Context In order to understand the biological causes of plant diversity and predict the functional consequences of losing plant diversity, we need to accurately measure the ecological processes that underpin our understanding. Species interactions like competition are the main deterministic forces that structure plant communities. The strength of interactions within and between species determines the types and number of species that stably coexist in diverse communities, and also the relative abundances of each species. Species interactions also drive the effects of diversity on ecosystem functioning by altering the per capita performance of species within the community.
The community-level properties that determine ecosystem functions are the product of which species are present in the community and the interaction between those species. Therefore, in order to develop a predictive understanding of how plant diversity influences the functioning of real-world ecosystems, we need a predictive understanding of species interactions in natural plant communities.
And in order to have a predictive understanding of species interactions, we need tried and tested methods for measuring species interactions, which consistently and accurately predict how plant communities respond when diversity is lost.
Here, I show that existing methods underestimate the impact of diversity loss on the remaining plant community. Chapter Summary Competition among neighbouring plants for shared resources is one of the key ecological forces that shapes plant communities. But measuring competition has always been a challenge, leaving controversy over the relative role of competition between species. Observational methods for measuring plant competition have become popular. This approach assumes that we can infer competitive effects from natural variation in the densities of co-occurring species.
The effect of competition between species is quantified by predicting how the population size of each species would respond to competitor removal.
However, this approach remains untested. We tested the predictive accuracy of this method by combining observational and experimental approaches. We grew four sand-dune annual species in monoculture and mixture. Their local compositions were left to naturally develop, making our data relevant to natural communities. We performed an observational analysis on the mixtures and predicted how each species would perform in the absence of competitors. We compared these predictions with our independent test: the monocultures, where each species was grown in isolation. We predicted that competitive ability increased with seed size, a well-known aspect of competition between these species. We occasionally predicted strong responses to competitor removal. Even so, we consistently underpredicted the effect of interspecific competition, for most species by at least half that observed. The method failed our test so we should infer competition from natural communities with care. We suggest that the method underpredicted the effect of competitor removal because the data lack information on fundamental niches.
Species are observed after they have been confined to realised niches by competition, so we lack the information to predict how they will respond to competitive release. Introduction Competition for shared limiting resources is the fundamental assumption that underpins community ecology. By understanding the nature of competition between species we can understand how they coexist, as coexistence requires that species limit themselves more than they limit others. This is the basis of the ecological niche concept, in which species are expected to evolve in a direction that will minimise interspecific competition, otherwise competitive exclusion is the inevitable outcome. While any farmer or gardener can confirm that competition depresses plant performance, it is less clear how best to measure the extent and nature of this competitive suppression in natural communities. One obvious way is to add or remove plants and measure the response of their neighbours. While seemingly straightforward, removal experiments have been heavily criticised because, among other things, species respond over a different timescale.
Hence, the immediate response to the removal of a particular species might differ greatly from a longer term outcome. Another common method is to experimentally grow focal plants surrounded by different numbers and types of neighbours. Such experiments often reveal that interspecific competition is strong and asymmetric. But it is not clear how to translate these measurements into the field, where densities and conditions could be very different. In short, all direct manipulative methods for measuring the strength of competition among plant species have been criticised, as either methodologically flawed or because they take place under unrealistic ecological conditions. Partly in response to these criticisms, plant ecologists have turned instead to observational approaches. Rather than manipulating the system, observational methods exploit natural variation in density and species composition found within real plant communities and can be used to estimate individual-level competitive effects.
For example, in neighbourhood modelling, detailed spatial maps of all plants allow focal plant size or fecundity to be modelled as a function of the number and identity of close neighbours. Using this method, estimates of individual-level competition coefficients have been obtained in both artificial and natural settings. Alternatively, counting the numbers of plants in permanent quadrats allow researchers to track changes in population sizes from year to year at small spatial scales. Changes in population size between years can then be modelled as a function of the number of neighbours, again allowing competition coefficients to be estimated. The pattern of interspecific interactions estimated from such observational analyses is mixed. But many studies have found that interactions between competing species in the field are extremely weak. However, this result throws up a problem. If competition between species is really so weak as to be negligible, then species would show little or no response to the removal of others. This was best illustrated by Martorell & Freckleton (2014) who parameterised a population model for each species in their community separately and then quantified the effect of removing the remaining species.
Their results showed that very little response was expected overall—though some species showed positive or negative responses, and rarer species seemed most suppressed by competitors. But this overall result, in turn, suggests that plant communities are not fundamentally competitive, a result clearly at odds with most experimental work. So are the weak interspecific interactions estimated using observational data simply some artefact of the method, or are plant communities in nature truly non-competitive? To resolve this paradox it is essential to combine observational methods for estimating competition coefficients with an independent test of model predictions within the same system. Here we present results from an experiment conducted under semi-natural conditions in which a community of annual plants was established and 2.27 allowed to grow and reproduce for several years. The communities were subdivided into small cells to which we could fit models of population growth using observed cell counts taken from the last two years of the experiment.
After fitting models and estimating competition coefficients, we predicted how each species would respond to the removal of the others, and similar to Martorell & Freckleton (2014), we predicted very little response to removal. However, we could then compare these predicted population sizes with those of monocultures of each species established at the same time. These comparisons revealed that the effect of interspecific competition had been grossly underestimated. Our work therefore reveals that when observational methods uncover weak interspecific interaction coefficients within natural communities, individual species might still suffer from strong interspecific suppression. Methods Overall approach Our overall approach is summarised in Figure. To test the accuracy of predictions made using observational approaches, we first needed a suitable dataset with which to fit appropriate models. In this case, we had established semi-natural communities consisting of seven species of sand-dune annuals subdivided into small cells (see Experiment).
Population sizes of all species were recorded in two consecutive years. For each of the five common species, we then fitted a population model in which changes in local population size from one year to the next are assumed to be a function of both its own density and the densities of other species. Depending on the details of model structure (see Models) interactions between species can be positive as well as negative. Figure. The method for estimating the effect of interspecific competition. Observational data on the population sizes of each species in a community is collected over multiple years. For each species, the change in population size from one year to the next is modelled as a function of its own density and the densities of other species. Once models are parameterised, they can be used to predict the population size of each species when: interacting species are present at their observed abundances, and interacting species are removed. These two predictions are compared with one another to quantify the effect of competition. Once the models are fitted, we can predict the effect of competitors on the focal species by setting population sizes of competitor species to zero and re-calculating the predicted population size of each focal species.
But to test whether these predictions are indeed accurate, we require additional data. In this case, our experiment included monoculture plots, which had been established at the same time. We therefore compared our predictions about the expected effect of the removal of competitors with observations of population sizes from monoculture plots (see Test). Experiment Seven species of sand-dune annuals were grown for four years (2010–13) in a common garden experiment in Zürich, Switzerland. The study species and their seed sizes were: Saxifraga tridactylites L. (0.006 mg), Arabidopsis thaliana Heynh. (0.025 mg), Cerastium diffusum Pers. (0.045 mg), Arenaria serpyllifolia L., Veronica arvensis L. (0.112 mg), Myosotis discolor Pers. (0.213 mg), and Valerianella locusta Laterr. (0.851 mg). They germinate in autumn and flower in spring. We analysed data for only five of these species, because Veronica and Valerianella were too rare. The experiment consisted of 80 (1 x 1 m) plots. A concrete lattice was inserted so that each plot consisted of 56 (7 x 7 cm) individual cells filled with a low-nutrient mixture of sand and compost. The lattice walls were sufficiently thick (2.5 cm) that plants in adjacent cells never overlapped aboveground. Thus, we assumed that plants within cells competed for resources, while plants in adjacent cells did not.
Plants dispersed seeds freely within plots, but barriers to dispersal prevented seed movement between plots. Subdividing the plots into cells provided the fine-grained information necessary for parameterising our models. We grew eight monocultures of each species and 24 mixtures containing all seven species. Figure 2.2. Example of an experimental plot, divided into 56 cells by a concrete grid. This is a mixture plot photographed immediately after seven cells were harvested in 2011. In order to create variation in density, a gradient of disturbance was applied across plots. This facilitated the fitting of nonlinear population models, which is often hampered by a lack of information at low density (Law & Watkinson 1987; Rees et al. 1996). Plots were disturbed by removing all plants from a fixed proportion of cells at the end of every growing season, just before the plants set seed. In mixture plots we applied five levels of disturbance: 12.5%, 25%, 50%, 75%, and 87.5%. In the monocultures there were only eight plots per species, so we imposed only three disturbance levels: 12.5%, 50%, and 87.5%.
We selected which cells to destroy in a stratified random way, destroying a fixed number of cells from each row in a plot grid. In 2012 and 2013 there was a highly significant negative relationship between disturbance and average density per cell, indicating that the disturbance treatment was successful in creating a density gradient (Supplementary Material SA1). The experiment was established from seed in 2010 using a constant total density of 1000 seeds per plot. The number of individuals in all cells was recorded at the end of the growing season for three years (2011–13), although only occupancy was recorded from the mixture plots in 2011. The transition 2012–13 is therefore the most completely sampled and was used for the model fitting. The end-season biomass of each species was estimated by destructively harvesting and weighing seven cells from each plot during application of the disturbance treatment. Models To ensure that our conclusions were not dependent on model choices, we fitted three models with varying assumptions about the nature of species interactions and the nature of dispersal within plots. We either assumed that: all seeds remain in their natal cells, or some fraction of seeds remain in the natal cell while the rest (1 – m) join a global seed rain.
The general form of model 1 (eqn 2.1) is: where Nt+1,i,c is the population size in year t+1 of focal species i in cell c. The population growth rate of species i in the absence of competition, ri, is modified by density-dependent interactions in the following way: where αij is the per capita effect of species j on species i. Thus, the first term in eqn 2.1 describes the expected number of individuals of species i in year t+1 that originated in the natal cell. Similarly, the average value of Fc among the cells within a plot can be calculated using: where p is the total number of cells within a plot. Thus, the second term in eqn 2.1 describes the expected number of immigrants arriving from other cells within the plot. Model 2 (eqn 2.4) contains only the first, within-cell-growth term from eqn 2.1, and thus assumes that no seeds disperse outside their natal cells: Model 3 (eqn 2.5) has a different structure. In this case we assume that within cells population growth is density-dependent, but is only sensitive to the density of conspecifics: where q is an index of cell quality. Other species affect the focal species by modifying the quality of cells.
This cell quality index is a logistic function of the densities of other species in year t+1 and their per capita effects on the focal species, βj. For each focal species we estimate a basal cell quality, β0, and the quality of each cell can deviate above or below this value depending upon the density of other species present in the same year. Model 3 allows species interactions to be positive as well as negative (eqn 2.6)—in contrast to models 1 and 2 where they are constrained to be negative. Positive interaction coefficients might indicate facilitation. But they might simply indicate that the seedling densities of both the neighbour and focal species tend to be positively correlated, perhaps because they share a preference for the same types of cells. All models were fitted using rjags v3-14 (Plummer 2014) in R v3.1.2 (R Core Team 2014). Each model assumed that Nt+1 was Poisson distributed. To estimate the competition coefficients we specified non-informative priors, assuming they had a normal distribution (μ = 0, σ2 = 1000). Competition coefficients were constrained to be positive—i.e. competitive—by applying an exponential transformation.
A common concern when parameterising these models is that the competition coefficients and the population growth rates in the absence of competition (ri) can be correlated, because they trade off against each other (Rees et al. 1996). This can produce an unstable estimation process, whereby both parameters increase or decrease together and yet give an equally good model fit. To avoid this instability we informed the estimation process on meaningful values of ri by specifying an informative prior for each species that used the best information we had on their maximum capacity for growth. We 2.34 specified these informative priors by assuming a gamma distribution with an expected value equal to the average 2012–13 population growth observed in high-disturbance monocultures (gamma: shape = mean 2012–13 growth; rate = 1; E[X] = shape/rate). When fitting model 3 to Myosotis, we fixed β0 at zero (basal cell quality = 0.5) to stabilise the estimation process, because there were significant trade-offs between ri and β0. We ran all models with three sampling chains.
We ensured each model had sufficiently converged on the target distribution by running an adaptation period of 40000 samples (plus 10000 burn-in). Following adaptation we monitored 10000 samples from the chains, thinning to every 10th sample to reduce autocorrelation— giving us 1000 samples from each posterior distribution. We checked that the chains had converged by plotting the sampling chains, posterior densities and chain autocorrelation. We used Gelman plots to check that chains had converged on the same target distribution (Brooks & Gelman 1998). We also checked models by: (i) testing that they can recover known parameters from simulated data, (ii) examining residual diagnostic plots, (iii) plotting the model fit, and (iv) comparing simulated and observed data to look for systematic differences between models and observations (Gelman & Hill 2007). Predicted data qualitatively resembled the observed data, although the observed data often showed a longer tail of right skewness.
Finally, we compared model performance using DIC (Plummer 2002). To facilitate comparisons among models, all models were fitted only to cells where Nt was positive. Analysis We examined interaction matrices from the parameterised models to look for patterns in competitive effects. We then used the parameterised models to quantify the effect of competition at the population level, by predicting population sizes in the presence and then in the absence of all other species (by setting populations sizes of other species to zero). We constructed intervals on the predicted population sizes without competitors from posterior samples within each cell. We averaged across these cell-level predictions to get the median predicted population size without competitors and its 95th percentile range. These median and interval values were then expressed relative to the average predicted population size when competitors are present. The predicted effect of competitor removal is thus the ratio between the focal population sizes with and without competitors (Nt+1 without / Nt+1 with).
We assessed the observed extent of competitive release by regressing the population sizes in 2013 on the population sizes in 2012 for both mixtures and monocultures. The slope of the regression line through the origin is therefore the population growth rate. We tested whether there was a significant effect of mixture vs monoculture on the growth rate of each species. If the regression slope in monoculture is, on average, steeper than in mixture, then there is a clear positive effect of removing competitors on population growth. In 2012 the range of population sizes in mixtures and monocultures was similar, so it was easy to compare treatments. The observed effect of competitor removal is thus the ratio between monoculture and mixture slopes (monoculture / mixture). Test Finally, to test whether our predictions matched our independent observations, we compared the predicted effect of competitor removal with the observed effect. We described each model’s predictive accuracy by expressing the predicted effect as a 2.36 percentage of the observed effect. We showed the credible range in each model’s predictive accuracy by using the interval for its predicted effect, which captures uncertainty in the estimation process.
Results Models Model 1 was the preferred model for three species—although for two species all models performed equally well (Supplementary Material SA1)—hence we focus on results from model 1. The competitive effects estimated by model 1 were asymmetric and structured by seed size (Figure 2.3). If a species had large seeds then it usually had a strong competitive effect on those with smaller seeds. In addition, for most species the strength of intraspecific competition was greater than the strength of competitive suppression by smaller seeded species, but weaker than competitive suppression by larger seeded species. Within the context of this seed-size pattern, Myosotis is anomalous. The model estimates that it is strongly affected by several of the smaller seeded species. This seed-size pattern was even more pronounced when the model did not include dispersal (model 2, see Supplementary Material SA1). When we allowed for positive interactions, however, the pattern disappeared: instead all interactions were scattered around zero, as many positive as there were negative (model 3). Broadly speaking, all models estimated the effects of interactions with high precision. Figure 2.3. Competition is asymmetric and related to seed size. The competitive effects of interacting species (columns) on the population size of each focal species (rows).
The highlighted diagonal are intraspecific competitive effects. Weak competitive effects are pale and stronger effects are darker (effects are log-scaled, so negative values describe more neutral effects). Species are ordered left to right and bottom to top by increasing seed size. Broadly speaking, competitive effects are linked to seed size, with large-seeded species exerting stronger effects. Model 2 shows even stronger seed-size structure (Supplementary Material SA1). Analysis Using these parameterised models we calculated the predicted effect of competitor removal within each cell. The seed-size structure of per capita interactions in Figure 2.3 is also clear in the population-level effects. For Saxifraga and Arabidopsis, model 1 predicted at least a doubling in population size in 50% of cells and they are predicted to increase by five-fold or more in 10% of cells. In contrast, larger seeded species are predicted to show a weaker response to competitor removal in most cells (75% of the time their ratio response is close to 1, i.e. no change). Myosotis is predicted to respond more strongly on average than Arenaria or Cerastium, reflecting the relatively strong competitive effects of other species on Myosotis.
Model 2 predicts smaller population-level responses of Myosotis, better conforming to the trend that large-seeded species respond less strongly to the removal of small-seeded competitors. Figure. Population-level effects of removing competitors. Distributions of the predicted effect of competitor removal at the cell level. An effect size of 2 means that the population size is predicted to double in response to competitor removal. In most cells the predicted effect is small but in some it is large. The x-axis has been truncated for clarity (removing <1% of cases). Species differences reflect the strength of competition shown in Figure 2.3. Predictions from model 2 show an even stronger seed-size structure. For the observed effects of competitor removal, there was a significant three-way interaction between species, diversity level and density. Inspection of the slopes revealed that in four out of five cases, the slope in the monoculture is much steeper than that in mixture: for most species, population growth at least doubled when grown in monoculture.
The only exception was Myosotis, whose population growth was higher in the mixture; although when we used biomass data rather than population sizes, the population growth in monoculture and mixture was the same (Supplementary Material SA1). Myosotis may have responded differently to interspecific competition because it was competitively dominant in mixtures. The hierarchy for average cell biomass in mixture was Myosotis > Arenaria > Cerastium > Saxifraga > Arabidopsis—broadly in decreasing order of seed size. It is clear that species densities are reduced by interspecific competition, especially if they have smaller seeds. Test Comparison of the predicted and observed effects revealed that the models made poor predictions about the population-level response to the removal of competitors. Models consistently underpredicted the effect of interspecific competition in four cases, but overpredicted in the case of Myosotis (Figure 2.6). The three different models had similar predictive accuracies, despite differences in the way they describe species interactions (Figure 2.6). Figure 2.5. Population growth rate is higher in monocultures than in mixtures.
The plot-level average cell population sizes in 2013 (Nt+1) versus 2012 (Nt) for each species. Blue dots show monocultures, red dots show mixtures. The regression lines, fitted through the origin, show the average population growth rate. Species are ordered by increasing seed size. Population growth rates were higher in monocultures than mixtures for four species. The exception was Myosotis, which was competitively dominant. In terms of population size Myosotis performed much better in the mixtures, but biomass data show no difference between diversity treatments for this species (Supplementary Material SA1). Figure 2.6. The effect of competition is consistently underpredicted. We assessed how accurate our predictions were by comparing the predicted effects shown in Figure 2.4 with the observed effects shown in Figure 2.5. Predictive accuracy is the predicted effect shown as a percentage of the observed effect (log-scaled). All three models behaved similarly. 2.41 Discussion We used tried and tested techniques to fit community models to observationalstyle data garnered in an experimental context. The models appeared to capture the relative competitive abilities of species, as the interaction matrices obtained are consistent with previous work.
This result, and other diagnostic tests, encourage us to believe that we fitted sensible models to the data. We then used the models to predict what would happen to each species once competitors were removed. Uniquely, we were able to provide an independent test of the model predictions, as the experiment included monoculture plots in which each species was free from interspecific competition. The models made poor predictions about the expected extent of competitive release. For most species the extent of competitive release was severely underpredicted, suggesting that we had underestimated the strength of interspecific interactions in multi-species communities. Why did we underestimate the strength of interspecific competition? The first possibility is that we fitted poor models, but this seems unlikely. The competition coefficients were well-estimated with small standard errors, from independent sampling chains that converged on the same posteriors. Model uncertainty was very low, reflected by the narrow intervals in Figure 2.6. The models were a good fit to the observed data. Distributions of cell population sizes in data simulated from the models closely resembled that of the observed data, further indicating that there was no systematic bias.
The three models we fitted described species interactions differently and yet all poorly predicted the effect of interactions in the same way. Our test was fair, as it expressed the same effect as our predictions—the mean change in population size in response to competitor removal—and did so over the same range of data. The wide variation in observed data meant that we avoided potential underestimation due to observing species only at high densities. These reasons lead us to believe that our analysis was not at fault for underestimating the strength of interspecific competition, but instead the underlying problem is more profound. The second possibility is that models which estimate the strength of competition in natural communities simply cannot be used to predict the effects of species loss. This might happen because species in natural communities are already confined by competition to realised niches. The fundamental niche represents all conditions in which a species can exist, whilst the realised niche is those conditions in which the species actually exists in the presence of interacting species.
If species are confined to parts of the habitat where they tend to compete best, then the strength of interspecific competition, as assessed by these methods, will be weak. In contrast, once competitor species are removed the remaining species may be able to expand their niche—assuming that their fundamental niche is wider than their realised niche. But without information on fundamental niches we cannot know the extent that species will respond to competitor removal. Therefore, to predict species responses from natural communities is to predict beyond the range of available information. This explanation for weakly interacting natural communities has previously been called the ghost of competition past. It may explain why interspecific competition measured in natural communities is often weaker than 2.43 that measured in experiments. Our results suggest this is a general problem that is likely to be present in any analysis using similar principles. Further simulation modelling is required to confirm this idea.
What are the implications? Ecologists have argued long and hard about the best way to measure competition; in particular, because the results of experimental work conflict with direct measurements of competitive interactions in natural communities. Our study potentially provides a resolution to this debate. In experiments plants are forced to compete, whereas in natural communities plants often display strong spatial aggregation that increases the chance of meeting conspecific neighbours. Species may aggregate in natural communities due to local dispersal. Freckleton & Watkinson (2000) recommended that the scale of sampling should reflect the dispersal abilities—and resulting clumping—of the species being monitored, to ensure that multiple species are observed within sampling units. But the larger the scale at which data are sampled, the more the effect of local interactions becomes blurred.
There are ways to incorporate dispersal into the modelling, as we have done. Aggregation can also be caused by species-specific requirements for particular ecological conditions. This has been suggested before as an explanation for the weak nature of estimated interspecific effects, but the magnitude of this problem has never been quantified. These methods have assumed a homogeneous environment. We believe this assumption was problematic even in our experimental setting—it was also considered by Mack & Harper (1977). Perhaps this problem could be addressed by measuring environmental variation, although it is not clear which variables are important to describe species preferences. But ultimately, if species rarely interact due to spatial aggregation then the effect of their interactions will be limited. If species weakly interact in natural communities because they have been confined to realised niches, then we should be wary of interpreting models parameterised using observational data to conclude whether such communities are strongly structured by interactions.
If much of the competition goes unseen we cannot claim whether or not communities are fundamentally competitive from such analyses. In particular, these models may give no information about how the community is likely to respond to the loss or removal of species, which is essential in a world where species are likely to be lost, for example, through new diseases. Future directions To understand more deeply why observational data are lacking, we need to combine experimental and observational approaches. Freckleton et al. (2000) used similar analytical techniques on a long-term dataset where densities were perturbed halfway through the sampling programme. However, they and others have criticised experimental approaches to estimate competition. Removal experiments are still practised, albeit more rarely and with acknowledgement of their caveats.
Perhaps experimental manipulations are more in need than recent studies would suggest. There is no method to measure competition that is not flawed. Much progress has been made in critiquing previous methods and developing new ones. We have shown that current observational methods also need refinement. If it is possible to devise a method that accurately predicts the impact of species losses from diverse communities, what extra information would be required? Traitbased approaches may be useful in predicting which species will respond most to the loss of another species. This approach would be most effective if we are able to identify which traits best explain how remaining species will expand their niche in response to competitor removal.
This could be combined with experimental approaches that remove one species at a time and measure the response of the remaining community. Experimental communities may also be useful for observing how species become confined to their realised niche if we can measure how species are affected by the gradual shift from homogenised to semi-natural conditions. Alternatively, we might need more detailed data on how species are affected by competition during specific life-history stages, rather than the more common observation of adult–adult transitions. Current observational data and methods are valuable tools, but we will need a greater combination of approaches to fully understand the role of competition between species in natural plant communities. Next Page – Ch 3: How Do More Diverse Plant Communities Increase Ecosystem Functions Previous Page – Ch 1: General Introduction