Ecological Modelling

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1 Ecological Modelling 222 (2011) Contents lists available at ScienceDirect Ecological Modelling jo ur n al homep ag e: The influence of soil community density on plant-soil feedbacks: An important unknown in plant invasion Anna G. Aguilera Biology Department, University of Massachusetts, 100 Morrissey Blvd., Boston, MA 02125, United States a r t i c l e i n f o Article history: Received 4 October 2010 Received in revised form 16 June 2011 Accepted 19 June 2011 Available online 29 July 2011 Keywords: Plant-soil feedbacks Invasion Competition a b s t r a c t Plant-soil feedbacks have been implicated in several successful plant invasions. However, simple identification of a feedback alone may not be enough to establish feedbacks as a mechanism behind plant invasion. I suggest that the relationship between soil community density and plant growth is an important unknown that strongly influences the impact of plant-soil feedbacks. I developed a mathematical model of two-plant species competition with plant-soil feedbacks. Each plant species obligately generates its own soil community. Each soil community then influences both plant species growth. The model allows for every possible combination of positive and negative effects of the soil community on plant growth. I model the relationship between soil community density and plant growth with non-linear functional responses. I use a range of plant competitive abilities and feedback scenarios from the literature to explore how different functional responses influence the outcome of plant competition. Sensitivity analysis of the model reveals that altering the relationship between feedback strength and soil community development can reverse the outcome of plant competition. Analysis of the model also shows how the importance of different feedback scenarios depends on the strength of plant competition Elsevier B.V. All rights reserved. 1. Introduction The growth rates of plants and their associated soil communities are tightly linked by feedbacks. The soil community is diverse; made up of bacteria, archea, protists, nematodes, and other invertebrates. Live plant biomass and exudates support both mutualistic and pathogenic invertebrate species. Mutualistic species directly supply plants with mineral nutrients in return for plant-supplied carbohydrate, as in the case of mycorrhizal associations. Negative plant-soil feedbacks occur when pathogenic microbes limit the growth of associated plant species. As a result, soil feedbacks have a strong influence on the composition of plant communities. Feedbacks can facilitate the coexistence of strong competitors and maintain diversity (Bever, 1994, 2003; Westover and Bever, 2001). However, recent publications have also implicated plant-soil feedbacks in the success of invasive plant species and reduced diversity (Borer et al., 2007; Bradley et al., 2008; Callaway et al., 2008; Jordan et al., 2008; Kourtev et al., 2002; Stinson et al., 2006). There are several feedback scenarios that have been put forth as driving mechanisms behind invasion. They include Enemy Release, Novel Weapons, what I refer to as Nutrient Availability, and the more recently proposed hypothesis Pathogen Fax: address: Anna.Aguilera001@umb.edu Accumulation. The Enemy Release hypothesis states that invasive species escape their natural enemies when they invade new ranges, and this causes their increase in distribution and abundance (Keane and Crawley, 2002). This hypothesis is easily applied to soil pathogens. Plants escape their soil pathogens when they arrive in a new range, presumably releasing them from a negative feedback. Such a theory has been supported by research showing that rare native plants accumulate more pathogens than invasive plants (Engelkes et al., 2008; Klironomos, 2002). The Novel Weapons hypothesis (Callaway and Ridenour, 2004) suggests that some nonnatives become invasive because they release chemicals that are novel in the invaded environment and that inhibit native plants. These chemical compounds can act directly upon native plants (as in cases of allelopathy), or they can disrupt microbe plant symbioses. The latter mechanism disrupts positive feedbacks between native plants and soil communities, giving the non-native plant an advantage that enables it to become invasive (Wolfe et al., 2008). Invasive plants can create soil feedbacks that change Nutrient Availability either positively or negatively. If the altered Nutrient Availability benefits the invasive plant over natives, it creates a Nutrient Availability feedback that may enable the invasive plant to dominate and spread. Finally, according to the Pathogen Accumulation hypothesis, invasive plants accumulate soil pathogens in their native soil that feed back negatively on their own growth. This negative feedback accelerates succession and replacement by other species. Eppinga et al. (2006) posit that in the invaded range the invasive plants still accumulate pathogens, but that the native /$ see front matter 2011 Elsevier B.V. All rights reserved. doi: /j.ecolmodel

2 3414 A.G. Aguilera / Ecological Modelling 222 (2011) plants are more sensitive to these pathogens than the invader. This disproportionate sensitivity to soil pathogens confers a relative advantage to the non-native plant, changing the competitive hierarchy and allowing it to become invasive. Clearly, these hypotheses depend on different combinations of positive and negative soil effects on plant growth. There is little known about actual mechanisms for these feedbacks and relative impacts that plant-soil feedbacks have on plant competition. Existing sensitivity analysis of mathematical models of plant competition with soil feedbacks can identify parameters and interactions that, when changed slightly, cause significant changes to the outcome of the model (Eppinga et al., 2006; Bever, 1999). Here I present a new model of plant competition with plant-soil feedbacks that is unique in its ability to accommodate all combinations of positive and negative feedback effects. As such it can be applied to any of the above feedback scenarios. I use this model to: (1) identify how soil feedbacks may alter competitive outcomes and, (2) identify important unknowns in our current understanding of plant-soil feedbacks and their role in plant invasion. Specifically, I examine how the relationship between soil community density and its effect on plant growth influences model outcomes. This relationship is rarely reported in the literature and has not been a focus of model sensitivity analysis. In previous models this relationship was considered linear (Bever, 1999) or assigned a functional response curve (Eppinga et al., 2006). I use 3 different functional responses to examine how the relationship between soil community density and plant growth influences two species plant competition. 2. Materials and methods 2.1. The model The model of competition with soil feedbacks presented is similar to, and builds upon, the model developed by Eppinga et al. (2006). The model is a modification of the Lotka Voltera two species competition model. This model includes two plant species: the native species represented by the index n, and the invasive species represented by the index i. Associated with each plant species is a density of a soil community, S i, S n (g m 2 ), that is obligately generated by its host plant. The density of the soil communities as a function of t is primarily described by the solution of the following logistic growth equations (shaded portions of (1a) and (1b)). ( ds i dt = r i S i 1 ds n dt = r n S n (1 ) S i k i in S i (1a) S n k n ) ni S n (1b) where r i and r n are the relative growth rates (day 1 ) of the soil communities S i, and S n, and k i and k n (g m 2 ) are the carrying capacities of the soil communities. In both equations, a small value (0.0001) is added to the carrying capacity to avoid singularities. The parameters in and ni (day 1 ) are unique to this model and represent a weighting term of the effects of the native plant on the invasive soil community and the invasive plant on the native soil, respectively. pq = max,pqsq x ωpq x + Sq x (2) Here max,pq is the maximum effect of plant species q that can be exerted on soil community p. The parameter ω pq (g m 2 ) is the half saturation constant, meaning the soil community density at which point plant species p experiences half of the maximum effect of soil community q. The x parameter in these equations determines the shape, and specific name of the functional response (Fig. 1; Holling, 1959). Fig. 1. Three Hollings functional response curves, type II (x = 1), type III (x = 2), and type III (x = 3). For these simulations xpq = 50, max,pq = 1. The parameters k i and k n are themselves functions of plant densities N i, N n (g m 2 ). k i = k n = N i N max,i S max,i N n N max,n S max,n (3a) (3b) Eqs. (3a) and (3b) describe how the soil carrying capacities are linearly dependent on the size of the plant populations. Here variables N i and N n are the host plant densities, constants N max,i and N max,n (g m 2 ) are the carrying capacities for the host plants, and constants S max,i and N max,n (g m 2 ) are the maximum carrying capacity for the specific soil communities. Host plant densities never exceed N max, therefore the fraction N/N max will always be less than or equal to one. To obtain the carrying capacity of the soil communities the maximum carrying capacity is multiplied by the proportion of actual host plant density to the host plant carrying capacity. When the density of the host plant is at carrying capacity, and there is no effect of plants on soil communities ( in = ni = 0), the density of its associated soil community can also reach its maximum carrying capacity. Eqs. (3a) and (3b) are based upon the assumption that microbial communities are always faithful to host plants. The model however, does not assume that there is no redundancy in microbe species between the two soil communities, as it is only concerned with the net effect of the microbial community of each. The host plant growth equations are as follows: dn i dt dn n dt = g i N i (1 = g n N n (1 ) N i + c in N n N max,i + ii N max,i + in N max,i ) N n + c ni N i N max,n + nn N max,n + ni N max,n (4a) (4b) Here g i and g n (day 1 ) are the relative growth rates of plant species i and n, and c in and c ni (g g 1 ) are the plant-only competition coefficients for species i and n. The parameter pq (day 1 ) is the effect of soil community q on plant species p. pq = max,pqs x q xpq + S x q Here max,pq is the maximum effect of soil community q that can be exerted on plant species p. Unlike the Eppinga et al. (2006) model that is concerned only with negative feedbacks, the equations allow for this parameter to be either positive or negative, thereby either increasing or reducing maximum N p potential. The parameter pq (g m 2 ) is the half saturation constant, meaning the soil community density at which point plant species p experiences half of the maximum effect of soil community q. As with Eq. (2), the x (5)

3 A.G. Aguilera / Ecological Modelling 222 (2011) Fig. 2. Conceptual schematic of the model. Arrows indicate direct connections between populations, and ± at the base of each arrow indicates positive or negative impacts on the receiving population. parameter in Eq. (5) determines the shape, and specific name of the functional response (Fig. 1; Holling, 1959). The general form of the feedback functions (Eqs. (2) and (5)) is that of Hollings functional responses. When x = 1 the equation produces a Hollings type II functional response. When x > 1 the resulting curves are known as Hollings type III functional responses. A Hollings type II response curve describes an initial strong effect of low densities of soil community that levels off. The Hollings type III responses describe an initial lag in effect on plant growth with increases in soil community density that then leads to an exponential increase that eventually levels off at the maximum effect. As the exponent increases from 2 to 3 in the Hollings type III functional response there is a longer initial lag in effect on plant growth with increasing soil community density (Fig. 1). The nature of this relationship in reality is unknown and all three curves (and more) can be expected to be present in nature. As the model is currently parameterized the soil effects on plant growth are greatest at low soil community densities when a Hollings type II functional response is used. This is reversed at high soil community densities, and the Hollings type III functional responses have the greatest effect on plant growth. This is a function of the model s parameterization rather than a fundamental difference between functional responses. However it is this difference in effect size relative to soil community density that is an unknown in the current feedback literature. I use the different functional responses to show that these differences cause changes in the outcome of competition; not to say that one functional response type will always have certain effects at specific soil densities. Taken together, the resulting set of differential equations makes a deterministic model, with no seasonality, that is not spatially explicit. Fig. 2 provides a conceptual schematic of the model Model analysis I parameterized the model using values from the literature (Table 1), and I set the initial conditions to simulate either Recolonization of Bare Ground (N i [0] = N n [0] = 5; S i [0] = S n [0] = 1; Fig. 4) or Invasion into an Established Native Population (N i [0] = 5, N n [0] = 400; S i [0] = 1, S n [0] = 80; Fig. 5). Besides competition (c in, c ni ), feedback ( pq ), and functional response values (x) all parameter values are equal for the two soil communities and plant populations. I assembled four feedback scenarios from the literature that each fit into one of the four categories, Pathogen Accumulation (PA), Enemy Release (ER), Novel Weapons (NW), and Nutrient Availability (NA) (Table 1). Fig. 3. Output from a single run of the model using Pathogen Accumulation feedback ( max,pq) values. For this simulation, N i [0] = 20, N n[0] = 20, S i [0] = 8, S n[0] = 8, xpq = 50, r i = r n = 0.03, g i = g n = 0.2, c in = c ni = 1.0, x = 2, t = 500. I analyzed each scenario separately, holding feedback values constant while changing competition coefficients. I varied competition coefficients over the interval in steps of I did this three times for each scenario each with different functional responses: Hollings type II (x = 1) and Hollings type III (with x = 2 and x = 3) functional response curves (Fig. 1). In this way I was able to examine how feedbacks change the outcome of plant competition and how altering the shape of the functional response affects that dynamic. Because each scenario (collection of feedback values) has a sample size of one, none can be assumed to be representative of the plant-soil feedback scenario it is named for. For example, every set of feedback values that conforms to a Pathogen Accumulation scenario cannot be assumed to behave as the Pathogen Accumulation scenario analyzed by this model does. However, I refer to each example with the scenario name for clarity. In addition, because the individual scenarios are not representative of the general plant-soil feedback I was not able to directly compare scenarios types. I used Matlab software to solve the system of ordinary differential equations using the Runge Kutta method to solve initial value problems. The total time for each run, t total, was 1000 (days), with a time step, t, of 0.1. Fig. 3 shows an example of an outcome from a single run of the model. Each run provides the density in g m 2 for both plant species and their associated soil communities. Running the model for every combination of competition coefficients, feedback values and functional response revealed thresholds that define when one plant species competitively excludes the other or when there is competitive coexistence. Results are presented as response planes for all combinations of competitive coefficients for each feedback scenario (Figs. 4 and 5). The axes of the response planes are the competitive effect of the native (c in ) and the non-native (c ni ) plants (Figs. 4 and 5). To visually assess these response planes it is helpful to consider that there are four zones in the plane (Figs. 4b and 5b). In zone I the native species is a weak competitor, and the non-native species is a strong competitor, in zone II both plant species are strong competitors, in zone III both species are relatively weak competitors, and in zone IV the native species is strong and the non-native species is weak. To understand how feedbacks influence competition it is also helpful to establish threshold values determining regions of competitive coexistence and competitive exclusion when there are no soil feedbacks at work (Figs. 4a and 5a). Both the zone delin-

4 3416 A.G. Aguilera / Ecological Modelling 222 (2011) Table 1 Values, units, and references for parameters used in the model simulations. Parameter Definition PA ER NW NA Units References a r i, r n Relative growth rate for invasive (i) and days 1 Ferris et al. (1996) native (n) soil communities a g i, g n Relative growth rate for invasive (i) and days 1 Hunt and Cornelissen (1997) native (n) plants c pq Competitive effect of plant q on plant p g g 1 Created based on reasonable range of values a S max,i, S max,n Maximum carrying capacities for invasive g m 2 Neher (1999) (i) and native (n) soil communities a N max,i, N max,n Carrying capacities for invasive (i) and native (n) plants g m 2 Olff et al. (2000), Blomqvist et al. (2000) a max,ii Maximum effect of invasive soil day 1 Jordan et al. (2008), Niu et al. (2007) community on invasive plant a max,in Maximum effect of native soil day 1 Jordan et al. (2008), Niu et al. (2007) community on invasive plant a max,nn Maximum effect of native soil day 1 Jordan et al. (2008), Niu et al. (2007) community on native plant a max,ni Maximum effect of invasive soil day 1 Jordan et al. (2008), Niu et al. (2007) community on native plant xpq Half saturation constant for soil community q on plant p g m 2 Arbitrarily set at half of the maximum density for all communities and simulations a max,ni Maximum effect of invasive plant on native soil day 1 Stinson et al. (2006) a Values were typically not presented in papers and were calculated from data provided. eations and no-feedback thresholds are displayed on each response plane. Each response scenario (Figs. 4c f and 5c f) has a form similar to the no soil feedback figure, with the feedback values and functional response values altering the relative size and exact shape of each region in the response plane (each panel shows a different response scenario; the pink, blue, and red lines show the model outcomes with the different functional response curves). Each response plane has three separate regions: (1) the area closest to the origin where there is competitive coexistence (here defined as both species having 10 or greater g m 2 after 1000 days), (2) the area underneath the threshold line where the outcome is competitive exclusion of the non-native plant by the native plant, and (3) the area above the threshold line depicting competitive exclusion of the native plant by the non-native plant. Figs. 4c f and 5c f illustrate how adding soil feedbacks alter the response plane Model assumptions For purposes of simplification this model makes several nonrealistic assumptions. To begin, it is a deterministic model with no seasonality. In addition, as presented here it only simulates competition between two species and is not spatially explicit. I also assume that the relationship between soil community density and plant growth is non-linear. Also, as mentioned earlier, microbial species are always faithful to their host plants, and the functional response describing the relationship between soil community density and plant growth is held constant for all plant-soil combinations for each simulation. Finally, I assume that competition coefficient values used for the model simulations represent the competitive ability of plants if they were to be grown in sterile soil (without the influence of soil communities). 3. Results 3.1. Colonization of bare ground Soil feedbacks confer advantages to non-native species in two ways. In some cases they lower the minimum competitive effect of the non-native on the native plant above which non-native plants will competitively exclude native species, thereby increasing the area of competitive exclusion by the non-native plant on the response plane. Feedbacks can also increase the area of competitive coexistence while reducing the area where native plants competitively exclude non-native plants (Fig. 4). In the Pathogen Accumulation, Novel Weapons, and Nutrient Availability scenarios, zone III clearly illustrates how feedbacks increase the region of competitive exclusion by the non-native species. In all three cases the type of functional response determines the severity of this effect. This is most clearly demonstrated in the Pathogen Accumulation scenario where the advantage to the non-native plant increases as the exponent in the Hollings function response equation increases from 1 to 3. Zones II and IV also show enlarged regions of competitive exclusion by non-native species for all four scenarios and all three functional response values. In this region where both plants have relatively high competition coefficients, feedbacks with a Hollings type II functional response confer the greatest advantage to nonnative species. Finally, the Enemy Release scenario illustrates well how feedbacks can increase the region of competitive coexistence in zone IV. In this extended area of coexistence competitively inferior nonnative plants are able to coexist with stronger native plants. In the Enemy Release scenario this effect is most exaggerated when the functional response exponent value is 3 (Hollings type III) and least pronounced when a Hollings type II functional response is used. However, in the remaining three scenarios the region of competitive coexistence is greatest with a Hollings type II functional response Invasion into an established native population When there is an established native population a small number of invasive plants are never able to exclude strong native competitors (zones II and IV). The Enemy Release feedback analyzed here reduces this region where strong native plants are able to resist invasion. In contrast the Novel Weapons scenario analyzed increases this region, thereby allowing relatively weaker native plants to resist invasion. The Novel Weapons scenario has positive soil-plant feedbacks for the native plant that are disrupted by the non-native plant. When the initial population of non-native plants

5 A.G. Aguilera / Ecological Modelling 222 (2011) Fig. 4. Competitive response plane for Recolonization of Bare Ground initial conditions: no plant-soil feedbacks (a), zones of relative competitive ability in the response plane (b), and competitive response planes for the four scenarios, Pathogen Accumulation (c), Nutrient Availability (d), Novel Weapons (e), Enemy Release (f). Planes c f are the result of running the model for every combination of both 0 < c in < 2 and 0 < c ni < 2 in steps of 0.01 for all three Hollings functional response curves. is small it is not able to significantly reduce the advantage the native plants receive from their soil communities. In zones I and III results of the invasion into an established community are very similar to those with initial conditions set to resemble recolonization of bare ground. In zone I, where the native plants are weak and the invasive plants are strong, there is competitive exclusion by the invasive plant. Feedbacks cause this area of competitive exclusion to continue well into zone III. Therefore the feedbacks allow weaker invasive plants to competitively exclude natives, thereby reducing the likelihood of coexistence. As was true for the Recolonization of Bare Ground initial conditions, the impact of the feedback changes with different functional response curves. 4. Discussion As expected the soil feedbacks alter the competitive outcomes of two species competition, however the nature of these conferred competitive advantages depends on the feedback values and the functional response modeling the relationship between soil community density and plant growth. The one advantage of soil

6 3418 A.G. Aguilera / Ecological Modelling 222 (2011) Fig. 5. Competitive response plane for invasion into an Established Population initial conditions: no plant-soil feedbacks (a), zones of relative competitive ability in the response plane (b), and competitive response planes for the four scenarios, Pathogen Accumulation (c), Nutrient Availability (d), Novel Weapons (e), Enemy Release (f). Planes c f are the result of running the model for every combination of both 0 < c in < 2 and 0 < c ni < 2 in steps of 0.01 for all three Hollings functional response curves. feedbacks for non-native species that is consistent across all of the Recolonization of Bare Ground feedback scenarios is that they lower the threshold above which a strong non-native plant competitor will exclude strong native species as seen in zone II. However, this effect is only present when a Hollings type II functional response is used in the model. When initial conditions are set to Recolonization of Bare Ground the Novel Weapons, Pathogen Accumulation, and Nutrient Availability scenarios show similar patterns of invader advantage due to soil feedbacks for weak non-native and native plant competitors (zone III). Zone III has an increased region where the invader completely excludes the native, where otherwise (with no feedbacks) the two plant species would coexist. With this pattern of advantage it becomes easier for relatively weak invasive species to exclude relatively weak native species. In the Enemy Release scenario this dynamic is not observed; however in this scenario the feedback generates a greater region of competitive coexistence where relatively weak invaders are able to persist in the presence of strong native species (zone IV). When the initial conditions simulate invasion into an established native populations all four scenarios show the same pattern of invader advantage due to soil feedbacks for weak non-native and native plant competitors (zone III), as is seen with the Recolonization of Bare Ground initial conditions. This effect increases as the exponent in the functional response increase from 1 to 3. However, unlike the recolonization of bare ground analysis, non-native plants are never able to become invasive when the established native population is a strong competitor. In addition the model suggests that

7 A.G. Aguilera / Ecological Modelling 222 (2011) the type of plant-soil feedback present in the native population changes the ability of native plants to resist invasion. When feedbacks are positive, relatively weaker native plants are able to resist invasion. This occurs even when the non-native plants disrupt the positive feedback. Using a spatially explicit multi-species simulation model in a pathogen-regulated community, Turnbull et al. (2010) found that successful invasion was not determined by whether the invasive species experienced a release from negative feedbacks in its own soil. Eppinga et al. s (2006) Pathogen Accumulation scenario posits that non-native plants gain the competitive advantage and become invasive by having some degree of release from negative soil feedbacks. Turnbull et al. (2010) assume that all negative feedbacks for each plant in its own soil are the same and that all away soils improve the growth of non-resident species equally. In contrast, Eppinga et al. (2006) assume each plant species responds to the negative feedbacks differently. The Eppinga et al. (2006) and Turnbull et al. (2010) models both explore the role of negative feedbacks in plant invasion and they come to different conclusions about how a release from negative feedbacks influences invasive plants. Taken with the range of results of the model presented here, this discrepancy highlights the importance of the unknown relationship between soil communities and different plant species. Soil feedbacks have been suggested as a mechanism that may explain plant invasion. However, simulations with this model suggest that even when feedbacks ( pq ) have been identified, it is still critical to understand the nature of the feedback (i.e., the shape of the relationship between soil community density and the soil community s effect on plant growth) and the relative competitive ability of the invader before asserting that feedbacks are a driving mechanism behind plant invasiveness. The common method to determine whether a plant generates a soil feedback is to pre-condition soil separately with invasive species and native species. Then, invasive and native plants are grown in each soil and/or sterilized soil. The difference in growth after a prescribed amount of time between plants grown in conspecific soil and foreign soil, or preconditioned soil and sterile soil, is taken as the effect of soil feedbacks on plant growth (Jordan et al., 2008; Niu et al., 2007; Stinson et al., 2006). A meta-analysis of plant-soil feedbacks (Kulmatiski et al., 2008) found that most soil-feedbacks ( pq ) reported in the literature are negative. Metaanalyses also revealed that invasive plants had the least negative plant-soil feedbacks ( pq ). However, evidence of feedback of this kind is still not sufficient to claim that the soil feedbacks are a mechanism behind invasion. For example this model shows that, when plant competitors are each strong (zone II), feedbacks only influence invasion when the relationship between soil community density and its effect on plant growth follows a Hollings type II functional response pattern. To begin to truly understand how feedbacks influence invasion we must know how plants respond to their own soil community as well as that of other plant species in the community. Clearly, we also need to consider relative competitive ability. Finally, we must understand how the effects on plant growth change with changes in soil community density. This model s strength is in its ability to be used as a tool to generate new hypotheses regarding plant-soil feedbacks that can be tested with field data. My results suggest that it would be useful to explore the little-researched relationship between soil community density and plant growth. One approach to testing this concept would be to pre-condition soil with different plant species, similar to experiments that identify plant-soil feedback. Then using sterilized soil, these conditioned soil can then be diluted to different concentrations of preconditioned soil. Growing plants in a gradient of conditioned soils can then begin to describe the nature of the relationship between soil community density and plant growth. However, this approach has drawbacks. To begin there is no temporal element. In addition, this approach would create unrealistically homogenous soils. Analysis of the model also highlights an interesting connection between plant-soil feedbacks and the concept of strong vs. weak invaders. Ortega and Pearson (2005) discuss the concept of weak vs. strong invaders in the light of the biotic resistance hypothesis (Elton, 1958) as a means to understand the positive relationships between native species diversity and invisibility that are reported in the literature (Levine, 2000). They point out that all invaders do not behave the same: some are weak, and others strong in their ability to impact native systems. Ortega and Pearson (2005) suggest that weak invaders are responsible for the positive relationships between native and non-native species in some studies, while strong invaders are the drivers of the negative relationships between native and non-native species reported. While others argue that this discrepancy in evidence for the biotic resistance hypothesis can be attributed to issues of scale, propagule pressure, and/or Nutrient Availability (Levine, 2000; Stachowicz et al., 2002) the concept put forth by Ortega and Pearson (2005) is simple and intuitive and clearly can be in part the reason for contradictory observations. Analysis of the model clearly shows how the relative strength of non-native competitors can influence whether invasion creates higher local diversity versus competitive exclusion of natives and reduced diversity for different feedback scenarios. The model analysis shows how soil feedbacks can aid in weak non-native plants ability to invade and persist among native species. The ability to persist in a native population is a critical step for successful plant invasion. In a heterogeneous environment persistent patches of non-native species can contribute propagules that support the continued existence of sink populations that would otherwise disappear. They also may behave as source populations for propagules that may ultimately land on patches that have more favorable conditions, where the non-native species will have stronger relative competitive interactions and/or stronger beneficial soil feedbacks that will allow it to exclude native species. Finally, the ability of an invasive plant to maintain itself in the population can have important consequences following disturbance. Depending on the soil s ability to stay conditioned for one species over another, the persistence of seedbanks, and the physical nature and location of disturbance, competitive coexistence by a non-native plant may ultimately be lead to its competitive exclusion of native species. Its ability to lay in wait for the opportunity to exclude natives may make the difference between non-native and invasive plants. In conclusion, analyses with this model demonstrate that even in the face of detectible plant-soil feedbacks, the role of plant competitive ability in plant invasions remains important. This model clearly shows that, regardless of the type of feedback, the competitive strength of both the invader and the native species will determine the impact that the feedback has on the outcome of two-species competition. In addition, the model demonstrates that to fully understand the influence of soil feedbacks on plant community dynamics and plant invasion the development of plantsoil feedbacks must be accurately described. Recent studies have identified novel plant-soil feedbacks generated by invasive plants (Stinson et al., 2006; Niu et al., 2007; Jordan et al., 2008). While this model supports the assertion that feedbacks influence plant invasion (and in doing so illustrates the importance of continuing these types of feedback studies), analysis of this model also shows that to determine the driving forces behind invasion future experiments must examine how plant-soil feedbacks develop and change with changing soil community densities. Furthermore, studies should continue to explore the relative competitive ability of invasive plants, as well as that of the different communities that they invade.

8 3420 A.G. Aguilera / Ecological Modelling 222 (2011) Acknowledgments This work was supported through a National Science Foundation Graduate Research Fellowship to AGA. I would like to thank Jeffrey S. Dukes, Timothy Killingback, and Karen Ricciardi for assistance with model development and for valuable comments on the manuscript. I am also grateful for the constructive and thoughtful advice of the anonymous reviewers. References Bever, J.D., Feedback between plants and their soil communities in an old field community. Ecology 75, Bever, J.D., Dynamics within mutualism and the maintenance of diversity: inference from a model of interguild frequency dependence. Ecol. Lett. 2, Bever, J.D., Soil community feedback and the coexistence of competitors: conceptual frameworks and empirical tests. New Phytol. 157, Blomqvist, M.M., Olff, H., Blaauw, M.B., Bongers, T., Van der Putten, W.H., Interactions between above- and belowground biota: importance for small-scale vegetation mosaics in a grassland ecosystem. Oikos 90, Borer, E.T., Hosseini, P.R., Seabloom, E.W., Dobson, A.P., Pathogen-induced reversal of native dominance in a grassland community. Proc. Natl. Acad. Sci.- Biol. 104, Bradley, D.J., Gilbert, G.S., Martiny, J.B.H., Pathogens promote plant diversity through a compensatory response. Ecol. Lett. 11, Callaway, R.M., Cipollini, D., Barto, K., Thelen, G.C., Hallett, S.G., Prati, D., Stinson, K., Klironomos, J., Novel weapons: invasive plant suppresses fungal mutualists in America but not in its native Europe. Ecology 89, Callaway, R.M., Ridenour, W.M., Novel weapons: invasive success and the evolution of increased competitive ability. Front. Ecol. Environ. 2, Elton, C.S., The Ecology of Invasions by Plants and Animals. Methuen & Co., London. Engelkes, T., Morrien, E., Verhoeven, K.J.F., Bezemer, T.M., Biere, A., Harvey, J.A., et al., Successful range-expanding plants experience less above-ground and below-ground enemy impact. Nature 456, Eppinga, M.B., Rietkerk, M., Dekker, S.C., De Ruiter, P.C., Van der Putten, W.H., Accumulation of local pathogens: a new hypothesis to explain exotic plant invasions. Oikos 114, Ferris, H., Venette, R.C., Lau, S.S., Dynamics of nematode communities in tomatoes grown in conventional and organic farming systems, and their impact on soil fertility. Appl. Soil Ecol. 3, Holling, C.S., Some characteristics of simple types of predation and parasitism. Can. Entomol. 91, Hunt, R., Cornelissen, J.H.C., Components of relative growth rate and their interrelations in 59 temperate plant species. New Phytol. 135, Jordan, N.R., Larson, D.L., Huerd, S.C., Soil modification by invasive plants: effects on native and invasive species of mixed-grass prairies. Biol. Invas. 10, Keane, R.M., Crawley, M.J., Exotic plant invasions and the enemy release hypothesis. Trends Ecol. Evol. 17, Klironomos, J.N., Feedback with soil biota contributes to plant rarity and invasiveness in communities. Nature 417, Kourtev, P.S., Ehrenfeld, J.G., Haggblom, M., Exotic plant species alter the microbial community structure and function in the soil. Ecology 83, Kulmatiski, A., Beard, K.H., Stevens, J.R., Cobbold, S.M., Plant-soil feedbacks: a meta-analytical review. Ecol. Lett. 11, Levine, J.M., Species diversity and biological invasions: relating local process to community pattern. Science 288, Neher, D.A., Soil community composition and ecosystem processes. Agroforest. Syst. 45, Niu, H.B., Liu, W.X., Wan, F.H., Liu, B., An invasive aster (Ageratina adenophora) invades and dominates forest understories in China: altered soil microbial communities facilitate the invader and inhibit natives. Plant Soil 294, Olff, H., Hoorens, B., De Goede, R.G.M., Small-scale shifting mosaics of two dominant grassland species: the possible role of soil-borne pathogens. Oecologia 125, Ortega, Y.K., Pearson, D.E., Weak vs. strong invaders of natural plant communities: assessing invasibility and impact. Ecol. Appl. 15, Stachowicz, J.J., Fried, H., Osman, W., Whitlatch, R.B., Biodiversity, invasion resistance, and marine ecosystem function: reconciling pattern and process. Ecology 83, Stinson, K.A., Campbell, S.A., Powell, J.R., Wolfe, B.E., Callaway, R.M., Thelen, G.C., et al., Invasive plant suppresses the growth of native tree seedlings by disrupting belowground mutualisms. PLoS Biol. 4, Turnbull, L.A., Levine, J.M., Fergus, A.J.F., Peterman, J.S., Species diversity reduces invasion success in pathogen-regulated communities. Oikos 119, Westover, K.M., Bever, J.D., Mechanisms of plant species coexistence: roles of rhizosphere bacteria and root fungal pathogens. Ecology 82, Wolfe, B.E., Rodgers, V.L., Stinson, K.A., Pringle, A., The invasive plant Alliaria petiolata (garlic mustard) inhibits ectomycorrhizal fungi in its introduced range. J. Ecol. 96,