Z theor BioL (1987) 125, 351-360
Partial Bird Migration and Evolutionarily Stable Strategies PER LUNDBERG
Department of Wildlife Ecology, Swedish University of Agricultural Sciences, S-901 83 Umed, Sweden (Received 13 October 1986) Partial migration in birds is analyzed from an evolutionarily stable strategy tESS) point of view and it is argued that frequency-dependent selection of tactics (i.e. migration and residency) should be considered. Since the empirical evidence for the condition-dependent choice due to individual asymmetries cannot be ignored, the possibility that partial migration is a mixed ESS at the individual level is excluded. Nonetheless, a mixed ESS at the population level (i.e. a genetic dimorphism) is possible, albeit that the experimental and logical evidence recently put forward are ambiguous. It is suggested that partial migration can be regarded as a conditional strategy with frequency-dependent choice. The individual asymmetries (e.g. age, sex, dominance position), acting against a complete fitness balancing of tactics, and the frequency-dependent choice, tending to equalize fitnesses, are analyzed. Whether this system will result in tactics with equal fitness payoffs is further discussed in relation to the life history consequences of migration and residency.
Introduction For birds in seasonal environments in north-temperate areas, breeding is restricted in time, and in winter the food resources are often so small that there usually is severe intraspecific competition for them. Given these resources, however, it is unlikely that an individual will fail to survive to the next breeding season (if we are ignoring predation). Suppose also that the individuals have the option to leave the breeding area in autumn for wintering elsewhere in order to reduce the increased risk of mortality due to food shortage. On the other hand, this round trip migration is costly as well. In this situation partial migration might evolve, i.e. some individuals stay in the breeding area the whole year (residents), whereas others migrate to areas where the intraspecific competition is relaxed (migrants). Partial migration is a rather common p h e n o m e n o n among temperate-zone birds (e.g. Lack, 1944, 1968; Gauthreaux, 1978, 1982; Ketterson & Nolan, 1982, 1983). Recently, attempts have been made to recognize how partial migration can be maintained by natural selection and how the two behavioural alternatives are chosen by the individual birds. The intraspecific variation in migratory habits has been summarized by for example Baker (1978), Gauthreaux (1982), Ketterson & Nolan (1983) and Swingland (1983). Partial migration is obviously a game between two behavioural (and consequently life history) alternatives within the population and one could argue that ESS (evolutionarily stable strategy) methodology might be appropriate for analyzing the evolution and stability of such a system. To my knowledge, only Swingland (1983) 351 0022-5193/87/070351 + 10 $03.00/0
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has tried to do this so far, albeit both conditional strategies and mixed ESSs at the population level have been implicitly suggested earlier. There are, however, examples of formal treatments of migratory behaviours in birds (e.g. Cohen, 1967; Baker, 1978). These are pure optimization models and have not considered frequencydependent selection. In this paper I explore the possibility of applying ESS thinking to partial migration in birds, hence introducing the suggestion that the decision between the alternatives is dependent on how all other members of the population are behaving. Analytical solutions will not be derived, the intention is merely to point out future ways of considering these problems. The reasoning has emerged with birds in mind, but might be valid for other creatures under similar circumstances.
Frequency-independent Partial Migration Currently, two main views dominate the literature on differential bird migration, both ignoring the fact that frequency-dependent selection might regulate the proportion of migrants and residents in a population. Here, as well as in the following, I will use ESS terminology although this has rarely been the case in the original studies. CONDITIONAL
It is commonly assumed that partial migration is a pure strategy specifying the two condition-dependent tactics. Certain asymmetries in individuals, e.g. age, sex, experience, body-size and dominance position specify the conditions on which the decision whether to migrate or not is based. Ketterson & Nolan (1983) and Swingland (1983) should be consulted for reviews. Common to most of the studies is that they explicitly have regarded intraspecific competition as the ultimate cause for the evolution of differential migration and that the proximate regulation depends on one or several of the factors mentioned above (e.g. Ketterson & Nolan, 1976; Gauthreaux, 1978; Myers, 1981; Dolbeer, 1982; Lundberg, 1985a). In a conditional strategy, the fitness payoffs of the two tactics do not necessarily have to be equal. As a matter of fact, they are often not (e.g. Dominey, 1984), and the inferior tactic is just a way of making the "best of a bad job" (Dawkins, 1980). The problem of fitness balancing between tactics has not been much discussed (but see Baker, 1978 and Ketterson & Nolan, 1982), although it has been considered for alternative dispersal strategies in other organisms than birds (e.g. Hamilton & May, 1977; Comins et al., 1980). As will be shown in later sections, there is probably no straightforward solution to the problem of fitness balancing for partial migrants. GENETIC
Here we meet one of the ambiguities in earlier versions of analyses of partial migration. A balanced genetic dimorphism, as proposed by Berthold & Querner (1981, 1982) and Biebach (1983), will only result if the fitness of the genotype is
related to its frequency (Fisher, 1930; Maynard Smith & Parker, 1976; Maynard Smith, 1982). This is not even implicitly assumed in the papers by Berthold & Querner and Biebach. However, Biebach (1983) suggested that the dimorphism would be maintained by a bet hedging strategy by the parents which produce offspring of the two morphs ensuring survival and subsequent reproduction of at least a fraction of the clutch, irrespective of varying winter conditions. How the proportion of migrant and resident offspring would be attained and whether the fitness of the two morphs would balance was not clearly stated. The bet hedging strategy will be critically examined in a following section.
Frequency-dependent Partial Migration There are probably good reasons to believe that partial migration in birds might be frequency-dependent, i.e. the fitness payoffs, and therefore the proportions of migrants and residents, are dependent on how other members of the population are behaving. There are at least three hypothetical possibilities as to how the frequencydependence could work. (1) Partial migration is a mixed (stochastic) ESS with two phenotypic alternative tactics in which payoffs are equal. (2) Partial migration is a balanced genetic dimorphism. This is a mixed ESS at the population level, i.e. the two strategies coexist in an evolutionarily stable state (ESSt). The formal analyses of the two kinds of mixed ESSs are identical, but the biological meaning is obviously very different. (3) Partial migration is regulated by frequency-dependent choice, i.e. a conditional strategy specifies tactics according to their relative frequencies (Dominey, 1984). It is still an open question whether the fitnesses of the tactics in this situation are indeed equal or if the asymmetries in individuals (making the choice conditional) can act against a complete equalization. MIXED
In the following I will develop a simple graphical model for partial migration without considering any conditional elements. However, it is a good starting point for the further discussion when asymmetries in individuals are included. Let p (0 -< p <- 1) be the proportion of the population that leaves the breeding area in autumn and returns the subsequent spring. The resident proportion is then 1 - p . Let also the winter conditions in the breeding area determine the survival chances of the residents. Sometimes the winters are mild, providing the individuals with a relatively large food supply and low thermal stress, and sometimes the winters are harsh with high mortality risks due to starvation. I here restrict the winters to be either mild or harsh, i.e. there is no continuous gradation of the winter conditions. This may be a quite unrealistic assumption but it does not seriously alter the principal reasoning. If the winters were always harsh, the periodicity of harsh winters (z) would be 1. On the other hand, if the winters were always mild, the periodicity of harsh winters would of course be 0. Finally, if the variation in winter conditions between years is purely stochastic, on average every second winter would be harsh ( r = 0 . 5 ) . Of course, ~" can take any number between 0 and 1 depending on local climatic conditions.
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FIG. 1. Partial migration as a mixed ESS. W,,, and W, are the fitness functions for migrants and residents, respectively, in relation to the proportion that leaves the breeding area in autumn (p). p* is the equilibrium proportion of migrants if the winter conditions vary randomly (r = 0.5), where r is the periodicity of harsh winters.
Let RS denote the reproductive success of an individual (i.e. the number of offspring produced in a summer and surviving to the beginning of the non-breeding season). Then RS,, < RSr, where m and r denote migrants and residents, respectively. RS,, is smaller than RSr since migrants generally start breeding later and are in a worse position with respect to choice of territories a n d / o r nest-sites (cf. Schwabl 1983). For migrants, the winter survival (s,,, 0<-s<-1) is constant, i.e. independent of how large a proportion that migrates from the breeding area. This might be a doubtful assumption but does not say that the winter survival is density-independent. The migrants are simply spread out over a relatively large wintering area and the densities of every particular wintering ground are only slightly influenced by the proportion that leaves the population we have in focus. The winter survival of the residents (st), on the other hand, is positively related to p since it is assumed that the food supply is strongly limiting the wintering population at the breeding grounds. The exact form of this function is not crucial here, but it is assumed to take the form of a sigmoid. Finally, let the fitness (W) of an individual be defined as
w = RSs.
Thus, Wm is constant for all p (since RS,, and s,,, are constant) and W~ is positively related to p. In other words, Wr is frequency-dependent. In Fig. 1 W,, and W~ are illustrated in relation to p. Wm is a horizontal line and independent of the winter conditions at the breeding ground. Three examples of W~ functions are shown. If r = 0 (always mild winters), the survival chances of the residents would be relatively high and W~ would be greater than W,, t'or all p. That is, individuals would always do better by being resident. If r = 1 (always harsh winters), the substantially reduced winter survival chances of individuals staying in the breeding area would shift the Wr function downwards, possibly so far that W,,, always lie above Wr for all p. In
Fig. 1, however, there is a p when IV,, = Wr, i.e. at this certain p both alternatives are equally profitable. This is also the case in the last example ( r = 0 . 5 ) , which could illustrate a possible situation in areas where partial migration is frequent. Thus, with varying winter conditions, there is an equilibrium proportion p* such that if the fraction p* migrates and l - p * is resident, both alternatives would be equally favoured. The same would be true if all individuals migrated with the probability p*. The system modelled above could either be maintained by a genetic dimorphism or as a mixed ESS with two phenotypic tactics. A genetic dimorphism would mean that the two strategies coexist in an ESSt with equilibrium proportions p* and 1 - p * . Irrespective of winter conditions, or for instance dominance position, migrants always migrate and residents always stay in the breeding area and individuals should not change behaviour between years. If the system is a mixed ESS at the individual level, no genetic determination should be found. The choice of tactics should be purely stochastic, finally adjusted so that the equilibrium frequencies are maintained. This case requires that there are no asymmetries between individuals and that they are perfectly capable of "playing the field" (Dawkins, 1980; Maynard Smith, 1982). FREQUENCY-DEPENDENT
Here the system has a conditional element and the tactics do not necessarily give equal fitness gain, i.e. the situation in a purely conditional strategy. Let, for instance, social dominance position be such an individual asymmetry specifying the condition on which the decision whether to migrate or not is based. There is support for such an assumption (e.g. Gauthreaux, 1978; Lundberg, 1985a), albeit there are reservations to this hypothesis (cf. Ketterson & Nolan, 1983). A conditional strategy, however, is not necessarily devoid of frequency-dependence (Dominey, 1984). Figure
FK;. 2. Partial migration as a frequency-dependent choice. In contrast to Fig. 1, asymmetries between individuals are here considered, i.e. they can either be socially dominant (dora) or subordinate (sub) which affects the fitness functions. In this particular case, dominant would do better if they stayed and subordinates would do better if they migrated. Note that the fitness payoffs for migrants and residents are not equal in this case.
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2 illustrates a situation where the fitness of residents and migrants are both frequencydependent and dependent on dominance rank. For simplicity, the population is divided into dominants and subordinates only, i.e. two extreme and oversimplified categories. Figure 2 is based on the same assumptions that produced Fig. 1, though without involving different winter conditions. In this particular situation residency would clearly be selected for (recall the situation when r = 0 in Fig. 1) if there are no asymmetries between individuals. However, subordinate residents, whose fitness is low for all p, would do better by adopting the alternative tactic, i.e. migration. In this situation we cannot explicitly predict any equilibrium proportion of migrants and residents, which in an unconditional strategy would be p * = 1. By their low ranks, the subordinates are forced to adopt a tactic which makes the "best of a bad job" and the proportion of migrants and residents is dependent on the relative frequencies of dominants and subordinates in the population. A situation when the fitness function for subordinate residents is shifted upwards, for instance, due to improved winter conditions, is shown in Fig. 3. For any p, dominants should still always stay in the breeding area, but now there will be an equilibrium proportion of migrants (p*) determined by the relative fitness payoffs for migrants and resident subordinates. Thus the fitnesses of migrant and resident subordinates is balanced, but will always be lower than for dominant birds. The frequency-dependent choice tends to balance the fitness payoffs of tactics, whereas the asymmetry between individuals (dominant or subordinate) tends to favour different payoffs for different tactics.
W r (sub)
Wm (dom, sub)
FIG. 3. A similar situation as in Fig. 2. Here the increased winter survival for residents has altered the fitness functions, p* denotes the equilibrium proportion of migrants, here determined solely by the relative fitness payoffs a m o n g the subordinates.
PARENTAL BET HEDGING Biebach (1983) suggested that partial migration in birds could be regulated by a genetic dimorphism in which the parents were producing both resident and migrant
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of[spring as to assure survival and high reproductive rate for at least some of the progeny irrespective of randomly fluctuating weather conditions. This would then be a way for the parents to optimize their inclusive fitness. The outcome of such a system is illustrated in the following, and is a more formal extension of Biebach's verbal version. Let the parents be able to regulate the proportion of migrants (q) and residents ( l - q ) in the brood. Let also "Next Generation Fitness" (NGF) be the genetic contribution that the parent's offspring make to the following generation (number of grand-children). Then N G F = (RS,,s,,q)/2 + (RSrsr(1 - q))/2
is the parent's contribution to the gene pool of the next generation. Let also RS, s and ~- vary in the same manner as described for the case of a mixed ESS. Then there is an optimal proportion (q*) of the brood that should become migrants and 1 - q* should become residents in order to maximize NGF. This is illustrated in Fig. 4. If ~"= 0, only a small fraction of the brood should be invested in migrants. If ~-= 1, the optimal investment would be to produce migrants only. With unpredictable winter conditions (~" = 0.5) q* is intermediate. If all individuals in the population would maximize N G F (i.e. producing q*% migrants and l - q * % residents), the proportion of migrants in the population would eventually be q*. However, in Fig. 1 the equilibrium proportion of migrants was predicted from the individual bird's point of view (p*) which does not necessarily equal q*. Numerical simulations, using equations (1) and (2), of hypothetical populations always result in q* greater than p* given equal numerical expressions for reproductive successes and survival in both cases. The parents' interest is hence to force more offspring to migrate than would be optimal from the individual's point of view. Suppose however, that the population is at q* ( q * # p*). Hence, the fitness of migrant and resident offspring are unequal because q * # p* (cf. Figs 1 and 4). Therefore, a female that abandoned the q* strategy and produced the fitter type of
FIe;.4. The optimal proportion of migrants (q*) in the brood if the parents were bet hedging and the winter conditions vary randomly ( r = 0.5), where T denotes the periodicity of harsh winters. Note that q* is usually not a stable equilibrium (see text).
offspring only, would be fitter than the average parent. Thus, q* is not a stable equilibrium frequency but will always eventually be equal to p* (Maynard Smith, in lilt.). Biebach's (1983) conclusion that partial migration has evolved as a bet hedging strategy thus cannot be so easily accepted. Discussion
In wintering bird populations in temperate areas, intraspecific competition for food resources is generally assumed to be significant (e.g. Fretwell, 1980; Pulliam & Millikan, 1982) which would be the ultimate cause for partial migration (Cox, 1968). By migrating, an individual would benefit from greater survival chances in benign wintering areas, but would face costs due to the hazardous migratory journey and possibly due to a somewhat delayed breeding the subsequent spring (Schwabl, 1983). Here, I have briefly discussed current ideas of how such a system of two alternative behaviours might be maintained in a population. I have also argued that the formerly neglected possibility of frequency-dependent selection should be considered. Surprisingly, this was not done in the original studies claiming that partial migration is a balanced genetic dimorphism (Berthold & Querner, 1981, 1982; Biebach, 1983). Notwithstanding the possible ambiguities of the kind of experiments supporting the dimorphism hypothesis, the fact that individuals may change from being migrant to resident (Schwabl, 1983), makes this idea equivocal, albeit its attractive simplicity. Moreover, as shown by Cade (1980, 1981) and discussed by Dominey (1984), the heritability of a trait does not necessarily mean that the behaviours are not conditiondependent. The genetic differences might merely reflect differences in switch point, i.e. when a certain condition is experienced as initiating, for instance, migration. Finally for reasons shown in the previous sections, the idea of parental bet hedging might be questionable. The empirical support for the condition-dependent partial migration is substantial (e.g. Gauthreaux, 1978, 1982; Myers, 1981; Dolbeer, 1982; Schwabl, 1983; Swingland, 1983; Lundberg, 1985a) and current discussion is mainly focused on the problem of determining the condition, or possibly conditions, on which the decision whether to migrate or not is based (Ketterson & Nolan, 1983). The point here has been to go beyond this discussion and to emphasize that the study of partial migration would benefit from ESS thinking. The way this has been done here is probably an oversimplification of the nature of the system, but I believe it is important to point out a slightly novel approach to these questions (cf. also Swingland, 1983). It should be important to understand whether in addition to the conditiondependence also frequency-dependence plays any role in the regulation of partial migration in birds. If so, how does that influence fitness balancing between the two alternatives? Earlier studies of the phenomenon emphasized the importance of fitness balancing (e.g. Lack, 1968; Haartman, 1968; Baker, 1978), but as shown here and by Dominey (1984) a complete equalization of the fitness payoffs is not a necessary condition for this system to persist. As Dominey puts it: "It would be
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interesting to consider the interaction between frequency-dependent choice, tending to balance the fitness gains of tactics, and internal and external asymmetries tending to favour different fitness gains for different tactics". In partial migratory birds this conflict has not yet been examined more closely. An understanding of the evolutionary mechanisms of partial migration would also give insight into the life history consequences of migration and residency, respectively. As pointed out by Greenberg (1980) and further discussed by O'Connor (1985), Pienkowski & Evans (1985) and Lundberg (1985b), there is a mutual interdependence between migration and reproduction in birds. For example, the productivity of migrants should be lower than in residents (e.g. Greenberg, 1980; Schwabl, 1983; Lundberg & Silverin, 1985), not only in terms of brood size, but also in the number of broods raised per year, partly because a somewhat delayed start of breeding. This should also hold true both between species as well as between and within populations of the same species. The delayed breeding probably also influences the asymmetry between individuals per se, since a later hatching might lower the chances to attain high dominance positions. Earlier hatching, on the other hand, would possibly make those nestlings more experienced and give them greater opportunities to develop site dominance than their later conspecifics (cf. Nilsson & Smith, 1985; Lundberg, 1985b). Again, if these asymmetries do skew the fitnesses or whether, for example, increased survival chances in benign wintering areas can be great enough to equalize the fitnesses of migrants and residents, is still uncertain. Torbj6rn Fagerstr6m and Jan Ekman criticized earlier drafts of the manuscript and I am particularly indebted to John Maynard Smith for invaluable comments.
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