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Keywords:

  • abrupt climate change;
  • alternative stable states;
  • community dynamics;
  • competition;
  • facilitation;
  • fire;
  • herbivore density;
  • nitrogen availability;
  • plant population;
  • tree–grass coexistence

Summary

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

1. Plant–plant interactions are known to vary with changing environmental conditions; however, we have little empirical knowledge of the impact of abrupt environmental changes on millennial scale plant–plant interaction outcomes for long-lived plant species. Here, we used palaeoecological data (13–7.6 k years bp) and a novel statistical modelling approach to determine the impact of multiple environmental drivers on predicted tree–grass population interaction outcomes from our study site in eastern England.

2. Changes from high to low herbivore density shortly preceded changes to low fire levels and a shift to warmer summers. These transitions occurred during a period of increasing nitrogen (N) availability. Shortly thereafter, there was a shift in landscape dominance from grasses to oaks and then a change to decreasing N availability.

3. Model predictions of tree–grass interaction outcomes varied over time with respect to all environmental changes. During the time of high disturbances and cool summers, grasses were predicted to out-compete oaks. After climate warming and the loss of regular disturbances, the predicted outcome was stable coexistence. However, changes in the N cycle corresponded with different predicted outcomes: unstable competition under increasing N availability and facilitation of oaks by grasses when N availability was declining.

4. Akaike Information Criterion weights indicate that climate warming and fewer fires were consistent with the best-fitting model of oak–grass interactions for the entire time series (i.e. competitive exclusion to stable coexistence). However, reconciling the conflicting model predictions with the observed population dynamics suggests that a temporary period of unstable competition preceded the predicted shift to stable coexistence. This dynamic behaviour is consistent with known patterns of shifts between alternative stable states.

5.Synthesis. We show that abrupt changes in environmental conditions over time lead to similarly abrupt changes in tree–grass interaction outcomes, which were shown to vary in contrasting directions with respect to resource versus non-resource variables. The approach described here allows plant ecologists to test hypotheses of plant–plant interactions over successional time scales for long-lived species and thus can lead to new knowledge about the structural role of these interactions in community dynamics.


Introduction

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

Plant–plant interactions play a key and complex role in structuring vegetation communities, yet our understanding of their role as drivers of community dynamics is complicated by the tendency of these interactions to vary with respect to prevailing environmental conditions (Bonsall, van der Meijden & Crawley 2003). While there is a large body of research on the effect of changing environmental conditions on plant–plant interaction outcomes (e.g. the stress gradient hypothesis, Brooker et al. 2008) the difficulty in obtaining observational data on population dynamics of long-lived species (e.g. trees) impedes our ability to assess the effect of environmental changes on their interactions. Thus, most work on plant competition and facilitation has been focused on short-lived species (Callaway 2007); however, recent studies have extended the time frame over which direct plant interactions can be assessed up to decades by using dendroecological data (Soliveres et al. 2010). To expand further the length of the observational record beyond the age of living trees (i.e. centuries to millennia) requires the use of the fossil record such as palaeoecological pollen data.

Millennial-scale ecosystem dynamics – as reconstructed by the fossil record – often demonstrate nonlinear shifts in the trajectory of drivers of vegetation change such that discrete disturbance, stress and climatic regimes can be observed on either side of a breakpoint in the time-series data (i.e. a threshold, Willis et al. 2010). Such thresholds can set off cascading changes through ecosystems including shifts between alternative stable states in population and community dynamics (Scheffer & Carpenter 2003), yet they are often difficult to predict (Scheffer et al. 2009). Here, we aimed to assess how plant–plant interaction outcomes respond to abrupt environmental changes: do they demonstrate gradual responses or sharp shifts between alternative stable states?

We achieved this goal by using a model-fitting and model-selection analysis of multiproxy palaeoecological data to generate predicted changes in interaction outcomes between two putative competitors –Quercus sp. (oak) trees and Poaceae (grass) species (Davis et al. 1999) – over time and across abrupt changes in climate, fire patterns, ungulate herbivore density and nitrogen (N) availability. Our study site was a shifting mosaic of chalk grassland and open deciduous woodland in eastern England during the late-glacial/early post-glacial period (i.e. 13–7.6 k years bp). This period is known for numerous abrupt environmental changes including changes in climate (Steffensen et al. 2008), nutrient cycles (Wolfe, Edwards & Aravena 1999), soil types (Willis et al. 1997), mega-herbivore density (Barnosky et al. 2004) and fire level (Marlon et al. 2009). This study introduces a novel approach to the analysis of plant competition and facilitation that greatly extends the time scale over which we can assess variation in plant–plant interaction outcomes with environmental change between long-lived plant populations.

Materials and methods

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

Palaeoecological Analysis

We reconstructed environmental changes that occurred around Quidenham Mere, Norfolk, England, UK (52°30′N, 1°0′E) over the late-glacial/early post-glacial transition (i.e. 13–7.6 k years bp) from lake sediments collected from the mere. The data we collected included vegetation, climate, fire level, herbivore density and N availability dynamics inferred from multiple independent proxies. Plant population density dynamics were inferred by fossil pollen accumulation rates (PAR) (Birks & Birks 1980). While all of the plant pollen taxa present in the sediments were identified during pollen analysis, here we focused on the population dynamics of oaks and grasses to allow for comparisons between our results and contemporary studies of plant–plant interactions in old-fields and savannas. The oak data were representative of the dynamics of all deciduous trees in the landscape over this time period (see Appendix S1 in Supporting Information). All proxies were analysed at the same levels of depth in the sediment core to determine the relative timing of changes in the environmental drivers without reliance on the radiocarbon dating.

Subfossil chironomid analysis was conducted and the resulting species assemblages were used to infer mean July air temperatures using a three-component weighted average partial least-squares transfer function based on the modern 153-lake Norwegian chironomid training set (Brooks & Birks 2000, 2001 and Brooks & Birks, unpublished data). Continuous changes in burning were reconstructed using microfossil charcoal contained in the sedimentary sequence and charcoal accumulation rates were calculated following the method of Tinner & Hu (2003). Changes in herbivore density were inferred from fossil dung-fungal spore accumulation rates (Davis & Shafer 2006). Nitrogen availability was reconstructed using stable isotope values of N from bulk sediments, which have been shown to correspond with changes in available N in trees across the landscape (McLauchlan et al. 2007). The chronology of the palaeoecological time series was established with a combination of radiocarbon dating of fossil pollen and climatic markers from the North Greenland Ice-core Project (Rasmussen et al. 2006) that were correlated with our chironomid-inferred climate dynamics (see Appendix S1).

Disturbance, Stress and Climatic Regimes

To assess the effect of abrupt environmental changes on grass–oak interactions at Quidenham Mere, we identified the point in time around which a major change-point in the time series of each environmental driver occurred. This change-point was used to separate the plant population density (i.e. PAR) data into discrete segments that represent the population density of oak and grass under different prevailing regimes. A plant–plant interaction model was fitted (described below) to each segment of the PAR data to generate the predicted interaction outcome for the corresponding time period.

Around 11.8 k years bp, a boundary was crossed in herbivore density dynamics which marked a change from relatively high herbivore densities (between 13 and 11.8 k years bp) to low densities (between 11.8 and 7.6 k years bp). The climate and fire time series both crossed a boundary around 11.7 k years bp, when summer air temperatures shifted from a cooling (13–11.7 k years bp) to warming trend (11.7–7.6 k years bp) and fire levels changed sharply from high to low. Taken together, these changes demonstrate a shift from a high- to a low-disturbance regime along with a change in the prevailing climate around 11.8–11.7 k years bp. In contrast, N availability passed a change-point over 1000 years after the abrupt changes in the non-resource variables. From 13 to 10.4 k years bp, N availability was increasing; then, after 10.4 k years bp, the resource began an initial decline (despite a temporary increase around 9.7 k years bp). Thus, the boundary around 10.4 k years bp marks a shift from decreasing resource stress to increasing resource stress.

Model-Fitting and Model Selection

The plant–plant interaction model used in this study was the Lotka–Volterra competition model:

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In this model, the rate of change in the population density of grass (x) and oaks (y) is described by the instantaneous growth rate (r) of each population, the carrying capacity (K) of each population and the interaction effect of grasses on oak population growth rate (α) and the effect of oaks on grass population growth rate (β) (i.e. the competition coefficients). The competition coefficients are treated as a rough proxy for competition intensity, defined here as the magnitude of the effect of population density of one species on the population growth rate of another species.

While this is a very simplified model of plant–plant interactions, it is suitable for the sparse time-series data (n = 77) we use here because: (i) it is bivariate (i.e. tri-variate models require many more data points to avoid problems of over-parameterization); (ii) it involves parameterization of only six model parameters (plus two variance and one covariance parameter) and (iii) it distils the complex interactions between the plant populations into an estimated competition coefficient value that summarizes the effect of one population on the population growth rate of another.

Ideally, we would be able to fit a complete model that simultaneously describes all of the interactions between the environmental variables and plant population dynamics such as the dependence of the oak–grass interaction on the level of disturbances in the landscape. However, the model-fitting approach is limited to fitting bivariate models. Therefore, to capture (albeit indirectly) the effect of changes in herbivory, fire level, climate and nitrogen availability on the oak–grass interaction, we split the PAR data into discrete periods of time which corresponded with major changes in disturbance, stress and climatic regimes. We then fitted the Lotka–Volterra model to each segment of the PAR data via maximum-likelihood estimation with a Gaussian likelihood function (Bonsall & Hastings 2004). This approach was replicated across each of the abrupt environmental changes so that we could compare the goodness-of-fit of the competition model to the data given each distinct breakpoint in the time series. The maximum-likelihood estimated (MLE) parameters from the model-fit for each segment were used to demonstrate the predicted changes in competition outcome over time. Additionally, we fitted a no-breakpoint model to the PAR data as a control. Confidence intervals for the MLE parameters were calculated from the likelihood profiles (Morgan 1999).

We used a model selection method to determine which environmental variable had the greatest impact on the oak–grass interaction over the whole time series. Since, model selection can only be conducted on comparable data sets (Burnham & Anderson 2002), we summed the log-likelihood (L) values estimated for each segment of the oak–grass PAR data as follows:

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This produced a single likelihood value (Lsum, i) that represented the goodness-of-fit of the competition model to the oak and grass PAR data over the entire time series given breakpoints in the PAR data coincident with abrupt changes in each environmental variable (i). We then calculated an Akaike Information Criterion (AIC) value (Burnham & Anderson 2002) associated with each of these breakpoints (AICi) in the PAR data using the equation:

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From the AICi values, we calculated AIC weights according to the formula:

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The AIC weights are a normalized indicator of the amount of evidence in support of each competition model-fit in terms of its ability to describe the long-term changes in the interaction between oak trees and grasses (i.e. from 13 to 7.6 k years bp).

To assess the goodness-of-fit over time of the AIC-inferred best interaction model to the oak and grass PAR data, we used a one-step-ahead-prediction procedure to generate predicted PAR values for the time series given the MLE parameters. This procedure uses the estimated parameter values and the current observed PAR value at a point in time to predict the PAR value in the next point in time in the series. We numerically integrated the Lotka–Volterra model over variable time lengths to obtain a set of one-step-ahead predictions. Then we calculated root mean square error (RMSE) values for both oak and grass PAR dynamics to demonstrate the average error in these model predictions across the time series.

Results

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

Time Series Data

Around 13 k years bp, the landscape was dominated by grasses (Fig. 1a) and herbs (see Appendix S1), while oak trees (Fig. 1b) were present at low densities. Herbivore densities – as inferred from dung-fungal spore accumulation rates – were relatively high until 12.2 k years bp (Fig. 1c), after which they began a gradual decline as the climate changed from the Allerød warm period to the Younger Dryas cool period (Fig. 1d). A hundred year prior to the end of the Younger Dryas cold period (11.8 k years bp), herbivore densities reached a low level that persisted through the remainder of the time series. The Younger Dryas ended around 11.7 k years bp and formed the boundary in the trajectory of climate dynamics as summer air temperatures shifted from a cooling to a warming trend.

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Figure 1.  Ecosystem dynamics at Quidenham Mere from 13–7.6 k years bp. Reconstructed population densities of grass and oak are represented by pollen accumulation rates (PAR). Herbivore density dynamics were inferred from dung-fungal spore accumulation rates (DFSAR), and mean July air temperatures were reconstructed from subfossil chironomid remains. Charcoal accumulation rates (CHAR) indicate changes in burning and stable isotopes of nitrogen (δ15N) represent changes in nitrogen availability. Abrupt changes are indicated by the change in colour in the bar above each environmental variable.

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As with herbivore densities, fire levels (Fig. 1e) were high throughout the cold Younger Dryas and there was a peak in burning that occurred immediately prior to the shift to warmer summer temperatures. Following this temporary peak in burning there was an abrupt shift to low-fire levels that remained in place throughout the early Holocene warm period when oak and other deciduous trees (see Appendix S1) became dominant in the landscape. This vegetation transition from a grass-dominated to a primarily oak-dominated landscape occurred about 500 years after the change in climate and disturbance regimes.

Nitrogen availability (Fig. 1f) had increased gradually from the start of the series through the change in disturbance and climate regimes and continued until around 10.4 k years bp when the time series shows that N availability began to decline. Although there was a temporary increase in N availability around 9.7 k years bp, the period from 10.4–7.6 k years bp was marked by increasing resource stress.

Change in Plant–Plant Interactions

With each regime change, there were corresponding changes in predicted interaction outcomes. Since these switch points occurred at different periods in time over the series, the results also demonstrate changes in the plant–plant interactions over time.

The first major change occurred in herbivore density (around 11.8 k years bp) and this transition corresponded with a change in the predicted interaction outcome from competitive exclusion of oak by grasses to stable coexistence (Fig. 2a). The change in predicted interaction outcome was attributable primarily to changes in each species’ model-estimated carrying capacity (Koak increased and Kgrass decreased) as there was little difference in the estimated competition coefficients between the regimes (Appendix S2). The next abrupt change occurred about 100 years later in the climate and fire time series (Fig. 2b) with a shift from high to low fire disturbances and to an ameliorating growing season climate. These shifts corresponded with the same predicted changes in interaction outcome as with the change in herbivore density (Figs 2a,b).

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Figure 2.  Predicted changes in interaction outcomes over time in terms of the predicted zero-net-growth isoclines of oak and grass pollen accumulation rates (PAR). The predicted oak–grass interaction outcome shifted from competitive exclusion of oak by grasses to stable coexistence with respect to abrupt changes in herbivory (a) and climate and burning (b). The oak–grass interaction model for the period 13–10.4 k years bp– the period of roughly continuous increases in nitrogen availability (c) – predicted that the oak–grass interaction outcome was unstable competition, with higher values of estimated competition coefficients and carrying capacities for both species relative to the predictions for the period 13–11.7 k years bp. After 10.4 k years bp, the modelled interaction outcome shifted to facilitation of oak by the grass population as nitrogen availability began to decrease.

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The N availability time series shows that a breakpoint occurred in the direction of change in this resource over 1000 years after the shift in the climate and disturbance regimes. The predicted interaction outcomes associated with this boundary contrasted with those predicted for the changes in the non-resource variables. The interaction outcome predicted for the period 13–10.4 k years bp was unstable competition between the populations (Fig. 2c); this means that any perturbation would have led to the extinction of one of the populations. The estimated model parameters for 13–10.4 k years bp indicated high values of Koak, Kgrass and competition coefficients compared with the estimated values of these parameters as predicted for the time period 13–11.7 k years bp when disturbances were low and summers were cool.

After the N availability boundary was passed and the resource was in decline, the predicted interaction between grass and oak was facilitation of oaks by grasses (i.e. for 10.4–7.6 k years bp). This prediction included an increase in the estimated Kgrass and a decrease in the estimated Koak as compared with the time period when nitrogen availability was increasing (i.e. 13–10.4 k years bp). The no-breakpoint model predicted unstable competition between the populations for the whole time series (see Appendix S2).

Model Selection

According to the AIC weights, the predicted shift from competitive exclusion of oaks by grasses to stable coexistence provided the best fit to the dynamics of oak and grass densities over the entire time series (Table 1). This was coincident with abrupt changes in climate and fire regime around 11.7 k years bp. The goodness-of-fit of this model to the grass and oak PAR data was estimated by the RMSE values of model-generated predictions from this model: 1081 grass PAR (grains cm−2 year−1) and 444 oak PAR (grains cm−2 year−1). The goodness-of-fit of the models to the data over time (Fig. 3) shows that there is a high correspondence between the predicted and observed values for each population. The greatest amount of error was clustered around the periods of time of high variability in the population density dynamics.

Table 1.   AIC weights for each application of the interaction model given different breakpoints in the environmental variables
Environmental variableBreakpoint in PAR data at:AIC weight
  1. PAR, pollen accumulation rates; AIC, Akaike Information Criterion.

Herbivory11.8 k years bp5%
Climate and fire11.7 k years bp95%
Nitrogen10.4 k years bp0%
No breakpointN/A0%
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Figure 3.  Plot of predicted (circles) and observed (line) values of pollen accumulation rates (PAR) as derived from the Akaike Information Criterion inferred best oak–grass interaction model compared with observed values of PAR over time. Predicted values were obtained by a one-step-ahead prediction procedure.

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The AIC weights showed that there was a small amount of support for the change in predicted interaction outcome across the herbivore density boundary around 11.8 k years bp, which occurred shortly before the climate and fire changes. However, there was no support for either the plant–plant interaction model prediction associated with the passing of the N availability boundary at 10.4 k years bp or the no-breakpoint model.

Discussion

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

The model selection results show that abrupt environmental changes had a significant impact on the predicted oak–grass interaction outcomes, relative to the control model. How did these environmental changes affect the plant interactions? And what aspects of these effects were unique to abrupt ecosystem dynamics?

Responses of Plant Interactions to Contrasting Environmental Changes

The breakpoints in the trajectory of the environmental variables occurred at different points in time (Fig. 4). The climatic and disturbance variables crossed boundaries between regimes around 11.8–11.7 k years bp. The first abrupt change was the loss of herbivores, which was shortly followed by a shift to a warming climate and a decline in burning. There was a coincident shift in the predicted interaction outcome from competitive exclusion of oaks (when the climate was cool and herbivory and fire levels were high) to stable coexistence (when the climate was warming and disturbances were low). The model selection results show that the changes in climate and disturbance regimes had the greatest effects on the joint dynamics of oak and grass density dynamics over the entire time series (Table 1). Thus, the competitive exclusion of oak trees predicted for this period (i.e. 13–11.7 k years bp) was likely enhanced by high levels of fire and herbivory in the ecosystem, which is consistent with the predictions of grass–tree interactions in contemporary savannas (Midgley, Lawes & Chamaille-Jammes 2010).

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Figure 4.  Summary diagram of changes over time in dominant vegetation, environmental drivers and predicted plant interaction outcomes.

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Following the shift to a low disturbance and warming climate regime after 11.7 k years bp, there was a change in landscape dominance whereby oaks became dominant by 11.2 k years bp after which grass density remained relatively low for the rest of the time series. Nitrogen availability had been increasing continuously until 10.4 k years bp, which suggests that the period from 11.7 to 10.4 k years bp was a time of low-resource stress as well as a benign environment in terms of growing season climate and disturbance levels. In these circumstances, trees are known to out-compete grasses (Baudena, D’Andrea & Provenzale 2010).

Interestingly, there were conflicting predicted interaction outcomes for this period: stable coexistence was predicted for 11.7–7.6 k years bp, while unstable competition was predicted for 13–10.4 k years bp. What was the prevailing interaction for the period 11.7–10.4 k years bp? The model-selection outcomes identified stable coexistence as the best-fitting oak–grass interaction outcome for the latter part of the time series; however, this result provides a poor explanation for the observed change in landscape dominance from grasses to oaks around 11.2 k years bp. Alternatively, it is possible that the unstable competition prediction associated with the time period 13–10.4 k years bp may have provided a better fit for the transition period between 11.7 and 10.4 k years bp. While further modelling is required to prove this assertion, there is some evidence in the data to support this claim.

The time-series data show that both oak and grass population densities increased following climate warming and the loss of disturbances while N availability was increasing. Therefore, it is reasonable to consider that these changes were consistent with an increase in competition intensity as indicated by the estimated competition coefficients for the period before 10.4 k years bp. Furthermore, the purported shift from competitive exclusion to unstable competition concurs with the timing of the change in landscape dominance around 11.2 k years bp (Fig. 4). However, since this model had a poor fit to the joint oak–grass density dynamics over the entire time series, it is likely that a shift to unstable competition was temporary, while the shift to stable coexistence was more durable (Vazquez et al. 2010).

Similarly, the predicted outcome of facilitation of oaks by grasses for the period 10.4–7.6 k years bp was in contrast with the stable coexistence outcome predicted for similar time period 11.7–7.6 k years bp. Following the shift to decreasing available N, the time-series data demonstrate a decline in the density of both populations. While there is little evidence of grasses providing a facilitative effect on trees via effects on the N cycle, there has been evidence of facilitation of trees by grasses via reduced soil-water stress during periods of high aridity (Berkowitz, Canham & Kelly 1995; Anthelme & Michalet 2009). Previous palaeoecological work on Quidenham Mere suggest that the early Holocene period was highly arid (Peglar 1993); therefore, the predicted facilitation of trees by grasses – if we can assume that it occurred – would likely have been due to the positive effects of grasses on soil-water retention. However, this line of reasoning remains speculative until further modelling of the direct responses of each population to changes in N availability is conducted.

Our finding of contrasting predictions in plant–plant interaction outcomes between biotic and abiotic drivers has previously been demonstrated by Smit, Rietkerk & Wassen (2009). Therefore, we now ask what distinctive qualities were evident in the response of the plant–plant interactions to abrupt changes in the environmental drivers.

Unique Effects of Threshold Changes in Stress Gradients

The results presented here demonstrate that grass–oak interactions responded in a discontinuous, abrupt way to changes in environmental drivers. This finding corresponds with past examples of empirical and theoretical shifts in ecosystem processes between alternative stable states given abrupt changes in environmental drivers (Scheffer et al. 2001). In particular, this was indicated by the short-term change to unstable competition that we presume occurred in between the two periods of stable interactions (i.e. between the shift from competitive exclusion to stable coexistence). This period of high-intensity competition was suggested by the predicted interaction outcome for the period 13–10.4 k years bp, which was found to be a poor fit to the whole time series but was consistent with the timing of the change in landscape dominance from grasses to oaks (Fig. 4). Rapid periods of instability are a common feature of shifts between alternative states as they tend to occur over very short time scales relative to the amount of time in which an ecosystem remains within each alternative stable state (Chapin et al. 2004).

An interesting aspect of our results is the finding that changes in competition intensity (as inferred from the Lotka–Volterra competition coefficients) were only evident for a short-term period. Long-lasting, stable interaction outcomes were marked only by differences in carrying capacity. Thus, the findings of this study suggest that changes in competition intensity may be a temporary aspect of model parameters while longer-term changes in interaction outcomes correspond more with the changes in carrying capacity. This assertion can be tested by investigating continuous changes in plant–plant interactions (as opposed to the discrete periods analysed here) which would also clarify the timing of the changes in plant–plant interactions with respect to abrupt changes in environmental drivers. Furthermore, the approach described here has important implications for research into plant competition and facilitation by utilizing millennial-scale information on plant population density dynamics that are available in the fossil record to extend the time frame over which we can analyse plant–plant interactions.

Acknowledgements

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

We acknowledge the support of the Royal Society. We would also like to thank Becky Bryant (Queen Mary, London) for collecting the sediment core; Fernando Maestre, José Carrión and an anonymous referee for comments that greatly improved this manuscript.

References

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

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

Appendix S1. Chronology development.

Appendix S2. Parameters of interaction models

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