Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=rajp20 Australasian Journal of Philosophy ISSN: (Print) (Online) Journal homepage: https://www.tandfonline.com/loi/rajp20 Multiple Realization and Evolutionary Dynamics: A Fitness-Based Account Graciela Kuechle & Diego Ríos To cite this article: Graciela Kuechle & Diego Ríos (2020): Multiple Realization and Evolutionary Dynamics: A Fitness-Based Account, Australasian Journal of Philosophy, DOI: 10.1080/00048402.2020.1839920 To link to this article: https://doi.org/10.1080/00048402.2020.1839920 Published online: 01 Nov 2020. Submit your article to this journal View related articles View Crossmark data Multiple Realization and Evolutionary Dynamics: A Fitness-Based Account Graciela Kuechle a and Diego Ríos b a Heilbronn University; b IIF - SADAF - CONICET ABSTRACT Multiple realization occurs when a natural kind is variably realized at more basic levels and the common physical structure of the realizers is not essential for supporting nomological statements. It has been suggested that this phenomenon may be an outcome of natural selection acting over multiple realizers that perform an adaptive function. In this paper, we make the following contributions. First, we present a revision of this model, characterized by stricter equilibrium conditions and superior explanatory power. Second, we present a typology of multiple realization that provides a plausible account of the di ff erences between across- and within-species multiple realization. Third, we perform a formal analysis of the dynamics of multiple realization that sheds light on the di ff erences between multiple realization at di ff erent levels of organization. ARTICLE HISTORY Received 25 March 2020; Revised 7 October 2020 KEYWORDS multiple realization; natural selection; evolutionary dynamics 1. Introduction Multiple realization occurs when a phenomenon is implemented by di ff erent realizers, and it is recalcitrant to a uniform physical explanation [Putnam 1967; Fodor 1974, 1997; Polger and Shapiro 2016]. A case in point is that of sex pheromones that attract individuals of the opposite sex, triggering the performance of behaviours related to sexual reproduction [Jacobson, 1972; Wyatt 2014]. In terms of chemistry, pheromones lack a common structure and consequently are not projectable. Yet, from the perspective of biology, pheromones constitute a natural kind and elicit a sys- tematic pattern of behaviours. Such biological regularities would pass undetected if regarded at the level of chemical implementation [Hoyningen-Huene 1997]. Multiple realization is the subject of considerable research engaging metaphysical, empirical, and theoretical perspectives. The literature on the metaphysics of multiple realization centres on the extent to which it is a sound alternative to reductive physic- alism [Loar 1981] and on how to specify the nature of the realizing relationship [Gillett 2003; Shoemaker 2007]. The research on the empirical underpinnings of multiple realization assesses evidence for or against it [Zangwill 1992; Polger 2004; Shapiro 2004, 2008; Aizawa and Gillett 2009], whereas the theoretical literature focuses mainly on its mechanism and scope. In the fi rst case, the goal is to fi nd an account spe- cifying how macroscopic invariances hold despite the absence of uniform realizers © 2020 Australasian Journal of Philosophy AUSTRALASIAN JOURNAL OF PHILOSOPHY https://doi.org/10.1080/00048402.2020.1839920 [Block 1997; Rosenberg 2001; Papineau 2010], in the second case, the aim is to explore species-speci fi c and species-wide instances of multiple realization [Block and Fodor 1973; Couch 2005, 2009]. The present paper is a contribution to these two streams of theoretical literature. In order to provide a mechanism for multiple realization, some authors postulate a model of selection in which realizers play an adaptive role [Macdonald 1992; Papineau 1992, 2009, 2010; Block 1997; Rosenberg 2001]. We call this the functional-cum-selec- tive account. The mechanism put forth by this approach relies on two features of natural selection — namely, variation and di ff erential replication. The main idea is that, whereas variation produces a continuous supply of potential realizers, di ff erential replication retains those that successfully perform an advantageous function [Rosen- berg 2001]. In this way, multiple realizers may come to coexist despite lacking a common physical property, and multiple realization is vindicated. In this paper, we argue that the functional-cum-selective approach needs revision. The main problem is that it focuses only on whether a realizer performs an adaptive function, disregarding the speci fi c fi tness of the realizers. We claim that, for this reason, the functional-cum-selective account is unable to explain why realizers that are apt to perform a task need not persist. To circumvent this problem, we provide a fi tness-based account of multiple realization whose upshot is that retained realizers that are subject to common selection pressures need to be equally fi t. We show that, with this requirement, the explanatory power of the functional-cum-selective approach becomes more restricted than previously thought. Furthermore, we argue that the condition of equal fi tness sheds light on the scope and the level of multiple realization. The former concerns the range of situations in which we can expect multiple realization to hold, and the latter relates to the organizational layer at which multiple realization occurs. With respect to the scope, the mainstream literature deals with across- and within-species multiple realization in a uniform way [Fodor 1974; Horgan 1993]. We argue that these two types of multiple realization should not be con fl ated when the within-species realizers are subject to common selection pressures. To support this claim, we develop a typology of multiple realization that speci fi es the dynamics of individual realizers, and show that the distinction between across- and within-species is inconsequential for the prevalence of multiple realization. What matters is whether the realizers compete within the same niche. Considering the levels of realization, the literature does not pin down the conditions under which di ff erent levels of organization may become multiply realized. To inves- tigate this matter, we model the dynamics of multiple realizers by means of an evol- utionary game theoretic set-up in which the evolutionarily stable equilibrium entails the coexistence of more than one realizer. Applying o ff -the-shelf evolutionary game theoretic results, we show that multiply realized behaviours at the population level may, but need not, entail multiple realization at lower levels of analysis. This result can be seen as a quali fi cation to Kim ’ s [1992] early insight concerning the coexistence of across-species multiple realization with species – speci fi c reduction. 2. Multiple Realization Model 2.1 Fodor ’ s Account of Multiple Realization In this section, we outline Fodor ’ s [1974] formalization of multiple realization. We adopt this characterization for two reasons. On the one hand, it is the canonical 2 GRACIELA KUECHLE AND DIEGO RÍOC representation in the literature, and, on the other, it provides a simple language with which to build up our argument concerning the mechanism behind multiply realized laws. We begin by presenting Fodor ’ s set-up. Let S be a law of a special science. In the language of fi rst-order logic, S can be written as follows: S 1 x S 2 x (1) According to this formula, all S 1 situations (that is, events in which x is an instan- tiation of S 1 ) induce S 2 situations (that is, events in which x is an instantiation of S 2 ). Keep in mind that, although this formula implicitly assumes that the relation- ship between S 1 and S 2 holds strictly, the laws of the special sciences are subject to exceptions [Fodor 1974, 1991]. In any case, the important feature for our purpose is that, because S is a law of a special science, neither S 1 nor S 2 is a predicate of basic physics. The mapping between realizers and special kinds is a central element of multiple realization. In this respect, multiply realized laws satisfy the following conditions [ibid.]: P 1 j x S 1 x , for j = 1 . . . n (2) P 2 j x S 2 x , for j = 1 . . . n (3) P 1 j x P 2 j x , for j = 1 . . . n (4) According to formulas (2) and (3), each P 1 j instantiates S 1 , and each P 2 j instantiates S 2 . The relationship between instantiation and realization should be understood in terms of metaphysical supervenience: saying that P 1 instantiates S 1 is tantamount to saying that S 1 supervenes on P 1 . This means that the occurrence of P 1 is a su ffi cient condition for S 1 [Kim 1992]. At the same time, the presence of S 1 does not entail the presence of P 1 , although it certainly entails the disjunction P 11 x _ P 12 x . . . _ P 1 n x . Finally, formula (4) states that, for j = 1 . . . n , each P 1 j is related to P 2 j in the same way that S 1 is related to S 2 in (1). Figure 1 represents this scheme. 2.2. An Extension of Fodor ’ s Account of Multiple Realization Fodor ’ s model presupposes a particular relationship between the realizers in the ante- cedent and the consequent. According to formula (4), each instantiation P 1 j of Figure 1. Standard multiple realization model (based on Fodor [1974]). AUSTRALASIAN JOURNAL OF PHILOSOPHY 3 predicate S 1 entails one and only one instantiation P 2 j of predicate P 2 ( j = 1 . . . n ). For instance, and in line with the example in the introduction, P 1 j ( j = 1 . . . n ) could rep- resent the di ff erent chemical instantiations of a mating pheromone ( S 1 ), and P 2 j ( j = 1 . . . n ) could represent species-speci fi c instantiations of mating behaviour ( S 2 ) triggered by each P 1 j ( j = 1 . . . n ). However, there are other types of relationships between predicates P 1 j and P 2 j that should be taken into account to fully understand the dynamics of multiple realization (section 4) in within and across species context (section 6). Figures 2 and 3 depict all possible cases of multiply realized laws for n = 2. Case 1 represents a situation in which the realizers of the antecedent and the con- sequent are linked by a bijective mapping. Case 2, on the other hand, represents a situ- ation in which those realizers are linked by a non-bijective relationship (that is, each realizer in the domain leads to any of the realizers in the codomain). Fodor ’ s model implicitly assumes that the realizers P 1 j ( j = 1 . . . n ) of predicate S 1 are independent of each other. The same holds for P 2 j ( j = 1 . . . n ) of predicate S 2 . The di ff erent realizers of the mating pheromone in our example are unrelated to each other. An important feature of the extension of the multiple realization model presented in this section is that it allows for di ff erent types of relationships among realizers, which are character- istic of certain cases of multiple realization. These interactions, when present, are indi- cated by means of dotted boxes. To appreciate this point, consider the scenario of an intrusion by a predator into the territory of a band of vervet monkeys and the corresponding defence by the latter [Cheney and Seyfarth 1990]. The aggression is multiply realized because any aggressor may invade the territory in two di ff erent ways, either by air ( P 11 ) or by ground ( P 12 ). This situation, in which the same individual can use either strategy, is indicated by putting both in the same dotted box. The behaviour of the owners of the territory is also multiply realized, as they may use two di ff erent behaviours to escape the intru- der — namely, jumping into a tree ( P 21 ) and hiding in the bushes ( P 22 ). The response of the territory owner is speci fi c to the intruder ’ s invasive behaviour in case 1, whereas, in case 2, each deterrent behaviour is a possible response to either form of attack. For instance, when velvet monkeys are attacked by ground, they can avoid the attack by jumping into a tree or by running further away. For this reason, the owner ’ s responses are in the same dotted box only in case 2. Case 1 situations can be illustrated by a law stating that the owners of the territory will jump into a tree when attacked by ground ( P 21 ) and will hide in the bushes when attacked by air ( P 22 ). The law depicted in case 2 states that the owners of the territory will jump Figure 2. Cases of multiple realization. 4 GRACIELA KUECHLE AND DIEGO RÍOC into a tree or hide in the bushes when attacked by ground ( P 21 ), and the same will happen when attacked by air ( P 22 ). If we consider Fodor ’ s account [1974], both cases are bona fi de instances of multiple realization. His main contention is that focusing narrowly on the type of intrusion and/ or the corresponding reaction would mean missing the generality of the mechanism behind territorial behaviour. The same would hold in the case of sex pheromones. The molecular composition of the pheromones and the chemical responses in the receiving organism will not provide information about the mechanism at hand. However, as we will see in sections 4 and 6, establishing a speci fi c connection between these realizers, as depicted by the dotted box, is important for understanding the workings of the selectional mechanism behind multiply realized laws. For this reason, we argue that it is not advisable to taxonomize them as equivalent. Figure 3 shows two further cases of multiple realization. In case 3, only S 1 is mul- tiply realized, meaning that all P 1 j ( j = 1 . . . n ) — namely, P 11 and P 12 — produce the same e ff ect P 21 . An example of case 3 would be a situation in which the intrusion is multiply realized but the deterrent behaviour is not. Finally, in case 4, S 2 is multiply realized but S 1 is not. In terms of the entry-deterrence example, the defender would use di ff erent strategies to deter the intruder, whose invasive behaviour would be invar- iant. We will return to these cases in section 5 and 6. 3. The Functional-cum-Selective Account of Multiple Realization According to Fodor [1974], multiple realization is a brute fact that need not be further analysed. However, many philosophers argue that the requirement that di ff erent rea- lizers cause similar e ff ects is problematic and that, unless a mechanism is found that explains how non-uniform realizers produce uniform results, multiple realization remains essentially puzzling [Macdonald 1992; Papineau 1992, 2010]. It is not obvious which mechanism could play that role. Common structure explanations would be the natural option, but they con fl ict with the very notion of multiple realiz- ation [Macdonald 1992]. If we account for S 1 x S 2 x in terms of common physical properties of the realizers, we certainly explain the special law. However, we do so at the price of abandoning multiple realization, because the latter requires disjunctive structures at the realizing level. To successfully explain multiply realized laws, two con- ditions must be satis fi ed: (i) a mechanism must be identi fi ed that is powerful enough to account for the uniformity expressed by S 1 x S 2 x , and (ii) this mechanism must not threaten the non-uniformity of the realizers in P 11 x _ P 12 x . . . _ P 1 n x or P 21 x _ P 22 x . . . _ P 2 n x . Common structure explanations satisfy only the fi rst condition. Figure 3. Cases of multiple realization. AUSTRALASIAN JOURNAL OF PHILOSOPHY 5 A signi fi cant strand of literature suggests that selective mechanisms may be able to account for the uniformity of special laws without compromising the requirement of non-uniformity at the level of the realizers [Rosenberg 1985, 2001; Papineau 2010]. In other words, advocates of the functional-cum-selective account argue that selectional explanations satisfy the above two conditions. Because the goal of our paper is to delve more deeply into this account, we present its main tenets. The fi rst tenet is that selection works as a fi lter within a certain population of traits, taking as input their exogenous variation and retaining those that are fi tter than their competitors in terms of producing an adaptive result [Godfrey-Smith 2014]. The concept of fi tness is crucial in selective explanations of multiply realized laws because it abstracts away from structural details and focuses only on outcomes [Sober 1984]. To illustrate its role, consider the case of gold fi sh sex pheromones. It is possible that, at some point, hormones that control egg development in female gold fi sh leaked into the water [Wyatt 2014]. As these hormones are a reliable cue of female sexual maturity, males whose olfactory receptors were sensitive to detect the hormones would fi nd females fi rst, thus gaining a reproductive advantage over other males. Female gold fi sh that secreted these hormones would bene fi t as well. In the long run, gold fi sh producing and detecting pheromones that coordinate these mating activities would outcompete those that neither produced nor received this information, thus increasing their share in the population [Sorensen 2015]. In addition to di ff erential reproduction guided by unequal fi tness, the functional- cum-selective account relies on phenotypic variation. That is, it assumes either the existence of di ff erent phenotypes or traits at some time or the presence of a mechanism continuously generating new ones. Going back to the example of sex pheromones, these are compound substances containing a rich array of molecules that can be rearranged through inclusion and exclusion in many di ff erent ways. The argument of the functional-cum-selective approach is that any arrangement of molecules that males can detect as a reliable signal of females ’ sexual maturity quali fi es for retention. If new con fi gurations emerge that fi t this description, physically non-uniform phero- mones may come to coexist. The reason is that selection is sensitive not to phero- mones ’ chemical structure but to their performance as mating coordinators. In fact, following the logic of this account of multiple realization, one could even argue that, because the list of molecular structures that support this coordination is open- ended, it would be surprising if pheromones were physically uniform. 1 In fact, there is an additional reason for the evolution of diversity in the chemical structure of pheromones. Animals live in ecosystems populated by other species. Therefore, they need to coordinate to compete not only with other conspeci fi cs but also with other species. In this respect, physically non-uniform pheromones provide the necessary speci fi city for animals to avoid sending information to the wrong species [Wyatt 2014]. In fact, very often, closely related species secrete pheromones that combine the same molecules in di ff erent ratios or that share some but not all of the molecules [ibid.]. This shows that, even in the presence of a basic chemical struc- ture, there are evolutionary pressures leading to diversity as a way of enhancing 1 According to the functional-cum-selective account, selection does not entail multiple realization. However, this account is committed to the presence of selection in instances of multiple realization. As David Papineau [2009] suggests, an argument against this account would be to identify a case of multiple realization that does not involve traits that are subject to either selection or intelligent design. 6 GRACIELA KUECHLE AND DIEGO RÍOC reproductive fi tness. Therefore, in addition to exogenous variation and blind selection, which are the pillars of the functional-cum-selective account, multiple realization may also be the result of the strategic nature of interactions among species. 4. The Fitness-Based Account of Multiple Realization 4.1 Modelling Fitness as a Continuous Measure The functional-cum-selective account measures the fi tness of each trait in terms of whether it is able to produce a given result or to perform a certain function [Papineau 1993, 2009]. In other words, the realizers retained by natural selection need to be apt to produce the outcome at stake. In this paper, we argue that this binary measure of fi tness misses an important aspect of the dynamics of multiple realization that bears on the conditions for the existence of multiple realization. In our entry-deterrence example of case 2, presented in section 2.2, all selected displays need to be e ff ective in protecting the territory. However, it is not hard to imagine that some displays will be more e ffi cient than others, either because they demand less e ff ort or because they repel the intruder faster or for a longer period of time. In any case, because deter- rence displays are likely to a ff ect the relative reproductive fi tness of the animals that adopt them, we can expect the eventual elimination of strictly dominated behaviours [Hofbauer and Sigmund 1998]. The main consequence of this dynamic is that the retained realizers P ij ( j = 1 . . . n ) will have to be — other things being equal — equally fi t (in reproductive terms) for the function for which they have been selected. In sym- bolic form, the condition for multiple realization is P ij F P ik ∀ j , k , and i = 1 . . . n , where the sign F denotes equal fi tness. If a certain display P ij were less fi t than another display P ik , then P ij would eventually be eliminated, meaning that it could not coexist with P ik In the sex pheromones example, males whose olfactory receptors are more sensitive at detecting reliable cues of female sexual maturity will fi nd females fi rst, thus gaining a reproductive advantage over other males with weaker detecting systems. As for females, those who produce pheromones that have a further reach and a stronger odour will enhance their chances of reproduction. In the long run, the di ff erence in the reproduction rates of female and male gold fi sh with a greater capacity to secrete and detect such odorant molecules, respectively, will lead to the elimination of rela- tively un fi t pheromones, even when the latter coordinate mating activities successfully [Wyatt 2014]. The continuous measure of the fi tness-based account imposes a novel constraint on multiple realization. We argue that this constraint bears on the di ff erences between the cases displayed in Figures 2 and 3. To illustrate this, in the remainder of this section we explore the repercussions of the equal fi tness condition on the typology introduced in section 4.1 by means of the intruder-defence game. In case 2, an intrusion of type P 11 can be averted by means of two deterrent beha- viours — either P 21 or P 22 . The same holds for an intrusion of type P 12 . We argue that, in this case, P 11 and P 12 are under competitive pressure to instantiate S 1 , and that, because both P 11 and P 12 can lead to either P 21 and P 22 , these last two will also be under competitive pressure to instantiate S 2 . According to our account, in this case multiple realization requires that P 11 F P 12 and P 21 F P 22 P 22 cannot be a better response to P 11 than P 21 when they coexist, because the fi tter realizer will eventually AUSTRALASIAN JOURNAL OF PHILOSOPHY 7 displace the other, leading to a single realizer in the consequent of the stated law. For the same reason, P 21 cannot be a better response than P 22 to P 12 Case 1, on the other hand, describes a situation in which each behaviour by the intruder elicits a unique and idiosyncratic response from the owner of the territory: an intrusion of type P 11 elicits response P 21 , and an intrusion of type P 12 elicits response P 22 . If we assume that strategies used against one type of attack will be even- tually tried (by error, perhaps) against another form of attack, we can expect P 22 to be a better response to P 11 than P 21 . Likewise, P 21 can be expected to be a better response than P 22 to P 12 . It is possible that, in the past, P 21 displaced P 22 as a response to P 11 , and that P 22 displaced P 21 as a response to P 12 . It is also possible that they were never under common selective pressures to respond to the same type of intrusion. In any case, we argue that, in case 1, P 21 and P 22 need not have the same levels of fi tness. Whereas the equal fi tness condition applies to P 21 and P 22 in case 2, it does not apply to them in case 1. The reason is that, in case 1, P 21 and P 22 do not compete with each other in the same niche (to facilitate the identi fi cation of realizers that are under common selective pressure, we enclose competing realizers in a dotted rectangle in every fi gure). A corollary of our analysis is that S 1 is multiply realized in cases 1 and 2, whereas S 2 is multiply realized only in case 2. In case 3, S 1 is multiply realized but S 2 is not. In an evolutionary set-up this could happen for two reasons. One is that, by sheer luck (for instance, a lack of su ffi cient vari- ation) or because of structural constraints [Gould 2002], no alternative realization of P 21 has emerged. Another reason is that P 21 has already been selected from a group of competing P 2 j s. Under any of these conditions, only the realizers of S 1 — namely, P 11 and P 12 — are subject to selection within the same niche. Therefore, multiple realiz- ation of S 1 requires that P 11 F P 12 . Finally, in case 4, only S 2 is multiply realized. Whereas there are no additional P 1 j s ( j = 2 . . . n ) competing with P 11 as realizers of S 1 , the realizers of S 2 — namely, the P 2 j s — are under competition. In this circumstance, multiple realization of S 2 requires that P 21 F P 22 Finally, notice that, in light of the typology spelled out in Figures 2 and 3, Fodor ’ s representation in Figure 1 could be interpreted in two di ff erent ways. It could display the case of realizers that are subject to common selection pressures — in the sense of competing against each other — or it could portray the situation of realizers whose dynamics are completely unrelated. Fodor and Papineau seem to be implicitly assum- ing the fi rst scenario, as they provide examples in which the realizers of the antecedent compete against each other. In section 6, we will return to the di ff erence between these cases after discussing across- and within-species multiple realization. 4.2. Evolutionary Dynamics of the Fitness-Based Account So far, we have looked at the dynamics of multiple realization informally by describing the selective process that will lead to the elimination of competing realizers with lower levels of fi tness. In this section, we analyse the dynamics in a formal setup to derive further conditions for the existence of multiple realization. Since we are interested in investigating the conditions for an equilibrium in which di ff erent phenotypes (rea- lizers) coexist, we analyse a game that has only one evolutionarily stable equilibrium in mixed strategies. Anti-coordination games, such as the hawk and dove game, are the canonical example of situations in which all the available phenotypes (realizers) coexist in the evolutionarily stable equilibrium. 8 GRACIELA KUECHLE AND DIEGO RÍOC Another reason for the introduction of a game theoretic analysis is that the entry- deterrence interactions discussed in section 4.1 assumed that the di ff erent types of intrusion were exogenously given. In general, both the invading and the deterring actions will be endogenously and conjointly determined. A valid set-up for these kinds of situation is a game-theoretic model. To illustrate this situation, which falls into our case 2, consider the scenario of animal contests, as discussed by Maynard Smith and Price [1973]. It is worth mentioning that, beyond animal contests, this game represents any situation where it is not a best response for every individual to adopt the same phenotype. In the simplest version of this game, animals meet pairwise to contest a territory and they have two possible strategies — hawk and dove . Hawk is a harsh strategy that an animal uses in an attempt to grasp the entire resource, by fi ghting for it if necessary. Dove, on the other hand, is an accommodating strategy oriented to sharing the resource. Call a the value of the resource and b the cost to obtain it ( a , b ). The four possible pay-o ff s are depicted in Figure 4. The pay-o ff s measure the value of the resource for the individuals, and this in turn a ff ects their reproductive potential. In this game, if two hawks or two doves meet, they share the territory. The di ff erence in pay-o ff s occurs because the hawks must bear the costs of fi ghting. If a hawk meets a dove, on the other hand, it wins the resource. According to these pay-o ff s, hawk is the best response to dove, and dove is the best response to hawk. If animals meet in pairwise encounters at random, the fi tness or pay- o ff of each strategy will depend on the chances of facing each behaviour, which in turn will depend on the proportion of animals employing each strategy. From a dynamic perspective, if we assume that the use of the two strategies increases in proportion to how well they performed in the previous period, relative to the mean population pay-o ff , then we observe that, at the population level, hawk will be advantageous if and only if the proportion of animals playing hawk is smaller than a / b . Under that circumstance, the proportion of animals using hawk will grow. Once the proportion of hawkish play exceeds a / b , dovish behaviour will bounce back, increasing its share in the population. The relative frequency of behaviours will reach an evolutiona- rily stable equilibrium when the proportion of hawks equals a / b = d At this point, if the population of animals is in fi nite, the strategies hawk and dove have the same expected fi tness. If we assume that P 11 ; Hawk , P 12 ; Dove , P 21 ; Hawk , and P 22 ; Dove , the realizers of the special kinds S 1 and S 2 can coexist if and only if the equal expected fi tness conditions, P 11 F P 12 and P 21 F P 22 , are satis fi ed. 2 Figure 4. One-shot hawk – dove game. 2 In fi nite populations, the condition of equal fi tness does not apply strictly. Relatively un fi t traits can persist over evolutionary time by genetic drift. AUSTRALASIAN JOURNAL OF PHILOSOPHY 9 Before discussing further implications of the fi tness-based account of multiple realization, we would like to make an additional comment concerning the evolutionary dynamics of the hawk – dove game. Although we assumed asexual reproduction, a poly- morphism may also occur in situations where phenotypes reproduce sexually. In this respect, Kokko et al. [2014] document the case of a species of birds with a two head- colour polymorphism where red-headed individuals produce signi fi cantly higher levels of testosterone and are behaviourally dominant over black-headed ones. The two types coexist, despite the fact that red-headed birds have higher reproductive success because they are less successful at rearing their o ff spring. To assess the theoretical validity of the hawk-dove model, Kokko et al. perform a simulation of the game with genetic inheri- tance. They fi nd that the polymorphism requires assortative mating, which is adaptive because of genetic incompatibilities of hybrid o ff spring fi tness. The bottom line is that the evolutionary dynamics of the hawk and dove game can be robust to genetic inheri- tance of traits. 5. Levels of Organization and Multiple Realization The condition of equal expected fi tness necessary for coexistence derived in the pre- vious section has several implications. First, even when a proportion d of the popu- lation uses hawk and a proportion 1 − d uses dove, there are in fi nitely many ways in which this proportion can be implemented at the individual level [Maynard Smith 1982]. We show two extreme cases in Figure 5. At one end of the spectrum (left-hand side of Figure 5), the population consists of two types — one always playing hawk and the other always playing dove. At the other end (right-hand side of Figure 5), the population consists of only one type: it sometimes plays hawk and sometimes dove. In the fi rst case, d per cent of the population will be pure hawks, and 1 − d per cent will be pure doves. In the second case, each individual in the popu- lation plays hawk and dove with probabilities d and (1 − d ), respectively [Maynard Smith 1974, 1982]. Between these extreme cases, there are in fi nite possible con fi gur- ations of polymorphic populations, yielding the same relative frequency of behaviours at the population level. An important upshot of the fi tness-based analysis is that multiply realized beha- viours at the population level need not be a sign of multiple realization at the individual level. A case in point is a population of individuals who are committed to the behaviours displayed on the left-hand side of Figure 5. At the individual level, there is a reduction in Figure 5. Multiple realization and levels of selection. 10 GRACIELA KUECHLE AND DIEGO RÍOC physical types. This is because some individuals always play hawk and others always play dove. In this case, the population is polymorphic, and the individuals are mono- morphic (namely, bound to one type of behaviour). In contrast, the right-hand side of Figure 5 shows a polymorphic population consisting of polymorphic individuals who play hawk and dove with probabilities d and 1 − d , respectively. In this con fi gur- ation, the evolutionarily stable outcome is reached by only one phenotype with variable behaviours. On the left-hand side, hawks and doves have the same expected fi tness, and, on the right-hand side, every individual is indi ff erent between these two behaviours, as they entail the same expected fi tness. Although the two populations are physically di ff erent, in equilibrium they have the same proportion of hawkish and dovish beha- viours, which are on average equally fi t (in terms of reproduction). The dynamics displayed on the right-hand side of Figure 5 are compatible with at least two causal mechanisms [Maynard Smith 1982]. Individuals may adopt multiple behaviours either because they have an internal mechanism that randomizes between hawkish and dovish behaviours or because they respond to external cues, such as size, arrival, and ownership, provided that these occur randomly and induce the equilibrium proportion of hawkish behaviour. Thus far, we have limited our analysis of the hawk and dove game to the symmetric (or one-population) case in which there are no discernible di ff erences among the players. This characterization is not always warranted. There are two main sources of asymmetry in this game. First, individuals who are otherwise identical might play di ff erent roles (one may be the owner of the territory and the other the intruder), and, second, some individuals might be physically di ff erent (one might be bigger than the other). Consider, again, the pay-o ff table in Figure 4. It is clear that players could earn more on average if they coordinated their actions by means of a conditional strategy such as ‘ play hawk if owner and dove otherwise. ’ With such a strategy, indi- viduals would earn a in one role and 0 in the other, thereby avoiding the costs of a fi ght. If the proportion of owners and non-owners was a / b , this strategy would yield an expected fi tness of ( b − a ) a b ( ) , which doubles the expected fi tness of the sym- metric game. For this reason, in the presence of asymmetry this behaviour would spread out and eventually displace any alternative behaviour [Selten 1980]. Individuals do not need alternate roles in order for this equilibrium to hold if they belong to di ff erent populations or if they have observable physical di ff erences (for instance, size). If pairwise interactions pit only one population or physical type against the other, then, in equilibrium, populations would specialize, thereby earning di ff erent pay-o ff s. If, on the other hand, interactions occurred within one population, as we assumed in section 4.2, the conditional strategy referred to above would be played by everyone. The upshot for multiple realization is that the equal fi tness con- dition derived earlier need not hold for asymmetric populations, because the pheno- types do not compete against each other. We will return to this issue in section 6. As an example of this last situation, consider a game in which the phenotypes (or realizers, from the point of view of multiple realization) are two possible chemical structures of a sex pheromone (S 1 and S 2 ) and two male receptor systems (M 1 and M 2 ) within the same species. Assume that M 1 is better than M 2 at detecting S 1 , and that M 2 has an advantage over M 1 at receiving S 2 . This is a coordination game with two evolutionarily stable equilibria (S 1 , M 1 ) and (S 2 , M 2 ). Under asexual replication — that is, when each phenotype produces replicas of its own type — the system will AUSTRALASIAN JOURNAL OF PHILOSOPHY 11 converge to one of the evolutionarily stable equilibria (depending on the initial con- ditions), thus averting a polymorphism. A polymorphism with two chemical structures that have their own male receptor systems could still occur if (S 1 , M 1 ) and (S 2 , M 2 ) belonged to two di ff erent species. Because the coordination with conspeci fi cs and the anti-coordination with other species is fi tness-enhancing, the evolutionary dynamics of this game may lead to chemical structures and receptors that vary across species. Finally, we would like to point out that games whose evolutionary dynamics converge to one strategy (most prominently, games with a dominant strat- egy) will not be relevant for multiple realization. 6. The Scope of Multiple Realization The typology of multiple realization presented in section 2.2 and the evolutionary dynamics discussed in section 4.2 set the stage for discussing further implications of our account that shed light on the distinction between within and across species mul- tiple realization. In the hawk-dove example, the potential deterrence displays ( P 1 j ) ( j = 1, 2) are under common selective pressures to perform a certain function. In other words, they compete within the same niche. This competitive relationship (illus- trated by the dotted boxes in Figures 2 and 3) means that the realizers can eventually substitute for each other. 3 Our argument is that if such competing traits coexist within a niche then they will have to be equally fi t. Note that this condition does bear on beha- viours that occur in response to di ff erent external or parametric conditions unrelated to the behaviour of the intruder. For instance, the deterrence display could depend on the size of the intruder, the health of the owner, the weather, or various features of the territory. These responses are probably adapted to speci fi c exogenous conditions, and are not ‘ alternative ’ , in the sense of competing within the same niche. For that reason, they do not need to provide an equally fi t response to intrusion. 4 As another example of this exception, consider, again, the example of sex phero- mones. The molecular structure of these pheromones has been found to vary according to how the message is sent (on wind versus water) and received (on the nose or the antenna of the recipient) [Wyatt 2014]. We can expect certain molecular structures to be more adequate for certain characteristics of the means of transportation and the detection system of the receptors. Such physical diversity does not fall into the cat- egory of competition within a niche, and it is therefore not subject to the equal fi tness condition. For this reason, this example is illustrated by case 1 in Figure 2. We use the c