SEARCH

SEARCH BY CITATION

Keywords:

  • hierarchical Bayesian analysis;
  • intraspecific variation;
  • mixed effects models;
  • permanova ;
  • PERMDISP ;
  • plant functional traits;
  • rosette diameter;
  • specific leaf area

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information
  1. The importance of intraspecific trait variation is increasingly recognized, but the ways in which this variation is quantified and compared have not been rigorously assessed.
  2. We reviewed 5 years of ecological literature quantifying intraspecific variation (64 published studies) and identified commonly applied statistical methods. Analysis of variance techniques (n = 43) was the most commonly applied method. Levene's tests (n = 14), linear techniques (both general and generalized models) (n = 12) and mixed effects modelling (n = 9) were also used. Qualitative comparisons of plant phenotype using descriptive statistics (n = 10) and coefficients of variation (n = 8) were also applied. Bayesian analysis was used in a single study.
  3. We compared the efficacy and interpretation of analysis of variance, tests for homogeneity of variance, qualitative comparisons, mixed effects models and Bayesian hierarchical modelling in a case study measuring variation in specific leaf area (SLA) and rosette diameter among 10 populations (n = 241 individuals) of Hypochaeris radicata. We also examined whether data base- and literature-based trait values provided good estimates for measured populations.
  4. Intraspecific variation was substantial, and significant differences existed in both means and variation across populations for both measured traits. There was a 27-fold variation in SLA (1·7–46·1 mm2 mg−1) and a 34-fold variation in rosette diameter (1·7–59·1 cm). The choice of statistical technique influenced the interpretation of results. Permutational anova was reasonably successful in detecting differences among populations, particularly when combined with a permutational test of dispersion within populations. Only Bayesian estimates were able to simultaneously quantify and compare variation within and across populations and to estimate trait values and variation on a larger, regional scale. Literature-based trait values had poor fit for four of 10 populations and differed from the estimated regional trait distribution.
  5. Synthesis. Although both classical and Bayesian techniques yielded similar results, Bayesian techniques were more sensitive to differences in intraspecific variation, could simultaneously examine variation within and across populations, could estimate regional trait distributions and did not require that the assumption of homogeneity of variance be met. Bayesian techniques and hierarchical models in particular represent a powerful analytical tool for studies of intraspecific variation.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information

Over the past several decades, plant ecology has moved from a reliance on strictly taxonomic classification of species towards the inclusion of functional trait-based methods (Calow 1987; Cadotte, Carscadden & Mirotchnick 2011). In describing plants by their functional traits, which indirectly or directly measure fitness, rather than their taxonomy, a fuller understanding of plant community ecology has emerged. Understanding of global trends in plant traits (Moles & Westoby 2003; Diaz et al. 2004; Wright et al. 2005; Moles et al. 2009), the effects of abiotic filters on trait community assembly (Diaz, Cabido & Casanoves 1998; Maharjan, Poorter & Holmgren 2011) and definitions of plant strategies (Westoby 1998; Laughlin et al. 2010) have all been extended in part by a functional trait-based approach. Definitions of diversity have also expanded to include the array of functional traits within ecosystems and landscapes (Petchey & Gaston 2002).

Much of the research about functional traits has focused on differences among species. This emphasis on interspecific variation is reflected in a commonly applied definition of a ‘useful’ trait in community ecology: one which shows high reproducibility, or low variation, within a species (McGill et al. 2006). While traits such as photosynthetic pathway are fixed and do not vary within species, recent research has shown that other traits can vary substantially (Karley & Hawes 2008; Lecerf & Chauvet 2008; Violle et al. 2009; Albert et al. 2010; Hulshof & Swenson 2010). Furthermore, this trait variation can have important implications for species coexistence (Clark 2010; Jung et al. 2010; Long et al. 2011; Pruitt & Ferrari 2011), other trophic levels (Karley & Hawes 2008; Ruhnke et al. 2009; Lankau 2011) and ecosystem functions (Pontes et al. 2007; Lecerf & Chauvet 2008). Intraspecific variation is an important element in functional diversity calculations (Cianciaruso et al. 2009; Albert et al. 2012).

Although defined generically as the variation within a species, intraspecific variation can be studied at different levels, such as within and across populations. While much trait variation can be linked to genetic differences (Begg et al. 2012), the levels of variation can also reflect different mechanisms. For example, variation within populations may reflect seasonal differences (Al et al. 2005; Prior, Bowman & Eamus 2005; Nouvellon et al. 2010) and ontogeny (Smith et al. 2011). Variation among populations may reflect climatic and resource gradients (Thuiller et al. 2004; Baruch 2011; Long et al. 2011), disturbance history (Kyle & Leishman 2009; Da Silveira Pontes et al. 2010; Mason et al. 2011) and niche partitioning due to differing community structure (Gubsch et al. 2011; Roscher et al. 2011).

The fact that intraspecific variation can be studied at different levels means that decisions about how data are collected, analysed and interpreted should be made carefully. However, the way in which this variation is quantified has not been rigorously assessed. In this paper, our objectives were to compare the efficacy and interpretability of methods used to quantify intraspecific variation and to assess the utility of published trait values. We conducted a literature review documenting current methods of quantifying and comparing intraspecific variation and then used six methods to quantify variation within and among populations of Hypochaeris radicata, a widespread weed. We focused on two traits and posed three questions: (i) How much trait variation exists within and between populations of H. radicata? (ii) Do different analytical techniques deliver different results or interpretations and what are their strengths and limitations? (iii) Are literature-based trait means an accurate representation of trait values in these populations? We hypothesized that large and statistically significant intraspecific variation exists within and across populations of this species and that different analytical techniques would yield different results. Furthermore, we hypothesized that the predicted high variation in plant traits would make literature-based trait means inaccurate.

Characterizing intraspecific variation

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information

We performed a literature review to identify the analytical methods used to quantify and compare intraspecific variation. These studies typically sought to directly quantify the intraspecific variation within a population, compare traits across populations of a species, or both. We searched the Thomson Reuters Web of Science data base (Thomson Reuters, USA) for the term ‘intraspecific variation’ (including wildcard terms such as vari*, var* and intra*) in articles published in peer-reviewed journals between January 2007 and October 2012. The full text of each article was searched for these terms. Studies were then reviewed to determine whether they were appropriate in scope and focus. We limited our review to studies that focused on plants and were drawn from plant ecology, plant evolution, forestry and agricultural journals. Sixty-four articles fit these criteria.

We reviewed each article to determine the method or methods used to analyse or interpret intraspecific variation. Most studies included a statistical test, usually an analysis of variance (anova) (43 of 64) (Fig. 1). Fourteen studies explicitly used a Levene's test to assess homogeneity of variance. Twelve studies used general or generalized linear mixed models, and nine used mixed effects models. One study used Bayesian analysis of variance. Roughly one-third of studies (20 of 64) did not conduct statistical tests of intraspecific variation, but summarized it using descriptive statistics such as standard errors, standard deviations or differences in average size. Eight studies compared coefficients of variation.

image

Figure 1. Techniques used to quantify or compare intraspecific variation drawn from peer-reviewed literature published between January 2007 and October 2012. Dark bars indicate quantitative statistical tests, and light bars indicate techniques that compare descriptive statistics. Sixty-four studies are included here, but some studies used multiple techniques and were tallied multiple times.

Download figure to PowerPoint

When evaluating the suitability of these techniques, it is important to recognize their assumptions, strengths and weaknesses (Table 1). Descriptive statistics used to characterize intraspecific variation include the standard deviation (SD), standard error (SE) and coefficient of variation (CV). While these measures provide useful information about the amount of variation present in populations, they are sensitive to sampling errors and methodological problems. Qualitative comparisons and reporting of plant trait values may provide a record of useful information for other trait-based analytical approaches. However, if these summaries are not accompanied by statistical tests, it is impossible to determine whether differences in observed intraspecific trait variation were statistically significant.

Table 1. Application, assumptions, strengths and weaknesses of statistical methods used to quantify intraspecific variation
MethodApplicationAssumptionsStrengthsWeaknesses
Descriptive statisticsComparison of means, standard deviations, standard errors and rangesMeasured values, standard deviations or standard errors are representative population and/or treatments effectsProvide information on values of traits of interestAnecdotal; no statistical test
Coefficient of variationCalculates the ratio of the standard deviation to the mean, quantifying data dispersionSuitable only for non-negative values on a ratio scaleDirectly quantifies and allows for direct comparison of varianceCannot be used for some data; no statistical test
Homogeneity of varianceTest for equality of variance; typically used diagnosticallyDependent on method usedDirect test for equality of varianceUnderlying data distribution cannot be quantified
PERMDISPTest for data dispersion from the mean using distance-based measuresAppropriate distance measures are used to construct the dissimilarity matrixA direct test for data dispersion around the mean, including significance and pairwise comparisonsChoice of distance measure is critical and can bias outcomes. Underlying data distribution cannot be inferred
Analysis of varianceTest for differences between means based on sums of squaresNormally distributed data; equal variance; independence of errorsCan indicate differences between populationsDoes not directly test whether populations differ in trait means and/or variation around the mean
permanova Test for differences between means using sums of squares and permutation testsWeak assumption: homogenous varianceNo distributional assumption; can detect differences between populationsUnderlying data distribution cannot be inferred from this test. Does not directly test whether populations differ in trait means and/or variation around the mean
Linear techniques
General linear mixed modelsRelate a continuous response to linear predictorsNormally distributed data; equal variance; independence of errorsCan indicate differences between populations or along gradientsDoes not directly test whether populations differ in both trait means and variation around the mean
Generalized linear mixed modelsRelate non-normal, non-continuous responses to linear predictorsMultiple families of distributions; independence of errors; interpretation of variance dependent on distributional formCan indicate differences between populationsVariance specified and is typically not quantified directly
Mixed effects modelsRelate non-normal, non-continuous responses to non-normal and non-continuous predictorsIncorporate both random and fixed effects; multiple families of distributions; independence of errors; interpretation of variance dependent on distributional formIndicates differences between populations; hierarchical estimation of population parametersCannot directly estimate variance for a given population
Bayesian techniquesDerives a posterior probability distribution for a variable based on a prior probability, and a likelihood function; estimation of parameters for direct comparisonPrior and posterior data must have some assumed and assigned distributional structureDirectly estimates both mean values and variance directly from data; allows for direct comparison of variance terms; allows for updating of distributions based on new data; assumptions about distributions can be assessed directlySensitive to improper or incorrect prior distributions; classic significance tests are not typically applied, computationally intensive

Linear mixed models were the most common method of analysing intraspecific variation. Classical anova compares populations based on the ratio of variation among and within populations. While this approach identifies differences among populations, mean trait values do not necessarily indicate, or correlate with, the degree of variation expressed in each population, and no inference about variation within populations can be made from trait means. In addition, anova and linear mixed models assume that residuals of the data are normally distributed; deviations from this assumption can bias the results of such tests. Other distributional forms can be analysed via generalized linear mixed models, or via permutational tests such as permanova (Anderson 2001), that make no assumptions about the distributional form of the data. Finally, these techniques assume homogeneity of variance, yet heterogeneous variance among populations may be one way that intraspecific variation is manifested.

It is well known that statistically significant anova results can indicate differences among populations in mean values, heteroscedasticity or both. Differences in variance among populations can be detected with a test of homogeneity of variance (e.g. Levene's test), though this test is typically used diagnostically rather than inferentially and is frequently not reported in the literature (only 14 of 64 studies reported diagnostic testing for equal variance). In addition, while this method can indicate which populations differ in variance, it does not provide a quantitative measure of the distribution of measured traits. A permutational equivalent of Levene's test has been developed (PERMDISP; Anderson 2004) that tests for differences in dispersion among populations, although this test suffers the same weaknesses of the traditional Levene's test.

Mixed effects models relax many of the assumptions of more commonly applied techniques, are appropriate for complex, non-normal data and include hierarchical models that can accommodate and estimate variation across multiple levels of organization (Zuur et al. 2009). The use of these models is growing in popularity in ecological studies (Bolker et al. 2009), and mixed effects models have been suggested for quantifying intraspecific trait variation (Albert et al. 2011). While mixed effects models do allow for an estimation of variance, they are unable to provide parameters for comparison between individual populations; such comparisons are necessary when identifying more or less variable populations.

Bayesian analysis of variance was used in a single study (Fig. 1). Bayesian parameter estimation and hierarchical models provide a flexible tool for addressing many ecological questions (Ellison 2004). They can simultaneously estimate trait distributions and variation within and across populations, as well as estimate trait distributions for the entire sample region. In addition, Bayesian parameter estimation is not constrained by the assumption of homogeneity of variance. An additional unique feature of Bayesian techniques is that prior information can be incorporated into models in the form of an ‘informative’ prior probability. The ability to use prior information – in the form of previously acquired data, expert opinion, or literature-based values – can strengthen models and reduce the time and cost associated with data collection (Kuhnert, Martin & Griffiths 2010). However, informative prior probabilities also draw the largest criticisms from those sceptical of Bayesian techniques (Lele & Dennis 2009) and should be implemented cautiously and appropriately (Choy, O'Leary & Mengersen 2009).

Case study

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information

Hypochaeris radicata is a short-lived perennial herb species common in grassland ecosystems throughout Europe, North America, Australia, New Zealand and Japan. It forms basal rosettes with oblong–lanceolate leaves and produces several upright, branching flower stalks during a long flowering period – June through October in the Pacific Northwest. Hypochaeris radicata is self-incompatible (Pico, Ouborg & Van Groenendael 2004), and its seeds are wind-dispersed up to a few hundred metres (Mix et al. 2006).

Trait measurements

In Summer 2011 and Spring 2012, specific leaf area (SLA) and basal rosette diameter were measured on 241 individuals in 10 populations, including one greenhouse-grown population. Individuals from the greenhouse-grown population were collected from a single source population. Greenhouse conditions were maintained at an average temperature of 20·7 °C and 50% humidity, and artificial lighting was provided from 0800 to 2200 h daily. The greenhouse population received weekly 10-10-10 NPK fertilizer plus micronutrients per manufacturer specifications. Field populations were at least 1 km apart and spanned a 480-km range from Corvallis, Oregon to Coupeville, Washington. Field populations were located in unmowed areas that received full to partial sun and included urban parks, roadsides and glacial outwash grasslands. In this article, populations are numbered from north to south in terms of their collection locations (see Fig. S1 and Table S1, Supporting Information).

Specific leaf area is the ratio of leaf area to leaf mass. It is a widely used functional trait (Wilson, Thompson & Hodgson 1999) because it is easily measurable for a variety of plant species and is correlated with exploitation of available resources, productivity, leaf life span and leaf quality (Reich, Walters & Ellsworth 1992; Westoby 1998). Plants with low SLA typically have longer-lived leaves and slower overall relative growth rates (Poorter 1990) because SLA influences the total amount of area available for photosynthetic capture. High SLA plants, in contrast, typically have short-lived leaves with high photosynthetic efficiency (Poorter 1998). SLA is also an important determinant of decomposition rates and nutrient return (Laughlin 2011); high SLA leaves break down more quickly. SLA is partially determined by genetic factors (Scheepens, Frei & Stöcklin 2010), but can also be affected by soil nutrient availability (Knops & Reinhart 2000) and light availability (Meziane & Shipley 1999). A mature, fully exposed, undamaged leaf was collected from each individual. Leaves were stored in Whirl-Pak plastic bags at 4 °C for no more than 48 h and then rehydrated following Cornelissen et al. (2003). After rehydration, leaves were scanned in a flatbed scanner at 200 dpi, dried at 60 °C for 7 days and weighed. One-sided leaf area was calculated from the scanned images using imagej version 1·45 (available at http://rsbweb.nih.gov/ij/). SLA was calculated as leaf area (mm2) divided by dry leaf mass (mg).

Basal rosette diameter was used as a measure of plant competitive ability. Plant height is more commonly used in this sense (Westoby 1998), but is less relevant for H. radicata because this species has a very flat, dense, exclusively basal rosette growth form and competes for light via physical exclusion rather than height growth. Devotion of resources to rosette diameter is assumed to be analogous to resource devotion to vertical height for other species: larger sizes represent greater access to light and greater carbon assimilation. For each individual, rosette diameter was calculated as the average of two measurements in perpendicular directions.

We searched the literature and the LEDA Trait Database (Kleyer et al. 2008) for published data about SLA and rosette diameter in H. radicata. We obtained four published mean values for SLA, three from Mokany & Ash (2008) and one from Kleyer et al. (2008). We did not find any literature-based values for rosette diameter. Literature-based values were compared with the posterior distributions produced from a Bayesian anova of our field-measured values.

Statistical analysis

Based on our literature review, we selected six methods of characterizing intraspecific variation: qualitative comparisons, including comparisons of coefficients of variation, anova-based techniques, tests of homogeneity of variance, linear mixed models and Bayesian anova. Qualitative comparisons were simple summaries of the data in terms of the extreme values, means and standard deviations. Coefficients of variation (CVs) were calculated as the standard deviation divided by the mean for each trait in each population.

Specific leaf area was log-normally distributed, while rosette diameter was normally distributed. Levene's test on transformed data indicated that both traits exhibited non-homogeneous variance between populations. Since data did not meet this key assumption of anova, we used permutational analysis of variance (permanova) with post hoc pairwise comparisons to test for differences among populations. Homogeneity of variance was tested using PERMDISP, a permutational analogue to Levene's test. These analyses were conducted using the permanova+ add-on to PRIMER-E (Clarke & Gorley 2006), with the Euclidean distance measure, type III sums of squares and 9999 permutations.

We fit linear mixed effects models using REML estimation with population designated as a random effect to quantify variation between and within populations. SLA data were transformed to meet assumptions of normality, and each trait was modelled separately. Analyses were conducted using the function ‘lmer’ in the lme4 package for r 2.14.2 (R Development Core Team 2011).

Bayesian anova provides a means of estimating the probability distributions of parameters of interest, including means and standard deviations. Our analysis methods are summarized here, but more detailed methods are provided in Appendix S1 (Supporting information), since we found this technique to be particularly powerful yet rarely used. In its most basic form, Bayesian statistics can be summarized as follows:

  • display math(eqn 1)

From the posterior distribution, point estimates of common moments, such as the mean, median and standard deviation, can be quantified, and distributions of parameters of interest can be directly compared with a variety of techniques. We used hierarchical random-effects Bayesian anovas (Gelman et al. 2004) with non-homogenous variance and non-informative priors. We assumed that SLA was log-normally distributed for the ith individual in the jth population with a population-level mean (θj) and variance (inline image):

  • display math(eqn 2)

We assumed that diameter was normally distributed with a population-level mean (θj) and population variance (inline image):

  • display math(eqn 3)

Analyses were conducted using Markov Chain Monte Carlo simulation techniques with Gibb's sampling as implemented in openbugs (version 3.2.2, Lunn et al. 2009) through r (version 2.14.2; for examples of code, please see Gelman et al. (2004) and Kery (2010)). Three chains were run for 5000 iterations. After visual inspection for convergence, the first 500 iterations were discarded. Differences within and across population means were evaluated by comparing effect sizes. Differences between mean and standard deviation parameters were evaluated by comparing 95% credible intervals (CIs), which are analogous to confidence intervals used in classical statistical approaches. Effect sizes were calculated as the differences between posterior parameter estimates of the mean for each population and the estimated grand mean for the regional population. Populations were considered to differ significantly from the regional population if their CI did not bound zero and from other populations if their CIs did not overlap. Posterior distributions were constructed for each population and for the regional population. For brevity, only the posterior distributions for SLA are shown below; posterior distributions for diameter are available in the supporting material (Fig. S2, Supporting information).

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information

Qualitative comparisons revealed large variation in both traits. SLA varied 27-fold among individuals, ranging from 1·7 to 46·1 mm2 mg−1, while rosette diameter varied 34-fold, ranging from 1·7 to 59·1 cm. Populations differed fourfold in mean SLA and fivefold in mean diameter (Fig 2).

image

Figure 2. Trait average (+SD) and coefficients of variation for specific leaf area (top) and rosette diameter (bottom) among 10 populations. Populations are numbered from north to south. P-value and uppercase letters denote significantly different groups as determined by permanova, and italicized lowercase letters denote significantly different groups as determined by PERMDISP. Note that the scale of the y-axis differs among panels.

Download figure to PowerPoint

There were significant differences among populations in both SLA and diameter (Fig. 2) when analysed using permanova. Pairwise comparisons identified four groups of populations for SLA. Differentiation among populations was stronger for diameter: four populations (1, 4, 6 and 8) were different from each other and all other populations. There was no significant difference in variance for SLA, but diameter variance was significantly different (P < 0·0001; PERMDISP). Populations 1, 4, 6 and 8 – the same ones identified as different via permanova – were significantly different from one another and from the other populations (Fig. 2).

Mixed models indicated that, for SLA, population identity explained 58% of observed variation, while 42% of variation was due to differences among individuals. For diameter, the same trend was observed: 65% of observed variation was due to differences in populations, while 35% of variation was due to differences among individuals.

Bayesian anova indicated that there was high intraspecific variation in SLA around the grand mean. Populations 2 and 4 had a significantly higher mean SLA than the grand mean, while populations 3 and 9 had significantly lower mean SLAs (Fig. 3). Estimates of SD for SLA demonstrated large differences among populations, as population 3 had a large estimated SD, while populations 4, 5, 6 and 9 had low estimated SD (Fig 4). We used our posterior distributions to compare estimated values with literature-based values for SLA. Four populations (1, 3, 7 and 9) had poor overlap with any of the published values, indicating that literature-based values poorly represented population-level mean trait values (Fig. 5) for these populations.

image

Figure 3. Effect sizes (magnitude of difference from the estimated grand mean, shown by the dashed horizontal lines) and 95% credible intervals for specific leaf area (top) and rosette diameter (bottom) among 10 populations. Populations are numbered from north to south. Populations differ significantly if their credible intervals for that statistic do not overlap.

Download figure to PowerPoint

image

Figure 4. Point estimates and 95% credible intervals for the mean (left) and standard deviation (right) for specific leaf area (top) and rosette diameter (bottom). Populations differ significantly if their credible intervals do not overlap.

Download figure to PowerPoint

image

Figure 5. Posterior distributions (solid lines) of specific leaf area for the regional population (top panel) and 10 populations of Hypochaeris radicata. The vertical lines in each graph indicate the literature-based trait estimates from fertilized pot-grown plants (thick dashed line), field-grown plants (dot-dashed line), unfertilized pot-grown plants (thin dashed line) and the LEDA Trait Data base (dotted line).

Download figure to PowerPoint

Bayesian anova also indicated that intraspecific variation for rosette diameter was high among populations (Fig. 3). Populations 4 and 6 had larger diameters than the grand mean, while populations 1 and 8 had smaller diameters than the grand mean. Mean values for diameter differed strongly among populations (Fig. 4). Estimates of SD for rosette diameter demonstrated a significantly different SD for only populations 2 and 8, although there was high uncertainty in the estimates for 6 and 10 (Fig. 4).

Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information

Our results demonstrate substantial intraspecific variation for commonly measured plant functional traits. Both SLA and rosette diameter showed high variation across populations (as evidenced by significant differences in mean values) and within populations (as evidenced by significant differences in estimated standard deviations). The large differences in both trait means (4- and fivefold variation for SLA and diameter, respectively) for measured populations, and trait values for individuals (27- and 34-fold for SLA and diameter, respectively), combined with significant statistical results indicate that this source of variation is biologically meaningful. Furthermore, the variation expressed in these traits is large, even when considering the range of trait values expressed across multiple plant species. For example, Wright et al. (2004) found that SLA [which we calculate from reported LMA, where LMA = 1/SLA (Cornelissen et al. 2003)] ranged from 0·6 to 71·4 mm2 mg−1 for 2548 measured vascular plant species. For our 10 measured populations of H. radicata, SLA ranged from 1·7 to 46·1 mm2 mg−1, which encompasses 63% of the range of trait values reported by Wright et al.(2004). However, this significant source of variation is typically unaccounted for when a single mean value is used for each species, as is common in many ecological studies. This variation likely influences how plants function within communities, suggesting that a failure to account for it may bias estimates of community-level traits and ecosystem functions.

The magnitude of variation in these functional traits is surprising considering that population samples were collected on small spatial scales and that, due to relatively long dispersal distances and proximity to major roadways, gene flow between measured populations is possible. Even populations that were geographically very close (i.e. <1 km apart) showed statistically significant differences in both means and variation in functional traits, and a number of populations differed significantly from trait values reported in trait data bases and the literature (Fig. 5). These results indicate that measuring traits in situ, rather than reliance on published values, is likely to be critical as intraspecific variation can be very high and is likely to be driven by local abiotic and resource conditions.

Choosing analytical methods

The choice of analytical method used to quantify intraspecific variation can strongly influence our understanding of its magnitude and importance. Qualitative techniques, while helpful in showing how much variation is present, are generally unsatisfactory as they do not provide insight as to whether the observed variation is statistically different among populations.

Although popular, and capable of identifying differences among populations, anova-based techniques require assumptions that are biologically unrealistic for some traits. When these assumptions are met, anova provides limited insight into how or why populations differ, though its utility is strengthened when accompanied by a test of homogeneity of variance. Furthermore, because these techniques assume equal variance across populations, sampling strategies are selected and data transformations are used that deliberately minimize variation, effectively eliminating it from analysis. permanova and PERMDISP are less influenced by these assumptions and therefore are more robust techniques for quantifying intraspecific variation. Mixed effects models can provide a great deal of insight into how variance is partitioned across levels of organization, and, like Bayesian methods, can be implemented hierarchically to estimate trait values on a regional level. While results from mixed effects models shed some light on the extent of intraspecific variation, this technique was not able to directly quantify variation within populations or how traits are distributed around population means. The Bayesian approach, on the other hand, was able to estimate regional and population means and trait distributions and allowed for direct comparison between populations and with the regional trait estimate (Fig. 5), as well as allowing for variance partitioning analysis.

The Bayesian and permanova approaches identified the same populations as differing from one another. However, the ability to not only estimate variance among populations but also to directly estimate variance within populations is a key strength of the Bayesian approach. The point estimates and credible intervals for standard deviations provide nuanced information regarding trait distributions that is not provided through any of the other techniques. However, Bayesian anova is relatively uncommon, in part because it is computationally intensive and because the underlying framework differs substantially from more commonly applied statistical methods. In addition, it may require more extensive data collection (although all statistical techniques can be biased by low sample size) and lacks the significance tests and values commonly used to interpret statistical tests. Overall, however, we suggest that this technique is best for quantifying intraspecific variation within and across populations and for incorporating this variation into larger ecological studies.

The importance and strength of a Bayesian approach

Recent work has called for an emphasis on distribution-based techniques for estimating and incorporating intraspecific variation (Albert et al. 2011; Violle et al. 2012) into community- and regional-level analyses and predictive models. Variation within and across populations likely has a measurable effect on both species and communities (Crutsinger, Strauss & Rudgers 2010; Jung et al. 2010).

At the species level, posterior probability distributions can be compared directly within and among populations. They can also be used as prior distributions in future analyses examining changes in trait distribution (e.g. increased or decreased variation) in response to changes in abiotic conditions or community composition. The posterior distribution for a given trait could be used to make predictions about a population's or species’ ability to cope with changing conditions. Furthermore, our understanding of community dynamics and biodiversity maintenance can be bolstered by a distribution-based approach. Fundamental questions about species competition and coexistence can be addressed iteratively with Bayesian techniques. For example, shifting means, distributions and overlap among trait distributions of species could be examined with a Bayesian approach. Furthermore, these distributions could be updated to reflect changing abiotic or biotic conditions and to make predictions about species presence or absence in response to such changes (e.g. Laughlin et al. 2012).

At the community level, posterior probability distributions can be used to compare among species, identify functional redundancy and develop predictions about the outcome of species interactions. It is common at present to calculate community-level trait averages by weighting the mean trait value for each species in a community by its relative abundance (e.g. Shipley, Vile & Garnier 2006). Community-weighted trait distributions should more accurately represent the functional traits of a community since they can include different distributional forms for each species. Such complete modelling of trait distributions, rather than the reliance on trait means, will allow for better quantification of critical ecosystem function concepts such as functional richness, evenness and divergence (Mason et al. 2005).

Although recent studies using plant trait data in a classical statistical framework have given insight into how traits and abiotic conditions mediate plant distributions (Pollock, Morris & Vesk 2012), incorporation of intraspecific trait variation using a Bayesian framework improves model predictions (Laughlin et al. 2012). Bayesian techniques provide more detailed and nuanced information than traditional statistical approaches and allow for comparison across multiple levels of organization. Furthermore, these parameters can be updated with new information and incorporated into larger, trait-based predictive models of community and ecosystem processes.

Future directions

We considered variation in one trait at a time, but a species’ ability to cope or adapt to changing conditions may be driven by a suite of functional traits, making a univariate approach incomplete. We suggest that future studies explore multivariate Bayesian techniques to identify how variation in a suite of traits influences species’ ability to cope with and adapt to changing conditions.

It was beyond the scope of this study to investigate the causes of the observed variation in traits, but local adaptation to microsite conditions through genetic variation or phenotypic plasticity, and differences in traits due to ontogeny are potential explanations for the different amounts of variation present. Abiotic gradients have been shown to induce plastic responses in traits of cork oak (Quercus suber) (Ramirez-Valiente et al. 2010), Patterson's curse (Ecium plantagineum) (Sharma & Esler 2008), Metrosideros polymorpha (Cordell et al. 1998) and many other species (Davidson, Jennions & Nicotra 2011). Genetic variation in populations has also been shown to create wide phenotypic and functional trait variation in some species (Pezzani & Montaña 2006; Leger et al. 2009; Bilton et al. 2010; Scheepens, Frei & Stöcklin 2010; Nakamura et al. 2011), which can have cascading effects on surrounding communities and ecosystem services (Crutsinger, Strauss & Rudgers 2010). Further study, likely in a greenhouse or common garden setting, would be necessary to tease out the factors influencing the observed differences in traits and variation and whether this variation is adaptive or beneficial.

Regardless of the source of observed trait variation, the extent of intraspecific variation present in a population may indicate a species’ or population's ability to adapt to changes in abiotic conditions, cope with invaders (or become invasive itself) or adapt to changes within the community. For example, taxa that demonstrate higher intraspecific variation in traits related to stress tolerance (e.g. water-use efficiency, growth rate) may be able to better cope with shifts due to climate change, while those with lower variation may be driven locally extinct. Taxa with high variation in certain functional traits may be more likely to become invasive when introduced to new habitats or may be able to compete or cope with newly introduced species. If high intraspecific trait variation indicates an increased ability to cope with biotic and abiotic stress, this may be of critical importance to conservation biology as efforts to preserve and expand variable populations may be of key importance in a shifting environment. In contrast, populations with low variability may be at higher extinction risk and require additional protection or assistance. Further research into the role of intraspecific variability in mediating species and population responses to biotic and abiotic stress should be conducted.

Regional-level trait estimates can be used to quantify species-level niche breadth and may be useful from a conservation standpoint. For example, species with low variation may have a greater risk of extinction due to global change. The effects of climate change, habitat disturbance, land use or conversion on species or ecosystems could also be quantified using model updating. More complex, community-level hierarchical models can be used to partition sources of variation between intra- and interspecific sources and across multiple levels of organization (e.g. Messier, McGill & Lechowicz 2010).

Conclusions

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information

Although intraspecific variation in important plant functional traits can be high, and likely has ecological consequences, techniques to adequately quantify this variation are not consistently implemented. Permutational anova was reasonably successful in detecting differences among populations, particularly when combined with a permutational test of dispersion within populations. Of the methods we considered, however, we suggest that Bayesian parameter estimation is most appropriate for quantifying intraspecific variation. The ability to directly estimate, incorporate prior knowledge about and statistically compare variation, as well as the opportunity to use estimated parameters for future predictions, represents an important step towards a more holistic and predictive view of functional ecology.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information

We thank Eric Delvin, Tom Kaye, Danielle Santamaria, O. Mitchell and Ty Robinson for their assistance with this research and Janneke Hille Ris Lambers, Soo-Hyung Kim, Sarah Reichard, Regina Rochefort and Daniel Laughlin for their advice and guidance. We also thank Lauren Sandhu, Alan Knapp and four anonymous referees for suggestions that improved this manuscript. Portions of this project were supported by the National Park Service under task agreement J8W07070010.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information

Supporting Information

  1. Top of page
  2. Summary
  3. Introduction
  4. Characterizing intraspecific variation
  5. Case study
  6. Results
  7. Discussion
  8. Conclusions
  9. Acknowledgements
  10. References
  11. Supporting Information
FilenameFormatSizeDescription
fec12167-sup-0001-LaySummary.pdfPDF document229KLaySummary
fec12167-sup-0002-AppendixS1.docxWord document33KAppendix S1. A summary of Bayesian methods.
fec12167-sup-0003-FigS1.docxWord document140KFig. S1. Map depicting collections sites for populations.
fec12167-sup-0004-FigS2.docxWord document95KFig. S2. Posterior distributions for rosette diameter.
fec12167-sup-0005-TableS1.docxWord document21KTable S1. Table of site name, population code and sample size.

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.