Testing predictions of a three-species plant–soil feedback model


Correspondence author. E-mails: afak@uaa.alaska.edu, andrewkulmatiski@hotmail.com


1. A growing number of experiments measure plant growth on soils cultivated by different species. Models show that the resulting plant–soil feedbacks (PSFs) can determine plant abundance and persistence; yet, quantitative tests of their importance in community dynamics are lacking.

2. Here, we use the growth of eight plant species on ‘self’ and ‘other’ soils to parameterize a three-species PSF model. Predictions from the parameterized model were compared to plant growth observed in a 3-month glasshouse experiment. Four types of three-species communities were simulated: native, non-native, nitrogen-fixing and non-nitrogen-fixing. Because the PSF model is founded on a competition model, removing PSF effects from the model allowed us to compare PSF model predictions to competition model predictions.

3. Mean plant biomass differed among soil types by 20% and differed among plant species by 101%.

4. The PSF model correctly predicted rank abundance in the four communities tested while the competition model correctly predicted rank abundance in the two communities with nitrogen-fixing plants. Furthermore, PSF model predictions of species abundances were closer to observed values than competition model predictions. Despite consistently improving upon the competition model, predictions from the PSF model were significantly different from observed values for three of four communities. Competition model predictions were different from observed values for all four communities.

5. Our three-species model described the plant and soil conditions that allow coexistence and competitive exclusion, but when parameterized with experimental data, no communities were predicted to result in long-term coexistence.

6.Synthesis. Results suggest that PSFs captured a mechanism of plant community development. However, because improvements in model predictions were consistently small, either PSFs were not a dominant mechanism determining plant community development or PSFs were underestimated by our experimental or modelling approaches. Further testing of PSFs and development of improved methods to measure PSFs are suggested.


Plant–soil feedback (PSF) studies are founded on the concept that plants change soil biology, chemistry and structure and that these changes affect subsequent plant growth (Van der Putten, Van Dijk & Troelstra 1988; Van der Putten, Van Dijk & Peters 1993; Bever 1994; Ehrenfeld & Scott 2001; Kyle, Beard & Kulmatiski 2007). When a plant species creates soils that increase growth of conspecifics, this is called positive individual PSF (Bever 1994). Positive individual PSFs are expected to increase species abundance, persistence and invasiveness (Callaway & Aschehoug 2000; Eppstein, Bever & Molofsky 2006; Inderjit & Van Der Putten 2010). When a plant species creates soils that decrease growth of conspecifics, this is called negative individual PSF (Bever 1994). Negative individual PSFs are expected to decrease a species’ abundance and persistence, increase successional replacements and maintain species diversity (Van der Putten, Van Dijk & Peters 1993; Klironomos 2002; Kardol, Bezemer & van der Putten 2006; Petermann et al. 2008).

While individual PSFs have been used to make assumptions about coexistence and competitive exclusion, plants typically grow in communities where they are affected by other plant species and the soils they cultivate (Bever et al. 2010). In some cases, these interactions may be more important in determining community development than individual PSFs. This concept was formalized in a foundational paper by Bever, Westover & Antonovics (1997). Bever, Westover & Antonovics (1997) developed a model (hereafter, Bever’s model) that describes how two plant species interact with each other and the soils they create (i.e. community-level PSF). Bever’s model identified the conditions under which community-level PSFs are more important than the direction or magnitude of individual PSFs for predicting coexistence and competitive exclusion (Bever 2003; Eppstein & Molofsky 2007). For example, a plant species, A, may increase its own growth by promoting the growth of a particular mycorrhizal species. This relationship may produce a positive individual PSF. However, if this same mycorrhizal species promotes the growth of a second plant, B, more than it promotes the growth of A, then B can be expected to outcompete A regardless of A’s positive individual PSF. In this way, commonly measured individual PSFs can be expected in some cases to produce incorrect predictions of plant community development while community-level PSFs address this problem.

Many researchers have measured the growth of plants on ‘self’ and ‘other’ soils (Kulmatiski et al. 2008), but we are not aware of any studies that have used these data for model parameters in simulations (i.e. a PSF model) to predict community dynamics (Eppstein & Molofsky 2007; Petermann et al. 2008). Furthermore, parameterized PSF models should be tested to determine how well they predict observed plant growth. As a result, the importance of PSFs to plant community development has been inferred, but not tested (Bever et al. 2010).

Our first objective was to develop a three-species PSF model similar to Bever’s two-species model. Using our model, we solve for constraints on model parameters that predict coexistence and competitive exclusion. Our second objective was to parameterize the model and test it using data from a glasshouse experiment. We parameterized the model with PSF values for four native and four non-native species. We tested model performance by comparing model predictions to observed species rank order and abundance in 2 three-species native and 2 three-species non-native plant communities. Because the PSF model is founded on a competition model, removing PSF effects allowed us to compare competition model predictions to PSF model predictions.

Materials and methods

Model development

Our model is founded on the assumptions of Bever’s model (Bever, Westover & Antonovics 1997). In our model, each species cultivates a soil type: plants A, B and C cultivate soils, sA, sB and sC, respectively (Fig. 1). Each species realizes a strictly positive growth rate on each soil type. For example, plant A has a specific growth rate on its own soil, αA, which may be smaller or larger than plant A’s growth rate on soil B or soil C, βA, or γA, respectively. At the same time, plants B and C will have a specific growth rate on soil A, αB and αC, respectively. An important consequence of this modelling approach is that a plant may realize a negative PSF, when calculated as the difference in plant growth on ‘self’ and ‘other’ soils, but our model does not produce negative growth rates, only smaller or larger growth rates. This modelling approach deviates from Bever, Westover & Antonovics (1997), which implies these growth rates can be negative.

Figure 1.

 Schematic of the three-species plant–soil feedback model. A, B and C represent three plants and SA, SB and SC represent three soils cultivated by plants A, B and C, respectively. α, β and γ represent the growth rates of a plant on a soil type (i.e. α represents the growth rate of plant A on SA). μ, ν and ω indicate that the rate at which soil occupied by a plant, for example A, is converted to a soil type (i.e. sA). Arrows represent the direction of fitness effect. Intrinsic growth rates on control soils are used to predict the effects of competition among species and the difference in growth rates between control and cultivated soils are used to predict the effects of plant–soil feedback.

The growth rate of each species in a three-species community is assumed to be a linear combination of the relative abundance of each soil type (as in Bever, Westover & Antonovics 1997). For example, if the growth rate of plant A is 7 g month−1 on soil A, but 10 g month−1 on soils B and C then plant A will have a weighted mean growth of 9 g month−1 on a soil community composed of soils A, B and C in equal parts. More specifically, changes in biomass of each plant were modelled as:


where A is plant biomass, A′ is the rate of change in plant biomass, and Si is the proportion of soil type i, e.g.


The relative abundance of each soil type changes as a function of plant biomass. For example, the change in plant A soil is modelled as sA= μPAsA, where μ is the constant of proportionality indicating the rate at which soil occupied by A is converted to sA. PA is the proportion of total plant biomass that is A [e.g. inline image]. The rate of change in the proportion of a soil type is given by:


The rate of change in the proportion of a plant biomass is given by a similar derivative.

From these basic equations, we derived the following six equations, which describe the change in proportions of plant biomass and soil type:


The derivation of this system of ordinary differential equations is described more fully in Appendix S1 in Supporting Information.

We compare results of this three-species PSF model with the results of a three-species competition model, where each plant is modelled with an exponential fit, without regard to soil type (i.e. A = αA, B′ = βB, C′ = γC). Here, α, β and γ are plant growth rates on control soil. Biomass estimates produced by this model were then converted to proportional abundance for the purpose of comparison with PSF model predictions. As an exponential growth model, this model will effectively predict competitive exclusion of two species unless two or three species have exactly the same growth rates and begin with exactly the same abundances.

Model assumptions and limitations

We used Bever’s model structure because it provided a good opportunity for parameterization of a PSF model based on empirical experiments. However, this modelling approach requires simplifying assumptions that may influence model outcomes. One key assumption in the model is that plant population growth can be modelled using positive exponential growth. An artefact of using strictly positive growth is that no species can go extinct. In addition, the community cannot have all species go extinct (i.e. zero biomass equilibrium). We used proportional abundance because it can approach zero and therefore can be used to predict competitive exclusion. A drawback to this approach is that it precludes inference on species and total biomass. In general, these assumptions should not be a problem when using short-term (i.e. our experimental) data, but may be problematic when communities start with low biomass (i.e. are likely to go extinct) or are modelled over long time periods (i.e. greater than one growing season where senescence becomes important). There are other assumptions to this model including no density dependence, competitive equivalence, no mixed soil types (i.e. α + β vs. αβ), and linear interactions between plants and soils that are discussed in detail elsewhere (Bever, Westover & Antonovics 1997; Kulmatiski & Kardol 2008).

Some of the limitations to this model have been addressed in more complex models (Bever 2003; Levine et al. 2006; Eppstein & Molofsky 2007). For example, Bever’s (2003) model incorporates competition coefficients that better describe plant–plant competition, Eppstein & Molofsky’s (2007) model relaxes assumptions of proportional abundance, and Levine et al.’s (2006) model addresses dispersal in plants with PSFs. These more realistic models may predict different outcomes for certain populations, but these models also require more data (i.e. competition coefficients) that can be difficult to collect (i.e. carrying capacity and dispersal rates).

Exploring model dynamics

Here, we explore model conditions that result in competitive exclusion and coexistence. Due to the dimensionality of the model, we did not attempt a global stability analysis. Rather, we considered the dynamics locally around fixed points (or equilibrium points) of the model using a linearized stability analysis. We explored the qualities of the fixed point by calculating a linear approximation of the nonlinear system near the fixed point (Wiggins 1990). This technique involved calculating the Jacobian matrix and evaluating the eigenvalues of the matrix at the fixed point. If the eigenvalues have negative real parts, the point was considered locally stable (or attracting) and the long-term behaviours of trajectories near this point tend towards the point. On the other hand, if at least one eigenvalue is a positive real value, the fixed point will no longer be stable and trajectories near the point will tend away from the fixed point. Our linearized analysis proved sufficient to describe observed dynamics because data from our communities did not produce multiple fixed points (Table 1).

Table 1.   Species combinations in the four experimental plant communities and the eigenvalues associated with the fixed points resulting from experimentally derived parameters. All eigenvalues are real numbers. Note that all eigenvalues must be negative for a fixed point to be attracting. See Model development
CommunitySpeciesFixed pointEigenvalues of JacobianStability
  1. *Nitrogen-fixing species.

Native 1 (N1)Hesperostipa comataX1,0,0(0.110, 0.141, −5, −5)Saddle
Koeleria cristataX0,1,0(0.882, 0.816, −5, −5)Saddle
Pseudoroegneria spicataX0,0,1(−0.085, −0.071, −5, −5)Asymptotically stable
Native 2 (N2)Hesperostipa comataX1,0,0(0.110, 0.685, −5, −5)Saddle
Koeleria cristataX0,1,0(0.882, 6.132, −5, −5)Saddle
Lupinus sericeus*X0,0,1(−0.487, −0.486, −5,−5)Asymptotically stable
Non-native 1 (X1)Agropyron cristatumX1,0,0(0.076, 0.205, −5, −5)Saddle
Bromus tectorumX0,1,0(−0.129, −0.594, −5, −5)Asymptotically stable
Centaurea diffusaX0,0,1(−0.225, 0.040, −5, −5)Saddle
Non-native 2 (X2)Agropyron cristatumX1,0,0(0.076, 0.852, −5, −5)Saddle
Bromus tectorumX0,1,0(2.238, 7.387, −5, −5)Saddle
Medicago sativa*X0,0,1(−0.714, −0.419, −5, −5)Asymptotically stable

We began our linearized analysis by examining solutions where only one species persists. An example of such a fixed point is X1,0,0 (i.e. PA = SA = 1 and PB = SB = PC = SC = 0). The eigenvalues of the Jacobian matrix associated with X1,0,0 are {0, 0, αB−αA, αC−αA, −μ, −μ}. Therefore, the point X1,0,0 is asymptotically stable when species A has a positive PSF on both heterospecific soil types (i.e. αA > αB and αA > αC) and trajectories tend towards the point or result in competitive exclusion (i.e. exclusion of plants B and C and their associated soil types). Conversely, the point X1,0,0 is no longer stable when A has at least one negative feedback (i.e. αA < αB or αA < αC) and trajectories near the point tend away from the fixed point. There are similar fixed points in the system representing species B dominance (i.e. X0,1,0) and species C dominance (i.e. X0,0,1).

The conditions that allow two-species coexistence can be defined with an interaction coefficient analogous to that proposed by Bever, Westover & Antonovics (1997) as a measure of the PSF between two species, Iab = αA − αB + βB − βA, Iac = αA −αC + γC − γA and Ibc = βB − βC + γC − γB. Just as in Bever’s model, two species will coexist when the value of the interaction coefficient is negative. For example, the interaction coefficient for two plant species is negative when both plant species realize negative PSFs.

Although not a necessary condition, universal negative PSF (i.e. all interaction coefficients are negative) proves sufficient for our model to predict three-species coexistence. However, unlike Bever’s model, our model also predicts three-species coexistence when interaction coefficients are all positive (universal positive), as long as there is still some negative PSF in the system. For example, Iab = αA − αB + βB − βA can be positive even if αA − αB is negative. We illustrate three-species coexistence with two examples in Fig. 2. The universal positive PSF criterion provides one example of coexistence that was not illustrated in Bever’s model; many others are likely to exist. Unfortunately, summarizing these parameter combinations is difficult because the interaction term describing three-species coexistence is too cumbersome for biological interpretation (see Appendix S2).

Figure 2.

 Two plates depicting trajectories of (a) stable and (b) oscillating three-species coexistence. (a) Occurs with universal negative PSF (i.e. all interaction coefficients are negative) and (b) occurs with universal positive feedback. Note that in (b) the points describing competitive exclusion (i.e. a proportion of one) are not attracting, which results in sequential predominance of each species. Initial plant proportions are (0.2, 0.2, 0.6).

Finally, there are fixed points for mismatched plant and soil compositions (i.e. exclusively plant A on exclusively soil type sB); however, none of these points are attracting, regardless of parameter values, and they do not make biological sense. So, we focused our attention on the seven fixed points that were relevant (i.e. X1,0,0, X0,1,0, X0,0,1, Xa,b,0, Xa,0,c, X0,b,c, Xa,b,c; see Appendix S2). All of these points can be attracting. As a result, our model can predict competitive exclusion or coexistence of two or three species. Our model can also predict multiple stable states (i.e. several different fixed points can be simultaneously attracting), although multiple stable states are not considered further here as they were not relevant to our experimental communities.

Plant effects on soils

The parameters μ, ν and ω describe the rate at which a plant creates its soil type. Because μ, ν and ω are strictly positive numbers, all of the fixed point coordinates uniquely defined by them are positive (see Appendix S2, equations 4–6 and 11). Moreover, the relative values of these parameters play no role in determining the stability of the fixed points. However, changing μ, ν and ω does affect the rate at which trajectories arrive at long-term solutions. Unfortunately, little is known about the specific rates at which different plant species create soil microbial communities (Peltzer et al. 2009; Maul & Drinkwater 2010). It may be possible to measure the rate at which different plants create their soils by repeatedly measuring PSFs over time.

Parameterizing the model

To parameterize our model, we conducted a glasshouse experiment using four native and four non-native plant species that are common in the Intermountain West, USA (Table 1; Bever, Westover & Antonovics 1997; Kulmatiski & Kardol 2008). Soils and seeds were collected from a shrub-steppe ecosystem in Winthrop, WA, USA (48°28′ N, 120°11′ W; for a more detailed site description, see Kulmatiski 2006). Non-native seeds were collected by hand from the study site and native seeds were purchased from BFI Native Seeds, Moses Lake, WA, USA. A three-species model was expected to be representative of plant dynamics because within any field at the study site three or fewer species typically represent > 50% plant cover (Kulmatiski 2006). Native and non-native plant communities were treated separately in the experiments because native and non-native species maintain alternate state communities, with little intermingling of species, at the study site (Kulmatiski 2006). One native and one non-native community contained a nitrogen (N)-fixing species because these species are common on the landscape.

In phase 1 of a two-phase PSF experiment, 600 pots (20 cm height) were filled with 1 L of a sterilized growth medium (a mixture of 7 : 1 sand and peat moss) that was inoculated with 50 mL of native- or non-native-dominated field soil, or 5% by volume. This approach provided a homogenous growth medium that contained microbial species from the field (Bever 1994). Five germinated seeds from each of the eight target species were planted into each of 60 pots. Seeds were assigned randomly to pots with the exception that native and non-native seeds were planted in pots inoculated with soils from native- and non-native-dominated fields, respectively. After 1 month, each pot was weeded to include the three largest individuals. After 3 months, above-ground biomass was harvested. This amount of time was comparable to a growing season. An additional 120 pots were left free of plant growth during phase 1. These pots provided 15 replicate control pots for each of the eight target plant species in phase 2.

At the beginning of phase 2, 16 mL of Hoagland solution was added to each pot to compensate for nutrients lost as a result of plant harvesting, minimize plant–nutrient feedbacks, and isolate plant–microbe feedbacks (as in Bever 1994). For each native species, five germinated seeds were planted into 75 pots: 15 pots that had been cultivated by each of the four native species including itself and 15 control pots. The same was done for each non-native species. After 1 month, plants were weeded to three individuals per pot as in phase 1. After 3 months above-ground biomass was harvested, dried to constant weight at 70 °C, and weighed. Plant growth on control soils was used to parameterize the competition model and plant growth on different soil types was used to parameterize the PSF model.

Translating empirical data to model input required several key assumptions. For example, both models were parameterized with plant growth rates. Growth rates of plants in pots are typically assumed to reflect the intrinsic growth rates; however, this measure includes a plant’s continuous affect on its own growth through the soil. Because of this, our competition model incorporated how a plant continuously affects itself through the soil. The PSF model differed from the competition model in that it also included measures of plant growth rates on different soil types (i.e. ‘self’ and ‘other’). A key assumption of the PSF model is that the growth of a plant on soils previously cultivated for 3 months by self or other species provides a good estimate of the continuous affects of each plant species on itself and other species during community development (as in Bever, Westover & Antonovics 1997).

Additional assumptions include seed mass at the beginning of the experiment and mean above-ground biomass at the end of the experiment were used to estimate exponential growth rates for each species on each soil type (e.g. αA, αB and αC); thus, we assumed growth rates could be derived from final biomass. The remaining parameters in the three-species PSF model, μ, ν and ω, were assumed to be equal to and fixed at 5. This was done because microbial growth is more rapid than plant growth. As a result, we assumed microbial abundance will increase or decrease faster than the plant species with which they are associated. We also assumed that final biomass equals proportional abundance. Parameter values were used to run a 3-month simulation of plant growth for two native and two non-native plant communities. Predictions were compared to plant growth observed in the same four communities.

To test model predictions, 120 pots (36 cm tall) were filled with 3 L sterilized growth medium and inoculated with 150 mL field soil (5% by volume). Each pot was randomly assigned to one of two native communities or one of two non-native communities for a total of 30 replicate pots for each community. Native and non-native communities were planted in pots inoculated with soils from native- and non-native-dominated fields, respectively. Five germinated seeds from each of three assigned plant species were sown into each pot. After 1 month, plants were weeded back to the three largest of each individual species. After 3 months above-ground biomass was harvested, dried to constant weight at 70 °C, and weighed. The biomass of each species at the end of the experiment was converted to proportional abundance.

Glasshouse experiments were conducted at the USDA-ARS Forage and Range Research Laboratory in Logan, UT, USA. Evaporative coolers and radiant heaters maintained a temperature about 20 °C from May to December 2007. Natural light was augmented with 14 h of light each day from sodium lamps. Pots were watered regularly to prevent water stress and minimize leaching. Pots were rotated every 2 weeks so that all plots spent equal time in each location on the glasshouse bench.

Plant biomass by species and soil type were compared using two-factor anovas. Transformations to meet assumptions of homogeneity and normality were used as necessary. A Tukey–Kramer adjustment was used to compare differences among means. To determine if PSF and competition model predictions differed from observed values, we conducted chi-squared tests for each plant community. Two tests were conducted to determine if the PSF model improved upon competition model predictions. First, a Student’s t-test on the absolute difference between observed and predicted values for the PSF and competition models was conducted. Secondly, predicted and observed results were regressed to determine the goodness-of-fit for the predictions from each model. Significant differences were accepted at < 0.05. All statistical analyses were conducted using sas v9 for Windows (SAS Institute, Cary, NC, USA).


Glasshouse experiment

The non-native N-fixer Medicago sativa had greater above-ground biomass and Agropyron cristatum had lower above-ground biomass than other non-native species (Table 2; F3,262 = 137.18, P < 0.001). The native N-fixer Lupinus sericeus had greater above-ground biomass than other native species (Table 2; F3,260 = 186.19, P < 0.001). Mean differences in plant biomass among species was 0.29 ± 0.06 g, which was larger than mean biomass of plants (0.28 ± 0.12 g), which reflected large differences in biomass between N-fixing species and other species.

Table 2.   Plant biomass of four native (a) and four non-native (b) species (n = 15) after 3-month growth in a glasshouse on soils that had been cultivated for 3 months by each of the other species in their group (i.e. native or non-native)
(a)Plant species
Soil typeHesperostipa comataKoeleria cristatumLupinus sericeusPseudoroegneria spicata
Control86 ± 13ab102 ± 10ab490 ± 52a70 ± 11a
Hesperostipa comata70 ± 13b85 ± 14ab455 ± 56a102 ± 24a
Koeleria cristatum67 ± 12b75 ± 9b591 ± 76a84 ± 15a
Lupinus sericeus120 ± 10a131 ± 18a538 ± 67a79 ± 10a
Pseudoroegneria spicata72 ± 8b72 ± 7b600 ± 78a90 ± 11a
(b)Plant species
Soil typeAgropyron cristatumBromus tectorumCentaurea diffusaMedicago sativa
  1. Plant growth on different soils (i.e. in columns) followed by the same lower case letter is not different at the α = 0.05 level.

Control74 ± 13ab163 ± 93bc253 ± 89a761 ± 81ab
Agropyron cristatum73 ± 10ab118 ± 28c167 ± 31a838 ± 75ab
Bromus tectorum47 ± 11b190 ± 19b143 ± 20a746 ± 102b
Centaurea diffusa86 ± 10a203 ± 29b173 ± 20a975 ± 98ab
Medicago sativa119 ± 19a355 ± 83a206 ± 32a1052 ± 152a

Plant biomass differed among soil types for Hesperostipa comata, Koeleria cristata, A. cristatum, Bromus tectorum and M. sativa (Table 2). When calculated as the difference in plant biomass on different soil types, mean differences among soil types were 0.05 ± 0.02 g, or 20% of plant growth (Table 2). In no case was the difference in plant growth between two soil types greater than the difference in plant growth between the two species that created those soil types. At the end of the experiment, all pots contained all three planted species (i.e. competitive exclusion was not observed in any pot).

Model predictions

Short-term model simulations

The PSF model correctly predicted rank order abundance in all four plant communities while the competition model correctly predicted rank order abundance in only two communities (Fig. 3). Despite improving predictions of rank order abundance, PSF model predictions for three of four communities were different from observations (d.f. = 2; N1: χ = 6.13, P = 0.05; N2: χ = 22.38, P < 0.001; X1: χ = 6.29, = 0.04; X2: χ = 52.29, < 0.001). Competition model predictions for all four communities were different from observations (d.f. = 2; N1: χ = 28.68, < 0.001; N2: χ = 22.79, P <0.001; X1: χ = 75.29, < 0.001; X2: χ = 10.65, = 0.005). Although predictions from both models were typically different from observed values, PSF model predictions were closer to observed values (t-test: d.f. = 11, < 0.001). Predictions from the competition (F1,11 = 5.46; = 0.042) and PSF models (F1,11 = 10.79, = 0.008) were correlated with observed values, but the PSF model had a better R2 (P < 0.001; Fig. 4).

Figure 3.

 Competition and plant–soil feedback (PSF) model predictions of plant abundances compared to observed plant abundances in four plant communities (a–d). Native community 1 (a) contained no nitrogen-fixing plant. Native community 2 (b) contained the nitrogen-fixing plant Lupinus sericeus. Non-native community 1 (c) contained no nitrogen-fixing plant. Non-native community 2 (d) contained the nitrogen-fixing plant Medicago sativa. Species names provided in Table 1.

Figure 4.

 Regressions of observed to predicted results for the competition (Comp.) and plant–soil feedback (PSF) models.

The PSF model predicted that dominant plant species will have disproportionately large effects on soil community composition (Fig. 5). In each community, there were 118–135% more of the soil type of the dominant plant than of the plant itself. Correspondingly, the least abundant species had a disproportionately small effect on soil community composition. In each community, soils of the least abundant species represented only 3–75% of the abundance of the plant that cultivated them. These responses reflected our assumption that microbial communities grow more quickly than plants (i.e. μ, ν and ω each equalled 5).

Figure 5.

 Plant–soil feedback model predictions of soil microbial community abundances in Native community 1 (a), Native community 2 (b), Non-native community 1 (c) and Non-native community 2 (d). AC, Agropyron cristatum; BT, Bromus tectorum; CD, Centaurea diffusa; HC, Hesperostipa comata; KC, Koeleria cristata; LS, Lupinus sericeus; MS, Medicago sativa; PS, Pseudoroegneria spicata.

Long-term model simulations

While it is not possible for either model to predict that any species will have zero proportional biomass, in effect both models predicted competitive exclusion of all but one plant species in all four communities. Table 1 lists the fixed points, their associated eigenvalues and their stability, when using glasshouse experiment data. We note here that the trends toward dominance measured in the 3-month experiment are consistent with the long-term predictions of the model. That is to say that each species with the highest proportional biomass after 3 months in the glasshouse is the species with the asymptotically attracting fixed point. While competitive exclusion is a necessary consequence of the competition model, this result suggests that PSFs either did not provide strong enough stabilizing pressure to allow coexistence or encouraged competitive exclusion.


Incorporating PSFs improved competition model predictions. The PSF model correctly predicted rank abundance in the four communities tested while the competition model correctly predicted rank abundance in the two communities with N-fixing plants. Furthermore, PSF model predictions were closer to observed values than competition model predictions: R2 = 0.35 and 0.52 for the competition and PSF models, respectively. Despite improving upon the competition model, predictions from the PSF model were significantly different from observed values for three of four communities. In general, the PSF model provided consistent, but quantitatively small improvements on competition model predictions. For example, in Non-native 2, the competition model underestimated B. tectorum abundance at 40.8% relative to an observed abundance of 57.2%. The PSF model prediction for B. tectorum (44.9%) was only slightly better.

The PSF model predicted that PSFs would have quantitatively small effects in most communities in this study. This suggests that PSF effects were small relative to other plant growth factors or that our experimental approach underestimated PSFs. On average, differences in plant growth among soil types represented 20% of plant biomass while differences in plant growth among species represented 101% of plant biomass. In no case was the difference in plant growth between two soil types greater than the difference in plant growth between the two species that created those soil types. These results indicate, as one would expect, that PSFs are of secondary importance to inherent differences in plant growth rates among species (i.e. density-independent fitness). A review of the literature suggests that the magnitude of PSF effects often observed in PSF studies (20+% of plant biomass; Klironomos 2002; Agrawal et al. 2005; Harrison & Bardgett 2010) should have observable effects on plant community development (Kulmatiski et al. 2008), but results from our model which actually incorporated PSF effects in a model with plant competition effects, suggest that PSFs of this magnitude may have only small quantitative effects on plant community development. Further model improvements are likely to require consideration of other plant growth factors, such as PSF effects on germination, allelopathy (Callaway et al. 2008) or niche partitioning (Adler, Ellner & Levine 2010).

The small, but consistent, improvements provided by the PSF model resulted from the incorporation of data that both increased and decreased inherent plant growth differences between species. For example, in Native 1, H. comata created soils that increased the growth of the superior competitor K. cristata. This interaction decreased PSF model predictions of H. comata abundance and increased predictions of K. cristata abundance and made them closer to observed values. Thus, improving competition model predictions for the species in this experiment required the PSF model, in some cases to increase competitive interactions and in other cases to decrease competitive interactions.

Soil microbial communities were not described as a part of this study, but our model suggested that soil microbial communities created by dominant plants will be over-represented and soils created by subdominants will be under-represented relative to plant abundance. These results provide an alternative to Grime’s (1998) mass-ratio hypothesis for why subdominant species may have little effect on ecosystem processes. More specifically, when microbial growth rates are greater than plant growth rates (i.e. μ, ν and ω > 1) plant dominance will be exaggerated in the soil because as a plant is increasing in abundance, its microbial community is increasing in abundance more rapidly. Because microbial communities have been associated with dominant plant species (Chen & Stark 2000; Eom, Hartnett & Wilson 2000; Belnap & Phillips 2001; Hawkes et al. 2005; Peltzer et al. 2009; but see Zak et al. 2003), these species may have disproportionate effects on microbial communities, otherwise it may be too difficult to discern the effect of a single plant species in a microbial community. As more measurements of plant effects on soil microbial communities are made, these measurements will provide a reasonable test for predictions from our model. If plants are found to have proportionate effects on microbial communities, the parameters μ, ν and ω in our model should be decreased.

Future research may demonstrate that μ, ν and ω should be either increased or decreased. Analyses of our model indicate that, as long as they are equal, changing μ, ν and ω will change the rate at which PSF effects are realized, but will not change the qualitative outcome of community dynamics. It is important to note, however, that small values of μ, ν and ω may have important implications for plants with different life histories. Where PSFs require more than one growing season to develop, for example, these feedbacks become a multigenerational process for annual plants but not for longer-lived plants. The effects of multigenerational time-lags on community development are not well understood (Farrer, Goldberg & King 2009). Furthermore, if μ, ν and ω are not equal, as is likely and has been found in at least one study (Peltzer et al. 2009), this could change the qualitative outcome of plant abundances predicted by PSF models.

We used the standard two-phase PSF experiment approach. Our results, therefore, may provide inference to other similar studies. In our case, we think the approach may have underestimated PSF effects. First, PSF effects were measured after 3 months. If PSF effects were realized in less time or if they become greater over more time, our model would underestimate PSF effects. Secondly, the two-phase approach measures legacy effects, although PSFs may be realized continuously by plants growing together. This is a key assumption of this approach and could be tested. Finally, fertilizing during phase 2 minimized plant–nutrient feedbacks and these may have been important (Ehrenfeld & Scott 2001).

Model predictions of plant abundances in communities with N-fixing plants provide an example of how the two-phase approach may underestimate PSF effects. Both the PSF and competition models underestimated the abundances of species growing with N-fixers. This was expected for the competition model because this model included no mechanism to accommodate facilitation. The PSF model, however, incorporated plant growth rates on N-fixing and non-N-fixing soils. We suggest two reasons the two-phase approach underestimated effects of facilitation by N-fixers. First, a nutrient solution was added to pots in phase 2 to isolate plant–microbe PSFs from plant–nutrient PSFs, so the facilitative effect of N-fixers was minimized. Secondly, N-fixation occurs continuously whereas the two-phase experimental approach measures only past effects of plant growth. It is likely, for example, that fixed N is rapidly immobilized in the soil and so the legacy effect of N-fixing plants having grown in a pot was not as important as the effect of N-fixing plants currently growing in a pot (Davidson, Dail & Chorover 2008). For these reasons, it is possible that our data and model may have underestimated the ability of PSFs to explain the difference between observed and predicted plant abundances.

Further assumptions and limitations inherent to the two-phase experimental approach for developing PSFs have been discussed elsewhere (Kulmatiski & Kardol 2008; Inderjit & Van Der Putten 2010). One major limitation is how to interpret the use of soil inocula in these experiments. We do not know if the microbial communities fully occupy the experimental soils or behave in ways similar to field soils. Whether or not microbial communities fully occupy soils may not affect interpretation of results from our experiment because our model was parameterized and tested using plant growth in the same sterilized, inoculated conditions, but it may limit inference about PSFs in whole field soils. Future experiments measuring PSFs on whole field soils can test this assumption, but are less likely to control for pre-existing conditions among soil types (Kulmatiski & Kardol 2008).


By parameterizing and testing a PSF model, we describe an important first step towards making PSF research quantitative. Because PSFs consistently improved model predictions, our results suggested that our measurements and model captured a mechanism of plant community development. However, because improvements in model predictions were consistently small, our results suggest either that PSFs were not a dominant mechanism determining plant community development or that PSFs were underestimated. Further testing of PSFs and development of improved ways to measure them are needed before conclusions can be made about their importance.


We thank the Utah Agricultural Experiment Station and Alaska EPSCoR NSF award #EPS-0701898 and the state of Alaska for support. We thank Tom Jones and the Agricultural Research Station for glasshouse use and G. Diamond, J. Wolfgram, T. Upton and K. Latta for help in the glasshouse.