormally distributed, the proportion f of individualsmet whose quality falls within such an interval rangecan be approximated as: ,where the function N stands for the cumulative normaldistribution (with the specified mean and standarddeviation). Given the definition of f, the mean meetingrate , and the proportion of singles s, we can thusapproximate the average value for tw as follows:

(4)

where corresponds to a residual uncertainty factorthat measures the likelihood that the found partnerwill accept the courtship proposal (because its aspira-tion level is not higher than the agent’s quality). As asimplification, we will assign a constant valueindependent of the agent’s quality (see discussionbelow). We can now define an update rule for asfollows:

(5)

In the above, qb represents the quality of the best indi-vidual in the alternatives list whose quality is lowerthan . This update rule essentially states that anindividual will drop his/her aspirations to the level ofthe best known individual whenever waiting for a bet-ter alternative does not provide any fitness benefits. Tobe more rigorous, and compliant with expected utilitymaximization approaches, different values of andfitness gains could be averaged in the above equationfor the different qualities within the interval range

. Still, if we assume that and differ onlyby a small amount (in the present case no more than

), the approximation of is reasonable, becausethere will be little variation between the relative fre-quencies f of individual quality values within thissmall interval range.

With this update rule, and the update rule used inthe flirting period, we can now define an aspiration-level-based decision rule for agents as follows:

(6)

The rule essentially states that agents will propose toany individual above the sought minimal quality, pro-vided that they are not too old. All variables have thesame meaning as before. We further define a strategyDnull that never changes partners once courtship starts.This allows us to define a strategy based purely ondynamically computed aspiration levels, ��rational = (Sra-

tional, Dnull).We could further refine the update rule for by

introducing additional factors in the computation ofthe residual uncertainty (e.g., the quality of theagent making the decision, an estimation of the distri-bution of aspiration levels of other individuals as afunction of their quality and age, the accuracy of therule used in the flirting period to estimate , and oth-ers). But instead we will next pursue a different route:finding a simple but efficient update heuristic for (Gigerenzer et al., 1999).

q*

y·( )

µ· σ·,( )y·( )

µ· σ·

q* q̂,[ ] q̂ min[ q* σ·+( )= Q· max]Q· max

q*

f N q̂ µ· σ·, ,( ) N q* µ· σ·, ,( )–=

y·

tw1

ρ f y· s⋅ ⋅ ⋅-----------------------=

ρ

ρ

q*

qnew* qb if F q* t K tw+ +,( ) F qb t K+,( )≤

qold* otherwise

=

q*

tw

q* q̂,[ ] q̂ q*

σ· tw

Srational qa q* t ta, , ,( )0 if ta K J L+>+

1 if qa q*≥0 otherwise

=

q*

ρ

q*

q*


5.2.2 Setting Aspiration Levels the Simple Way Analternative approach to regulate the drop in the valueof the aspiration level is to keep track of the timean individual has been waiting for a partner and tolower his/her aspiration when a waiting time thresholdtmax is reached. This approach is more parsimoniousthan the one presented in the previous section, becauseestimating an appropriate value for tmax does notrequire knowing environmental factors such as themeeting rate or distribution of qualities. Specifically,we will define this threshold tmax as a fixed fraction of the maximum waiting time for which there arefitness gains by mating with an individual with quality

rather than qb (as defined above). Intuitively, theconstant can be interpreted as a risk factor thatspecifies how much the individual is willing to bet inthe attempt to court an individual with the currentminimal sought quality—rather than the best (attaina-ble) alternative that is likely to be already available tohim/her. The value can be computed straightfor-wardly by solving the algebraic equation: F( , t +K + ) = F(qb, t + K), where t is the current age ofthe agent. This yields:

(7)

The constant can be interpreted, once again meta-phorically, as a risk factor that specifies how much theindividual is willing to bet on its current aspirationlevel—the minimal quality partner sought, rather thanthe best (attainable) alternative that is likely to bealready available to him/her. Although the aboveexpression appears complex and therefore as difficultto implement in an agent as Srational, if we assume thatevolution would endow agents with “innate” knowl-edge of the approximate value of the parameters J andL, then the information gathering demands on theagent are minimal. Specifically, an agent only needs tokeep track of the highest quality individual seen so far.

We can now define a decision rule Sfrugal as equiv-alent to Srational but with the following update rule for

:

(8)

In the above, tw represents the number of time steps anindividual is waiting for a date of the minimal soughtquality. Whenever the value of is changed, tw isreset to 0. A key feature of this strategy is thatalthough statistically speaking the time an individualwill have to wait for a partner of the sought minimalquality is independent of the time he/she is alreadywaiting, this value reflects (albeit in a highly aggre-gate way) many relevant aspects of the social environ-ment. Namely, it provides a summary of the effects ofthe quality of the agent, the accuracy of the qualityestimate, the meeting rate, the availability of partners,and the lost fitness due to wasted reproductive time—all without making explicit observations or computa-tions of these values.

Finally, a new strategy ��frugal can be defined as��frugal = (Sfrugal, Dnull). This is again a strategy basedpurely on aspiration levels, which never makes agentschange partners after they start courtship.

5.3 Combining Aspiration Levels with Partner Switching

To investigate the advantages of combining partnerswitching strategies with aspiration level strategies,we define a new strategy ��mix = (S'frugal, Dswap). Thisstrategy combines Dswap with a slight variation of Sfru-

gal in which the update rule is modified such that out-comes of broken relationships are also used in settingthe values for : Specifically, if an agent was previ-ously courting and the partner took the initiative ofbreaking the relationship, is updated to ,where qd is the quality of the agent’s departing partnerand is a correction factor to decrease theagent's expectations to slightly below the quality ofthat partner (we will use the value .8). This procedureis likely (although not certain) to assign an appro-priate value, because the agent’s partner will break therelationship only to start courting a higher qualityindividual—and this gives a rough indication that theagent is aiming too high and is unable to retain part-ners of quality qd. This will be the case whether thevalue of goes down or goes up—as might happenwhen the agent was lucky getting a high-quality mateoriginally. Additionally, because the partner switch-ing decision rule Dswap gives partnerships a tentativecharacter, it makes sense to have drop in valuefaster by decreasing the risk factor in Equation 7.

q*

κtmax

′

q*

κ

tmax′

q*

tmax′

tmax = κ tmax′×

= κ J L+( ) t K+( )–[ ] 1qb

q*-----–

××

κ

q*

qnew* qb if tw tmax>

qold* otherwise

=

q*

q*

q* ω * qd

ω 0 1,[ ]∈

q*

q*

q*

κ


6 Results—Comparing the Strategies

In this section, we investigate how the strategies justspecified perform over a wide range of parameter set-tings, and what qualitative and quantitative aspects ofthose strategies explain the differences in perform-ance. More specifically, we explore the strategic rolethat courtship plays in mate choice behavior, lookingat the advantages of switching partners during court-ship. We also ask how the simplicity of decision rulesfor setting aspiration levels impacts their efficiencyand robustness, and what the consequences are ofusing combined strategies that rely both on aspirationlevels and partner switching.

In Table 1, we present a summary of the modelparameters with the (default) values used in the simu-lations and an indication of the rationale for thosechoices. For those model parameters where the actualvalue is likely to be highly contingent on the specificsof particular environmental ecologies, we present theinterval ranges for which we performed sensitivityanalysis. We set 10 time steps to correspond to oneyear. The parameters for the (quasi) normal quality

distribution were set by equating agent quality withthe total number of offspring produced during a com-plete (female) lifetime using a data set from a particu-lar human population, the Ache (Hill & Hurtado,1996)—although similar values apply to other socie-ties without significant contraceptive use. The inti-macy constant I was set to 2.0 to model a quadraticreduction of interaction capabilities, which corre-sponds to a super-linear increase in couples’ intimacyas courtship develops. Note that for the results shownin the next section, all of the strategies use a courtshipperiod of K = 10, even when no swapping is allowed(in ��rational and ��frugal); this is to reflect the cost ofcourtship for assessing the likelihood of desertion, asdiscussed in Section 3.2, even though we do notexplicitly model desertion here. Furthermore, we startby assuming that the flirting period A coincides withthe juvenile period J, thus instantiating the first agentlife-history depicted in Figure 2 (we consider otherlife-histories later). Each simulation was run until20,000 agents were created, and the results shown cor-respond to averages across 10 runs (except when men-tioned otherwise).

6.1 Strategy Comparison Across Parameter Settings

To compare the efficiency of the strategies, we use asa heuristic measure the average fitness (F(qd, t) = qd ×

[(J + L) – t]/L) of individuals with quality equal to orabove average ( ). Figure 3a shows these meas-ures for the four strategies defined in Section 5: ��swap,��rational (with uncertainty factor ), ��frugal (withrisk factor ), and ��mix (with a lower risk factor

Table 1 Parameter settings: base values and interval ranges used in sensitivity analysis.

Parameter Description Value(s) Range Note

P Population size/2 100 – Small community

L Reproductive lifetime 200 – 20 years (typical for women)

J Juvenile period 30 – 3 years (early adolescence)

Quality distribution 8,2 – No. offspring for

Qmin, Qmax Lower,upper bound 4,12 – Ache women

A Adolescence period 30 [20, 40] 3 years (same as J)

K Courtship time 10 [0, 40] 1 year

I Intimacy constant 2 – (see text)

Y Meeting rate .5 [.1, 1] 5 people met / year (× 2, for M&F)

N Max. size of alt. list 5 [2, 12] No. simultaneous options

µ σ,

qi µ≥

ρ .5=κ .3=


to take into consideration the possibility ofswitching partners as discussed in Section 5.3), with theparameter settings otherwise as specified in the previ-ous section. The rationale for this measure is that moreefficient strategies should move the fitness of individu-als of high quality further above chance level (i.e., thelevel obtained by mating with the first individualencountered) than less efficient ones that select lowerquality individuals. With our current parameter settingsrandom mating would give all individuals a fitnessvalue of about 8. In fact, as can be seen from Figure 3b,the small gains in the fitness of high quality individualsabove the chance level is achieved in all strategies at theexpense of a much greater reduction in the fitness oflow quality individuals. Furthermore, since higher qual-ity individuals have higher fitness they will delivermore replicas (offspring) to the next generation. Thus,the strategies that perform better for these individualsare the ones most likely to invade a population overevolutionary time. While a complete analysis of strat-egy performance and evolutionary stability wouldrequire a full-fledged game-theoretic analysis, becausethe fitness of individuals is contingent on the relativefrequency of the different strategies existing in the pop-ulation (Smith, 1982; Dugatkin & Reeve, 1998); herewe focus on the above heuristic measurement as a con-siderable simplification, but still useful first step.

Figure 3a shows several important results. First,��swap performs slightly better than ��rational. This isinteresting because with ��swap, individuals do not tryto estimate their own quality, but instead only try toretain partners and switch to better ones. Furthermore,��swap performs efficiently in spite of a relatively smallcourtship time, along with a realistic reduction ininteraction possibilities as courtship progresses.

To analyze the extent to which this result holdsacross parameter values, we present in Figures 4a and4b how the performance of ��swap varies as a functionof meeting rate Y and size of alternatives list N(keeping the courtship period K constant and equal to10). As can be seen when N = 5 (Figure 4a), ��swap

performs almost at the same level as ��frugal (and betterthan ��rational), for all values of Y presented—and withslightly increasing performance as Y increases. On theother hand, with Y = .5 (Figure 4b), ��swap requires aminimal value of N = 5 to reach a performance closeto ��frugal—with no important changes in performanceafter N reaches the value 6. Thus, ��swap can work as aneffective mating strategy, but at the expense ofkeeping track of (at least) a small number ofalternatives. If agents could strategically choosewhich individuals to keep track of (e.g., only the oneswith higher quality than the current partner), then thismemory requirement could be reduced. Elsewhere wehave shown that ��swap also performs rather well, interms of producing mated pairs with high interpairquality correlation (see beginning of Section 2), formost values of Y, with very little gain from increasingcourtship time beyond a small value (Simão & Todd,2001). This indicates that ��swap allows individualindividuals to make good mating decisions withreasonably few encounters. Intuitively, the power of��swap arises from the fact that holding partners shieldsindividuals against the uncertainty of whether or notthey will be able to find better (and attainable)alternatives soon enough in the future.

Moving away, temporarily, from our focus onhumans, we can see the relevance of these results onthe effectiveness of ��swap for other animal species.First, the life-history of many species is such that their

κ .1=

Figure 3 Fitness comparisons between the mate choice strategies. (a) Average fitness of individuals with qualityabove average using each strategy. (b) Average fitness of individuals using each strategy, as a function of their matequality.


juvenile period cannot be easily used by individuals toevaluate their own quality accurately without losingimportant reproductive time. This will be the caseespecially if an individual’s absolute and relativequality varies between breeding periods—as canoccur for seasonal birds (Johnstone, 1997; Alcock,1997; Krebs & Davies, 1993). Second, the social andecological constraints might be such that the relevantintersex interactions are too rare to allow a good esti-mation of one’s own quality (although some animalsmay also rely on internal “gauges” such as health con-dition). Thus, aspiration-level-based strategies maynot make sense for many species, but ��swap is a goodalternative.

Wittenberger (Wittenberger, 1983) proposed arelated mating tactic available to many animals, calledthe sequential-comparison tactic: Search for matesonly until there is a drop in the quality of the next indi-vidual found, and then attempt to go back to the previ-ous individual. If we think of previously visitedindividuals as tentative dates, then this strategy hassome parallels with ��swap (when N = 2). The main dif-ference is that the trigger for mating in the sequential-comparison tactic is finding a lower quality individ-ual, while in ��swap a fixed courtship time is used.Because both strategies present drawbacks that theother can address—namely, ��swap requires severalindividuals to be met or be available during the court-ship period to perform well, and the sequential-com-parison strategy is prone to prolonged search times ifthe meeting rate is very low and might lead to baddecisions due to precocious mating—combinations ofthe two kinds of strategies can be envisioned (e.g., usea threshold time to find the next alternative, and usethe quality of the alternatives found as a trigger for

mating). Empirical studies have indicated that somespecies use even more elaborate strategies, involvingthe sampling of increasingly restricted subsets of indi-viduals before a choice is made (Patricelli & Borgia,2001).

Another interesting aspect to be observed fromFigures 3 and 4 is that ��frugal performs better than��rational for many parameter values. In Figure 4b wecan see that, when Y = .5, this holds when N < 8.Above N = 8 ��rational gains an advantage because theupdate rule it uses potentially changes the aspirationlevel in every time step, and so can profit by seeinga larger and more representative pool of alternatives.In contrast to this, ��frugal only updates after a cer-tain waiting time has elapsed, and so is virtually unaf-fected by changes in N.

In a similar vein, Figure 4a that shows that ��frugal

is very robust to changes in the value of Y, while��rational exhibits a steep decrease in performance forvalues of Y greater than .5. This is somewhat surpris-ing given the fact that the strategy directly estimatesthis meeting rate itself (see Section 5.2.1). But becausethe increased meeting rate makes all individuals morepicky, waiting longer before lowering their aspirationlevels (see Equation 4), this reduces the likelihood thatthe alternatives an agent meets that match or surpassits aspiration level will accept the agent in turn. Itturns out that assigning a constant value to the uncer-tainty parameter in Equation 4 is insufficient toimplement a good strategy across the range of valuesfor Y. The value chosen at the beginning ofthis section provides the best performance for Y = .5,but for higher values of Y we found that smaller valuesof deliver better performance. On the other hand,for small values of Y, higher values of perform bet-

Figure 4 Average fitness for individuals with above-average quality (q > µ) using the four strategies. (a) Comparingperformance across changes in meeting rate Y (with N = 5). (b) Comparing performance across changes in maximumnumber of simultaneous alternatives N (with Y = .5).

q*

q*

ρ

ρ .5=

ρρ

��

ter. This shows that ��rational is very sensitive to propersettings of .

A tentative conclusion to derive from theseresults is that ��rational, by trying to guess what thefuture might bring in terms of partnerships, becomesvery sensitive to variations or errors in the estimationof the wide range of factors involved in this calcula-tion. As mentioned, this could be remedied by takinginto account more factors in the computation of theparameter in Equation 4, in a sense creating amore complex (implicit) model of the world. Thiswould require, though, that agents collect even moreinformation (unless a fixed value of is adequatefor all parameter values, or environmental settings,the agent might be exposed to). Not only would thisbe temporally and computationally expensive, itwould also be highly prone to overfitting (Gigeren-zer et al., 1999). ��frugal, on the other hand, by exploit-ing the information available in a single good pieceof evidence—the time the agent is waiting for a part-ner—becomes robust to possible environmental fluc-tuations.

A further key aspect to draw from Figure 3a isthat ��mix, by combining the advantages of Sfrugal in set-ting minimal aspiration levels with the ability to swappartners during courtship as directed by Dswap, is ableto outperform the individual use of these rules in thetwo strategies ��frugal and ��swap. From Figures 4a and4b, we can see that this result is robust across changesin Y and N. Intuitively, ��mix performs better becausesetting aspiration levels allows low-quality individu-als to be avoided, while swapping allows the agentnot to be too picky about the quality of the firstaccepted partner because of the possibility of laterswitching to a better partner. This result suggests thatdelaying mating with courtship—often interpreted informal models of mating behavior solely as a signalof male commitment (Dawkins, 1976/1990; Schuster& Sigmund, 1981; Mylius, 1999; Wachtmeister &Enquist, 1999)—can also be used effectively (by bothsexes) for mate selection. Moreover, given the dualcomposition of ��mix and its good performance, itmight be argued that (at least for complex social spe-cies like humans) mate choice behavior and itsunderlying psychological mechanisms could be com-posed of not just one strategic component, but sev-eral elements which are activated in different periodsor contexts in the individual’s life. Together, the com-bination of these elements is orchestrated to produce

effective lifespan mating behavior. Although in thisarticle we explore only strategic behavior that lastsuntil the time of first mating, we are currently work-ing on further models of mate choice that extend thetime frame under consideration (e.g., including rulesto decide if a partner should be deserted once off-spring have been produced). (See Simão & Todd,2002, for further analysis of robustness of modelresults.)

��

��

In the previous section, we found that being able toswitch partners during a courtship period is superior tocourtship without partner switching (that is, ��mix out-performed ��frugal and ��rational). This was not so surpris-ing, as being able to swap upward in mate qualityshould clearly be beneficial. But that result did indi-cate another adaptive role for courtship—holding onto good potential mates, at least until a better one isfound—beyond the usual proposal of courtship fortesting male fidelity (see Section 3.2). Here we wantto test this role for courtship more thoroughly, askingwhether the ability to hold and switch partners canactually make using a courtship period better than notusing any coursthip period. That is, we will comparethe mixed strategy ��mix with a courtship period includ-ing partner switching, against a variation of the ��frugal

strategy that needs no courtship at all and just allowsindividuals to mate immediately after the juvenileperiod. Can delaying mating via courtship possiblyoutperform immediate mating, given the time costpaid by the former? If so, then we can infer that court-ship can have an important strategic role in matechoice through the possibility to hold good partnersand switch to better ones, in addition to its usefulnessin assessing mate “honesty” (intention of not desertingafter mating).

To test this question, we introduce two strategyvariants that draw upon the different life-histories pre-sented in Figure 2. First, we define the strategy to be equivalent to ��frugal ( = .3), but with the court-ship period removed by setting K = 0 (thus corre-sponding to a degenerate case of the first life-historypresented in Figure 2). Second, is defined asequivalent to ( = .1), with the exception that itmakes use of a reduced flirting period A = J – K (= 20)so that courtship can begin while individuals are not

ρ

ρ

ρ

��frugal–

κ

��mix–

��mix κ


yet fully mature (thus corresponding to the secondlife-history presented in Figure 2). This means that

does not pay as big a cost in terms of matingdelay as would (otherwise there are no benefitsof delaying mating and using the courtship period toswitch partners—compare the plots for inFigure 4 where the fitness values are for most parame-ter setting below 8.4 with those in Figure 5 for where the values are higher than this). With these twostrategies, we can compare mate choice without court-ship (i.e., beginning immediately following the juve-nile period) using with mate choice includingcourtship and partner switching using .

Figures 5a and b depict the performance of thestrategy variants and (along with ,which is described below), as a function of Y (withN = 5) and N (with Y = .5) as in Figure 4. As can beseen, for all values of and , alwaysperforms better than . Only for very low meet-ing rates does the strategy of courting and part-ner switching not prove beneficial. This is animportant result, because it indicates that even in theideal case where no courtship is required to evaluatethe commitment of potential mates (i.e., here with K =0), the costs of courtship in terms of delayed matingcan still be outweighed by its benefits in finding andswitching to better partners. In other words, courtshipcan serve not only the function of selecting for honestmates, but also selecting for good mates. Thus, mod-els of the battle of the sexes (see Section 3.2) andmodels of sequential mate choice can profit from inte-gration into more complex and realistic theories ofreproductive behavior.

Finally, we can ask whether simply extending theadolescent flirting period (A) of could make

this courtship-less strategy outperform the strat-egy with courtship. Will the opportunity to learnlonger and set a better informed aspiration level be aseffective as the opportunity to hold onto and switchpartners during courtship? To find out, we created thestrategy , defined to be equivalent to butwith an extended flirting period A = 40 (and still withK = 0). This strategy corresponds to a degenerate caseof the third life-history in Figure 2. By comparing theperformance curves of and in Figure 5with those of in Figure 4, we see that extendingthe flirting period beyond the juvenile period (usingtime otherwise used for courtship) is not particularlyadvantageous. This is because only a small number ofencounters are required for reasonable set-up of theaspiration level, and therefore delays matingunnecessarily. Note that this is in contrast to the find-ings of Mazalov et al. that longer learning leads to bet-ter mate choice (Mazalov et al., 1996). This resultindicates that partner switching during courtship playsa qualitatively different role from just obtaining betterestimates of one’s own quality during an equivalenttime period.

7 Testing Model Predictions

Now that we have compared the performance of plau-sible mating strategies, the next step is to use ourmodel to generate predictions about human relation-ship patterns and evaluate those (whenever possible)against known empirical evidence. It is also of interestto inspect the concordance (or not) between the modelpredictions and those of more informal theories pre-sented in the social sciences literature. Due to its high

Figure 5 Average fitness for individuals with above-average quality (q > µ) using four variant strategies. (a) Comparingperformance across changes in meeting rate Y (with N = 5). (b) Comparing performance across changes in maximumnumber of simultaneous alternatives N (with Y = .5).

��mix–

��mix

��mix

��frugal–

��frugal–

��mix–

��mix– ��frugal

– ��frugal+

Y .2≥ N 3≥ ��mix–

��frugal–

��mix–

��frugal–

��mix–

��frugal+ ��frugal

–

��frugal+ ��frugal

–

��frugal

��frugal+


performance, robustness, and plausible psychologicalassumptions, we will take the strategy as a rea-sonable candidate to model human behavior (at thelevel of abstraction of interest to us). In the rest of thissection, we use with the same base parametersettings as specified at the beginning of Section 6.

Figure 6a depicts the linear correlation betweenthe qualities of individuals in mated pairs as a functionof rate-of-meeting Y and courtship time K. The resultsshow, as intuitively expected, that the more alterna-tives individuals are meeting (as Y × K gets bigger),the more likely they will mate with an individual closeto them in quality. In fact, only very small meetingrates and courtship times are required to produce thereasonably high correlation coefficients empiricallyobserved (mostly between .6 and .7) in sampledhuman populations (Kalick & Hamilton, 1986). Thissuggests that individuals are making good use of theirmating potential even though they have no initial,direct knowledge of their own mate value.

Figure 6b shows the mean number of dates indi-viduals engage in—including the very last one—untilthey settle down and mate (again as a function of Yand K). Our results show that for a wide range ofparameter values most individuals mate with rather lit-tle search. For example, with K = 8 and Y = .2, wefound that 98% of the individuals in the populationwere able to mate (and reach a correlation of qualitiesof .54), even though they only went through a smallnumber of dates—1.26 on average. These findings arein accord with demographic data—it is estimated thatin most human populations from 85 to 95% of theindividuals are able to mate at least once in their lives(typically under the official seal of the marriage insti-tution) (Coale, 1971; Fisher, 1989; Buss & Schmitt,1993; Kalick & Hamilton, 1988). While the meannumber of individuals courted may seem low, the

actual distribution should be compared with data fromsocieties without contraceptive use, something we arestill looking for. In any case, it should be stressed thatthe model’s realistic combination of statistics—rea-sonably high correlation of qualities in mated pairs,most of the population being able to mate, and lownumber of courtships—was never obtained with previ-ous models of human mate choice (Kalick & Hamil-ton, 1986; Todd & Miller, 1999).

Our simulations also gave some indication thatthe average duration of terminated relationships isnegatively correlated with the difference in qualitybetween courting partners, as one might expect. Tomore clearly highlight this trend, we run a simulationwith a much higher number of runs—50. In Figure 7a,we show the results for a particular setting of Y(= .5)and K(= 10). We can see that the higher the differenceis in the qualities within a couple, the more unstable(less durable) the relationship is. Moreover, if individ-uals differ too much in quality they will never court.(The absolute quality of individuals taken alone is aless important predictor of the duration of relation-ships.) Similar findings were obtained in a number ofempirical studies (see Kalick & Hamilton, 1986, for ashort review).

On a more theoretical level, this result matchesinsights from well-established (but nonformal) socialpsychology theories about factors underlying satisfac-tion and stability in relationships, such as the theory ofinterdependence in close relationships and its exten-sion, the investment model (Berscheid & Reis, 1998;Rusbult, Martz, & Agnew, 1998; Rusbult & Buunk,1993). In this theory, three factors are identified asassociated with commitment to a relationship, andconsequently its stability: satisfaction, quality ofalternatives, and investment. Subjective satisfactionand investment are known to be positively correlated

Figure 6 Predictions of the model across a range of settings for parameters Y (meeting rate) and K (courtship time).(a) Correlation of qualities in mated pairs. (b) Mean number of courtships before mating.

��mix–

��mix–


with relationship stability, while quality of alternativesis negatively correlated. Although in Rusbult’s invest-ment model these three factors have a broad holisticinterpretation and they have not been interpreted asaspects of individual adaptive strategies for findinggood mates, our model suggests that such an interpre-tation is reasonable. As depicted in Figure 7a, the rela-tive quality of alternatives (compared to the currentpartner) is the most important variable in controllingpartner switching behavior—and therefore the termi-nation of relationships. Furthermore, if we equatecourtship time in our model with investment, then wecan also functionally explain the positive correlationbetween an individual’s investment in a relationshipand their commitment to maintain that relationship.Regarding the degree of satisfaction in relationships, itis empirically known that intensity of romantic feel-ings is higher when an individual perceives his/herpartner as more attractive (Bunk, 1996; McKnight &Phillips, 1988). This is consistent with an evolutionaryfunctional interpretation, such as the one we endorsehere, where individuals seek and have a preference forhigh quality partners.

We also found that in our model, as expected,lower quality individuals are more likely to be“dumped” by their partners, with higher quality indi-viduals taking the initiative of breaking relationships(Figure 7b). Furthermore, lower quality individuals onaverage need more courtships and more time to find amate. This is because these individuals are morelikely to be courting somebody with a higher quality,who will often take the initiative of breaking off therelationship.

8 Discussion and Future Work

In the previous sections, we presented a detailed per-formance analysis of alternative mating strategies andselected the most efficient one as a tentative candidateto explain (part of) human mating behavior. Methodo-logically speaking, we embraced an iterative processesof designing and evaluating plausible psychologicalmechanisms as an attempt to reverse-engineer thefunctional structure of the mechanisms making up thehuman mind. This approach goes very much in theprogrammatic direction of evolutionary psychology, inthe strict sense defined by Tooby and Cosmides morethan one decade ago but still little explored (Tooby &Cosmides, 1989).

Our results show that our model better fits empiri-cal data concerning patterns of human mating than doprevious models. Our model demonstrates that indi-viduals can make successful mating pairs after a rela-tively few encounters with potential mates. Incontrast, Kalick and Hamilton’s attractiveness-prefer-ence model requires a high number of courtships (or atleast individuals met) to achieve a realistic intracouplequality correlation and a realistic proportion of matedindividuals (Kalick & Hamilton, 1986). This isbecause individuals in their model do not try to esti-mate their mate quality and use it in tuning their(probabilistic) aspiration level. Still, our model con-firms Kalick and Hamilton’s intuitions that a greatdeal of assortative mating in human populations canbe explained by a common preference for the mostattractive or “best” mates (also called “type” prefer-ences). This does not exclude the possibility that forsome quality dimensions there may be “homotypic” or“like prefers like” preferences instead (e.g., height,Ellis, 1992).

Figure 7 Relationship stability. (a) Average duration of relationships; (b) Average number of breaks (K = 10; Y = .5).


In our model, most individuals are able to findmates. Todd and Miller’s model only produced unre-alistically low proportions of individuals mated (Todd& Miller, 1999), because the aspiration-guided indi-viduals miss too many opportunities, rather than tak-ing an initial mate and possibly swapping later to abetter one. Individuals in our simulations used simpleheuristics to learn about the qualities of available part-ners during mutual search with unknown costs and nofixed time horizon. The learning model of Mazalovand colleagues concerned optimized single-sex search-ing with no search costs, fixed environmental distribu-tion of mates, and known search time (Mazalov et al.,1996). Finally, while Johnstone’s model produces sta-tistics similar to ours, this is only accomplished bygiving individuals initial knowledge of the distributionof qualities in the population and their own exact qual-ity, and by assuming that the cost of waiting or search-ing for a potential partner is constant (Johnstone,1997).

Beginning with such unrealistic assumptions doesnot allow us to learn much about the actual design ofthe psychological mechanisms regulating mating deci-sions. Our model and the strategies described here, onthe other hand, rely on plausible socio-ecologicalassumptions and feasible psychological designs. Inparticular, we found that the use of ecologically validinformation such as “waiting time” allows individualsto make efficient and robust decisions without requir-ing substantial information gathering or computation.Moreover, the possibility of switching (tentative) part-ners during courtship periods adds to the mating suc-cess of individuals. Overall, our methodologicalcommitment to psychologically and environmentallyplausible mate choice mechanisms allowed us to makea set of substantial predictions that matched empiricaldata, and thereby better understand the nature of theadaptive problem.

We are currently working to develop further ourconceptual framework of human mate choice and toextend our model in several directions. First, we areinterested in studying the nature of preferences andthe effect of including extra preference dimensions inthe models (e.g., age of partners). Multi-dimensionalpreferences are likely to make it harder to set upappropriate aspiration levels, because different ruleswill apply to different dimensions and trade-offs willoften be involved. Therefore, we expect to find thatthe complementary ability to switch partners during

courtship is even more advantageous in this case. Thisis, because the trade-offs in different dimensions canbe made based on comparisons between specific pairsof values (the values of the current partner and thealternative), instead of trying to estimate appropriateaspiration levels for all dimensions by taking intoaccount what the future might bring. Second, becausepartnerships frequently do not last for the completereproductive period of individuals—for example, peo-ple get divorced—we are currently working on amodel that includes strategic behavior beyond the firstmating and is conditional on the number and paternityof existing offspring (and can also be affected by con-traceptive use). We also aim to explore the conditionsin which different mating systems characteristic ofhuman populations emerge, and the extent to whichcultural distinctions and similarities can be captured ina broader model.

9 Conclusions

In this article, we have shown how an evolutionary(functional) analysis of mate choice can be combinedwith an agent-based modeling approach to gaininsights into the processes underlying human sexual/romantic relationships. In particular, by buildingextended courtship processes, the ability to switchpartners, and other key aspects of the mating gameinto our model, we have accounted for existing dataand generated predictions in ways unattainable by ear-lier models or verbal theories. We hope that our workwill motivate further research on more realistic andinformative models of the psychological mechanismsunderlying social behavior in humans (and other spe-cies). This should in turn help social psychology toescape the dangers of theory-blind empiricism andturn more to theory-guided experiments. Finally, wehope that the design and engineering insights thatcome from building computational models will helppush forward a new view of ecologically rationalsocial cognition: social beings as effective decisionmakers using simple mechanisms tuned to specificenvironmental contexts, rather than as general-pur-pose utility-maximizing calculators pounding at allsocial problems with the same big stick.


Notes

1 This would also require the additional modification of notreplacing mated individuals, so that the breeding poolshrinks over time (see Section 4).

2 Since the rule is applied to both sexes, the average numberof individuals met in each time step by each agent is infact 2 × Y.

3 An alternative and more realistic way of modeling this dif-ferential meeting probability is to do it explicitly by hav-ing two different meeting rates. We will use only one tokeep the set of model parameters to manageable size.

4 It is possible for instance to imagine a decision mecha-nism that will tend to accept dates of higher quality(despite the higher risk of later abandonment), unless reli-able information about future rejection becomes available.

5 Similar kinds of heuristics are presented in (Todd &Miller, 1999), but these also use information from encoun-ters that are unlikely to happen in the real world (namely,those where neither of the parties is interested in flirting orcourting). Moreover, these heuristics are not combinedwith other update rules that regulate the drop in value of

to compensate for wasted reproductive lifetime if part-ners are not found (as we do below).

Acknowledgments

This work was partially supported by a PRAXIS XXI scholar-ship. We would like to acknowledge the scientific and intellec-tual support and/or comments on earlier draft versions of thispaper to John McNamara, John Hutchinson, Paulo Gama Mota,Luis Moniz Pereira, João Sousa, Rainer Hilscher, Luis Cor-reira, and Monique Borgerhoff-Mulder.

References

Alcock, J. (1997). An introduction to behavioral ecology (6th

ed.). Sunderland, MA: Sinauer.Aron, A. (1988). The matching hypothesis reconsidered

again—comment on Kalick and Hamilton. Journal of Per-sonality and Social Psychology, 54(3), 441–446.

Barkow, J. H., Cosmides, & L. Tooby, J. (1992). The adaptedmind: Evolutionary psychology and the generation of cul-ture. New York: Oxford University Press.

Bateson, P. (1983). Mate choice. New York: Cambridge Uni-versity Press.

Bergstrom, C., & Real, L. (2000). Towards a theory of mutualmate choice: Lessons from two-sided matching. Evolu-tionary Ecology Research, 2(4), 493–508).

Berscheid, E., & Reis, H. T. (1998). Attraction and close rela-tionships. In D. T. Gilbert, S. T. Fiske, & G. Lindzey

(Eds.), Handbook of social psychology (pp. 193–281).New York: McGraw-Hill.

Bunk, B. P. (1996). Affiliation, attraction and close relation-ships. In M. Hewstone, W. Stroebe, & G. M. Steohenson(Eds.), Introdaction to social psychology (2nd ed.) (pp.345–373). Oxford: Blackwell.

Burley, N. (1983). The meaning of assortative mating. Ethologyand Sociobiology, 4(4), 191–203.

Buss, D. (1994). The evolution of desire. New York: Basic Books.Buss, D. M., & Schmitt, D. P. (1993). Sexual strategies theory:

An evolutionary perspective on human mating. Journal ofPersonality and Social Psychology, 100(2), 204–232.

Coale, A. J. (1971). Age patterns of marriage. Population Stud-ies, 25, 87–94.

Dawkins, R. (1990). The selfish gene. Oxford: Oxford Univer-sity Press. Originally published 1976.

Dombrovsky, Y., & Perrin, N. (1994). On adaptive search andoptimal stopping in sequential mate choice. AmericanNaturalist, 144(2), 355–361.

Dugatkin, L. A., & Reeve, H. K. (Eds.). (1998). Game theoryand animal behaviour. New York: Oxford University Press.

Ellis, B. J. (1992). The evolution of sexual attraction: Evaluativemechanisms in women. In J. H. Barkow, L. Cosmides, & J.Tooby (Eds.), The adapted mind: Evolutionary psychologyand the generation of culture (pp. 267–288). New York:Oxford University Press.

Epstein, J. M., & Axtell, R. (1996). Growing artificial socie-ties: Social science from the bottom up. Cambridge, MA:MIT Press.

Fisher, H. E. (1989). Evolution of human serial pairbonding.American Journal of Physical Anthropology, 78, 331–354.

Gigerenzer, G., & Selten, R. (2001). Bounded rationality—theadaptive toolbox. Cambridge, MA: MIT Press.

Gigerenzer, G., Todd, P. M. & the ABC Reserach Group.(1999). Simple heuristics that make us smart. New York:Oxford University Press.

Hammerstein, P. (2001). Evolutionary adaptation and economicconcept of bounded rationality—a dialogue. In G. Gigeren-zer, & R. Selten (Eds.), Boundeded rationality—the adap-tive toolbox (pp. 71–81). Cambridge, MA: MIT Press.

Hammerstein, P., & Riechert, S. (1988). Payoffs and strategiesin territorial contest: Ess analyses of two ecotypes of thespider Agelenopsis. Evolutionary Ecology, 2, 115–138.

Hill, K., & Hurtado, A. M. (1996). Ache life history—the ecol-ogy and demography of a foraging people. Chicago:Aldine de Gruyter.

Jeugd, H. P., van der, & Blaakmeer, K. B. (2001). Teenage love:The importance of trial liaisons, subadult plumage andearly pairing in barnacle geese. Animal Behaviour, 62(6),1075–1083.

Johnstone, R. (1997). The tactics of mutual mate choice andcompetitive search. Behavioral Ecology and Sociobiology,40(1), 51–59.

q*


Johnstone, R., Reynolds, & J. Deutsch, J. (1996). Mutual matechoice and sex differences in choosiness. Evolution, 50(4),1382–1391.

Kalick, S. M., & Hamilton, T. E. (1986). The matching hypoth-esis reexamined. Journal of Personality and Social Psy-chology, 51(4), 673–682.

Kalick, S. M., & Hamilton, T. E. (1988). Closer look at amatching simulation: Reply to Aron. Journal of Personal-ity and Social Psychology, 54(3), 447–451.

Kenrick, D. T., & Keefe, R. C. (1992). Age preferences inmates reflect sex differences in reproductive strategies.Behavioral and Brain Sciences, 15(1), 75–133.

Krebs, J. R., & Davies, N. B. (1993). An introduction to behav-ioral ecology (3rd ed.). Oxford: Blackwell Science.

Low, B. S. (1997). The evolution of human life histories. In C.Crawford, & D. L. Krebs (Eds.), Handbook of social psy-chology: Ideas, issues, and application. Mahwah, NJ: Erl-baum.

Mazalov, V., Perrin, N., & Dombrovsky, Y. (1996). Adaptativesearch and information updating in sequential matechoice. American Naturalist, 148(1), 123–137.

McKnight, T. W., & Phillips, R. H. (1988). Love tactics. Lon-don: Penguin.

McNamara, J., & Collins, E. (1990). The job search problem asan employer candidate game. Journal of Applied Proba-bility, 27(4), 815–827.

Miller, L. C., & Fishkin, S. A. (1997). On the dynamics ofhuman bonding and reproductive success: Seeking win-dows on the adapted-for human-environmental interface.In J. A. Simpson, & D. T. Kenrick (Eds.), Evolutionarysocial psychology (pp. 197–235). Mahwah, NJ: Erlbaum.

Montemayor, R., Adams, G. R., & Gullotta, T. P. (Eds.).(1994). Personal relationships during adolescence. Lon-don: Sage Publications.

Moore, P. J., & Moore, A. J. (2001). Evolution reproductiveaging and mating: The ticking of the biological clock infemale cockroaches. Proceeding of the National AcademySciences. USA, 98(16), 9171-9176.

Mylius, S. D. (1999). What pair formation can do to the battleof the sexes: Towards more realistic game dynamics. Jour-nal of Theoretical Biology, 197, 469–485.

Parker, G. A. (1983). Mate quality and mating decisions. In P.Bateson (Ed.), Mate choice (pp. 141–166). New York:Cambridge University Press.

Patricelli, J. A. C. U. G. L., & Borgia, G. (2001). Complexmate searching in the satin bowerbird ptilonorhynchusviolaceus. American Naturalist, 158(5), 530–542.

Pepper, J. W. Smuts, B. B. (2000). The evolution of cooperationin an ecological context: An agent-based model. In T. A.Kohler, & G. J. Gumermman (Eds.), Dynamics in humanand primate societies—agent-based modeling of socialand spatial processes (pp. 45–76). New York: OxfordUniversity Press.

Pfeifer, R. Scheier, C. (1999). Understanding intelligence.Cambridge, MA: MIT Press.

Plous, S. (1993). The psychology of judgment and decisionmaking. New York: McGraw-Hill.

Real, L. (1990). Search theory and mate choice 1. model of single-sex discrimination. American Naturalist, 136(3), 376–405.

Reed, E. S. (1996). Encountering the world: Toward an ecolog-ical psychology. New York: Oxford University Press.

Rusbult, C. E., & Buunk, B. P. (1993). Commitment processesin close relationships: An interdependence analysis. Jour-nal of Social and Personal Relationships, 10, 175–204.

Rusbult, C. E., Martz, J. M., & Agnew, C. R. (1998). Theinvestment model scale: Measuring commitment level,satisfaction level, quality of alternatives, and investmentsize. Personal Relationships, 5, 375–391.

Schuster, P., & Sigmund, K. (1981). Coyness, philandering andstable strategies. Animal Behaviour, 29, 186–192.

Simão, J. P., & Todd, P. M. (2001). A model of human matechoice with courtship that predicts population patterns. InSixth European Conference on Artificial Life. Heidelberg:Springer-Verlag.

Simão, J. P., & Todd, P. M. (2002). Modeling mate choice inmonogamous mating systems with courtship (Tech. Rep.).Center for Adaptive Behavior and Cognition, Max PlanckInstitute for Human Development, Berlin.

Smith, J. M. (1982). Evolution and the theory of games. Cam-bridge: Cambridge University Press.

Symons, D. (1979). The evolution of human sexuality. NewYork: Oxford University Press.

Todd, P. M. (1996). Searching for the next best mate. In R.Conte, R. Hegselmann, & P. Terna (Eds.), Simulatingsocial phenomena (pp. 419–436). Heidelberg: Springer-Verlag.

Todd, P. M., Fiddick, L., & Krauss, S. (2000). Ecologicalrationality and its contents. Thinking and Reasoning, 6(4),375–384.

Todd, P. M., & Miller, G. F. (1999). From pride and prejudice topersuasion: Satisficing in mate search. In Simple heuris-tics that make us smart (pp. 287–308). New York: OxfordUniversity Press.

Tooby, J., & Cosmides, L. (1989). Evolutionary psychologyand the generation of culture—part I. Theoretical consid-erations. Ethology and Sociobiology, 10, 29–49.

Trivers, R. L. (1972). Parental investment and sexual selection.In B. Campbell (Ed.), Sexual selection and the descent ofman (pp. 1871–1971). Chicago: Aldine de Gruyter.

Wachtmeister, C.-A. (2000). The evolution of courtship rituals.Unpublished doctoral dissertation, Stockholm University.

Wachtmeister, C.-A., & Enquist, M. (1999). The evolution offemale coyness—trading time for information. Ethology,105, 983–992.

Weisfeld, G. (1999). Evolutionary principles of human adoles-cence. New York: Basic Books/Wayne State University.


Wittenberger, J. F. (1983). Tactics of mate choice. In P. Bateson(Ed.), Mate choice (pp. 435–447). New York: CambridgeUniversity Press.

Zeifman, D., & Hazan, C. (1997). Attachment: The bond in pair-bonds. In J. A. Simpson, & D. T. Kenrick (Eds.), Evolution-ary social psychology (pp. 237–264) Mahwah, NJ: Erlbaum.

About the Authors

Jorge Simão completed his Licenciatura and masters degree in computer science andengineering at the College of Sciences and Technology at the New University of Lisbon(FCT/UNL). He is currently completing his Ph.D. on the topic of computer modeling andsimulation of human social behavior at the same university. This research was carried outat the Center for Artificial Intelligence (CENTRIA) in association with the computer sci-ence department at FCT/UNL, at the Center for Adaptive Behavior and Cognition at theMax Planck Institute for Human Development in Berlin, and at the anthropology depart-ment at the University of Coimbra, Portugal. His research interests include studyingaspects of human (social) behavior at the neuropsychological, behavioral, and societallevels, and connecting these three levels within a biocomputational and evolutionaryframework.

Peter M. Todd was born in Silicon Valley and studied mathematics, computer modeling,and cognitive science at Oberlin College, Cambridge University, and UC San Diegobefore receiving a Ph.D. in psychology at Stanford University. His thesis research there,working with David Rumelhart, used neural network models to explore the evolution oflearning. After developing artificial life simulations while a postdoctoral researcher at theRowland Institute for Science in Cambridge, Mass., he joined the psychology departmentat the University of Denver. In 1995 he moved to Munich to help found the Center forAdaptive Behavior and Cognition (ABC) at the Max Planck Institute for PsychologicalResearch under director Gerd Gigerenzer. His research interests there and at the ABCResearch Groups current home in Berlin have focused on modeling the interactionsbetween decision making and decision environments, including how the two interact andcoevolve over time. Todd has cowritten one book on adaptive decision mechanisms,coedited three books on neural network and artificial life models in music, and writtenpapers on topics ranging from social decision processes in rats to the impact of matechoice on macroevolution. Address: Center for Adaptive Behavior and Cognition, MaxPlanck Institute for Human Development, Lentzeallee 94, 14195 Berlin, Germany. E-mail:[email protected]

Documents

Modeling Mate Choice in Monogamous Mating Systems with …abcwest/pmwiki/pdf/simao.adaptbehav... · 2016-01-08 · Simão & Todd Mate Choice in Monogamous Systems with Courtship 3