Evol Ecol (2010) 24:479–489 DOI 10.1007/s10682-009-9320-6 ORIGINAL PAPER
Adaptive branching in source-sink habitats Jennie Nilsson Æ Jo¨rgen Ripa
Received: 9 June 2008 / Accepted: 7 August 2009 / Published online: 29 August 2009 Ó Springer Science+Business Media B.V. 2009
Abstract Evolution and ecological diversification in a heterogeneous environment is driven by an often complex interplay between local adaptation and dispersal between different habitat types. Heterogeneous environments also easily generate source-sink dynamics of populations coupled by dispersal. It follows that local adaptation and possible adaptive radiation almost by necessity involves adaptation to a (pseudo-)sink habitat, which is considered unlikely. We here study a model of ‘parapatric branching’ with this special focus on the spatial ecology of the process. We find that evolutionary branching can display a sequence of alternating adaptations to the source or the sink. In some circumstances a true sink can become a pseudo-sink through adaptation to the corresponding source habitat. The evolutionary endpoint is a spatially structured community consisting of two source populations with one corresponding sink or pseudo-sink each. Our results shed new light on the interpretation of extant source-sink systems and the process of parapatric branching. Keywords Source-sink dynamics Local adaptation Parapatric branching Migration Dispersal
Introduction Adaptation to a heterogeneous environment is often considered one of the major processes generating diversity of organisms on earth (e.g., Schluter 2000). Local adaptation, gradually leading to increased ecological divergence and potentially new species, is however not as straightforward as it might seem. There is a strong tension between the arising of local adaptations on the one hand, and dispersal or migration between different types of habitats on the other hand (Lenormand 2002). A too low rate of dispersal will
J. Nilsson (&) J. Ripa Department of Theoretical Ecology, Ecology Building, Lund University, 22362 Lund, Sweden e-mail:
[email protected]
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prevent the exposure to novel environments and thereby preclude selection for traits better suited in such environments. It is also hard for a species to adapt to an environment in which the local population is dependent on immigrants for its persistence, a so called sink population (Holt and Gaines 1992; Kawecki and Holt 2002). In a sink population all individuals have negative fitness (Holt 1985). A so called pseudo-sink population would persist without immigration but is kept above carrying capacity due to a net inflow of migrants, which again gives all individuals negative fitness (Holt 1985; Watkinson and Sutherland 1995). Mutant types will also experience negative fitness in both types of sinks, as long as mutations are small and generate only small deviations from existing phenotypes. Consequently, a gradual adaptation to a sink habitat requires dispersal in both directions between the ancestral source population and the sink, such that an individual in a sink has a fair chance to disperse to a source and get positive fitness on average (Kawecki and Holt 2002). However, if the rate of dispersal is too high, migrants from a source population will swamp a local gene pool and thus prevent local adaptation (Lenormand 2002). Put another way, a too high dispersal will reduce selection for local habitats and instead favour an intermediate, generalist strategy (Brown and Pavlovic 1992). Despite the possible hurdles to local adaptation inflicted by dispersal between habitats, local adaptation is most likely a common evolutionary process, at times also leading to parapatric speciation. If the necessary emergence of reproductive isolation is put aside for a moment, parapatric speciation involves precisely the processes described above—adaptation to habitats of different character despite considerable gene flow between them. Several theoretical studies have investigated the possibility of what we will call parapatric branching—the evolutionary branching (sensu Geritz et al. 1998) of a single, asexual, type into two ecologically diversified types, each specialised on one of the two habitats connected by migration. Brown and Pavlovic (1992), Mesze´na et al. (1997) and Day (2000) all came to the same general conclusion: parapatric branching will occur if: (1) the evolutionary trade-off between the two habitat types is of intermediate strength and (2) migration rate is not too high. A too strong trade-off makes the intermediate, generalist type an evolutionary repellor and prevents branching. A too weak trade-off makes the generalist strategy a global ESS, i.e., no other strategy can invade the system. Finally, too much dispersal can also weaken selection for specialisation on one habitat or the other and make the generalist strategy an ESS. Although parapatric branching has been analysed in some detail already, little attention has been paid to the spatial ecology of the two incipient species. More precisely, we ask: What are the predicted patterns of source-sink dynamics before and during the branching? Will there be adaptation to a source habitat or sink? What is the final outcome? Assuming migration continues, both types will be represented in both habitats even after the branching, but will it necessarily be one source and one sink population? Here we investigate a model similar to earlier models, but with added biological realism and this different perspective. Also, we examine the properties of the final coalition. We find that the process of parapatric branching involves periods of source-sink dynamics with adaptation to the source or the sink, or both, driven by selection for local adaptation or evolutionary character displacement. The end result is two specialist types with one source and one sink, or possibly pseudo-sink, population each. During branching, adaptation to the source habitat may ‘drag’ a corresponding sink population through an adaptive valley to be converted from a true sink to a more ecologically persistent pseudo-sink. Our results give new insights about the origin of natural source-sink systems and the process of parapatric speciation.
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Fig. 1 A schematic figure of the model. Two habitats have the same kind of resources but differ in local abundance (white and black bars). The habitats are connected by two-way migration
The model We here present a model of a consumer feeding on two discrete resources in two habitats connected by migration (see Fig. 1). The fact that both resources are present in both habitat types makes possible (for some parameter values) the local coexistence of two specialist consumers, even in the absence of dispersal. We point this out because it is an important model feature to some of our results. A similar model with discrete resources, but only one habitat, was analysed by Rueffler et al. (2006). The consumer individuals in this model compete through resource utilisation. All individuals are assumed to have a heritable, continuous trait u, which determines their resource specialisation. We also assume asexual reproduction. At u = -1/2, a consumer is specialised on the first resource, R1 (uR1 = -1/2), and u = ?1/2 implies specialisation on the other resource, R2 (uR2 = ?1/2). The consumer morph is able to change its trait value through gradual evolution of u between these two specialist strategies. For simplicity, we assume that the resource dynamics are much faster than the consumer dynamics, such that they can be analysed on separate time scales. If only one consumer morph (u) is present, the fast dynamics of resource i within patch j are given by: dRi;j ¼ Ii;j ai ðuÞNj ðuÞRi;j ðtÞ di Ri;j ðtÞ; i; j ¼ 1; 2 dt
ð1Þ
where Ri,j is local resource abundance, Ii,j is a constant inflow of resources, ai(u) is the attack rate of the consumer on the resource, di is the death rate or outflow rate of the resource and Nj is local consumer population size, which is considered constant on this time-scale. The attack rate ai(u) is determined by the distance in trait space between the consumer with trait value u and the resource i with trait value uRi , and is given by the Gaussian function:
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ai ðuÞ ¼ a0 e
ðuuRi Þ 2r2n
;
ð2Þ
The closer u is to uRi the more likely is the consumer to eat from resource i. a0 sets the maximal attack rate and is here chosen equal to one without loss of generality (rescaling of resource or consumer density allows an arbitrary choice of a0). The parameter rn is the niche width of the consumer, which has a tight correspondence to ‘trade-off strength’ in earlier models. A large rn makes an intermediate phenotype (u close to 0) reasonably good at consuming both resources, and therefore corresponds to a weak trade-off. By the same token, a small rn corresponds to a strong trade-off. Setting Eq. (1) equal to zero and solving for Ri,j gives the equilibrium resource level: Ri;j ðu; NÞ ¼
Ii;j ai ðuÞNj ðuÞ þ di
ð3Þ
On the longer time scale of consumer growth, the per capita growth rate of the consumer subpopulation in patch j is given by: f u; R1;j ðu; NÞ; R2;j ðu; NÞ ¼ c1 a1 ðuÞR1;j ðu; NÞ þ c2 a2 ðuÞR2;j ðu; NÞ: ð4Þ Given that the resource will be at ecological equilibrium, we can write: fj ðu; Nj Þ ¼ f u; R1;j ðu; Nj Þ; R2;j ðu; Nj Þ ¼
c1 a1 ðuÞI1;j c2 a2 ðuÞI2;j þ a1 ðuÞNj ðuÞ þ d1 a2 ðuÞNj ðuÞ þ d2
ð5Þ
which introduces fj as the local fitness function in patch j. Next, we include passive migration between the two habitats. The total consumer population dynamics follows: ( N1;tþ1 ðuÞ ¼ ð1 mÞN1;t ðuÞf1 u; N1;t þ mN2;t ðuÞf2 u; N2;t ð6Þ N2;tþ1 ðuÞ ¼ mN1;t ðuÞf1 u; N1;t þ ð1 mÞN2;t ðuÞf2 u; N2;t where m is the proportion of individuals migrating between the habitats each time-step. The only way in which the habitats differ is in the relative amounts of resources. We assume that the inflows to the resources are in inverse relation to each other, i.e., q¼
I1;1 I2;2 Ilarge ¼ ¼ : I2;1 I1;2 Ismall
ð7Þ
A ratio q = 3 gives that the inflow of resource 1 in patch 1 is three times larger than the inflow of resource 2 in patch 1, whereas the relationship is the opposite in patch 2. Since the numbering of the resources is arbitrary, we can assume q C 1 without loss of generality. In a sense, q is a measure of habitat heterogeneity, where q = 1 implies no difference between habitats and larger q values represents larger heterogeneity. To summarise, the complete dynamics of a single consumer population are driven by its local dynamics in the two habitats (Eq. 6), which in turn depend on the fast dynamics and equilibrium levels of the local resources (Eq. 3). It is straightforward to calculate the local equilibrium consumer population sizes, N*1 and N*2, but the mathematical expressions are rather complex and uninformative. A rare type u0 invading a resident population with trait value u will face the local resource levels determined by the resident population, but will utilise them according to its
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own attack rates. Assuming the resident population is at ecological equilibrium, the mutant per capita growth rate in habitat j is given by: 0 fj ðu0 ; uÞ ¼ f u0 ; R1;j u; Nj ; R2;j u; Nj ð8Þ c1 a1 ðu0 ÞI1;j c2 a2 ðu0 ÞI2;j ¼ þ : a1 ðuÞNj ðuÞ þ d1 a2 ðuÞNj ðuÞ þ d2 Mutant fitness, as long as it is rare, is independent of mutant density, which means its global dynamics are linear: n1;tþ1 ¼ ð1 mÞf 01 ðu0 ; uÞn1;t þ mf20 ðu0 ; uÞn2;t ð9Þ n2;tþ1 ¼ mf10 ðu0 ; uÞn1;t þ ð1 mÞf20 ðu0 ; uÞn2;t where nj,t is the number of mutants in patch j at time t. The linear growth implies that the total growth rate, the invasion fitness, of a rare mutant strategy is given by the dominant eigenvalue of the matrix (cf. Holt and Gaines 1992; Mesze´na et al. 1997; Kawecki and Holt 2002): mf20 ðu0 ; uÞ ð1 mÞf10 ðu0 ; uÞ : ð10Þ F¼ mf10 ðu0 ; uÞ ð1 mÞf20 ðu0 ; uÞ It is here assumed that the invasion of a mutant is slower than the migration process, such that a stationary distribution of mutants across the habitats is established for most of the invasion process. By calculating the invasion fitness of all possible mutants for all possible resident morphs, a Pairwise Invasibility Plot (PIP, Geritz et al. 1998, see also Fig. 2a, b) can be constructed. In a PIP, the invasion fitness for every pair of a resident and an invader is represented as a surface, and it is indicated where the invader has higher fitness than the resident or vice versa.
Results Single morph evolution We assume the system is initially invaded by a single morph, arbitrarily positioned in the u trait space. Its subsequent evolution can be predicted from the corresponding PIP, for example Fig. 2a. The x-axis represents the resident trait and the y-axis the possible mutant invading trait. On the diagonal (thick solid line), the mutant is equal to the resident and has neutral fitness. In regions marked with ‘‘?’’ the mutant has a fitness advantage to the resident and is assumed to invade and eventually replace the resident population (except cases of mutual invasibility, see below). Conversely, regions with ‘‘-’’ represent mutants unable to invade. The thick, curved, line is a fitness null-cline—just like the diagonal it marks the boundary between mutant advantage and disadvantage, compared to the resident. The thin lines in Fig. 2a and b are local fitness null-clines, representing selection within each habitat (Eq. 8), although the resident equilibrium population sizes still take migration into account. Here, it is obvious that selection in the two habitats can differ substantially. The consumer morph will respond to global selection (as given by the thick null-cline), which will often be in opposite direction to local selection in one of the habitats.
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(a)
(b)
(c)
(d)
Fig. 2 Pairwise invasibility plots (PIPs), a and b, and mutual invasibility plots (MIPs), c and d, of the twohabitat model. In a and b the x-axis gives the resident trait value and the y-axis represents that of the invading type. In the areas denoted ‘‘?’’ the invader will have higher fitness than the resident and will thus be able to invade, and eventually replace, the resident. In the areas denoted ‘‘-’’ the invader will have lower fitness than the resident, and will then not be able to invade. The thick line is the global null-cline, i.e., the separation between invader advantage (?) and disadvantage (-), taking global fitness into account. The thin lines represent local null-clines, where the invader and the resident have equal fitness in one habitat or the other. In c and d the stationary points after branching are depicted with stars. In the white area the populations are not mutually invasible. In the dashed area the populations are globally mutually invasible. In the light grey area the populations are mutually invasible in one of the habitats. In the dark grey area the populations are mutually invasible in both habitats and all populations are thus self sustained. Parameters: a and c rn = 0.75, m = 0.05; b and d rn = 0.35, m = 0.05. Other parameter are q = 3, d1 = d2 = 0.1, c1 = c2 = 0.5 and Ismall = 50
The expected endpoint of the gradual evolution of a single morph is most strongly influenced by the niche width of the consumer, rn, in relation to the distance in trait space between the two resources, which here is fixed to 1. Figure 3 summarises some of the dependence on rn. For a very narrow niche width (approx. rn \ 0.23) the two specialist strategies are both locally convergent stable. The intermediate, generalist strategy is either not viable (dashed area in Fig. 3), a repellor or locally convergent (for *0.16 \ rn \ 0.23). Above rn & 0.23, the generalist strategy is globally convergent stable (Fig. 3). Any invader will adapt to become a resource generalist, irrespective of previous specialisation. The trade-off is now so weak that it always generates selection towards the (globally) least utilised resource. The details of Fig. 3 naturally depend on the other parameters of the model, like the migration rate m or the ratio between resource influxes, q. The dependence at these narrow niche widths is however surprisingly weak. Even dramatic changes in parameter values gives only minor shifts of the boundaries drawn in Fig. 3 (see also the grey areas in Fig. 4). m and q nevertheless have a large influence on when the intermediate trait value becomes an ESS (grey are in Fig. 3, black area in Fig. 4). Finally, it is straightforward to show that above rn = 0.5, the generalist strategy is always convergent stable.
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Fig. 3 Stationary points (solid lines) for m = 0.1, q = 4 and rn \ 1.2, other parameters as in Fig. 2. The arrows indicate the direction of monomorphic evolution. Large arrows denote adaptation to the (pseudo-) sink habitat, and small arrows indicate adaptation to the source habitat. For trait values smaller than -0.5 or larger than 0.5, adaptation to both habitats increase. In the dashed area the population is not viable. The grey area indicates when the intermediate trait value is an ESS (which will be determined by the migration rate, m, and asymmetry of resource inflow, q)
(a)
(b)
Fig. 4 Properties of the two population scenario after branching, for a m = 0.05 and b q = 3, other parameters as in Fig. 2. Black area denotes when the intermediate trait value is an ESS, and no branching will occur. The grey areas show when the specialist trait values are attractors, and the dark grey area when the intermediate trait value is a repellor (cf Fig 3). The white and light grey areas indicate when the intermediate trait value is a branching point. The sink population will be a true sink at the evolutionary endpoint in the horizontally dashed area, and a pseudo-sink in the vertically dashed area. Would migration cease, the local populations will be able to coexist ecologically, but not evolutionary, above the dotted line within the vertically dashed area
Source-sink evolution of a single morph A single morph invading our model system will initially be best adapted to one of the resources, which here means it will have a larger population in the habitat where that resource is most abundant. Since migration is purely passive, symmetric and proportional to the population size, the larger population will also produce the most migrants and net migration flow will be from the larger population to the smaller. At equilibrium the larger population will thus act as a source population. If migration would cease, any morph would persist in both habitat (except for populations with trait values within the dashed area in Fig. 3), hence the sink population will always be a pseudo-sink for a single morph
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scenario. The results illustrated in Fig. 3 show that an invading population can become more adapted to the source (small arrows) or to the pseudo-sink (large arrows), depending on its niche width (rn). A morph with a narrow niche width will specialise on the resource closest in trait space and therefore adapt to the habitat of its source population. A wider niche width, on the other hand, entails evolution to a generalist strategy, i.e., a strategy better adapted to the habitat which is initially a pseudo-sink habitat. This is possible since migration is bidirectional—individuals that survive passive migration to the sink habitat and back again have an advantage compared to individuals that will perish in the sink habitat due to specialisation on the source habitat. It pays off more to increase the low fitness in the sink, compared to increasing the high fitness in the source (cf. Holt 1996). ESS:s and branching points If a specialist strategy is convergent stable, it is also a local ESS, i.e., no similar morph can invade, but any morph specialised on the other resource can readily invade. In other words, gradual evolution by small mutations stops, but the system is open to invasion from the outside. The intermediate, generalist strategy can on the other hand be both an ESS (grey area in Fig. 3) and a branching point (Fig. 2a, b). A branching point is characterised by convergent stability and a local fitness minimum, i.e., once gradual evolution has taken the consumer to this point in parameter space, any mutant strategy can invade. Branching points are known to induce evolutionary branching and protected polymorphisms (Geritz et al. 1998). At niche widths above 0.5, the evolutionary properties of the generalist strategy depend on the amount of migration between the habitats (m) and the asymmetry of the resource inflow (q = Ilarge/Ismall, Fig. 4). Dimorphic evolution after branching If the generalist strategy is a branching point, the single morph is expected to branch into two morphs, each slightly more specialised on one of the resources. Each morph will because of this have a large source subpopulation (in the habitat were it is best adapted to the resource with larger inflow) and a smaller sink subpopulation. Moreover, the sink will be a true sink—without immigration from its source it will be completely outcompeted by the other morph, which is best adapted to the locally most abundant resource. Local selection is still directional (Fig. 2a, b), which does not allow for coexistence. The question is, will this relation last, will there always be one source and one sink population of each morph until the ecological divergence is completed to full specialisation? To investigate this we made Mutual Invasibility Plots, MIP:s, as can be seen in Fig. 2c and d. Here, the two coordinate axes correspond to one consumer strategy each, and the colour coding shows which configurations are mutually invasible, i.e., are able to coexist locally or globally. Global mutual invasibility (horizontally dashed area) means the two morphs can coexist globally, taking migration between the habitats into account. Regions of local mutual invasibility on the other hand (light grey), indicate where two morphs can coexist locally, within a habitat, even if migration ceases. In the darker grey areas, finally, the two morphs can coexist locally in both habitats. As noted above, there is no local coexistence immediately after branching—each morph consists of a source and a true sink population. This can also be concluded from Fig. 2c and d since the area just above and to the left of the global branching point (on the diagonal) is not shaded, i.e., there is no local coexistence. In this region each morph
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gradually adapts to its source population. As divergence proceeds, however, there may be or may not be room for local coexistence. The endpoint of dimorphic evolution is a convergent stable coalition of two highly specialised morphs (denoted with stars in Fig. 2c, d). Due to symmetry they will be situated on equal distance from the branching point. Figure 2c shows the MIP for the same scenario as the PIP in Fig. 2a. The convergent stable coalition (stars) is well within the white area, which means the evolutionary endpoint is two habitat specialists, each supporting a true sink population in the reciprocal habitat type. Figure 2d illustrates the same scenario as the PIP in Fig. 2b. Here the convergent stable coalition is found in the area of local mutual invasibility (the dark grey area). Thus, the ‘mal-adapted’ subpopulation of each morph is only a pseudo-sink and would persist without immigration. Whether a sink population in the final constellation will be a pseudo-sink or a true sink depends mainly on the niche width (rn, see Fig. 4). If the niche width is broader than approx. 0.55 the sink is a true sink (horizontally dashed area in Fig. 4). A broad niche means the locally best adapted morph imposes strong competition on the other morph and local coexistence is impossible. For a narrower niche width the sink will be a pseudo-sink (vertically dashed area in Fig. 4)—the ecological diversification is now large enough to prevent competitive exclusion. The migration rate (m) and asymmetry of resource inflow (q) only have minor influence on whether the sink population will be a pseudo-sink, but a decreased q or increased m can turn the intermediate strategy into an ESS, which prevents branching altogether (black area, Fig. 4). So far, we have only considered the ecological coexistence of specialised morphs should migration between the habitats cease. Ecological coexistence does however not guarantee long term, evolutionary coexistence. In some circumstances the convergent stable coalition after branching is in the area of mutual local invasibility, but coexistence is not evolutionary robust to a haltered migration. As long as migration is upheld, the local boosting of the pseudo-sink population keeps local competition strong and the morphs are kept apart due to evolutionary character displacement. If migration stops, however, the former pseudo-sink will decrease to a new ecological equilibrium, which decreases competition and opens a new evolutionary path for the locally best adapted morph—it can gradually evolve towards a more generalist strategy and eventually outcompete the other, smaller, population. Such ‘evolutionary sinks’ occur in our model in a quite narrow interval of the niche width parameter rn (Fig. 4, above the dotted line, within the vertically dashed region). We find this scenario interesting but somewhat unlikely, due to the limited parameter space.
Discussion First of all, we conclude that a high migration rate, small habitat differences and a broad niche width increase the likelihood that the intermediate, generalist trait value is a globally stable ESS. The reverse conditions make the intermediate strategy a branching point, which makes parapatric branching a plausible outcome. For very narrow niche width the intermediate trait value becomes a repellor, and specialisation on one habitat or the other will be the final outcome. These conclusions conform well to previous studies on similar models (e.g., Brown and Pavlovic (1992); Mesze´na et al. (1997); Day (2000); Ronce and Kirkpatrick (2001); Parvinen and Egas (2004); Rueffler et al. (2006)). We have also shown that a parapatric branching, driven by habitat differences, most likely involves periods of source-sink dynamics and adaptations towards firstly the sink
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habitat and secondly the source habitat. When the initial colonisation takes place there is a larger equilibrium population size in the habitat where the invading type is best adapted to the most productive resource, and the subpopulation in the other habitat will be smaller because of less resources. This produces a net migration from the larger population, which makes the other population a pseudo-sink. Despite this fact, selection in the sink habitat is stronger than selection in the source habitat. The population will thus evolve towards the intermediate trait value even though this decreases adaptation to the source habitat. Evolution will generally favour adaptation to a source habitat as opposed to a sink (Holt 1996), but if selection in the source is relatively weak adaptation to the sink is still possible. In a study of asymmetric migration in a two habitat system, Kawecki and Holt (2002) concluded that adaptation to a pseudo-sink happens most easily if migration from the source is low. Our results of adaptation to the sink habitat do not depend on migration rate; it will occur even for very high migration rates. It should be noted here that which habitat is a source and which is a pseudo-sink to some extent depends on their relative sizes, since a larger population produces more migrants. In our model an evolving morph will always have the largest equilibrium population in the habitat to which it is best adapted, which gives a net migration to the other habitat and makes it a pseudo-sink. An asymmetric situation is not analysed here but would make branching less likely due to the stronger selection for adaptation to the larger habitat (Kisdi and Geritz 1999). It is still unclear, however, to what extent the convergence of a single morph to an intermediate generalist strategy always implies adaptation to a pseudo-sink habitat, especially beyond the assumptions on symmetry made here. Right after the branching event there will be a source and a true sink in each habitat. The ecological divergence implies gradual adaptation to the source habitat of both morphs and consequently a loss of adaptation to the sink habitat. Despite this, the sink population can eventually become a pseudo-sink, since ecological divergence also reduces local competition between morphs (cf. Fig. 2d). A sink population can thus become a source, or at least pseudo-sink, through two different processes: either it adapts to local conditions or its mere presence causes evolutionary character displacement of competing species. In the model presented here, we see both mechanisms at work. Once a sink is converted to a pseudosink, ecological coexistence is guaranteed even if dispersal from the source should stop. However, subsequent evolution may in the absence of dispersal in some cases revert the process and drive the previous pseudo-sink population to extinction. A pseudo-sink population may thus not depend on immigration for its immediate persistence, but if long-term evolutionary consequences are taken into account immigration may be just as vital as to a true sink population. We thus call it an ‘evolutionary sink’. A relatively broad niche width (a weak trade-off) can generate an ESS configuration with two source populations and two true sinks (Fig. 2c, horizontally dashed area in Fig. 4), while narrower niche width (stronger trade-off) is more likely to produce a configuration with two source populations with pseudo-sinks, that would allow for ecological coexistence should migration cease (Fig. 2d, vertically dashed area in Fig. 4). Migration rate and habitat heterogeneity seem to have only a minor influence on the properties of the sink population, but are important for the possibility for branching. Brown and Pavlovic (1992) made the point that dispersal should not be considered as a force opposing (local) adaptation, but rather as ‘‘part of the context to which natural selection should respond’’. From a local perspective, much dispersal prevents local adaptation, but from a global perspective the intermediate phenotype can the best adapted to such a scenario. Whether a genotype is adapted or maladapted thus depends on the scale at which it is evaluated. Local selection in two habitats can be in opposite directions (e.g.,
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compare the thin lines in Fig. 2a, b). However, if these habitats are connected by migration they cannot be considered on their own, but must be put in a larger perspective. It is thus the global environment, of which migration is a part, that will determine the route of evolution. We have here generated new predictions and possible interpretations of source-sink dynamics in natural systems. Source-sink dynamics is shown to be an inevitable part of parapatric branching in a heterogeneous environment, including both true sink populations and pseudo-sink populations. There might even be transitions from a true sink to a pseudosink population through adaptation to the source habitat, where the source population ‘drags’ the sink population through an adaptive valley. Over all, we have highlighted the spatial population ecology of parapatric branching, which we hope will inspire future work by both theoreticians and empiricists. Acknowledgments We thank two anonymous reviewers for useful suggestions which helped improve an earlier version of this manuscript. This work was financially supported by the Swedish Research Council.
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