NONRANDOM LARVAL DISPERSAL CAN STEEPEN MARINE CLINES

Evolution, 59(12), 2005, pp. 2509–2517

NONRANDOM LARVAL DISPERSAL CAN STEEPEN MARINE CLINES MATTHEW P. HARE,1,2 CHRISTOPHER GUENTHER,3

AND

WILLIAM F. FAGAN1

1 Department

of Biology, University of Maryland, College Park, Maryland 20742 2 E-mail: [email protected] 3 Graduate Program in Applied Math and Scientific Computation, University of Maryland, College Park, Maryland 20742 Abstract. Sharp and stable clinal variation is enigmatic when found in species with high gene flow. Classical population genetic models treat gene flow as a random homogenizing force countering local adaptation across habitat discontinuities. Under this view, dispersal over large spatial scales will lower the effectiveness of adaptation by natural selection at finer spatial scales. Thus, random gene flow will create a shallow phenotypic cline across an ecotone in response to a steep selection gradient. In sedentary marine species that disperse primarily as larvae, nonrandom dispersal patterns are expected due to coastal hydrodynamics. Surprisingly sharp phenotypic and genotypic clines have been documented in marine species with high gene flow. We are interested in the extent to which nonrandom dispersal could accentuate such clines. We model a linear species range in which populations have stable and uniform densities along a selection gradient; in contrast to random dispersal, convergent advection of larvae can amplify phenotypic differentiation if coupled with a semipermeable dispersal barrier in the convergence zone. The migration load caused by directional dispersal pushes the phenotypic mean away from the local trait optimum in downstream populations, that is, near the convergence zone. A dispersal barrier is possible as a result of colliding currents if the water and larvae are mostly displaced offshore, away from suitable settlement habitat. Disjunctions in a quantitative trait were enlarged in the convergence zone by faster current flows or a more complete dispersal barrier. With advection of larvae per generation one-third as far as the average dispersal distance by diffusion, convergence on a dispersal barrier with 40% permeability generated a trait disjunction across the convergence zone of two phenotypic standard deviations. Without directional dispersal, similar clines also developed across a habitat gap, where population density was low, or across dispersal barriers with less than 1% permeability. These findings suggest that the types of hydrographic phenomena often associated with marine transition zones can strongly affect the balance between gene flow and selection and generate surprisingly steep clines given the large-scale gene flow expected from larvae. Key words.

Adaptation, advection, gene flow, maladaptation, migration load, population model, selection. Received March 17, 2005.

Accepted September 29, 2005.

Dispersal and selection interact to shape evolutionary change in quantitative traits along environmental gradients. This interaction often generates smooth genetic and phenotypic clines that are broader than the environmental discontinuity (Slatkin 1973; May et al. 1975; Endler 1977; reviewed in Lenormand 2002). Local maladaptation results when dispersal creates a migration load by moving genes from areas where they have high relative fitness to areas where they experience lower fitness. Maladaptation is avoided along an environmental gradient under two general conditions (for a more detailed review see Lenormand 2002). First, if the selection gradient is broader than a characteristic length, then dispersal does not limit populations’ local responses to selection. Characteristic length is defined by the ratio of dispersal distance, measured as the standard deviation in parentoffspring distances (s), and the square root of selection (Slatkin 1973). Second, if dispersal is homogeneous and random among a linear array of populations of uniform abundance, a trait mean will evolve to the optimum value at each locality because the migration loads from each direction are balanced (Felsenstein 1977). Effects of migration load become interesting, then, in relatively sharp ecotones and when dispersal is nonrandom. For example, in species with strong gradients in abundance, random dispersal will produce a net flux of gene flow from high-density to low-density populations (Nichols 1989). Theoretical models of species ranges with an abundance peak in the center of the range and low-density peripheral populations, when subject to a selection gradient, can generate migration loads that constrain local adaptation in peripheral populations (Garcia-Ramos and Kirkpatrick

1997) and limit species range distributions (Kirkpatrick and Barton 1997; Case and Taper 2000). Empirical evidence for migration load has come mostly from terrestrial systems (Camin and Erlich 1958; Via 1991; Riechert 1993; Lenormand et al. 1999; Storfer et al. 1999). For example, two recent studies of Parus major, a bird species with high gene flow, demonstrated that phenotypic clines at small spatial scales resulted from differential gene flow across a selection gradient (Garant et al. 2004; Postma and van Noordwijk 2004). These studies make the important point that nonrandom gene flow can emerge for different reasons (proximity to a source population and a population density gradient, respectively) and accentuate differentiation over small spatial scales rather than homogenize populations. Migration load may be a common constraint on local adaptation in other species that experience directional dispersal. Coastal marine species, in particular, many of which experience high gene flow via dispersal as larvae (Jablonski and Lutz 1983), are subject to the combined influences of directional current flows and sharp coastal environmental gradients that could generate migration loads and maladaptation. Diffusion and hydrographic transport are both important factors determining larval dispersal (Jackson and Strathmann 1981; Scheltema 1986; Roughgarden et al. 1988; Cowen et al. 2000; Siegel et al. 2003), although vertical larval swimming across stratified flows can also have a large speciesspecific affect on dispersal patterns (Hill 1991; Baker and Mann 2003). The maximum scales of average dispersal for marine species with sedentary adults (i.e., primarily larval dispersal) were recently estimated to be hundreds of kilometers, more than an order of magnitude greater than that in

2509 q 2005 The Society for the Study of Evolution. All rights reserved.

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terrestrial plants (Kinlan and Gaines 2003). Genetic estimates of average dispersal distance were also significantly associated with the species-specific length of time larvae remain in the plankton before settlement (Siegel et al. 2003). Many marine species are also highly fecund, so they are producing large numbers of larval migrants with the capacity to disperse broadly. Given that north–south coastlines often have temperature gradients that are steep on a regional scale (Briggs 1974), and local gradients in salinity, temperature, and intertidal exposure can have strong biotic effects in estuaries (Bilton et al. 2002), marine processes will often transport larvae to habitats in which they are maladapted. In marine species with high fecundity, strong viability selection each generation has been shown to maintain differentiation in the face of dispersal along local environmental gradients (Koehn et al. 1980; Bertness and Gaines 1993; Wilhelm and Hilbish 1998; Schmidt and Rand 2001). Thus, many local marine clines appear to conform to the classic model (Endler 1977) of population homogenization through dispersal countered by spatially heterogeneous directional selection (Williams 1975). Although the theoretical consequences of nonrandom dispersal on cline shape are well known (May et al. 1975; Nagylaki 1978; Slatkin 1978), its influence on cline dynamics rarely has been measured in the context of marine clines (but see Wares et al. 2001; Gilg and Hilbish 2003). Because dispersal barriers within a selection gradient will strengthen migration load by generating or amplifying a local asymmetry in the source of migrants, coastal barriers to larval migration may be particularly likely to show these effects. Gaylord and Gaines (2000) explored the consequences of directional larval dispersal on species range limits in the absence of selection. Several population dispersal models of converging or diverging along-shore currents generated barriers to range expansion by deflecting dispersal propagules offshore (Gaylord and Gaines 2000). Gaylord and Gaines (2000) noted that the confluence of major current systems is often associated with clustered species range limits separating marine zoogeographic provinces (Briggs 1974; Hayden and Dolan 1976), although narrowly distributed endemics also occur at such convergence zones (Olson 2001). Converging currents typically carry water with very different properties, creating relatively sharp thermal or chemical gradients that constrain range distributions for marine invertebrates (Hutchins 1947; Hedgpeth 1957; Hall 1964; Valentine 1966; Suchanek et al. 1997). The results of Gaylord and Gaines (2000) demonstrate that advective currents could create dispersal barriers that limit species ranges even without a selection gradient (also see Wares et al. 2001). At the intraspecific level, when there is selection along an environmental gradient, directional dispersal can strongly influence the balance between dispersal and selection that determines cline shape (May et al. 1975; Nagylaki 1978; Slatkin 1978). Although both larval supply and postsettlement community ecology influence population recruitment (Connolly and Roughgarden 1998), directional dispersal can make larval supply a dominant force (Possingham and Roughgarden 1990) and potentially cause striking deviations from a centerabundance population density distribution (Sagarin and Gaines 2002). When these effects of nonrandom dispersal are

coupled with the type of dispersal barriers modeled by Gaylord and Gaines (2000), gene flow can become a force generating spatial differentiation rather than homogenization. In particular, convergent patterns of directional dispersal along a selection gradient may bring different alleles (producing very different trait values) into proximity from distant source populations. This dynamic can create spatially narrow clines, as described by Garcia-Ramos and Kirkpatrick (1997), but would result from the nonrandom dispersal caused by coastal current flows, not the net dispersal down a population density gradient. Because larval dispersal will result from a complex interaction between larval behavior and hydrography, the potential for advective forces to accentuate coastal marine clines (Gardner 1997; Sotka and Palumbi 2006) may not be obvious based on the strongest or average oceanographic flow fields along the continental shelf. For example, in an eastern Pacific barnacle (Balanus glandula) allele frequencies shift strikingly over 475 km of coastline despite a capacity for dispersal at an equivalent scale during a 21 week larval stage (Sotka et al. 2004). The hydrography along the U.S. west coast is neither simple nor stable, but surface drifter tracks suggest that along-shore dispersal may be convergent over a broad geographic scale (Fig. 1a, summarized from Sotka et al. 2004). Similarly, eastern oysters (Crassostrea virginica) have larvae in the plankton for 2–3 weeks, yet populations along the Atlantic coast of Florida have a dramatic 50–75% shift in allele frequencies over just 20 km (Hare and Avise 1996). The oyster cline is centered on Cape Canaveral, and nearshore currents converge toward this locality at least seasonally (Bumpus 1973; Fig. 1b). In both examples the intraspecific cline is spatially coincident with interspecific range limits (Briggs 1974; Suchanek et al. 1997), suggesting that nonrandom gene flow may be shaping patterns of diversity at both population and community levels. To our knowledge, the impact of convergent dispersal along a selection gradient has not been modeled in such a way that its effects can be distinguished from gradients in population density. Classical cline theory predicts that directional gene flow, whether by advection or a net asymmetry down a density gradient, will shift a cline downstream (May et al. 1975; Endler 1977). Density troughs can sharpen a dispersal-dependent cline (Barton 1979; Nichols 1989), but this effect is presumably due more to the dispersal barrier imposed by poor habitat than to opposing density gradients (Barton 1980). Here we use a single model to demonstrate three mechanisms by which migration load induces spatial discontinuities in a quantitative trait mean. We demonstrate that a semipermeable dispersal barrier, population density troughs, and convergent current flows all can enhance the sharpness of a cline formed by spatial variation in natural selection. Our model is an extension of that by Garcia-Ramos and Kirkpatrick (1997; GRK hereafter) in which the optimum trait value varies linearly across a species range and there is local stabilizing selection for the optimum trait value. GRK examined several population density distributions and examined the impact of a complete barrier to dispersal at different locations, but partial barriers and advection were not modeled. Our results demonstrate that the extent to which a quantitative

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FIG. 1. Mitochondrial DNA allele frequency clines for the barnacle Balanus glandula on the west coast (a) and the oyster Crassostrea virginica on the east coast of the United States (b), shown with a latitude scale and proportional to diagrammatic maps of local hydrographic features. In both cases mitochondrial DNA is representative of clinal patterns at one or more nuclear loci and the clines span broad environmental and ecological gradients. West coast solid arrows depict the latitudinal extent of multiple surface drifter trajectories over 40 days after release from within the open circles (for details see Sotka et al. 2004). Dashed arrows show predominant drifter locations after 40 days. Over the potential duration of barnacle larval dispersal, drifters from the north and south converge toward Cape Mendocino and San Francisco, but tend not to meet between these localities. Eastern Florida arrows show the prevailing direction of near-shore surface currents (black) and the Florida Current (gray) as depicted in Bumpus (1973) and on U.S. pilot charts (National GeospatialIntelligence Agency, http://pollux.nss.nima.mil/pubs/pubspjpapcplist.html).

trait cline is steepened by convergent advection is inversely proportional to permeability of the convergence zone to migrants. Partial barriers to gene flow that would have trivial effects under random dispersal can instead generate extreme disjunctions in quantitative traits at convergence zones. METHODS Basic Model We expand upon a quantitative genetic model developed by Pease et al. (1989) and subsequently used by GRK. The basic model assumes that a species is distributed continuously across its linear range and that the pattern of selection acting on the quantitative trait varies spatially. An individual’s phenotypic value is z, and among individuals, values for z and

the corresponding breeding values have Gaussian distributions (Falconer 1989). The phenotypic values are rescaled so that the population-level phenotypic variance is 1.0. This rescaling also means that the additive genetic variance equals the heritability, denoted h2. Juveniles are assumed to disperse randomly along the linear species range, resulting in simple diffusive spread with dispersal variance s2. Dispersal variance can be empirically measured as the mean squared displacement of each offspring from its parent (Kareiva 1983). The root-mean-square of dispersal variance, s, roughly approximates the average displacement of offspring from parents in a single generation, disregarding dispersal directionality (Barton and Hewitt 1989). The juveniles experience postdispersal selection on viability where the selection intensity at location x, denoted

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b˜ (x), acts against the mismatch between the phenotypic trait mean z¯(x) and the local ecological optimum for the trait u(x). The model of Pease et al. (1989) assumes soft selection (Christiansen 1975) in which population regulation is sufficiently strong to maintain a local population at its carrying capacity regardless of the local population’s mean fitness. Thus, selection against individuals with low fitness does not change population density, but instead acts only on the phenotypic trait values. Furthermore, the local population density, denoted n(x), is assumed to be large enough that genetic drift is negligible. The resulting model is ]z¯ s 2 ] 2 z¯ ] ln n ]z¯ 5 1 s2 1 h 2b˜ , ]t 2 ]x 2 ]x ]x

(1)

where t is in units of generations. The first term reflects the effects that diffusive dispersal has on the phenotypic trait mean, the second term captures the interplay of dispersal and density (making the mean trait in a local population more like that of a neighboring area with higher density), and the third term reflects the impacts of selection. Following GRK, we assume that the phenotypic and additive genetic variances are constant in both time and space (which is reasonable if many loci control the trait; Barton and Gale 1993). The ecological optimum for the trait, u(x), varies linearly with space according to u(x) 5 bx. We scale the units of z and x such that at x 5 0, the ecologically optimum value for the trait is z 5 0. Selection acts against individuals whose traits differ from the local optimum such that the probability of survival for a juvenile with phenotype z at location x is w(z, x) } exp[2(bx 2 z)2/2v],

(2)

where v, which quantifies the width of the fitness function, is assumed constant in time and space. As in GRK, this pattern of survivorship means that the strength of directional selection at point x is b˜ (x, t) 5

bx 2 z¯ (x, t) . v11

(3)

GRK used equation (1) to study phenotypic evolution before and after vicariant events. They demonstrated that, in the absence of any barrier to dispersal, and with a Gaussian distribution for local density (centered at x 5 0), a stable equilibrial solution to equation (1) was the linear cline given by zˆ (x) 5

s 2 (v

bh 2 x . 1 1) 1 h 2

(4)

The cline resulted from the interplay of dispersal and selection, which varies spatially as a function of density. Peripheral populations (on the tails of the Gaussian distribution of local densities) were unable to attain their local optimum for the phenotypic trait mean because of migration load from the higher density populations near the center of the species’ range (GRK). In contrast, after the imposition of a vicariant event that completely blocked gene flow at one point in the cline (e.g., between northern and southern portions of a species’ range along a coastline), populations in the two regions each evolved to a new equilibrium. A phenotypic step cline resulted at the location of the vicariant event; the population

trait mean was no longer linear but instead jumped abruptly between values on either side of the blockage to gene flow (GRK). Mathematically the vicariant event was modeled as a reflecting (i.e., Neumann) boundary condition in the interior of the species’ range. This boundary condition meant that there was zero dispersal across the blockage. Investigating Convergent Advection Via Changes to the Basic Model Because center-abundance distributions may not be representative of coastal populations (Sagarin and Gaines 2002) and barriers to dispersal are usually porous, we extended the basic model along three lines, each of which is motivated by the empirical observations concerning convergence zones for along-shore currents as presented in the introduction (Fig. 1). First, we asked how the model predictions would change if a dispersal barrier was imperfect and permitted passage of some fraction of the individuals that encountered it. Second, we asked how the model predictions would change if, instead of a vicariant barrier to dispersal, there was a region of lowquality habitat where population densities were lower but the dispersal of individuals was unimpeded. Third, we asked what effect a pattern of converging current flow would have on the formation and maintenance of the phenotypic step that formed across a dispersal barrier. Throughout our analyses we used rectangular (i.e., uniform) distributions (or variants) rather than Gaussian distributions for the population densities. (GRK compared the behavior of their model for Gaussian and rectangular density profiles and demonstrated that at equilibrium, the rectangular distribution produced a curvilinear cline that more closely approximated the spatially varying phenotypic optimum than did the Gaussian distribution. Thus, the rectangular distribution of densities used here provides a conservative starting point for investigating the three modifications to the GRK model.) To ease comparisons of our results with those found previously, we adopted the same numerical values for several key parameters as were used by GRK. Specifically, we set v 5 10, b 5 1.5, s2 5 0.1, and h2 5 0.5 throughout this paper. Empirical justifications for these choices can be found in GRK. In the absence of any boundary effects, a dispersal variance of 0.1 yields a root-mean-square displacement of 0.32 units, or 5.3% of the total species range (six units on the x-axis of Figs. 2–5). To model the first scenario, an imperfect dispersal barrier, we substituted a Robin boundary condition (also called ‘‘mixed’’ or ‘‘third-kind’’ boundary condition) for the reflecting boundary condition used by GRK. A Robin boundary condition for (each side of) the dispersal barrier can be written as pw ¯ 1 (1 2 p)

]w ¯ 5 0, ]h

(5)

where p (constrained such that 0 # p # 1) can be interpreted as the permeability of the barrier to dispersal (Fagan et al. 1999). The term ]w ¯ /]h is the flux across the barrier, where h is an outward unit normal vector (in two- and three-dimensional models, this vector is used to relate the direction of dispersal to the orientation of a semipermeable boundary, but the issue is not critical in this one-dimensional model).

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FIG. 2. Population density profile used in the models. The x-axis represents a linear species range totaling six spatial units. Rectangular density distributions (solid gray line) were used in the gene flow barrier and advection scenarios. The two rectangular blocks and a gap distribution (dotted line) was used to model a gap of low-quality habitat in the interior of the species’ range. A gapwidth, g, of 20% of total range size is shown. Population density in the gap was always 10% that outside the gap, but the gapped density profiles were scaled so that they have the same area under the curve (i.e., the same total population size) as the ungapped distribution.

FIG. 3. Effects of dispersal barrier permeability on trait means under conditions of random dispersal (i.e., simple diffusion) as in equation (1). A barrier at position x 5 0 allows a fraction of migrants, p, to cross from one side to the other per generation (as in eq. 5). The trait mean, zˆ, measured in phenotypic standard deviations, is shown for each spatial position relative to the local trait optimum, u. Local maladaptation due to migration load is represented as the deviation of zˆ from u at a particular locale. Increasing the permeability of the vicariant barrier (i.e., making p larger), even by a small amount, lessens the magnitude of the disjunction in mean value of the phenotypic trait across the barrier.

The reflecting boundary condition that GRK used corresponds to the case p 5 0 (an impermeable boundary). To model the second scenario, a density trough within lowquality habitat, we changed our distribution of population densities from a rectangular function to a density distribution consisting of two blocks and a gap (Fig. 2). Population density in the gap of low-quality habitat was always 10% of that in the good-quality habitat on either side. The parameter g (expressed as a percentage of the total species range length) governed the width of the gap. To model the third scenario, converging current flow, we added an advection term to the right side of equation (1). Pease et al. (1989) briefly mentioned how one might use an advection term to study how the effects of preferential dispersal toward higher-quality habitat would change conclusions about evolution in a changing environment. The simple advection coefficient c(x) (units: space 3 time21) below can be used to model the effects of directed, along-shore flows that spread genes from two upstream populations toward the center of the range (x 5 0). The resulting equation has the form

An advection coefficient of c 5 0.1 corresponds to 0.1 spatial units per generation, equivalent to directional displacement across 1.7% of the species range. Initially, we assume an impermeable vicariant barrier exists at the center of the range, but then relax this assumption to explore the interplay between converging currents and dispersal across the barrier. We solved equations (1) and (6) and their corresponding boundary conditions numerically, using finite difference methods. As was true for GRK, we found that numerical solutions to our governing equations stabilized quickly and that, depending on the model, step clines or pronounced phenotypic disjunctions developed within only a few dozen generations.

]z¯ s 2 ] 2 z¯ ]z¯ ] ln n ]z¯ 5 1 c(x) 1 s 2 1 h 2b˜ , 2 ]t 2 ]x ]x ]x ]x

(6)

where c(x), the current velocity, is defined as 2c



c(x) 5 0  c

for x . 0 for x 5 0 for x , 0.

(7)

RESULTS We found that semipermeable dispersal barriers, gaps of low-quality habitat, and advective along-shore dispersal converging on an absolute barrier were each capable of inducing disjunctions of substantial magnitude in phenotypic trait means. The permeability of dispersal barriers influenced the magnitude of the phenotypic disjunctions observed (Fig. 3). The strongest disjunctions were observed when the barriers were completely impermeable (reflecting boundary conditions), and even slight increases in the permeability of the barrier weakened the disjunction in the phenotypic trait mean that existed across the barrier. Increased permeability of the barrier allowed the cline to more closely approximate the op-

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FIG. 4. Effects of gap width on phenotypic trait means. Population density in the density trough is 10% of that in the surrounding habitat and phenotypic trait values are plotted for gaps of different width following Figure 1. The trait mean, zˆ, measured in phenotypic standard deviations, is shown for each spatial position relative to the local trait optimum, u. Local maladaptation due to migration load is represented as the deviation of zˆ from u at a particular locale. In these results, there is no dispersal barrier (i.e., p 5 1) and the step cline results only from the reduction in gene flow caused by a pocket of reduced population density. For a given gap width, curves on the right are connected with those on left to differentiate these results from those in Figures 3 and 5, where there is a dispersal barrier.

timum trait value near the barrier at the center of the species range (Fig. 3). Equilibrium trait means in peripheral populations diverged from the trait optimum in every case because the edge of the species range was essentially an absolute dispersal barrier. Gaps of low-quality habitat (where equilibrial population densities are 10% of those in the high-quality habitats) also generated step clines under random dispersal (Fig. 4). In these cases, there was no vicariant barrier to dispersal and the step cline resulted only from the reduction in gene flow due to the zone of reduced population density. All but one of the gap widths modeled were larger than the root-mean-square dispersal distance. Even the narrowest gap in good-quality habitat, constituting 4% of the species range and 75% of the root-mean-square dispersal distance (s), proved sufficient to generate a sharp disjunction in the phenotypic trait mean. Larger gaps of low-quality habitat extending across 8% of the species range (1.5s) resulted in disjunctions exceeding two phenotypic standard deviations in magnitude. Advective dispersal, such as would occur from currents converging toward the interior of a species range along a coast, can also generate a step cline in the phenotypic trait mean when coupled with an absolute dispersal barrier (Fig. 5). Note that in the absence of advection (c 5 0), random dispersal will pile up migrants at a dispersal barrier to produce a step cline (as shown by GRK and similar to Fig. 3). The magnitude of the disjunction in trait mean increased as advection was increased (i.e., stronger currents). The largest advection coefficient modeled, c 5 0.1, yielded an advective displacement per generation that was one-third as great as the root-mean-square displacement due to diffusive spread.

FIG. 5. Effects of nonrandom dispersal, modeled as convergent advection using equation (6) on phenotypic trait means. The advection coefficient, c, corresponds to the number of x-axis units larvae are displaced per generation. The trait mean, zˆ, measured in phenotypic standard deviations, is shown for each spatial position relative to the local trait optimum, u. Local maladaptation due to migration load is represented as the deviation of zˆ from u at a particular locale. Directional dispersal converging toward an absolute dispersal barrier at the center of the species range (x 5 0) can generate a dramatic step cline in the phenotypic trait.

Nonetheless, advection had a strong effect such that the phenotypic trait mean more closely matched the phenotypic optimum at the outer ends of the species range and deviated strongly from the optimum near the barrier. This effect arose because the advective component of dispersal (i.e., directional movement) overrode the diffusive component (i.e., random movement that operates both up- and downstream equally). Effectively, downstream dispersal prevented populations near the barrier from contributing as much gene flow to the upstream populations as occurred in the opposite direction. Thus, the phenotypic deviation from local trait optima (migration load) was greatest where migrants were advected into a barrier than with advection away from a barrier (compare central barrier to species range edge, Fig. 5). When both the permeability of the dispersal barrier and the strength of the advective gene flow were considered, the magnitude of the phenotypic disjunction depended jointly on both factors (Fig. 6). The largest disjunctions occurred for cases where the dispersal barrier was only slightly permeable and advective gene flow was high. Strong advection can offset the homogenizing effects of a semipermeable dispersal barrier, allowing disjunctions in the phenotypic trait mean to persist under permeability conditions that would otherwise lead to a weak cline. DISCUSSION Our simulation results show that with random dispersal, physical barriers to movement and habitat gaps can each create a discontinuity in the mean of a quantitative trait along a selection gradient because migration load becomes asymmetrical. Populations on each side of the barrier or gap receive migrants primarily from one direction along the selec-

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FIG. 6. Surface plot showing the combined effects of convergent advection and barrier permeability on the magnitude of phenotypic trait disjunction at the barrier (x 5 0). Model conditions are identical to those in Figure 5, except that now the barrier is permeable. Magnitude of disjunction is measured in standard deviations.

tion gradient and therefore become maladapted relative to the local trait optimum. The dispersal constraints create a step cline in quantitative trait values, with the magnitude of phenotypic discontinuity for a given dispersal rate dependent on permeability of the barrier and width of the habitat gap. However, our results indicate that each of these mechanisms acting alone is unlikely to have a strong affect on local adaptation or induce sharp clines, except in extreme cases where dispersal across the selection gradient is almost entirely prevented. Our results are consistent with previous conclusions about the importance of these factors under random dispersal (Endler 1977; Barton 1980; GRK). Anything that increases the asymmetry of gene flow will either displace the trait mean downstream relative to its optimum (Slatkin 1978) or, if coupled with a barrier, will amplify the migration load and trait disjunction (GRK). Not surprisingly, in the special case of converging advection toward a complete barrier, the trait disjunction was amplified in proportion to the amount of advection (Fig. 5). When the barrier was made permeable, converging advection would move propagules across the barrier where they experienced advection in the opposite direction. Under this regime, even strong advection did not generate much of a phenotypic disjunction when the barrier was largely permeable (p 5 0.5 in Fig. 6). This is because random diffusion was broad in these models compared with advection (s2 5 0.1 in all cases, corresponding to root-mean-square dispersal distances due to diffusion encompassing 5.3% of the species range each generation, whereas the strongest advection corresponded to downstream displacement across 1.7% of the species range per generation). Thus, the balance between converging ad-

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vection and diffusion is not expected to generate sharp clines without some barrier to dispersal in the convergence zone. One of the most significant results of the model is that a convergence zone barrier need not be highly impermeable to create phenotypic disjunctions of more than four standard deviations (e.g., permeability of 10% and c 5 0.1, Fig. 6). In reality, conservation of mass requires that colliding flow fields displace water somewhere. In relatively shallow nearshore shelf waters, much of the flow will be deflected offshore, potentially carrying larvae away from suitable settlement habitats. Examples of this at a large geographic scale include the Labrador and Gulf Stream near Cape Hatteras or the Peru Current and North Equatorial Countercurrent on the west coast of South America. To the extent that offshore trajectories result in larval mortality, convergent currents can create a dispersal barrier (Gaylord and Gaines 2000). The along-shore permeability of a convergence zone between colliding currents and the degree to which larvae can return to the coast after movement offshore (Shanks 1995) are important empirical questions raised by our results. Our model does not take into account any of the life-history and behavioral factors that determine how advection influences larval dispersal (see Gaylord and Gaines 2000 and references therein). We have also made simplifying assumptions about how selection operates. Our simplifications are not meant to imply that these factors are unimportant—these biotic properties are likely to produce wide variation among species in their sensitivity to advection within environmental gradients. Rather, the simplicity of our model makes it more general, suggesting that random dispersal should not be assumed in marine clines because advection of larvae, coupled with partial barriers to dispersal such as from habitat gaps, can have nontrivial affects on cline shape as well as location. The relative spatial scales of dispersal, habitat patchiness, hydrographic flow fields and selection gradients are going to influence the dynamics examined here. Our model considered the full range distribution of a species with a linear selection gradient and constant advection imposed across the entire range. These forces often act over large portions of species’ ranges (e.g., Fig. 1a). Their importance, however, is not expected to diminish at smaller scales, where selection gradients can be steeper and flow fields might be locally stronger or more constant. Implications and Prospects for Further Analysis The present analysis highlights the potential significance of convergent advection among factors that may sharpen coastal marine clines relative to extrinsic selection gradients. Convergent advection is a special case among the many ways that coastal oceanography and larval behavior can create nonrandom patterns of larval dispersal (e.g., Shanks 1995). These factors need to be taken into account when trying to explain marine clines or estimate population parameters from cline shape. Dispersal-dependent cline theory (also known as tension zone theory; Barton and Hewitt 1985) has recently been promoted as an underused approach for estimating gene flow in marine species with clinal variation (Sotka and Palumbi 2006). Sotka and Palumbi argued that measures of linkage disequilibrium between genetic polymorphisms at indepen-

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dent loci, when coupled with an estimate of cline width, can be used to generate useful estimates of average gene flow. A major assumption of dispersal-dependent cline theory, however, is random dispersal with negligible genetic drift (Barton and Gale 1993). If there are steep population density gradients, then random dispersal has a net directionality and, coupled with genetic drift in pockets of small population size, cline width becomes an unreliable indicator of selection (Nichols 1989). If dispersal has a directional as well as diffusive component and advection can be estimated independent of the cline shape, improved estimates of selection may be possible based on cline width (May et al. 1975) and linkage disequilibrium. Alternatively, repeated measures of cline shape and disequilibrium can be used to jointly estimate selection and nonrandom dispersal (Lenormand and Raymond 2000). In any case, to make accurate estimates of larval dispersal within marine clines we will generally need to account for nonrandom movements caused by advection and/or larval behavior. The likelihood that multiple factors combine to influence cline shape argues for close scrutiny of individual cases, but experimentally isolating the individual effects of these factors will be challenging (e.g., Sotka et al. 2004; also see Connolly and Roughgarden 1998). Fortunately, when sharp clines occur in species with sedentary adults, it facilitates experimental methods that can distinguish between patterns produced by dispersal barriers versus postdispersal selection (Koehn et al. 1980; Bierne et al. 2003; Gilg and Hilbish 2003; Toro et al. 2004). Also, directional gene flow has been detected in several marine systems (Wares et al. 2001; Billot et al. 2003) and estimates should improve through the use of high-resolution genetic markers (Estoup et al. 1999; Mountain et al. 2002) and analyses designed to take advantage of them (Falush et al. 2003; Wilson and Rannala 2003; Hey et al. 2004). Thus, the experimental tools exist to test for patterns of nonrandom gene flow that could accentuate differentiation within a species. Strong advection will have similar affects on codistributed species dispersing primarily as larvae, so comparisons across species provide another method of testing for their influence. Of course, exceptions are also expected from differences among species in larval biology (Shanks 1995; Baker and Mann 2003), seasonality of reproduction, and postsettlement ecology (Connelly and Roughgarden 1998), and these exceptions should prove equally enlightening about the mechanisms shaping clines and the spatial scale of local adaptation. ACKNOWLEDGMENTS We appreciate comments provided by D. Olson, S. Palumbi, E. Sotka, and two anonymous reviewers that helped improve this paper. LITERATURE CITED Baker, P., and R. Mann. 2003. Late stage bivalve larvae in a wellmixed estuary are not inert particles. Estuaries 26:837–845. Barton, N. H. 1979. Gene flow past a cline. Heredity 43:333–339. ———. 1980. The hybrid sink effect. Heredity 44:277–278. Barton, N. H., and K. S. Gale. 1993. Genetic analysis of hybrid zones. Pp. 13–45 in R. G. Harrison, ed. Hybrid zones and the evolutionary process. Oxford Univ. Press, New York.

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