On in the Presence of Multiple Costly Displays Clifford Bohm1,3,4, Acacia L. Ackles1,3,4, Charles Ofria2,3,4 and Arend Hintze1,2,3,4

1Department of Integrative Biology 2Department of Computer Science and Engineering 3BEACON Center for the Study of Evolution in Action 4Michigan State University, East Lansing, MI 48824 [email protected] Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal2019/31/247/1903563/isal_a_00170.pdf by guest on 26 September 2021 Abstract Robertson, 1979), sexual conflict (Chapman et al., 2003) and the (Zahavi, 1975). While these are often Sexual selection is a powerful yet poorly understood evolu- viewed as competing theories, a growing community is de- tionary force. Research into sexual selection, whether bio- veloping that argues that they are actually complementary, logical, computational, or mathematical, has tended to take a top-down approach studying complex natural systems. Many each explaining some aspect of sexual selection dynamics simplifying assumptions must be made in order to make these (Kokko et al., 2002). systems tractable, but it is unclear if these simplifications re- Here we study sexual selection using a dynamic agent- sult in a system which still represents natural ecological and evolutionary dynamics. Here, we take a bottom-up approach based system composed of many parts that can each be de- in which we construct simple computational systems from signed independently. Our approach is not to attempt to subsets of biologically plausible components and focus on ex- model any particular natural system, but rather, to define amining the underlying dynamics resulting from the interac- system parts that each simulate different aspects of naturally tions of those components. We use this method to investigate occurring sexual selection. This ‘system of parts’ will allow sexual selection in general and the sexy sons theory in par- ticular. The minimally necessary components are therefore for modeling of both naturally occurring as well as plausi- genomes, genome-determined displays and preferences, and ble, but not currently existing phenomena. As each part of a process capable of overseeing parent selection and . the model is validated, we will develop new parts to increase We demonstrate the efficacy of our approach (i.e we observe the complexity of the phenomena that can be studied and im- the evolution of female preference) and provide support for prove the systems applicability to nature. Since the system sexy sons theory, including illustrating the oscillatory behav- ior that developed in the presence of multiple costly display of parts will be built up rather then designed to mimic spe- traits. cific natural systems, we can also remove parts to determine if they are critical to a particular phenomenon. We have chosen to focus on the sexy sons theory (see be- Introduction low) because of its simplicity. In order to observe sexy sons Sexual selection occurs when a member of one sex selects behavior we needed only a small number of elements: (1) mates based on traits displayed in individuals of another mutable and heritable genomes, (2) genetically determined sex. The effects of sexual selection are clearly evident in preferences and displays (with assignable costs), and (3) a natural systems, from the bright coloration of male cichlid process capable of overseeing parent selection and mating. fishes (Payne and Krakauer, 1997) to the sweeping antlers In particular to investigate sexy sons, we did not need to con- of cervids (deer, elk and moose) (Clutton-Brock, 1982) to sider significantly more complex system parts that would be the brilliant tail feathers of peacocks (Petrie et al., 1991). needed to allow for phenomena such as condition dependent In addition to being attractive to mates, such display traits displays, developmental processes or, complex behaviors re- can be costly both to produce (Hunt et al., 2004) and to se- lated to life histories, nuptial gifts, or parental care. lect for (Pomiankowski, 1987; Head et al., 2005). Despite an abundance of literature, a unified understanding of the mechanisms that drive and maintain sexual selection in the Sexy Sons Theory face of costs has not yet been formulated. A number of theories have been developed to explain first proposed the idea of runaway sexual se- some mechanisms of sexual selection based upon observa- lection, a condition in which a trait that signals fitness be- tions of natural and theoretical systems. Primary among comes preferred by sexual selection and subsequently is ex- these theories are runaway selection (Grier, 1930), good aggerated to such an extent that the trait becomes costly. The (Rowe and Houle, 1996), sexy sons (Weatherhead and sexy sons theory extends Fisherian selection with the idea

247 that a female’s preference for a potentially costly male trait1 mined sex, sexual preferences, and sexual displays. MABE could increase the offspring production of males with that is a general-purpose evolutionary computation and artificial trait. It logically follows from sexy sons theory that it would life research tool that allows researchers to construct exper- be beneficial for a female to select these preferred males so iments by combining different modules. Modules in MABE that her male offspring can inherit their father’s attractive- have five different types: Brains (neural/cognitive digital ness (sexy sons) and those sons’ increased offspring count architectures), Genomes (sources of mutable and heritable would improve her long term fitness. information), Worlds (problem descriptions/environments), While sexy sons is generally accepted as theory, few em- Optimizers (parent selection and population management) pirical studies have tested its critical hypothesis (Huk and and Archivists (data tracking and recording). For this work Winkel, 2008) and significant doubts remain (Kirkpatrick, we developed an optimizer called Two Sexes Optimizer that 1985). This lack of empirical evidence is due primarily to manages detection, sex determination, parent selection challenges that limit testing sexy sons in biological con- and reproduction. Aside from the Two Sexes Optimizer we texts. For example, how can an experimenter ensure that were able to rely on existing modules. We used the Circular a male display is a sexy sons trait? (i.e., that the trait pro- Genome and Default Archivist modules. Due to the simple Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal2019/31/247/1903563/isal_a_00170.pdf by guest on 26 September 2021 vides no beneficial information). Even if such a trait can be nature of our experiments we did not need to use either a identified, assessing the reproductive success of organisms brain or world module. would require long-term, highly controlled experiments, ex- The digital organisms in this work each had a hap- tensive genotyping, and accurate phylogeny reconstruction. loid genome (a list of 1000 integers valued 0 to 255). A computational approach, however, will be faster and pro- An organism’s sex, sexual preference, and sexual display vide perfect data collection, allowing for clearer insight into level were determined by scanning its genomes for spe- the dynamics of sexual selection. cific genes, each indicated by a different sub-sequence (start In this paper we turn to computational agent-based evo- codon). Sex genes used a 4-digit start codon (the values lution to investigate sexy sons. Previous research has em- 101,102,103,104) with the parity of next site determining ployed theoretical methods, both mathematical and compu- the sex. Preference genes also used a 4-digit start codon tational, to attempt to understand the sexy sons hypothesis (105,106,107,108) with the value of the next site determin- (see Kokko et al. (2006) for a survey of the topic), but prior ing which trait is preferred in a mate (using the modulus op- work has tended to model only a single sexy sons trait reg- erator and the number of available display traits). Organisms ulated by a single genetic loci and then investigate under were required to have one and only one sex gene and one what conditions that trait will be selected. Pomiankowski and only one preference gene or they were removed from and Iwasa (1998) did examine multiple trait sexual selection the population without having an opportunity to reproduce. using a system of equations to model two traits, but their Display genes each had a unique 2-digit start codon and the formulation was not agent based and did not included either number of each display gene start codon found within the inheritance or mutation. Interestingly, even though Pomi- genome was used to determine the level of the associated ankowski’s system is quite different from ours, it did pro- display. While an organism could have any number of genes duce cyclic display and preference behavior that aligns with for each display trait in their genome, the display values our results. We and others (Mead and Arnold, 2004) argue were capped at 50 (i.e. an organism with 51 or more genes of that the two loci approach and other simplifications that are a particular display appears to females as though they had 50 often employed in generating models lack the complexity genes of that display). Random selection was implemented needed to model sexual selection properly. by adding a display trait with a fixed value of 0, which was Here, we ask: What effect does the number of costly not associated with any gene, to all males. This constant dis- traits have on the dynamics of sexual selection? Using play trait allowed for random selection; as all males had the this system we show that the behavior generated by sexual same display value for this trait, females selecting based on selection when only a single costly display trait is available this trait were selecting randomly. creates a illusion of stability. We then show that when mul- Each organism received a score, S, which determined the tiple equally costly display traits are available, female pref- organism’s number of mating opportunities relative to the erence will oscillate between the available traits. rest of the organisms of the same sex in the population. In all of the experiments in this manuscript, we allowed one ben- Methods eficial display trait, and zero or more costly display traits. We used the MABE (Modular Agent Based Evolver) frame- Females scores (SF ) were calculated by work (Bohm et al., 2017) to implement and evaluate popu- lations of evolving digital organisms with genetically deter- SF = min(tb, 60) (1) 1In this paper we will use the convention that females act as selectors and males are selected. This division is common in nature where tb is the number of beneficial display trait genes in due to differential offspring investment costs, but is not universal. their genome.

248 Male scores (SM ) were calculated by display trait genes, one beneficial, and four costly. For con- sistency, we seeded genomes with the five different display S = min(t , 60) C max(0, t 10) (2) trait genes in every condition even though not all five were M b − − t Tc used in all experiments. X∈ We evolved each population for 10,000 generations. Ev- where tb is as above, C is the cost coefficient (which sets ery generation each organism’s sex, sexual preference and to cost of costly traits), and Tc is the number of display trait genes in their genome for each display trait in the set of display trait levels were read from that organisms genome. costly traits in the current experiment. In other words, both Organisms that did not have exactly one sex gene and one males an females receive a base score equal to the level of preference gene were considered to have experienced a their beneficial trait (to a maximum of 60). Females pay no lethal mutation and were discarded. We then divided the costs, and males pay a cost relative to the number and level remaining population into females and males. A female was of their costly displays but only for those displays that are selected using roulette selection (fitness proportional) and above 10. then a collection (a lek) of 20 males were selected, also us- While exploring parameter values (such as cost coefficient ing roulette selection, for that female to choose from. The Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal2019/31/247/1903563/isal_a_00170.pdf by guest on 26 September 2021 and population size) there were a number of essentially arbi- female mated with the male in the collection with the highest trary decisions we needed to make. Two of these decisions, display level matching the females preference (or a random while not necessary to generate the effects observed, did sig- male from the collection if the female had no preference) nificantly improve the consistency of the results. and produced an offspring. This process was repeated many First, the score cap for the beneficial display trait was times to produce the next generation of 1000 organisms. The set at 60 but the value for display traits where females can parents were then discarded; that is, organisms lived for ex- no longer detect differences was set at 50. This difference actly one generation. means that the beneficial display trait continued to provide Mating consisted of crossing the selected parents benefits even after changes to the trait were undetectable to genomes and applying mutations to the resulting genome. females. As a result, if the beneficial display trait were to We setup genomes to have to have 19 equally-spaced drift away from its optimal value (60) it would not immedi- crossover points, generating 20 genome segments. For each ately create a signal that was detectable to females, which pair of segments, the system selected a random parent from might become a focus for selection. Similar beneficial traits the mating pair and used that parents genome for the first are likely found in nature; perhaps fur color, where preda- genome segment of the offspring genome. Then the second tors have more sensitivity to the color range then females, genome segment was contributed by the other parent. This or a vocalization that acts both as a warning and a mating process of was repeated for the remaining segments. This call where the auditory range of the target of the warning is process is comparable to a 10-chromosome genome where 1 greater then that of the females. each parent randomly contributed 2 of each of their chro- Secondly, costs were not applied on male display traits mosome to each offspring chromosome. when they were less then or equal to 10 because we found Two types of mutations were possible: point mutations that if these displays were costly at any level, then the as- and indel mutations. Point mutations changed the value of sociated genes generally would be purged from the genome one site from its current value to a random number in the when not being selected for. Once a gene had been entirely range of 0 to 255. Indel mutations copied a section of the purged a rare mutation would be required for it re-appear. genome (from 2 to 12 sites) and replaced another section The costly display traits describe traits that at low levels are of the genome of the same length with the copied values. not significantly costly. This type of costly display can be Note that these mutation types were selected because they thought of as tail length in a species where short to medium maintain genome length. We found that if insertion mu- tail length has no significant fitness effect, but beyond some tations were allowed the system would produce extremely limit, tails become costly either because of upkeep, preda- large (and therefore slow to convert) genomes. Point muta- tion risk, or some other factor. tions occurred at a rate of 0.001 per genome site (on average To initialize each run, we generated a population with 1 per genome). Indel mutations occurred at a rate of .0001 1000 organisms with randomized genomes. We seeded each per genome site (on average 1 per 10 genomes). organism’s genome with one sex gene at genome location We chose to define display traits with 2-digit start codons 250 and one preference gene at location 750. The spacing so that there would be a non-trivial chance for them to spon- between sex and preference genes ensured that these genes taneously emerge as the result of mutation. Specifically, 1 would be able to be inherited separately (i.e. low linkage). there is a 65,536 chance that two randomly selected numbers Since the sex and preference of each organism was based on will generate a specific pair. With a population size of 1000 the site following the start codons, the sex and preference of organisms evaluated for 10,000 generations the creation of each initial organism were random. The genomes were also display start codons by mutation, while rare, becomes likely. seeded with five randomly positioned copies of each of five Of course, once one or more genes exist, indel mutations can

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40 Figure 2: The results of a typical replicate from Condition 1. 2.a, display 20 shows the % of random selection. 2.b, shows the level of the bene- ficial display trait (black) and the % of selection for that trait (red). 0 200 400 600 0 2000 4000 6000 8000 10000 Selection for the beneficial trait is high until it reaches 50, after generations generations which selection drifts between random selection and the beneficial display trait. Figure 1: Average results of 100 replicates of Condition 1. 1.a

and 1.b show percent of females selecting either for a beneficial Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal2019/31/247/1903563/isal_a_00170.pdf by guest on 26 September 2021 trait (red) or randomly (black dotted) over 10,000 generations (1.a files and instructions for generating the data presented in provides a detail of the first 600 generations). 1.c and 1.d show the display level of the beneficial trait over the same time scales. this paper (see: http://github.com/cliff-bohm/ Initially selection for the beneficial trait is high, but as the trait ALIFE-2019-On-Sexual-Selection). passes 50 (the greatest value at which females are able to detect trait variation) selection drifts, eventually to a level equal to random Results selection. The trait eventually achieves a value slightly above 60 (the greatest value at which trait increases are rewarded). Shaded The results of Condition 1 (one beneficial trait) are shown in areas display 95% confidence. Fig.1. We observed that selection tended to fix on the benefi- cial display trait and remain fixed until that trait reached 50, the level over which females are unable to detect variation. copy these and the likelihood of an indel mutation resulting Female preference then appeared to drift. Fig 1.b illustrates in a copied gene increases as there are more of that gene that random selection and selection for the positive trait ap- present. On the other hand, we did not want a high rate of pear to stabilize at approximately 50% each for remainder of creation of sex and sex preference genes. The 4-digit sex and the 10,000 generations. Condition 1 demonstrates that sex- preference start codons are far less likely to arise by muta- ual selection in our system can target displays and will select tion ( 1 ) and so additional copies of these genes 4,294,967,296 for a beneficial display when there is detectable variation in would most likely be the result of indel mutations. the display and furthermore that if the beneficial trait’s vari- We tested five conditions. ation is undetectable to females, then the trait will be as at- Table 1: Experimental Conditions. tractive as random selection. Fig 2 shows behavior of a sin- gle replicate of Condition 1 and illustrates that the apparent Condition Num. Costly Traits Trait Cost selection stability between random selection and selection 1 0 NA for the beneficial trait is really the result of averaging drift 2 1 1.0 3 1 0.1 with higher variance across 100 replicates. 4 4 1.0 The results of Condition 2 (one beneficial trait and one 5 4 0.1 costly trait at high cost) are shown in Fig 3. We observed that like Condition 1, sexual selection tended to select for the In all five conditions, one beneficial display trait was vis- beneficial display trait early, but where Condition 1 resulted ible to selection, as was the option for females to choose a in drift once the beneficial display trait has reached 50, we mate randomly. Condition 1 served as a control, with no see selection for the costly display trait develop. Once this costly traits. Conditions 2 and 3 examine when a single trait reaches 50, we did not see the system tending to drift costly trait was also available at a high or low cost, respec- as in Condition 1. Rather, we observed persistent selection tively. Conditions 4 and 5 expanded this test to four costly for the costly display trait and low occurrences of selection traits, again with high or low cost, respectively. for the beneficial display trait or random selection. Fig. 5.a Costs were manipulated by altering the cost coefficient (C through c. show the behavior of an arbitrary replicate of from equ. 2). Condition 2. We ran 100 replicates of Condition 1 and 300 replicates In Condition 3 (one beneficial trait and one costly trait at each of Conditions 2,3,4, and 5. Each replicate was run with low cost), shown in Fig. 4, the reduced cost coefficient re- a different random seed for 10,000 generations with a popu- sulted in lower interest on the part of females for the costly lation size 1000. display trait. As opposed to Condition 2 where selection Readers wishing to replicate the results from this paper for the costly display trait was consistently at or near 100%, are directed to the supplemental materials which include in Condition 3, selection for the costly display trait hovered

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3.b show the percent of females selecting either for a beneficial condition is identical to Condition 2 except that in Condition 2 the Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal2019/31/247/1903563/isal_a_00170.pdf by guest on 26 September 2021 trait (red), a costly trait (black solid), or randomly (black dotted) cost coefficient was 1.0 and here it is 0.1. See Figure 3 for descrip- over 10,000 generations (3.a provides a detail of the first 600 gen- tion. erations). 3.c and 3.d show the display level for the beneficial trait a d (red) and the costly trait (black) over the same time scales. Initially 1.0 selection for the beneficial trait is high, but as the trait passes 50 0.5

(the greatest value at which females are able to detect trait varia- selection 0.0 tion) selection shift to the costly trait. The beneficial trait eventu- b e 1.5 75 ally achieves a value slightly above 60 (the greatest value at which 1.0 50 trait increases are rewarded) while the costly trait stabilizes around 0.5 25 display 50. Shaded areas display 95% confidence. selection 0.0 0.0 c f 1.0 50

0.5 25 display selection 0.0 0.0 around 75% after the beneficial display trait had exceeded 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 50. Random selection and selection for the beneficial dis- generations generations play trait both maintain values near 12%. Interestingly, se- Figure 5: The results of two typical replicates, one from Condition lection for the beneficial trait seemed to behave in the same 2 and one from Condition 3. 5.a, 5.b, and 5.c show the results of manner as random selection supporting the idea that selec- a Condition 2 replicate (one beneficial display trait and one costly tion for the beneficial display trait provides the same benefit display trait with cost coefficient = 1.0). 5.a, shows the % of ran- as random selection once the beneficial trait exceeded the dom selection, 5.b, the level of the beneficial display trait (black) level of female detection. 5.d though f. show the behavior and the % of selection for that trait (red), and 5.c, the level of the costly display trait (black) and the % of selection for that trait (red). of arbitrary replicate of Condition 3 and illustrate that the 5.d, 5.e, and 5.f show the same data for a replicate from Condition selection levels are not in fact stable and that the apparent 3 (cost coefficient = 0.1). In both conditions, selection for the bene- stability in Fig. 4 is a the result of averaging replicates. ficial trait is high until it the beneficial trait reaches 50, after which The results of Condition 4 (one beneficial trait and four selection is predominately focused on the costly display trait. The primary differences between conditions is the consistency of selec- costly traits at high cost) are shown in Fig 6. We observed tion for the costly display trait (more focused when the cost is high) the same early preference for the beneficial display trait that and, to a lesser extent, the consistency for the level of the costly trait was seen in Conditions 1 and 2. Once the beneficial display itself. It can be observed in the low costly condition both random trait reached 50 though, we did not observe a single costly selection and selection for the beneficial trait appear to be targeted trait being selected for, but rather we observed that all four frequently when selection is not focused on the costly trait. of the 4 costly display traits are being selected for at compa- rable levels, about 25% and that the display levels all seem display traits as was observed in Condition 4, but higher lev- to be approximately the same, at a level of about 12. Fig. els in the costly display traits themselves. Perhaps these 8.a through f. show the behavior of an arbitrary replicate of higher levels resulted from a slower decay rate due to the Condition 4. Looking at the single replicate it is evident that reduced selection pressure exerted by the decreased cost co- the 4 costly traits are not at equilibrium as Fig. 6 suggests, efficient. 8.g though l. show the behavior of an arbitrary but rather preference and trait values are constantly shifting. replicate of Condition 5. Here again like in Condition 4, os- Note, that the averaged lines of the four traits overlap in Fig. cillations between different preferences and traits were seen. 6, suggesting that each trait spent similar time under selec- tion when compared across replicates. Discussion In Condition 5 (one beneficial trait and four costly traits Costly display traits can be a preferred target for sexual at low cost), shown in Fig. 7, the reduced cost coefficient re- selection. More surprisingly, they can even be preferred sulted in comparable rates of selection among the four costly over neutral or even beneficial traits particularly when those

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Figure 6: Average results of 300 replicates of Condition 4. 6.a Figure 7: Average results of 300 replicates of Condition 5. This and 6.b show the percent of females selecting either for a benefi- condition is identical to Condition 4 except that in Condition 4 the cial trait (red) or randomly (black dotted) over 10,000 generations cost coefficient was 1.0 and here it is 0.1. See Figure 6 for descrip- (6.a provides a detail of the first 600 generations). 6.c and 6.d show tion. the display level for the beneficial trait over the same time scales. 6.e and 6.f show the percent of females selecting for each of 4 costly traits. 6.g and 6.h show the levels of these four traits. The a high level (slightly above 60) is reasonable as those organ- four costly traits all have the same cost and so are not individually isms who have this display at a higher then average level are labeled. Initially selection for the beneficial trait is high, but as provided more mating opportunities. Fig. 2 shows a typ- the trait passes 50 (the greatest value at which females are able to detect trait variation) selection drifts and appears to be evenly di- ical replicate of Condition 1 and illustrates that preference vided among the four costly traits (each approximately 25 percent). is not actually balanced between random selection and the The beneficial trait eventually achieves a value slightly above 60 beneficial trait, but rather drifts between the two. (the greatest value at which trait increases are rewarded) while the In Conditions 2 and 3 we observe the system with a single costly traits each stabilize near 12. Shaded areas display 95% con- fidence. beneficial display and a single costly display. These con- ditions demonstrate that a sexy sons trait can (and in this system will) become the target of selection, once it is the traits fail to provide discriminatory information. This work only available target for selection. Females could have se- demonstrates this result conclusively. The costly display lected for either the beneficial display trait or accepted ran- traits were designed to provide no benefit, but clearly they dom mates. Instead, when presented with a collection of must, and the most logical explanation for that benefit is the males, females overwhelmingly chose to mate with the male sexy sons hypothesis. that had the lowest probability to have been selected to be In the introduction we posed the question, What effect do part of that collection. the number and cost of costly traits have on the dynamics The increased rate of selection for the costly trait in Con- of sexual selection? We designed a series of experiments to dition 2, versus Condition 3, may seem counter intuitive; demonstrate both the efficacy of our system and then to in- Should we not observe lower levels of selection for the crementally add complexity in the form of costly displays to costly display when the display is more costly? We hypoth- explore system dynamics. We will now provide conjecture esize that when the costly display value reaches 50 or above, for what we believe are the driving factors that explain the selection for that trait begins to drift. At high cost, as female observed behavior. preference drifts there is greater pressure for males to reduce In Condition 1 we observe that selection for the benefi- the level of their costly display which creates a greater vari- cial display is high only when the beneficial display has de- ation and this creates a stronger signal and thus provides a tectable variation. Moreover, we observe that female prefer- larger sexy sons benefit. ence for the beneficial trait behaves in the same manner as In Condition 4 and 5 we considered the system with a sin- random selection, once that beneficial trait no longer has de- gle beneficial display and four costly displays. Fig. 6, sug- tectable variation. The fact that the beneficial trait maintains gests that the system stabilizes at around 25% selection for

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0.5 25 Figure 9: Compares the lengths of periods where a significant ma- display selection 0.0 0.0 jority of females are selecting for a single display trait in Condi- e k tions 4 and 5 - one beneficial trait and four costly traits at high cost 1.0 50 (4) and low cost (5). A period begins when the % of selection for Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal2019/31/247/1903563/isal_a_00170.pdf by guest on 26 September 2021 0.5 25

display a trait exceeds 90% and ends when it drops below 50%. All repli- selection 0.0 0.0 cates from each condition were averaged, so values show average f l 1.0 50 counts per replicate. The x-axis lists length of the periods from 1

0.5 25 generation to 1000 generations and the y-axis shows the average display

selection number of runs which were at least this long among all replicates 0.0 0.0 0 2000 4000 6000 8000 10000 0 2000 4000 6000 8000 10000 in the higher cost Condition 4 (solid line) and lower cost Condition generations generations 5 (dashed line). The results illustrate that while Condition 4 had less overall runs they tended to be longer. Shaded areas are 95% Figure 8: The results of two typical replicates, one from Condi- confidence. tion 4 and one from Condition 5. 8.a through 8.f show the re- sults of a Condition 4 replicate (one beneficial display trait and four costly display traits with cost coefficient = 1.0). 8.a, shows 9 shows that at higher cost (in Condition 4) there are fewer the % of random selection, 8.b, the level of the beneficial dis- play trait (black) and the % of selection for that trait (red), and total runs (defined as a period when a single display trait is 8.c through 8.f, the level of each of the costly display traits (black) being selected for by a majority of females), but these runs and the % of selection for that trait (red). 8.g through 8.l show tend to last longer. We argued that in Condition 2, the rel- the same data for a replicate from Condition 5 (cost coefficient = atively high cost of display causes a rapid decay in display 0.1). In both conditions, selection for the beneficial trait is high once selection for that display begins to drift and this faster until it the beneficial trait reaches 50, after which selection os- cillates among the four costly traits. The primary differences be- rate of decay, in turn, results in a stronger signal. We ex- tween conditions is the duration of the periods of selection for each pect that the same phenomena may explain the relationship costly display trait (more focused when the cost is high) and the between cost and run length here. The stronger signal gener- slower rate at which the costly display traits fall when not un- ated by higher cost results in more focused selection on the der selection. Unlike Fig. 8, random selection or selection for trait that is currently preferred. the beneficial trait are rare. Data from additional replicates can be found in the supplemental material (http://github.com/ What about the Handicap Principle and the Good cliff-bohm/ALIFE-2019-On-Sexual-Selection). Genes Theory? Two models often cited to explain the existence of costly displays are the Handicap Principle and the good genes the- each of the four costly traits. This apparent result is not the ory. We would be errant not to address these directly. case though. Fig. 8 shows the behavior of typical replicates The Handicap Principle, argues that evolution may result of Conditions 4 and 5 and reveals that rather than stability, in some costly displays that ”serve as marks of quality” since we observe oscillations among the four costly display traits. an organism would need to be fit in order to survive with In Conditions 2 and 3, once the costly trait maxed out and such handicaps (Zahavi, 1975). The handicap principle can begin to decay, there was no other viable option for female not apply here since it requires the existence of condition preference (neither the random option nor the beneficial trait dependant displays and the displays here are entirely genet- had detectable variation), so any small variation in the costly ically based. trait was the only signal that selection could target). In Con- The Good Genes theory, posits that an arbitrary display ditions 4 and 5 when one costly display trait maxes out, there may be linked with some beneficial hidden gene. Essen- are always three other, equally viable, options. This is the tially, the good gene provides an honest signal that a male primary result in this paper: when there are multiple costly contains a particular beneficial gene. Clearly the beneficial traits the stable state of the system is a state of constant display trait in our experiments is a good gene. It is directly change. observable and is directly associated with mating opportu- How does the difference in the cost coefficient explain the nity. On the other hand, the costly display traits are clearly differences between the results in Conditions 4 and 5? Fig. not. Good genes theory can not be used to explain the se-

253 lection of costly displays that we observe. It may be reason- In Artificial Life Conference Proceedings 14, pages 76–83. able to argue that costly display traits are sometimes good MIT Press. genes. If females find a particular costly display trait at- Chapman, T., Arnqvist, G., Bangham, J., and Rowe, L. (2003). tractive and select for that display to such an extent that it Sexual conflict. Trends in Ecology & Evolution, 18(1):41– outweighs the cost then the presence of the gene in a male 47. does (for a time) communicate that the male’s offspring are Clutton-Brock, T. (1982). The functions of antlers. Behaviour, likely to have higher than average reproductive success. Is 79(2-4):108–124. there room in good genes theory for transient good genes? Grier, N. (1930). Fisher. the genetical theory of natural selection For a different approach to the same argument, see Kokko (book review). Social Forces, 9(1):295. (2001). Head, M. L., Hunt, J., Jennions, M. D., and Brooks, R. (2005). The indirect benefits of mating with attractive males outweigh the Conclusion direct costs. PLoS biology, 3(2):e33. In this work we demonstrated that sexual selection on costly Huk, T. and Winkel, W. (2008). Testing the sexy son hypothe- Downloaded from http://direct.mit.edu/isal/proceedings-pdf/isal2019/31/247/1903563/isal_a_00170.pdf by guest on 26 September 2021 traits can occur and that sexy sons provides a sound expla- sisa research framework for empirical approaches. Behav- nation. We also demonstrated that multi-trait sexual selec- ioral Ecology, 19(2):456–461. tion can result in a semi-stable state of constant change. This Hunt, J., Brooks, R., Jennions, M. D., Smith, M. J., Bentsen, C. L., work investigated only a subset of parameters possible in the and Bussiere, L. F. (2004). High-quality male field crick- system used. From here we will continue to investigate the ets invest heavily in sexual display but die young. Nature, sexy sons theory, examining how this system responds to 432(7020):1024. different costs, including female search costs and develop- Kirkpatrick, M. (1985). Evolution of female choice and male ing methods to investigate genetics effects such as how sexy parental investment in polygynous species: The demise of sons and trait oscillation affects genomic rates of change. In the ”sexy son”. The American Naturalist, 125(6):788–810. the longer term, we will extend our system to include more Kokko, H. (2001). Fisherian and good genes benefits of mate complex features of sexual selection such as threshold se- choice: how (not) to distinguish between them. Ecology Let- lection, condition dependant traits, parental care, and sexual ters, 4(4):322–326. display signal fidelity. Kokko, H., Brooks, R., McNamara, J. M., and Houston, A. I. Understanding sexual selection is not only important to (2002). The sexual selection continuum. Proceedings of understanding biology’s history and predicting its future, but the Royal Society of London. Series B: Biological Sciences, also may provide dynamics that could support open-ended 269(1498):1331–1340. evolutionary processes. Deeper understanding of the os- Kokko, H., Jennions, M. D., and Brooks, R. (2006). Unifying and cillatory behaviors generated by costly selection and how testing models of sexual selection. Annu. Rev. Ecol. Evol. this phenomena alters genomes and phenotypes may explain Syst., 37:43–66. how some species have been able to navigate away from lo- Mead, L. S. and Arnold, S. J. (2004). Quantitative genetic mod- cal optima or across seemingly impossible fitness valleys. els of sexual selection. Trends in ecology & evolution, Finally, if we were able to control sexual selection it could 19(5):264–271. even be used in engineering and machine learning contexts Payne, R. J. and Krakauer, D. C. (1997). Sexual selection, space, as a more naturalistic form of diversity search. and speciation. Evolution, 51(1):1–9. Petrie, M., Tim, H., and Carolyn, S. (1991). Peahens prefer pea- Acknowledgements cocks with elaborate trains. Animal Behaviour, 41(2):323– 331. We wish to thank Vincent Ragusa, Jory Schossau, Alexan- der Lalejini, and Emily Dolson who all provided insights Pomiankowski, A. (1987). The costs of choice in sexual selection. that helped develop this work. CB would like to particularly Journal of theoretical Biology, 128(2):195–218. thank Jason Bundy for sharing his enthusiasm on the topic Pomiankowski, A. and Iwasa, Y. (1998). Runaway ornament diver- and for acting as the initial catalyst in a process that eventu- sity caused by fisherian sexual selection. Proceedings of the ally resulted in this document. This work was supported by National Academy of Sciences, 95(9):5106–5111. the National Science Foundation (NSF) through the BEA- Rowe, L. and Houle, D. (1996). The lek paradox and the capture of CON Center (Cooperative Agreement DBI-0939454). Com- genetic variance by condition dependent traits. Proceedings putational resources critical to this work were provided by of the Royal Society of London. Series B: Biological Sciences, 263(1375):1415–1421. Michigan State University’s Institute for Cyber-Enabled Re- search. Weatherhead, P. J. and Robertson, R. J. (1979). Offspring quality and the polygyny threshold:” the ”. The References American Naturalist, 113(2):201–208. Bohm, C., C G, N., and Hintze, A. (2017). Mabe (modular agent Zahavi, A. (1975). Mate selection - a selection for a handicap. based evolver): A framework for digital evolution research. Journal of theoretical Biology, 53(1):205–214.

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