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Abstract

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

A fundamental question in ecology is how are species added to the phenotypic or functional trait space when one moves from a species poor to species rich assemblage. Specifically, the functional volume of an assemblage can expand and/or be packed more tightly to accommodate an increasing number of species. Quantifying the packing and filling of trait space therefore provides critical information regarding the generation of species richness gradients, but it is also informative for our understanding of community assembly as the functional volume is expected to be constrained by abiotic factors while the degree of the packing of the volume should be limited by biotic interactions. In this investigation we quantify the packing and filling of trait volumes in tree assemblages in eastern North America. We demonstrate that both the functional volume and the degree of packing both increase with increasing species richness. However, the increase in the functional volume is less than expected suggesting that the overall functional space is constrained. We then show that null models that incorporate a functional volume constraint uncover a greater degree of separation in trait space than expected suggesting the importance of biotic interactions within an abiotically defined functional volume.

The spatial distribution of biotic diversity is a frequent topic of study for ecology and evolutionary biology. Much of this research focuses on how species richness, the number of species counted at a place, is correlated with other variables. A common approach is to regress species richness on climatic variables to infer whether present day climatic gradients might explain the distribution of species richness (Currie 1991, O'Brien 1998). Less common is research that focuses on deeper dimensions of biodiversity such as the attributes of the species counted at a place. The majority of the hypotheses that attempt to explain species richness gradients explicitly or implicitly invoke distributions of the phylogenetic, functional and genetic dimensions of biodiversity. Therefore, it may be best to take our eyes off of gradients in species richness per se and focus on gradients in phylogenetic, functional and genetic diversity in order to understand the underlying processes that generate and maintain species richness gradients (Swenson 2011, 2013).

A simple and useful approach for studying species richness gradients is to ask: as the species richness of assemblages along a gradient increases, how does the functional volume the assemblages occupy change? The classic approach is to examine how the overall volume and packing of functional traits change as species richness increases (Ricklefs and O'Rourke 1975, Roy et al. 2000). Limiting similarity theory (MacArthur and Levins 1967) predicts that the functional trait volume, defined as the multi-dimensional trait space, must increase as the number of species increases if the limits to similarity are invariant along a species richness gradient. An alternative outcome could be that the functional volume simply becomes more tightly packed. Tighter packing could result from a lack of biotic interactions, low population sizes reducing the encounter rate of species and/or finer partitioning of local scale environmental gradients.

The volume and packing of functional space in species assemblages arrayed along broad regional-scale species richness gradients has been quantified in several animal systems. Early work on the functional volume occupied by moth and bird assemblages was consistent with limiting similarity theory (Ricklefs and O'Rourke 1975, Ricklefs and Cox 1977, Ricklefs and Travis 1980), but more recent work has suggested the moth results were likely biased due to a low number of sampling sites (Ricklefs 2009). Research from mammalian assemblages has also suggested an increase in the functional volume occupied as species richness increases (Shepherd 1998). Contrary to some of the above empirical examples and in agreement with Ricklefs (2009), simulations suggests that the functional volume should saturate as species richness increases in model food webs (Stegen and Swenson 2009). Lastly, there is relatively little information on changes in functional trait volume and packing with increasing species richness in plant assemblages. Recent work has quantified the dispersion of plant traits on broad scales (Swenson and Enquist 2007, Swenson et al. 2012), but these studies do not explicitly quantify functional volumes.

The research that has occurred on functional volumes and their packing aligns conceptually with recent trait-based investigations of community assembly. Specifically, the majority of trait-based assembly studies ask whether assemblage trait distributions are constrained by the abiotic environment, thereby increasing the packing of species, or whether species are more evenly arrayed in trait space due to biotic interactions (Weiher et al. 1998, Grime 2006, Kraft et al. 2008, Swenson and Enquist 2009). It is important to note that it is likely that both abiotic and biotic interactions may be acting to structure assemblages. Strong biotic interactions can take place within a functional volume that has been constrained by the abiotic environment. An approach that acknowledges this particular problem is to first consider whether the overall functional volume is smaller than expected given the species richness as would be expected by an abiotic filtering process. One could then consider whether the species within that volume are evenly distributed in the functional trait space possible given the larger abiotic constraint as would be an expected outcome of processes such as facilitation, competition and/or shared enemies. This framework could then be implemented along a species richness gradient to quantify whether the relative magnitude of these processes changes with the species richness. In other words, using a hierarchical conceptual model to guide the analytical workflow for quantifying the expansion and packing of functional trait volumes in assemblages varying in their species richness values is likely a more robust approach for detecting the dual importance of abiotic filtering and biotic interactions.

Here we use a large trait and spatial distributional dataset of eastern North America tree assemblages to quantify the degree to which the functional volume expands and/or is packed along a species richness gradient. Specifically, we first ask does the functional volume expand as expected by limiting similarity theory? We then use null models to ask whether the observed functional volume and packing are higher or lower than expected under random trait distributions and for the observed species richness. If the abiotic environment constrains the functional traits that can colonize an assemblage, we expect that the observed functional trait volume will be smaller than expected. If limiting similarity is important for defining functional volumes, we expect that the observed functional trait volume will be larger than expected. We then use a different null model for the mean nearest neighbor distance analyses. Given a model of community assembly where species must first pass an abiotic filter and then are biotically filtered, we argue that null model analyses of trait packing that do not constrain the analysis by the observed functional volume likely underestimate the importance of biotic interactions. Specifically, if the observed functional volume is smaller than expected as predicted by abiotic filtering, then a null model that is not constrained by this observed volume will be biased towards inferring that species are more tightly packed than expected. Conversely, null models that take into account the (abiotically constrained) smaller than expected functional volume will be more likely to detect the signal of biotic interactions in assemblages. We test this expectation and discuss the results in the context of the hierarchical conceptual framework for community assembly.

Methods

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

Forest inventory data

Plot level data produced by the United States Forest Service Forest Inventory and Analysis Program (FIA; <http://fia.fs.fed.us/>) was used in this study. Each FIA plot is composed of four circular subplots with 0.017 ha in area where all free-standing woody stems with diameter ≥ 12.7 cm were inventoried. Within each subplot there is a 0.001 ha ‘microplot’ where all stems with diameter ≥ 2.54 cm were inventoried. Previously Swenson and Weiser (2010) have taken from the FIA dataset more than 18 000 individual plots located in eastern North America to test geographic patterns of functional trait distributions. This study utilized a geographically rarefied subset of the original data used in Swenson and Weiser (2010) to remove sampling effects. Specifically we divided eastern North America into 1° × 1° grid cells and randomly selected 17 plots in each cell to build the new dataset. Non-native species were removed from the dataset before conducting any further analyses. These non-native species were removed because the species richness gradients of interest are predominantly the result of long-term interactions that did not involve these species. Lastly, those map grid cells containing no more than 17 plots were eliminated.

Functional trait data

Four functional traits that indicate where a species falls along spectra of plant ecological strategies were used in this study. Maximum height was used as it relate to the adult light niche of species, the ability to tolerate xeric environments, and recruitment (Moles et al. 2009). Seed mass was used as it is related to the regeneration niche of species and represents a fundamental tradeoff between producing many small seeds and few large seeds (Venable 1996, Moles and Westoby 2006). Wood density was used because it is often the best predictor of growth and mortality rates in tree datasets and represents a tradeoff between rapid volumetric growth and mechanical instability versus slow volumetric growth and mechanical stability (on the tissue and organismal scale) (Chave et al. 2009). Leaf nitrogen was used to represent the leaf economics spectrum where species with high leaf nitrogen typically have higher mass based photosynthetic rates while having reduced leaf life spans (Wright et al. 2004). The trait data for this study were primarily collected from the literature (Swenson and Weiser 2010), but were supplemented through field collection of additional trait values and through the measurement of traits on herbarium vouchers by NGS.

Quantifying the packing and filling of functional space

The central goal of this work is to quantify the packing and filling of functional trait space in tree assemblages in relation to species richness. To accomplish this goal we first quantified the functional volume by calculating a multivariate convex hull volume also known as the functional richness (FRic; Laliberte and Legendre 2010). The convex hull volume is simply a multidimensional volume that is maximally convex given the trait data. In other words, it is the smallest volume possible that still contains all data points. To quantify the packing of trait space we measured the mean nearest neighbor distance using the Euclidean distance between species in multivariate trait space. We calculated both metrics using principle component axes and raw trait values. Because the traits were not strongly correlated, both approaches gave similar results. We therefore only report the results from the raw trait values.

Unconstrained null model analysis

The multivariate trait volume or functional richness is expected to be positively correlated with species richness while the mean nearest neighbor distance is expected to negatively correlate with species richness. To determine whether observed values were significantly different from a random expectation we first used an unconstrained null model. The unconstrained null model shuffled species names on the trait matrix 9999 times and recalculated the functional richness and mean nearest neighbor metric for each assemblage for each iteration. This generated a null distribution of 9999 values for each metric. The observed values and this null distribution were used to calculate a standardized effect size for each metric for each assemblage. The standardized effect size was equal to the observed functional richness or mean nearest neighbor value minus the mean of the null distribution divided by the standard deviation of the null distribution. Therefore positive standardized effect size values indicate higher than expected observed functional richness or nearest neighbor values, while negative standardized effect size values indicate lower than expected values.

Constrained null model analysis

Statistical and conceptual problems arise when using the unconstrained null model to quantify both trait volumes and nearest neighbor distances. That is, if the observed volume is lower than expected given the global trait pool, it is very difficult to find a higher than expected nearest neighbor value. This is not only a statistical nuisance, but biologically it is also a problem as plant community ecologists often view community assembly in a hierarchical manner where species first pass through an abiotic filter and then a biotic filter. In other words, we first expect the trait volume to be reduced and once this has occurred biotic interactions begin to ‘play out’. For these reasons a global unconstrained null for both volume and nearest neighbor is likely not appropriate and should only be used for trait range. This leaves the problem of how to generate a statistically and biologically appropriate null model for nearest neighbor distance.

Here we argue that the most appropriate null model for nearest neighbor distance constrains the pool by the observed trait volume and from this constrained pool the random assemblages can be generated to generate a null distribution and standardized effect size values. We implemented this null model by generating 9999 random assemblages for each observed assemblage. Each random assemblage was constrained such that the observed local species richness was maintained and the only species that could colonize the assemblage had trait values within the observed multivariate convex hull volume.

Power analysis

The mean nearest neighbor standardized effect size results from the constrained null model were found to be significantly negatively related to the observed species richness and were converging towards a standardized effect size value of zero at high species richness values (Results). This result could be biologically ‘real’ or a null modeling artifact. Specifically, as the observed species richness increases and approaches the species richness of the pool used to construct the null model a decrease in statistical power may be expected (Colwell and Winkler 1984). We therefore conducted a power analysis to quantify which mean nearest neighbor standardized effect size analyses had enough statistical power to produce a reliable result.

The power analyses were accomplished by modifying the approach of Colwell and Winkler (1984) and Kraft et al. (2010). Specifically, these two works simulated assemblages with maximal limiting similarity and therefore the maximal expected mean nearest neighbor distance given the observed constraints – the pool and observed species richness of the assemblage. Next random assemblages are generated that also observe the pool and richness constraint, but do not observe any limits to similarity. Generating 1000 simulations for both the limiting similarity and random scenarios generates a distribution of mean nearest trait neighbor values. If the mean nearest neighbor metric has 95% power to detect a non-random result, then it is expected that the distributions of the 1000 simulations do not overlap by more than 5%. This can be tested by quantifying whether the mean nearest neighbor value in the 5th percentile of the limiting similarity simulation is larger than the 95th percentile of the random assemblage simulation.

In previous work by Kraft et al. (2010) the pool did not vary across the study similar to our unconstrained null model. Here, in our constrained null model the pool varied between assemblages due to our constraining of the values to the observed range of traits observed in the assemblage. Thus, we modified the R code published by Kraft et al. (2010), which was adapted from Colwell and Winkler (1984), to perform simulations for each individual pool rather than one simulation for a single global pool.

Results

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

Observed multivariate functional volume and nearest neighbor distances

The present study quantified the multivariate functional volume (i.e. functional richness) of the species observed in a map grid cell. The functional volume was positively correlated with species richness (Fig. 1; Pearson's r = 0.825). The relationship between the functional volume and species richness was linear and did not appear to saturate. The mean nearest functional neighbor distance was calculated between all species in each assemblage using the Euclidean distance separating species in multivariate trait space. The mean nearest neighbor distance was negatively correlated with species richness (Fig. 1; Pearson's r = −0.735).

image

Figure 1. The relationship between the tree assemblage species richness and the multivariate functional richness or volume (top) and the mean nearest neighbor distance (MNND) in multivariate trait space (bottom). The r values are Pearson correlation coefficients and are significant at the p < 0.05 level.

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Unconstrained null model analyses

We were interested in determining whether the observed functional volume and mean nearest neighbor distances deviated from that expected given the observed species richness of the assemblage. To address this issue we first performed a null model analysis that was ‘unconstrained’. Specifically, we shuffled the names of species on the trait matrix and recalculated the functional volume and nearest neighbor distances for each assemblage 9999 times and calculated a standardized effect size. The standardized effect size results for the functional volume were generally negative and weakly correlated with the observed species richness (Fig. 2; Pearson's r = 0.146). Negative standardized effect size values indicate an observed functional volume that is smaller than that expected given the observed species richness.

image

Figure 2. The results of the unconstrained null model analysis. On the top are the standardized effect size (SES) results for functional richness where negative values indicate a lower than expected observed functional richness given the species richness. On the bottom is the SES of the mean nearest neighbor distance (MNND) where negative values indicate a lower than expected observed MNND given the species richness. The r values are Pearson correlation coefficients and are significant at the p < 0.05 level.

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The unconstrained null model was also used to assess whether the observed mean nearest neighbor distance in an assemblage deviated from that expected given the observed species richness. The standardized effect size results from this analysis were generally negative and were weakly negatively correlated with the observed species richness (Fig. 2; Pearson's r = −0.197). Thus, the observed mean nearest neighbor distance between species was generally smaller than that expected given the species richness and the magnitude of this packing of species in trait space increased with the species richness.

Constrained null model analyses

A potential problem with the unconstrained null model analysis is that the randomizations for the mean nearest neighbor analyses were not constrained by the observed functional volume. A lack of this constraint may bias the results towards an overestimation of how tightly packed species are into trait space. To explore this statistical and conceptual problem we ran a second null modeling analysis for the mean nearest neighbor analyses where we constrained the randomization to only draw from species that were known to occur within the observed multivariate functional volume. The standardized effect size results from this constrained randomization were generally positive (Fig. 3). Thus, when constraining the null model analyses by the observed functional volume the observed mean nearest neighbor in the assemblages was generally higher than that expected. The standardized effect size values from the constrained null model were still negatively correlated with the observed species richness (Pearson's r = −0.402) indicating that degree to which species are packed within the observed multivariate functional volume increases with the number of species in an assemblage.

image

Figure 3. The results of the constrained null model analysis. The standardized effect size (SES) of the mean nearest neighbor distance (MNND) is plotted against the species richness of the assemblage. Positive values indicate a higher than expected observed MNND given the species richness and negative values indicate a lower than expected observed MNND. The r value is a Pearson correlation coefficient and is significant at the p < 0.05 level.

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Power analyses

The negative correlation between the standardized effect size values from the nearest neighbor null modeling analyses could be a ‘real’ result or could be an artifact. Specifically, the statistical power to reject the null expectation will decrease as the number of species in the assemblage approaches the number of species in the species pool. We therefore conducted a power analysis where we asked whether there was sufficient statistical power to reject the null hypothesis given the observed species richness, the observed functional volume and the number of species in the species pool that were inside the observed functional volume. We retained only those assemblages that were expected to have at least 95% power to reject the null hypothesis. The remaining assemblages still demonstrated that the observed mean nearest neighbor distance in an assemblage was still generally positive, but negatively related to the observed species richness (Fig. 4; Pearson's r = −0.271). Thus, the general inferences that are drawn from our constrained null model analyses are not an artifact of a loss of statistical power in relation to the species richness of the assemblage.

image

Figure 4. The results of the constrained null model analysis for only those assemblages where sufficient statistical power (> 95%) was present to reject the null expectation of random assembly. The standardized effect size (SES) of the mean nearest neighbor distance (MNND) is plotted against the species richness of the assemblage. Positive values indicate a higher than expected observed MNND given the species richness and negative values indicate a lower than expected observed MNND. The r value is a Pearson correlation coefficient and is significant at the p < 0.05 level.

Download figure to PowerPoint

Discussion

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

A fundamental question in ecology is how are species added to the functional space occupied by an assemblage as there is an increase in species richness (Fischer 1960, Stevens et al. 2003, Ricklefs 2009, Stegen and Swenson 2009). Specifically, is species richness increased via the expansion of the functional volume occupied or by an increase in the packing of the functional volume? If the magnitude of the limits to similarity (MacArthur and Levins 1967) is consistent across species richness gradients, then the functional volume is expected to increase with species richness. The present work began by analyzing the change in the multivariate functional volume across a species richness gradient in eastern North American tree assemblages. We found that the multivariate functional volume increases with the species richness observed (Fig. 1). This relationship did not saturate and therefore did not suggest there was a hard limit to the functional volume as species richness increased. The packing of this volume was then quantified as the mean nearest neighbor distance in multivariate trait space. The results show that as species richness increased the mean nearest neighbor distance decreased (Fig. 1). In other words as the species richness increased from one assemblage to the next in this study system the functional volume increased, but the packing of species also increased. Thus, as species are ‘added’ to assemblages along the species richness gradient they tend to pack the functional volume to a greater degree than they expand the volume. This suggests that a consistent limit to the functional similarity of species does not underlie the increase in species richness from one assemblage to the next. Rather, species are generally added to the existing functional volume suggesting that species in rich assemblages either more finely divide that volume due to biotic interactions or overlap broadly within that volume with diffuse or biotic interactions though determining which of these situations occurs would require additional information regarding the intra-specific distribution of function within and across assemblages.

The observed patterns of how the functional volume and packing changes with species richness could be simply due to a sampling effect and not a biological process per se. For example, as the species richness increases we might expect the packing of trait space to increase even if species are assembled at random from some pool of species (Ricklefs and O'Rourke 1975). Thus, we conducted a null modeling analysis where we asked whether the observed functional volume and mean nearest neighbor distance deviated from that expected by randomizing the names of species on the trait matrix. The results of the null modeling analysis showed that the observed functional volume was generally smaller than that expected given the species richness as indicated by the negative standardized effect sizes in Fig. 2. Thus, although the functional volume increased with species richness, that increase in volume was generally constrained. The standardized effect sizes values for the mean nearest neighbor analyses were also generally negative (Fig. 2) indicating that the observed value was lower than that expected given the species richness observed. Thus, these results appear to confirm that as the species richness increases from one assemblage to the next in our study system, species are generally added to the interior of the existing functional volume thereby packing this volume more than expected given the pool of possible colonists. We therefore infer that the functional volume of tree species assemblages in our study system is the result of broad scale abiotic filtering that is evident across the entire species richness gradient and there is little evidence for consistency the degree to which species can be functionally similar across the species richness gradient.

The species also appear to be consistently packed more tightly into the functional volume of assemblages than expected potentially indicating the importance of abiotic filtering and a diminished importance for biotic interactions. However, we expected this result could simply be an artifact of how we conducted the null modeling analysis. Specifically, the null model analysis above was relatively unconstrained where the observed functional volume was not constrained or fixed in the nearest neighbor null model. This is problematic particularly because we know that the observed functional volume was on average significantly smaller than that expected given the species pool. Thus, by not constraining the nearest neighbor null model by the observed functional volume it is very likely that we are overestimating the packing of species in functional space (Colwell and Winkler 1984). This is not only statistically important, there is also a biological and conceptual basis for why we may not want to implement a null model for nearest neighbor distances that does not constrain by the observed functional volume. Specifically, it is generally expected that the assembly of species is initially constrained by the abiotic environment. The species that can tolerate the abiotic environment then interact with their biotic environment, which determines their co-existence (Weiher and Keddy 1995, Swenson et al. 2006). In this framework, the functional volume is constrained by the abiotic environment while biotic interactions dictating the patterns of mean nearest neighbor distance take place within the abiotically defined functional volume (Weiher et al. 1998). Thus, it is likely conceptually and biologically more appropriate to fix the observed functional volume in null model analyses of mean nearest neighbor distances.

We explored the degree to which constraining our null model analyses by the observed functional volume altered our inferences regarding nearest neighbor distances and the packing of functional space. When constraining the null model by the observed functional volume we found that almost all observed mean nearest functional neighbor distances were higher than that expected given the species richness and the functional volume as indicated by the positive standardized effect sizes values in Fig. 3. Thus, the functional volume of tree assemblages in our study system is smaller than that expected, but within this constrained functional space, species are more distantly spaced than expected though the magnitude of this spacing was not as great at the highest species richness values (Fig. 3). We were concerned that this null modeling result could be due to a loss of statistical power as the assemblage species richness approached the species richness in the species pool used to construct the null model (Colwell and Winkler 1984, Kraft et al. 2007, 2010). A power analysis was utilized to explore this possibility and while some results were found not to have sufficient statistical power those data points that had sufficient statistical power upheld our general finding of a higher than expected mean nearest neighbor distance within the observed functional volume (Fig. 4).

The results in this study are consistent with a conceptual model where species first pass through an abiotic filter, which constrains their functional volume. Next the species pass through a biotic filter that maximizes the possible functional diversity, given the abiotic filtering present, via competition, facilitation or shared enemies. Thus, the results strongly support the dual importance of both abiotic and biotic filters for the structuring species assemblages and their functional diversity. It is likely that similar patterns will be detected across taxa on broad scales once appropriate null models are formulated and implemented. Thus, it is important that our quantification of the functional packing of assemblages is quantified and conceptualized within the given functional volume produced by the abiotic constraints. This has a critical statistical importance with respect to how we should constrain null models by the observed functional volume, but more importantly this result highlights the need to align conceptual frameworks for community assembly processes and the null models used to infer these processes.

Acknowledgements

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References

NGS was supported by a National Science Foundation Advances in Bioinformatics Award (DBI 1262475). MDW was supported by National Science Foundation Macrosystem Biology Grant EF-1065844. The authors would like to thank Nathan Kraft for making his R code available.

References

  1. Top of page
  2. Abstract
  3. Methods
  4. Results
  5. Discussion
  6. Acknowledgements
  7. References