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Keywords:

  • coexistence;
  • competition;
  • dispersal;
  • keystone predation;
  • life-history trade-offs;
  • resource productivity

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
  • 1
    I investigated the effects of dispersal on communities of keystone predators and prey. I obtained two key results.
  • 2
    First, a strong trade-off between competitive ability and predator susceptibility allows consumer coexistence over a large resource productivity range, but it also lowers the predator-susceptible superior competitor's abundance and increases its risk of extinction. Thus, unexpectedly, dispersal plays a more important role in coexistence when predator-mediated coexistence is strong rather than weak. The interplay between the trade-off, small population sizes resulting from transient oscillations, and dispersal leads to qualitatively different species distributions depending on the relative mobilities of the consumers and predator. These differences yield comparative predictions that can be tested with data on trade-off strength, dispersal rates, and species distributions across productivity gradients.
  • 3
    Second, there is an asymmetry between species in their dispersal effects: the predator-resistant inferior competitor's dispersal has a large effect, but the predator-susceptible superior competitor's dispersal has no effect, on coexistence and species’ distributions. The inferior competitor's dispersal also mediates the predator's dispersal effects: the predator's dispersal has no effect when the inferior competitor is immobile, and a large effect when it is mobile. The net outcome of the direct and indirect effects of the inferior competitor's dispersal is a qualitative change in the species’ distributions from interspecific segregation to interspecific aggregation.
  • 4
    The important point is that differences between species in how they balance resource acquisition and predator avoidance can lead to unexpected differences in their dispersal effects. While consumer coexistence in the absence of dispersal is driven largely by the top predator, consumer coexistence in the presence of dispersal is driven largely by the predator-resistant inferior competitor.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Communities in which species share common resources and predators are widespread in nature (Mills, Soule & Doak 1993; Menge et al. 1994; Chase et al. 2002; Chase & Leibold 2003). Diversity in such communities is thought to be enhanced by keystone predation: preferential predation on superior resource competitors prevents the exclusion of inferior competitors (Paine 1966; Mills et al. 1993; Menge et al. 1994; Chase et al. 2000, 2002; Chase & Leibold 2003; Schmitz 2003). Predator-mediated coexistence occurs via a trade-off between competitive ability and predator susceptibility: the superior resource competitor must be more susceptible to predation (Leibold 1996; Chase & Leibold 2003; Noonberg & Abrams 2005).

Recent theory suggests that predator-mediated coexistence may not be as strong as previously thought (Abrams 1999; Noonberg & Abrams 2005). There are two reasons for this. First, the competition–predation trade-off is expressed only at intermediate levels of resource productivity and/or predator mortality (Leibold 1996; Noonberg & Abrams 2005): spatial or temporal variation in productivity (mortality) can cause exclusion of the consumer species with the overall disadvantage. Thus, a competition–predation trade-off does not guarantee coexistence in variable environments. Second, even when productivity/mortality regimes allow the trade-off to be expressed, transient dynamics may limit coexistence (Noonberg & Abrams 2005). This occurs because invasion by the predator-resistant inferior competitor causes a large decline in the abundance of the predator-susceptible superior competitor, thus predisposing it to extinction via demographic stochasticity and/or Allee effects; furthermore, transient oscillations following such invasion can lead to low densities of the predator-resistant inferior competitor as well as the predator, further compromising coexistence (Noonberg & Abrams 2005). The fact that such frequent extinctions are not typically observed in nature (Menge et al. 1994; McCauley & Briand 1979; Proulx & Mazumder 1998; Chase et al. 2000; Shurin & Allen 2001; Chase & Leibold 2003; Schmitz 2003) suggests that long-term coexistence must involve additional mechanisms besides a competition–predation trade-off.

While dispersal provides an obvious mechanism for coexistence in spatially structured environments (Amarasekare 2003; Leibold et al. 2004), its role in keystone predation is not well studied. The one study that I am aware of (Shurin & Allen 2001) investigated dispersal effects on regional coexistence using a patch occupancy model (Levins 1969, 1970). However, because this study focused on extinction–colonization dynamics while ignoring local dynamics, it could not investigate dispersal effects on within-patch competition and predation.

Here, I present a spatial model with explicit population dynamics that incorporates species interactions, spatial heterogeneity and extinction due to small population size. I investigate the interaction between dispersal and keystone predation, in particular whether dispersal can increase local diversity by preventing competitive exclusion and extinction during transient dynamics.

The model

  1. Top of page
  2. Summary
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

I consider a patchy and spatially heterogeneous landscape where suitable habitat patches are separated by an uninhabitable matrix. Each habitat patch is occupied by a local community consisting of a resource, two intermediate consumer species and a top predator. The following model describes the dynamics of such a community in the absence of dispersal:

  • image(1)

where Rj is the resource abundance, Cij is the abundance of consumer species i, and Pj is the predator abundance in patch j (i = 1, 2, j = 1, 2, 3). The parameter rj is the per capita rate of resource production in patch j, and K is the spatially invariant resource carrying capacity; ai is consumer species i's attack rate on the resource, ei is the number of its offspring resulting from resource consumption, and di is its background mortality rate. The parameter αi is the predator's attack rate on consumer i, fi is the number of resulting predator offspring, and dP is the predator's background mortality rate.

I consider the consumers and the predator as having linear functional responses. This is because I want to investigate dispersal effects on consumer coexistence in the absence of confounding mechanisms such as coexistence via resource fluctuations. Such mechanisms arise when consumers exhibit saturating functional responses with the superior resource competitor having the more nonlinear response (Armstrong & McGehee 1980).

I nondimensionalize equation (1) using scaled quantities. Nondimensional analysis reduces the number of parameters and highlights biologically significant scaling relations between parameters (Nisbet & Gurney 1982; Murray 1993). I transform the original variables into nondimensional quantities by using the following substitutions.

  • image

(Note that I have separated the nondimensional parameter  = ei/fk, (i, k = 1, 2, i ≠ k) into êi = ei/fi and  = f1/f2 because it allows for a more biologically meaningful scaling relationship.) These quantities have the advantage of being independent of the units used in the analysis. Hence, the expressions ‘small’ and ‘large’ have clear relative meaning (Murray 1993). The nondimensional time metric τ expresses time in terms of the superior competitor's death rate, which allows for comparison between systems that vary in their natural time-scales. Resource abundance is expressed as a fraction of the resource carrying capacity, and varies from 0 to 1. The two consumers’ abundances are scaled by their respective conversion efficiencies (ei) and the resource carrying capacity. Large Cij and small Ckj signify that for any given resource carrying capacity, consumer i has a lower conversion efficiency than consumer k. The nondimensionalized attack rates of the consumers (âi) depend on the resource carrying capacity, conversion efficiency (ei) and the consumer's death rate (di). Similarly, the nondimensionalized attack rate of the predator on consumer i (inline imagei) depend on the predator's conversion efficiencies (fi), consumer i's mortality rate and the resource carrying capacity. The parameter δ is the ratio of the consumers’ mortality rates, and P is the predator's mortality rate relative to that of the superior competitor.

I substitute the nondimensional quantities into (1) and drop the hats for convenience. Unless otherwise noted, all variables and parameters from this point on are expressed as nondimensional quantities. This yields the nondimensional system:

  • image(2)

local dynamics

I focus on aspects of local dynamics that are key to the study of spatial dynamics. Additional details are given in the Supplementary Material Appendices S1 and S2.

Local coexistence via a competition–predation trade-off

Local (within-patch) coexistence of the two intermediate consumers is possible if each consumer species can invade a food chain consisting of the resource, predator and the other consumer species. Mutual invasibility requires that the superior resource competitor (i.e. the species with the a lower R*; Tilman 1982) is more susceptible to predation (see Supplementary Appendix S1 for mutual invasibility criteria). From Equation (2) R* is 1/ai, and hence competitive superiority translates into having a higher attack rate on the resource. Similarly, greater predator susceptibility translates into being subject to a higher attack rate by the predator and yielding more predator offspring per attack. I use ai as the measure of competitive ability and αi as the measure of predator susceptibility. Without loss of generality, I consider consumer species 1 to be the predator-susceptible superior competitor and consumer species 2 to be the predator-resistant inferior competitor. For brevity, I will refer to the two species as superior and inferior competitors.

The strength of the trade-off between competitive ability and predator susceptibility can be quantified in terms of ai and αi. A strong trade-off involves large trait differences between species (e.g. a1 >> a2, α1 >> α2 and f > 1), and allows mutual invasibility over a much larger parameter space than a weak trade-off (Supplementary Appendix S2 and Fig. S2.1a).

A key feature of the competition–predation trade-off is that its expression depends on variability in resource and/or predator traits. Spatial variation in resource productivity and predator mortality in particular have strong effects on the trade-off, restricting its expression to intermediate levels of productivity and mortality (Appendix S2; Fig. S2.1b and c).

Trade-off strength and transient dynamics

In the model considered here (equation 2), conditions that allow both consumer species to invade when rare also guarantee stability of the four-species coexistence equilibrium (Appendix S1; see also Noonberg & Abrams 2005). However, transient dynamics that precede coexistence can involve large-amplitude oscillations, during which species’ abundances can fall to very low levels (Noonberg & Abrams 2005). In real communities, such low-density phases can cause species extinction via demographic stochasticity and/or Allee effects. Noonberg & Abrams (2005) show that such extinction greatly reduces the parameter space allowing coexistence following successful invasion. Interestingly, while it is the inferior competitor's invasion that causes the community to undergo large-amplitude fluctuations (Noonberg & Abrams 2005), it is the superior competitor, because of its inherently low abundance, that is more prone to extinction during transient dynamics.

The strength of the competition–predation trade-off has an important effect on transient dynamics. This occurs primarily via the trade-off's effect on the consumer species’ abundances. For instance, the superior competitor’a abundance is much lower under a strong trade-off than under a weak trade-off (Appendix S2; Fig. S2.2a–d). Coexistence is possible over a wider productivity/mortality range when the trade-off is strong, but it is not guaranteed because of the increased extinction risk for the superior competitor (Appendix S2; Fig. S2.2e and g). Coexistence is limited to a narrow productivity/mortality range when the trade-off is weak, but it is guaranteed because of the minimal extinction risk for the superior competitor (Appendix S2; Fig. S2.2f and h). This interplay between trade-offs that allow local niche partitioning, and small population sizes resulting from transient oscillations has important consequences for spatial dynamics (see below).

spatial dynamics

I envision an environment that is both spatially structured and heterogeneous. Spatial heterogeneity is manifested through variation in resource productivity. I consider resource productivity rather than predator mortality as exhibiting spatial variation for two reasons. First, productivity gradients are ubiquitous in nature, and they have important effects on diversity patterns (Chase 1999a,b; Chase & Leibold 2003); second, it allows comparisons with previous studies of communities with competition and predation, many of which have focused on productivity effects on species coexistence (e.g. Holt & Polis 1997; Chase 1999a,b; Diehl & Feissel 2000, 2001; Mylius et al. 2001; Amarasekare 2006).

The simplest mathematical representation of a metacommunity with spatial variation in resource productivity is a three-patch model with one patch having a productivity level too low for the inferior competitor to invade, one patch having a productivity level too high for the superior competitor to invade, and one patch having a productivity level at which both species can invade and co-exist via a competition–predation trade-off. I consider the resource species as being immobile. Examples of such immobile resources include plants and immobile life stages of insects and aquatic invertebrates. The two consumers and the predator disperse randomly. Spatial dynamics of such a metacommunity are given by:

  • image(3)

where βi and βP are, respectively, the emigration rates of consumer species i and predator scaled by their respective death rates.

I consider the situation where each consumer can support the predator in the absence of the other consumer, that is, each of the three-species food chains is viable. Species’ abundances in these food chains are not so low as to cause extinction. It is when the food chain is invaded by the other consumer species (particularly the inferior competitor) that species’ abundances fall to the levels where demographic stochasticity and/or Allee effects become important (Noonberg & Abrams 2005). Thus, considering both food chains as being initially viable is a reasonable starting point for studying spatial dynamics.

Because the spatial model does not lend itself to analytical results, I used numerical methods to investigate invasibility and coexistence. Equation (3) was numerically integrated for 75 000 time steps using the method of Runge-Kutta step 5 with an adaptive step size (Press et al. 2002). I investigated the effects of extinction during transient dynamics by considering a species as having gone extinct from its resident patch if its abundance fell below 0·0001 (i.e. 1/1000th of the resource carrying capacity for a conversion efficiency ei or fi of unity) during any time step. Long-term abundances were calculated as the average over the last 1200 time steps (Supplementary Appendix S3 gives more details on the simulations).

I introduced spatial variation by setting the patch-specific resource productivity to levels leading to the three outcomes observed in the absence of dispersal: (i) patch 1: inline image (food chain with resource, intermediate consumer 1 and predator), (ii) patch 2: inline image (food web with resource, two intermediate consumers and predator), (iii) patch 3: inline image (food chain with resource, intermediate consumer 2 and predator), where rmax is the maximum resource productivity. I used inline image, inline image, inline image as the baseline productivity variation.

Because the focus is on the interplay between keystone predation and dispersal, I assumed that the two consumer species differ in their attack rates (ai), predator susceptibilities (αi, f) and dispersal propensities (βi) but have similar background mortality rates (i.e. δ = 1) and conversion efficiencies (e1 = e2). The assumption of equal mortality rates allows all important life-history traits to be scaled relative to the common mortality rate; it is biologically realistic because competitors within a guild are often subject to the same density-independent mortality factors (Zwolfer 1971; Mills 1994; Amarasekare 2000). The conversion efficiency ei is the reproductive benefit to consumer species i from resource consumption scaled by the reproductive benefit to the predator via consumption of consumer species i. If the superior resource competitor is more susceptible to predation, it will get more reproductive benefit per unit of resource consumed than the inferior resource competitor, and it will also provide more reproductive benefit to the predator on a per capita basis. Thus, when a competition–predation trade-off operates, the scaled conversion efficiencies of the two consumer species are likely to be comparable (i.e. e1 > e2 and f1 > f2 in equation 1[RIGHTWARDS DOUBLE ARROW]inline image in equations 2 and 3).

I consider four cases of spatial dynamics: (i) predator is immobile, (ii) inferior competitor is immobile, (iii) superior competitor is immobile, and (iv) all three species are mobile. I analyze dispersal effects on the coexistence and abundance patterns when the competition–predation trade-off varies from very weak to very strong.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

effects of dispersal on transient dynamics

I highlight the essential points here and defer the details and the figures to Appendix S3. Dispersal can both increase and decrease the extinction risk due to small population sizes, depending on which species is mobile. Dispersal has the strongest effect on reducing extinction risk when the predator is immobile (Supplementary Fig. S3.1d–f and S3.2d–f). When the competition–predation trade-off is strong, consumer dispersal prevents extinction and ensures global persistence of the four-species food web; when the trade-off is weak, the predator goes extinct from the low-productivity habitat (Fig. S3.1d and S3.2d), but the two consumers can co-exist because the inferior competitor's dispersal allows it to maintain a small sink population. This dispersal scenario leads to the greatest enhancement of diversity, with consumer coexistence resulting from both local (trade-off mediated) and spatial (source-sink) mechanisms.

Dispersal has the strongest effect on increasing extinction risk when the superior competitor is immobile. When the trade-off is strong, extinction of the superior competitor effectively limits its distribution to the intermediate productivity habitat (compare Fig. S3.1J-1 with Fig. S3.2J-1); when the trade-off is weak, the superior competitor can persist in both intermediate- and high-productivity habitats. An increase in extinction due to small population size is expected when the superior competitor is immobile because it is the species whose abundance reaches the lowest levels during transient oscillations. What is unexpected is that dispersal of the predator and the inferior competitor appear to increase superior competitor's extinction from the low-productivity habitat where it has the highest abundance in the absence of dispersal (compare Fig. S3.2a and S3.2j).

The interplay between competition–predation trade-off, dispersal and extinction due to small population size leads to qualitatively different species distributions depending on the relative mobilities of the consumers and the predator (Table 1).

Table 1.  The productivity ranges that allow the persistence and coexistence of the predator-susceptible superior competitor (consumer 1) and predator-resistant inferior competitor (consumer 2) for various dispersal scenarios
Dispersal scenarioTrade-off strengthConsumer 1's distribution*Consumer 2's distribution*Coexistence region**
  • *

    The productivity ranges over which each consumer species can persist. Global means that the species persists over the entire productivity range that allows it to invade when rare despite extinction at low abundances.

  • **

    The productivity range over which the two consumer species can coexist, which is determined by the consumer species with the narrower distribution over a productivity gradient.

  • 1–6

    The five dispersal scenarios yield six unique spatial distributions depending on trade-off strength (Appendix S3, Fig. S3.1 and S3.2). Cases where different dispersal scenarios yield the same distribution (e.g. distributions 1 and 2) can be distinguished by the trade-off strength that yields each distribution. For instance, the same distribution results when all species are immobile and when the predator-resistant inferior competitor is immobile, but the former situation occurs regardless of trade-off strength while the latter occurs only when the trade-off is strong.

All species immobileWeak-strong1Low-mediumMedium-highMedium
Predator immobileWeak-strong2GlobalGlobalGlobal
Consumer 2 immobileStrong1Low-mediumMedium-highMedium
Weak-moderate3GlobalMedium-highMedium-high
Consumer 1 immobileStrong4MediumGlobalMedium
Weak-moderate5Medium-highGlobalMedium-high
All species mobileStrong6Low-mediumGlobalLow-medium
Weak-moderate2GlobalGlobalGlobal

dispersal-mediated coexistence

The inferior competitor's dispersal has a much stronger effect on coexistence than dispersal of the predator or the superior competitor. When the inferior competitor's dispersal is low relative to the within-patch mortality rate (e.g. β2 < 0·2), coexistence in the low-productivity patch occurs via source-sink dynamics in the inferior competitor, and coexistence in the high-productivity patch occurs via source-sink dynamics of the superior competitor. In both cases, the intermediate productivity patch, where trade-off mediated local niche partitioning occurs, acts as the source population. Thus, coexistence at low dispersal rates occurs via a combination of trade-off mediated local niche partitioning and source-sink dynamics in both species. When the inferior competitor's dispersal rate is intermediate (0·2 < β2 ≤ 1) to high (β2 > 1) relative to the within-patch mortality rate, coexistence in the high-productivity patch can occur even when the superior competitor is immobile. This occurs because emigration of the inferior competitor from the high-productivity patch (where it has the highest abundance) far exceeds immigration into it, which allows the superior competitor to invade that patch. In contrast, the superior competitor's net emigration from the low-productivity patch, where it has the highest abundance, does not allow the inferior competitor to invade that patch when the latter is immobile. Coexistence in the low-productivity patch therefore requires source-sink dynamics of the inferior competitor. Thus, coexistence at high dispersal rates occurs via a combination of trade-off mediated local niche partitioning, net emigration of inferior competitor from the high-productivity patch, and source-sink dynamics of the inferior competitor. The key point is that the inferior competitor's dispersal rate determines which combination of local and spatial coexistence mechanisms operates in the metacommunity (Table 2).

Table 2.  Effects of the predator-resistant inferior competitor's dispersal in coexistence and species distributions
Inferior competitor's dispersal1Coexistence mechanisms2Abundance-productivity relationshipSpecies distributions
Superior competitorInferior competitor and predator
  • 1

    Relative to the within-patch mortality rate;

  • 2

    2 when trade-off mediated local niche partitioning also operates.

LowSource sink in both species[DOWNWARDS ARROW] with[UPWARDS ARROW] productivity[UPWARDS ARROW] with [UPWARDS ARROW] productivityInterspecific segregation
MediumEmigration of inf. competitor, source sink in inf. competitorHump-shaped, highest abundance at intermediate productivity[UPWARDS ARROW] with [UPWARDS ARROW] productivityPartial interspecific segregation
HighEmigration of inf. competitor, source sink in inf. competitor[UPWARDS ARROW] with[UPWARDS ARROW] productivity[UPWARDS ARROW] with [UPWARDS ARROW] productivityInterspecific aggregation

dispersal-mediated changes in species’ distributions

The inferior competitor's dispersal has a much stronger effect on species’ distributions than dispersal of the predator or the superior competitor. Specifically, the inferior competitor induces a qualitative change in the superior competitor's abundance–productivity relationship, both directly through its own dispersal and indirectly through the predator's dispersal. For instance, when the inferior competitor is immobile, the superior competitor's abundance–productivity relationship is qualitatively similar to that in the absence of dispersal (Fig. 1a vs. 1d); when the inferior competitor is mobile, the superior competitor's abundance–producitivity relationship is qualitatively different (Fig. 1a vs. 1g), an effect that becomes stronger when the predator is also mobile (Fig. 1a vs. 1m). The predator's dispersal has no effect on the superior competitor's abundance–productivity relationship when the inferior competitor is immobile (Fig. 1a vs. 1d), and a strong effect when the inferior competitor is mobile (Fig. 1a vs. 1j, 1d vs. 1j). The superior competitor's dispersal has no effect on any species’ abundance pattern (Fig. 1a–c vs. 1d–f). These effects are robust to extinction during transient oscillations.

image

Figure 1. Long-term abundances as a function of resource productivity for the various dispersal scenarios. In each panel, multiple values at each productivity level reflect abundances at different trade-off strengths (see raw data in Fig. S3.1 and S3.2). Each circle represents the average abundance over a unit trade-off strength, e.g. the abundance corresponding to a trade-off strength of 4 is the average over the trade-off strength range 4·00–4·99. Trade-off strength was calculated for varying values of a1 and α1 (1 ≤ a1 ≤ 10, 1 ≤ α1 ≤ 10) while holding other parameter values constant (a2 = 2, α2 = 1, e1 = e2 = 1, δ = 1, f = 2 and dP = 0·5; see Appendix S3 for details).

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These results suggest an asymmetry between species in their dispersal effects. This asymmetry can be investigated further by looking at the effect of variable dispersal rates on species’ abundance–productivity relationships (Fig. 2). This analysis confirms that the inferior competitor's dispersal induces a qualitative change in the superior competitor's abundance–productivity relationship, causing it to increase rather than decrease with increasing productivity. As a consequence, species’ distributions across the landscape also undergo a qualitative change, from interspecific segregation to interspecific aggregation (Fig. 2, Table 2).

image

Figure 2. Abundance–productivity relationships under variable dispersal rates of the inferior competitor. When the inferior competitor is immobile, the superior competitor's abundance pattern is qualitatively similar to that in the absence of dispersal, regardless of the predator's dispersal rate (βP). When the inferior competitor is mobile but the predator is immobile, the superior competitor's abundance pattern is qualitatively similar to that in the absence of dispersal for low β2, but qualitatively different for high β2. When the inferior competitor and the predator are both mobile, the superior competitor's abundance pattern is qualitatively different even for low β2. The inferior competitor's and the predator's abundance patterns are insensitive to the dispersal scenario as well as to the inferior competitor's dispersal rate. The predator has only a weak abundance gradient when the inferior competitor is immobile but a strong gradient when the inferior competitor is mobile. Parameter values used are: a1 = 9, a2 = 2, α1 = 9, α2 = 1, e1 = e2 = 1, δ = 1, f = 2, dP = 0·5 and β1 = 0·5; βP = 0·5 for all cases except when the inferior competitor is immobile.

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What is the mechanism by which the inferior competitor's dispersal changes the superior competitor's abundance–productivity relationship? Because the inferior competitor's abundance increases with increasing productivity in the absence of dispersal, its net movement occurs in the direction of decreasing productivity. Net emigration of the inferior competitor from the high-productivity patch allows the superior competitor to invade that patch and attain high abundances. When the predator is immobile, the inferior competitor's net immigration into the low-productivity patch decreases the superior competitor's abundance via a mass effect. This effect, however, is relatively weak. It becomes much stronger when the predator is also mobile. Then, the predator's net movement into the low-productivity patch imposes high mortality on the superior competitor and decreases its abundance. Thus, the inferior competitor's dispersal has the direct effect, through emigration, of increasing the superior competitor's abundance in the high-productivity patch, and the indirect effect, through the predator's dispersal, of reducing the superior competitor's abundance in the low-productivity patch.

This last result begs the question of how the inferior competitor's dispersal mediates the effects of the predator's dispersal. When the inferior competitor is immobile, the predator's abundance is only weakly related to productivity. This is because the predator's abundance depends on consumers’ traits rather than the basal resource's traits. When the inferior competitor is mobile, its net movement into the low-productivity patch causes an overabundance of the less palatable prey. This causes a decrease in the predator's abundance in the low-productivity patch, thus creating an abundance gradient in the direction of increasing productivity. The resulting influx of predators into the low-productivity patch causes a further decline in the superior competitor's abundance in that patch.

The last question to address is why the superior competitor's dispersal does not affect the predator's or the inferior competitor's abundance. Because the superior competitor's abundance decreases with increasing productivity in the absence of dispersal, its net movement is in the direction of increasing productivity. However, the superior competitor's net emigration from the low-productivity patch does not allow the inferior competitor to invade that patch. This is because the inferior competitor's poor resource exploitation ability prevents it from maintaining self-sustaining populations in resource-poor areas; it can only maintain a small sink population, via dispersal, in such habitats. The superior competitor's net immigration into the high-productivity patch has no effect on the inferior competitor, because the latter's abundance is much higher than the former's in the presence of the predator. These two constraints also prevent the superior competitor's dispersal from altering the predator's abundance pattern.

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Predator-mediated coexistence has long been considered an important mechanism of diversity maintenance (Paine 1966; Mills et al. 1993; Menge et al. 1994; Chase et al. 2000, 2002; Chase & Leibold 2003; Schmitz 2003), but recent theory shows that its effectiveness may be limited by demographic stochasticity and environmental variability (e.g. Leibold 1996; Abrams 1999; Noonberg & Abrams 2005). A previous study shows that high predator colonization rates can increase regional coexistence of consumers (Shurin & Allen 2001). However, because it focused on extinction–colonization dynamics, this study could not investigate dispersal effects on the local dynamics of competition and predation.

Here, I present a model that explicitly investigates the interplay between dispersal and the local dynamics of keystone predation. I obtained two key results. First, a strong trade-off between competitive ability and predator susceptibility allows consumer coexistence over a large resource productivity range, but it also predisposes species to extinction (via demographic stochasticity and/or Allee effects) during community assembly. This yields the unexpected outcome of dispersal being more important in maintaining diversity when predator-mediated coexistence is strong rather than weak.

The second key result is an asymmetry between species in their dispersal effects and responses. Dispersal of the inferior competitor has a large effect, but dispersal of the predator and the superior competitor have little or no effect, on coexistence and species’ distributions. For instance, the inferior competitor's dispersal determines the type of spatial coexistence mechanisms that operate within the metacommunity. Moreover, the inferior disperser's dispersal changes species’ distributions from interspecific segregation in low- and high-productivity habitats to interspecific aggregation in high-productivity habitats.

Previous studies of dispersal effects on intraguild predation found a similar asymmetry with the intraguild predator's dispersal having a much larger effect on the intraguild prey than vice versa (Amarasekare 2006, 2007). However, because the two species are competitors who also engage in a trophic interaction, it could not be determined whether the asymmetry resulted from the intraguild predator's role as a competitor or predator. The crucial contribution of the present study is in elucidating the combinations of life-history traits and vital rates that allow some species to have a disproportionately large effect (relative to their trophic status) on other community members via dispersal. By separating the competitive interactions that occur within a trophic level from the predator–prey interactions that operate between trophic levels, this study shows that it is not the predator but the predator-resistant intermediate consumer whose dispersal drives coexistence and species distributions.

This asymmetry in dispersal effects arises from the differences between two consumer species in how they solve the problem acquiring resources in the face of predation: one species is better at resource acquisition while the other species is better at predator avoidance. These differences in turn cause species-specific responses to spatial variation in resource productivity (or predator mortality) such that the superior competitor's abundance decreases, and the inferior competitor's abundance increases, with increasing productivity. Random dispersal in the face of opposing abundance gradients causes a net movement of the superior competitor from areas of low to high productivity, and a net movement of the inferior competitor from areas of high to low productivity. The asymmetry results from the inferior competitor's net movement occurring in a direction that simultaneously exerts a large impact on the superior competitor (both directly, and indirectly via the predator), and prevents the superior competitor from having an impact on the inferior competitor. For instance, the inferior competitor is more limited by resources than predation and hence cannot invade the low-productivity habitat despite the superior competitor's net emigration from it. Thus, the superior competitor's dispersal induces no qualitative change in the inferior competitor's abundance pattern. In contrast, the superior competitor is limited less by resources than by predation, and hence, the inferior competitor's net movement from high- to low-productivity habitats allows the superior competitor to invade the high-productivity habitat and attain high abundances even in the absence of its own dispersal. The inferior competitor's net movement from high- to low-productivity habitats also reduces predator abundance in the low-productivity habitat and creates an abundance gradient in the direction of increasing productivity for the predator. The ensuing net predator movement from high- to low-productivity habitats inflicts high mortality on the superior competitor in the low-productivity habitat. This in turn decreases the superior competitor's abundance in the low-productivity habitat below that in the absence of dispersal. The net result is a qualitative change in the superior competitor's abundance gradient, with abundances now increasing with increasing productivity. This in turn induces a qualitative change in the species’ distributions across the landscape, from interspecific segregation to interspecific aggregation.

The important implication of these results is that differences between species in how they balance resource acquisition and predator avoidance can lead to unexpected differences in their dispersal effects. While consumer coexistence in the absence of dispersal is driven largely by the top predator, consumer coexistence in the presence of dispersal is driven largely by the predator-resistant inferior competitor. This suggests that there may exist keystone dispersers, species whose dispersal has a disproportionately large effect on community dynamics.

The fact that the species exerting keystone effects via dispersal are not necessarily those exerting keystone effects in the absence of dispersal is critical in understanding and predicting spatial community dynamics. The typical keystone species is a generalist predator that, through its preference for a particular prey species, has a large effect on species occupying lower trophic levels. In contrast, a keystone disperser is likely to be an intermediate consumer with low resource exploitation efficiency and high predator resistance/tolerance that, through its response to spatial variation in resource or predator traits, has large effects on species occupying its own trophic level as well as levels above and below. Such species are most likely to be found in communities of small-bodied predators/parasites that attack prey/hosts of same or larger sizes (e.g. insects and aquatic invertebrates). Insect herbivores that are relatively invulnerable to predation or parasitism are particularly likely candidates.

While these theoretical insights are interesting, their true significance lies in the extent to which they capture the interplay between species interactions and dispersal in real communities. The model analysed here yields qualitatively different species distributions depending on the relative mobilities of the consumers and the predator (Table 1). These differences yield comparative predictions about the interplay between the competition–predation trade-off, small population sizes during transient oscillations, and dispersal in determining spatial coexistence and species’ distributions. These predictions can be tested with data on trade-off strength, dispersal rates and species distributions across productivity gradients.

Finally, the model analysed here considers the effects of random dispersal on interspecific interactions. It does not consider intraspecific interactions such as inbreeding or kin competition that may favour non-random dispersal. For instance, inbreeding avoidance may select for sex-biased dispersal while kin competition, and intra-specific competition in general, may select for density-dependent dispersal (Ronce 2007). Such nonrandom dispersal strategies may well change the patterns of coexistence and species abundances predicted under random dispersal. Investigating the consequences of dispersal driven by intraspecific vs. interspecific interactions is an important next step.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

This research was funded by a grant from NSF (DEB-0717350). I thank two anonymous referees for many constructive comments on the manuscript.

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  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information
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Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. The model
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Supporting Information

Appendix S1. Invasion criteria and local stability analysis for the four species food web with keystone predation

Appendix S2. Local dynamics of keystone predation: key aspects of the competition–predation trade-off

Appendix S3. Spatial dynamics of keystone predation: effects of dispersal on transient dynamics and species’ abundance patterns

Figure S2.1. Key aspects of the trade-off between competitive ability and predator susceptibility

Figure S2.2. The interplay between trade-off strength and extinction during transient oscillations

Figure S3.1. Long-term abundances of the two consumers and the predator as a function of trade-off strength in low-, intermediate- and high-resource productivity habitats for the various dispersal scenarios when extinction due to small population size is not considered

Figure S3.2. Long-term abundances of the two consumers and the predator as a function of trade-off strength in low-, intermediate- and high-productivity habitats for the various dispersal scenarios when extinction due to small population sizes is taken into account

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