Download how do different measures of functional diversity perform?

Ecology, 85(3), 2004, pp. 847–857
q 2004 by the Ecological Society of America
HOW DO DIFFERENT MEASURES OF FUNCTIONAL
DIVERSITY PERFORM?
OWEN L. PETCHEY,1,3 ANDY HECTOR,2,4
2
AND
KEVIN J. GASTON1
1Department of Animal and Plant Sciences, University of Sheffield, Western Bank, Sheffield, S10 2TN, UK
Natural Environment Research Council Centre for Population Biology, Imperial College London, Silwood Park Campus,
Ascot, Berkshire, SL5 7PY, UK
Abstract. Biodiversity can influence ecosystem functioning through changes in the
amount of resource use complementary among species. Functional diversity is a measure
of biodiversity that aims to quantify resource use complementarity and thereby explain
and predict ecosystem functioning. The primary goal of this article is to compare the
explanatory power of four measures of functional diversity: species richness, functional
group richness, functional attribute diversity, and FD. The secondary goal is to showcase
the novel methods required for calculating functional attribute diversity and FD. We find
that species richness and functional group richness explain the least variation in aboveground biomass production within and across grassland biodiversity manipulations at six
European locations; functional attribute diversity and FD explain greater variation. Reasons for differences in explanatory power are discussed, such as the relatively greater
amount of information and fewer assumptions included in functional attribute diversity
and FD. We explore the opportunities and limitations of the particular methods we used
to calculate functional attribute diversity and FD. These mainly concern how best to select
the information used to calculate them.
Key words: biodiversity; biomass production; complementarity; ecosystem; functional groups;
resource use differentiation; species richness.
INTRODUCTION
Interest in whether biodiversity determines ecosystem functioning (Schulze and Mooney 1993) spawned
experimental studies specifically designed to answer
that question (reviewed in Tilman 1999, Kinzig et al.
2001, Loreau et al. 2001, 2002). Whether these demonstrated functional consequences of biodiversity depended on factors such as trophic complexity (Raffaelli
et al. 2002), temporal scale (Petchey et al. 2002), and
spatial scale (Wardle et al. 1997, Loreau 2000), to name
but a few (Hughes and Petchey 2001). Recently, attention has turned to why biodiversity matters (when
it does): what are the functionally significant components of biodiversity (Dı́az and Cabido 2001, Hooper
et al. 2002)? This attention is currently (Naeem and
Wright 2003) focused on the concept of functional diversity, which Tilman (2001) defined as ‘‘those components of biodiversity that influence how an ecosystem operates or functions.’’ Theory predicts that increased functional diversity will increase ecosystem
functioning due to greater resource use complementarity (Hooper 1998, Petchey 2003) among the species
in a local community, all else being equal (Trenbath
1974, Harper 1977, Tilman et al. 1997b, Loreau 1998).
Manuscript received 7 April 2003; revised 22 July 2003; accepted 25 July 2003. Corresponding Editor: M. Loreau.
3 E-mail: [email protected]
4 Present address: Institute of Environmental Sciences,
University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland.
Such theory is closely related to niche models, where
separation in niche space allows coexistence through
lack of competition for similar resources (e.g., MacArthur and Levins 1967). For example, species that
exhibit a large diversity of above and below ground
architectures should coexist, capture light, and forage
resources more completely and efficiently than a community containing species all with similar architectures
(Berendse 1983, Naeem et al. 1994). Hence, an accurate
measure of functional diversity could help explain and
predict changes in ecosystem functioning that might
result from extinctions (Petchey and Gaston 2002 a),
for example. Yet the explanatory power of different
measures of functional diversity remains largely unexplored.
Experimental manipulations of biodiversity provide
one method for assessing different measures of functional diversity by comparing how well they explain
variation in ecosystem functioning. These experiments
typically manipulate one or both of species richness
and functional group richness (e.g., Tilman et al.
1997a, Hector et al. 1999). Species richness typically
has low explanatory power perhaps because it ignores
similarities or differences in the functional traits of
species (Root 1967, Hooper et al. 2002). Indeed, when
used as a measure of functional diversity, species richness implicitly assumes that all species are equally different (addition of any species to a community will
increase functional diversity by one unit) and that the
contribution of each species to functional diversity is
independent of species richness.
847
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Ecology, Vol. 85, No. 3
PLATE 1. The BIODEPTH biodiversity manipulation experiment at Silwood Park, near
London UK, after three years showing plots
with different plant diversity, composition, and
productivity. The plot in the center foreground
is a monoculture of Hypochaeris radicata. Photograph by Andy Hector.
Functional group richness (FGR) also has limitations. It relies on an arbitrary decision about the level
at which interspecific differences among species are
functionally significant (Simberloff and Dayan 1991,
Vitousek and Hooper 1993). It assumes that species
within groups are functionally identical, that is, species
within groups are entirely redundant (Lawton and
Brown 1993). It also assumes that all pairs of species
drawn from different functional groups are equally different. In other words, adding a species from a novel
functional group to a community adds unity to functional group richness, regardless of the identity of
group(s) that are present and the identity of the novel
group.
The explanatory power of two recently developed
measures of functional diversity has never been measured in a biodiversity experiment. These are functional
attribute diversity (Walker et al. 1999) (hereafter FAD)
and FD (Petchey and Gaston 2002b). Both of these
measures have the traits of species as their foundation
and estimate some component of the dispersion of species in trait space. For FAD this dispersion is estimated
as the sum of the distances between species in trait
space (Walker et al. 1999) and need not be limited to
plant assemblages. For FD, dispersion is estimated as
the total branch length of the functional dendrogram
that results from clustering the species in trait space
(Petchey and Gaston 2002b). The implications of this
difference are covered in the Discussion section of this
paper. They both require an assumption about how to
measure distance (e.g., Euclidean or Manhattan) and
FD requires an assumption about how to cluster species
(e.g., unweighted pair group method using arithmetic
averages or minimum variance clustering) (see Pielou
1984). Previous analyses show that the qualitative behavior of FAD and FD are not sensitive to a range of
distance measures and cluster methods (Petchey and
Gaston 2002b).
Several properties of these two measures predict that
they will explain greater variance in ecosystem func-
tioning than either species richness or FGR. Unlike
FGR, FAD and FD require no arbitrary decision about
the functional significance of interspecific differences
among species (because they do not assign species to
groups) (Walker et al. 1999, Petchey and Gaston
2002b). They include the large functional differences
that might delineate groups and the small functional
differences that groups ignore. Consequently, both can
be continuous measures of functional diversity, whereas species richness and FGR are discrete; this could
enhance their explanatory power if natural interspecific
variation is continuous (Hooper et al. 2002). We used
data from the BIODEPTH project (Hector et al. 1999)
to compare the performance of these four measures of
functional diversity: species richness, functional group
diversity, FAD, and FD. We also discuss the novel
methods used to calculate FAD and FD.
MATERIALS
AND
METHODS
The BIODEPTH project manipulated plant species
and functional group richness at eight European sites
(Plate 1); the methods are described in detail elsewhere
(Hector et al. 1999). Here we consider only aboveground plant biomass production (g/m2) at six of these
sites in the second year as the ecosystem process of
interest. We used the same classification of species into
three functional groups (legumes, grasses, herbaceous)
as in the original study (Hector et al. 1999).
We performed four separate analyses of the BIODEPTH project: (1) an analysis of all polycultures
across all sites simultaneously; (2) an analysis of all
polycultures at each separate site; (3) an analysis of
all four-species mixtures across all sites, and (4) an
analysis of all two-species mixtures across all sites.
We performed analyses A and B for consistency with
previously published analyses (Hector et al. 1999).
We performed analyses C and D to assess the explanatory power of functional diversity in the absence
of the interpretive difficulties caused by variation in
species richness among communities (Aarssen 1997,
March 2004
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849
TABLE 1. The candidate traits that were used to calculate FD (Petchey and Gaston 2002b) and FAD (functional attribute
diversity).
Source of traits
Unpublished measurements
BIODEPTH monoculture
measurements
Additional
Trait
number
Trait
1
2
3
4
specific leaf area
leaf area
leaf thickness
dry matter content
5
canopy structure
6
canopy height
7
lateral spread†
8
seed mass
continuous measure; mm2/mg
continuous measure; mm2
continuous measure; mm
continuous measure; percentage of saturated
mass
categorical measure; leaves all basal or plant
prostrate, semi-rosette (stems leafy but largest leaves at base), leafy
categorical measure: ,100 mm, 100–200 mm,
300–500 mm, 600–1000 mm, 1–3 m
categorical measure: therophytes, ,100 mm,
100–250 mm, 250–1000 mm, .1 m
continuous measure; log(mass [in mg])
9
biomass†
continuous measure; g/m2
10
11
vegetation cover†
canopy height
continuous measure; %
continuous measure; cm
12
legume or not†
binary measure
Details
Notes: Trait numbers are used in the text for brevity. Daggers (†) indicate the four traits that were used in a separate
bootstrap analysis.
Huston 1997). Sample sizes were not large enough to
warrant analyses within any other levels of species
richness.
Each analysis comprised the same four steps. (A) A
matrix of candidate traits was compiled (candidate
traits sensu the candidate function groups of Vitousek
and Hooper [1993]). (B) Each possible combination of
candidate traits was used to calculate a candidate measure of FAD and FD of each experimental plot in the
analysis. (C) The amount of variance in ecosystem
functioning explained by each candidate measure of
FAD and FD was recorded. (D) The analysis was bootstrapped to test statistical significance of relationships
between ecosystem functioning and FAD or FD.
Candidate traits.—Eight traits collected from various sources (J. P. Grime, J. Hodgson, K. Thompson, P.
Wilson, and R. Ceriani, unpublished data), three measurements from the BIODEPTH monoculture plots, and
a legume/non-legume trait were the candidate traits
used to calculate FAD and FD (Table 1). The first eight
traits, such as leaf thickness, were typically measured
from individual plants. BIODEPTH monoculture measurements were the ecosystem-level properties that
were also measured in species mixtures (measurements
that contained missing values were not included as candidate traits). Monoculture measurements from all
Northern European BIODEPTH sites were pooled and
where there was more than one monoculture of a species, the mean across plots and sites was calculated.
We were only able to compile traits for the species used
in the six most-northern BIODEPTH sites, consequently the Greek and Portuguese sites were excluded from
all analyses. These two sites show nonsignificant and
significant relationships between species richness and
biomass production, respectively, so excluding them
should not bias conclusions in a particular direction.
Calculating FAD and FD.—Each of the 212 possible
combinations of the 12 candidate traits was used to
calculate candidate measures of FAD and FD of all
plots across the experiment. The rationale for this is as
follows. An assumption of any measure of functional
diversity is that the traits/criteria used to calculate it
are functionally important; that is, they inform about
interspecific differences in resource use differentiation.
We were unsure of which candidate traits met this criterion. Rather than make a more or less subjective decision about the functional importance of each trait, we
calculated a separate candidate measure of FAD and
FD for each possible combination of candidate traits.
This equates to weighting the candidate traits by zero
or one, in all possible combinations. Using zero/one
weights (and no fractional weights) was a pragmatic
solution to reducing the number of trait combinations
to manageable levels (4096). There would have been
531 441 possible combinations of trait weightings if
we had used 0, 0.5, and 1 as weights, and the analyses
would have taken months of computer time. As mentioned, both FAD and FD require an assumption about
the measure used to quantify distance in trait space and
the algorithm used to cluster species. We used Euclidean distance and the unweighted pair-group method
using arithmetic averages (UPGMA) clustering method
and standardized all candidate traits to have a mean of
zero and variance of one.
Estimating the explanatory power of FAD and FD.—
The amount of variance in aboveground biomass production explained by each separate candidate measure
of FAD or FD was estimated as the R2 of the appropriate
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Ecology, Vol. 85, No. 3
FIG. 1. Relationships between aboveground biomass production and (a) log2(species richness), (b) FGR (functional group
richness), (c) FAD (functional attribute diversity), and (d) FD (Petchey and Gaston 2002b) across the six analysed BIODEPTH
sites. Lines show the fitted relationships of analysis of covariance (which included the interaction term between diversity
and site).
statistical model. For analyses A, C, and D, this was
analysis of covariance (ANCOVA) with FAD or FD as
a continuous explanatory variable and European location as a categorical explanatory variable. For analysis B, the model was linear regression. The explanatory powers of models with log2(initial species richness, S) and functional group richness (the number of
grasses, legume and herb functional groups represented) as continuous explanatory variables were also estimated.
Estimating statistical significance by bootstrap.—To
estimate statistical significance of FAD and FD we
bootstrapped each analysis (Manly 1997). This tested
whether high amounts of variance explained by either
FAD or FD resulted from chance or not; a parametric
test was not appropriate because multiple candidate
explanatory variables were tested in step 3. We first
randomized the trait matrix: values were randomized
among species and within traits. That is, trait values
were not allowed to swap between traits. We then calculated the maximum explanatory power of FAD (or
FD) given the randomised trait matrix. Repeating this
1000 times produced a bootstrapped distribution of
maximum explanatory powers for each measure of
FAD and FD against which the observed maximum
explanatory power could be compared for statistical
significance. In addition, we repeated each analysis
while including only four traits in the analyses to see
if the number of candidate traits affected the bootstrapped significance level (Table 1). The four traits
EXPLAINING ECOSYSTEM FUNCTIONING
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TABLE 2. The explanatory power (R2) in analysis B of linear relationships between biomass production and log2(species
richness, [S]), FGR (functional group richness), both log2(S) and FGR fitted simultaneously, FD (Petchey and Gaston
2002b), and FAD (functional attribute diversity) across the n plots at each site.
FGR
Log2(S )
1 FGR
FAD
FD
FD last
FAD last
NS
0.34***
0.34**
0.35
0.79
Legume
P , 0.001
P , 0.001
0.05
NS
0.22*
0.22*
0.16
0.67
Legume
P , 0.001
P 5 0.45
50
0.02
NS
20.01
0.03
NS
Legume
P 5 0.13
P 5 0.99
34
Monoculture
biomass
Vegetation
cover
Lateral spread
P , 0.001
P 5 0.40
P , 0.001
P 5 0.99
P , 0.05
P 5 0.32
Site
n
Log2(S )
Bayreuth, Germany
Lupsingen,
Switzerland
Riverstick, Ireland
Röbäcksdalen,
Sweden
Sheffield, England
Silwood, England
30
,0.01
28
Trait
,0.01
NS
0.02
0.19*
0.10
NS
0.19*
0.2
0.43
NS
30
0.49***
0.40***
0.50***
0.39
0.70
NS
32
0.03
0.06
0.06
0.05
0.11
NS
NS
NS
NS
NS
Notes: Standard parametric P values are denoted as follows: NS, P . 0.05; *P , 0.05; **P , 0.01; ***P , 0.001; or the
exact value. Bold type indicates that the relationship between FD and biomass production was significant when the observed
R2 was compared with a bootstrapped distribution of R2. The last two rows show the standard parametric significance levels
when FD or FAD is fit after species richness and FGR.
used were those that maximized explanatory power in
analysis B (see Tables 1 and 2).
RESULTS
Analysis A: all polycultures, all sites
The overall R2 values of the analysis of covariance
with log2(species richness), FGR, FAD, or FD as the
continuous explanatory variable were respectively
0.33, 0.40, 0.40, and 0.55 (Fig. 1). Each explanatory
variable was significantly associated with aboveground
biomass production, whether probabilities were calculated by F tests in the case of log2(species richness)
and FGR or by bootstrapping in the case of FAD and
FD.
The maximum explanatory power of both FAD and
FD was attained by including only one trait in the matrix, the legume/non-legume trait. Two other combinations of traits produced significant explanatory power of FD (Fig. 2), both of which included the legume/
non-legume trait and one other trait (either trait 5 or
10; see Table 1). The vast majority (99.6%) of all possible trait combinations resulted in a measure of FD
with greater explanatory power (though not necessarily
significant explanatory power) than FAD (when comparing FAD and FD models with the same traits; Fig.
2).
Including only four candidate traits (instead of 12)
lowered the critical R2 value for FAD and FD, which
resulted in no change in the significance of the most
powerful trait combination at a 5 0.05 (Fig. 2). The
number of significant trait combinations increased to
seven for FAD (including traits 3, 4, 5, 6, 8, and 12)
and 13 for FD (including traits 1, 2, 3, 4, 5, 7, 8, 10,
11, and 12), all of which included the legume/nonlegume trait. The next most common trait was vegetation cover and was present in only six of the 20 combinations.
Analysis B: all polycultures, each site separately
At each site, the explanatory variable with greatest
power was FD; the relative explanatory powers of other
variables varied across sites (Table 2). Within any one
site, the maximum explanatory power of FD and FAD
was always attained by including a single trait, though
the identity of this trait differed between sites (Table
2). The explanatory power was only significant by
bootstrap test at two sites, Germany and Switzerland,
where the only trait included was legume/non-legume.
This supports the results of analysis A, where the effect
of FAD and FD varies across sites (Fig. 1c and d).
In Germany, only one of the 4096 different trait combinations resulted in a measure of FD and FAD with
significant bootstrapped explanatory power. In Switzerland, four trait combinations resulted in a measure
of FD with significant explanatory power and all of
these included the legume/non-legume trait (the other
traits were 5, 9, and 10). Similarly, the two significant
combinations of traits for FAD both included the legume/non-legume trait (the other trait was 10). The
next most common trait occurred in a maximum of one
of the four combinations for both FD and FAD. F tests
indicated that FD explains variance that is not accounted for by log2(species richness) or FGR, more frequently (at five of six sites) than does FAD (one of six
sites) (Table 2).
Including only four candidate traits (instead of 12)
sometimes decreased and sometimes increased the critical R2 value for FAD and FD (Fig. 3). In only two of
12 cases did the change in critical value cause a change
in significance at a 5 0.05: FAD at Riverstick, Ireland
included the legume/non-legume trait and FAD at Sheffield, England included the vegetation cover trait (Fig.
3c and e). In Switzerland, the number of significant
trait combinations increased from four to eight for FD;
all but one included the legume/non-legume trait and
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Ecology, Vol. 85, No. 3
the next most common trait was included only twice
(other traits were 3, 4, 5, 9, 10, and 11). Otherwise,
there were no changes in the numbers of significant
trait combinations.
Analysis C: four-species mixtures, all sites
FIG. 2. A comparison of the explanatory power of FD
(Petchey and Gaston 2002b) and FAD (functional attribute
diversity) in analysis A. Each data point represents the explanatory power of a particular combination of traits. The
solid line represents equal explanatory power of FD and FAD.
The vertical dashed (dotted) line is the 95th percentile of the
bootstrapped explanatory power for FD with 12 (four) candidate traits; the horizontal dashed and dotted lines are the
same except for FAD.
The overall R2 values of analysis of covariance with
FAD or FD as the continuous explanatory variable were
high (R2 5 0.62 and 0.68, respectively). They were not,
however, statistically significant when compared to the
bootstrapped analyses. That is, given the large number
of tests (4096), the high explanatory power was relatively likely by chance alone. The explanatory power
of FGR was lower, though significant, with an R2 of
0.32. Notably, FAD and FD have more similar explanatory power than in analyses A and B and changes in
trait combinations have a similar effect on the explanatory power of both measures of functional diversity
(Fig. 4a). The maximum explanatory power of both
FAD and FD resulted from including the legume/nonlegume trait and three (FAD; traits 3, 4, and 10) or one
(FD; trait 9) other trait(s).
Including only four candidate traits (instead of 12)
reduced the critical R2 value for FAD and FD (Fig. 4a).
In both cases, this changed the statistical significance
FIG. 3. A comparison of the explanatory power of FD (Petchey and Gaston 2002b) and FAD (functional attribute diversity)
at each site (analysis B). All details are as for Fig. 2. The relative positions of the dotted and dashed lines differ between
sites, indicating that changing the number of traits had different effects on the 95th percentile at different sites.
EXPLAINING ECOSYSTEM FUNCTIONING
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853
FIG. 4. A comparison of the explanatory power of FD (Petchey and Gaston 2002b) and FAD (functional attribute diversity)
in (a) analysis C and (b) in analysis D. All details are as for Fig. 2.
of the results so that both FAD and FD were significantly associated with biomass production as a result
of including the legume/non-legume trait.
Analysis D: two-species mixtures, all sites
Again, no combinations of traits produced a measure
of FAD or FD that explained greater variance in aboveground biomass production than expected by chance.
Maximum R2 was 0.71 for both FAD and FD. The
explanatory power of FGR was lower, though significant (P , 0.01), with an R2 of 0.48. Again, FAD and
FD have more similar explanatory power than in analyses A and B and changes in trait combinations have
a similar effect on the explanatory power of both measures of functional diversity (Fig. 4b). The maximum
explanatory power of both FAD and FD resulted from
including the legume/non-legume trait and no (FAD)
or two (FD; traits 7 and 10) other traits.
Including only four candidate traits (instead of 12)
reduced the critical R2 value for FAD and FD (Fig. 4b).
In both cases this changed the statistical significance
of the results so that both FAD and FD were significantly associated with biomass production and both
result from including the legume/non-legume trait.
DISCUSSION
These results suggest that species richness and functional group richness explain a relatively small proportion of local-scale variation in ecosystem functioning of experimental grassland plots. Other measures of
functional diversity, such as functional attribute diversity (Walker et al. 1999), that incorporate trait information about species tend to explain greater variance.
These findings are consistent with theoretical predictions that functional differences among species are the
basis of biodiversity effects on ecosystem functioning
(Tilman et al. 1997b, Loreau 1998). They also reinforce
recent opinion that a better understanding of the determinants of local-scale ecosystem functioning may
be developed by considering the diversity of trait values among species (Bengtsson 1998, Dı́az and Cabido
2001, Hooper et al. 2002, Schmid et al. 2002, Naeem
and Wright 2003). In other words, a better understanding will result from considering information about the
natural history and strategies of different species.
The results also suggest that the effects of biodiversity on ecosystem functioning, albeit only the diversity of nitrogen fixing ability, depend on geographic
location. Such context dependence is predicted by theory and demonstrated by varying environmental conditions at a single site (Cardinale et al. 2000, Jonsson
et al. 2001, Fridley 2002). Such findings caution against
using any single-site experiment, or single relationship
between biodiversity and ecosystem functioning to predict regional-scale consequences of biodiversity loss.
The remainder of this discussion addresses potential
reasons for the differences in explanatory power among
the four measures of functional diversity, notable features of the novel analyses used to calculate FAD and
FD, and alternate explanations for the results.
Reasons for differences in explanatory power
The relative explanatory power of species richness
and FGR varied, so that species richness was a more
powerful explanatory variable at some sites, but not at
others. This may result somewhat from the design of
the BIODEPTH project experiments, where the species
richness and FGR treatments were correlated, so that
they share some explanatory power in common (Naeem
2002). Indeed, previous analyses of the BIODEPTH
project experiments shows that the explanatory power
of species richness and FGR overlaps strongly, and
each explains a similar amount of variance in ecosystem functioning that the other does not (Hector 2002).
Though we did not make exactly the same comparisons,
deviation of our results from these previously published
results are most likely a consequence of not including
monocultures in our analyses. For example, Hector et
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OWEN L. PETCHEY ET AL.
al. (1999) found a significant effect of species richness
at the German site, whereas we did not.
Differences in explanatory power between FGR and
FAD or FD could result from a variety of sources. First,
FGR in this paper results from different information
than FAD and FD. The division of species into functional groups in the BIODEPTH project was a qualitative exercise quite different to using quantitative
traits to assign species to groups (e.g., Dı́az and Cabido
1997). Indeed, if we use the same information for FGR
as for FD, whether species are legumes or not, both
result in two values of biodiversity, low and high, and
exactly the same explanatory power.
Second, FGR makes the assumptions (mentioned in
the introduction) that result from grouping species,
whereas FAD and FD make no such assumptions. Our
data provide little evidence regarding this explanation
because a binary trait resulted in measures of FAD and
FD with the greatest explanatory power. Many combinations of continuous traits did, however, produce
greater (and significant) explanatory power than FGR,
suggesting that grouping may reduce explanatory power by producing a distorted measure of continuous natural interspecific variation.
Differences in explanatory power between FAD and
FD can only be explained by differences between these
measures, since exactly the same data and analyses
were used for both. Fig. 1 illustrates that these two
measures differ significantly: the binary legume/nonlegume trait results in only two values of FD but several
values of FAD (Fig. 1). The two values of FD correspond to experimental plots that contained only nonlegumes and plots that contained legumes and nonlegumes, independent of how many species of each
type were present. The several values of FAD result
from whether a legume was present or not, and also
how many legume and non-legume species were present.
This difference can be explained by considering species as points in n-dimensional trait space. Here, FD
is a measure of the volume of space occupied by these
points. Adding a species that lies at exactly the same
point as an existing species causes no increase in the
total volume occupied. In contrast, FAD is a measure
of the total distance between all pairs of points. Here,
adding a new species that coincides exactly with an
existing species adds all the new pair-wise distances.
Consequently, FAD is a function of both trait differences among species and total number of species present, while FD is only a function of trait differences
among species. When there is no variation in number
of species (e.g., analyses C and D) there is much tighter
correlation between FAD and FD within a site (mean
R2 across sites 5 0.84 6 0.01 [mean 6 1 SD] for the
most significant trait combination) than when variation
in species richness is present (e.g., analyses A and B)
(mean R2 across sites 5 0.50 6 0.19 [mean 6 1 SD]
for the most significant trait combination). These pat-
Ecology, Vol. 85, No. 3
terns support the verbal argument presented above, that
variation in species richness per se (i.e., without and
irrespective of functional differences) affects FAD, but
not FD.
Furthermore, the relatively horizontal spread of
points in Figs. 2 and 3 indicates that the variance in
explanatory power of FAD (across different combinations of traits) is affected less by the particular combination of traits used than is the explanatory power
of FD. Presumably this occurs because the explanatory
power of FAD is constrained by the effect of species
richness on FAD, which remains relatively constant
regardless of trait combinations. In contrast, the explanatory power of FD is only affected by the trait
combination used. When effects of species richness on
FAD are eliminated (e.g., in analyses C and D), the
explanatory power of both measures changes similarly,
again supporting the argument that species richness
contributes to FAD, and that this results in the lower
explanatory power for FAD. These results suggest that
a measure of functional diversity that is not influenced
by number of species per se will be a better predictor
of ecosystem functioning than otherwise.
Analyzing biodiversity-ecosystem functioning
experiments using FAD and FD
We are aware that our methods of relating FAD and
FD with aboveground biomass production are previously untested. Consequently, we will highlight some
of the more important considerations surrounding the
approach. First, it is worth pointing out that our analyses are conceptually similar to more traditional analyses that assign species a priori to candidate functional
groups and test whether ecosystem functioning increases with increases in FGR (Bengtsson 1998) and with
the proposed iterative selection of important functional
characteristics (Hooper et al. 2002). The difference
here is that we test many possible functional difference
schemes/traits within a single experiment.
A critical property of both FAD and FD is that they
must include the functionally important traits (Petchey
and Gaston 2002b). This property focuses attention on
the question of what these traits are. We took the approach of compiling a set of candidate traits and testing
their explanatory power to find traits that when used
to calculate FAD or FD explained significant variation
in ecosystem functioning. This approach should be
used with caution, however, because omission of important traits and inclusion of unimportant traits could
influence the ecological interpretation of the results.
For example, we cannot be sure that we included all,
or indeed any of the functionally important traits in the
candidate trait matrix. We did not have access to traits
relating to belowground characteristics of plants, where
much resource acquisition occurs. Furthermore, none
of the candidate traits were collected with our use in
mind. The eight unpublished traits (Table 1) were collected primarily to distinguish between species typical
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EXPLAINING ECOSYSTEM FUNCTIONING
of different stress and disturbance habitat types (Grime
2001) and the BIODEPTH monoculture traits were the
measures of ecosystem functioning taken across the
entire experiment.
Any of these features of the candidate traits could
explain why none were functionally important at four
sites when analysed separately (analysis B; Table 2).
Perhaps we did not include any of the traits that are
functionally important at these sites. That is, FAD and
FD are powerless if they are not supplied with functionally important traits. A direction for future research
will be to collect trait information specifically for the
purpose of explaining and predicting ecosystem functioning. Such candidate traits could be selected on the
basis of independent information about the likelihood
that they are important descriptors of resource use partitioning among species.
Similarly, including unimportant traits can influence
the interpretation of the results. The number of candidate traits used influences the likelihood of finding
strong correlations between FAD (or FD) and ecosystem functioning by chance alone. This seems intuitive,
since the number of possible trait combinations to
search in each bootstrap iteration increases as the number of candidate traits increases. Reducing the number
of candidate traits from 12 to four sometimes increased
and sometimes decreased the bootstrapped significance
value in analyses A and B in which there was variation
in species richness. This idiosyncrasy could result because variation in species richness allows other processes to operate (such as sampling probability effects)
with which FAD and FD derived from random traits
will always correlate. The effect of this on bootstrapped
significance may dominate over any effect of changing
the number of candidate traits. In the absence of variation in species richness (analyses C and D), bootstrapped significance values always decreased to the
extent that the ecological interpretation of the results
changed. For example, the legume/non-legume trait
was either interpreted as significant or not in analysis
C depending on whether four or 12 candidate traits
were used. Without variation in species richness, there
is no possible correlation of FAD and FD derived from
random traits with sampling probability effects, and
changing the number of candidate traits consistently
alters bootstrapped significance values.
Another notable characteristic of these analyses is
their correlational nature. So called ‘‘soft’’ traits could
be selected because they are correlated with functionally important traits (so called ‘‘hard’’ traits), rather
than because of any direct link with mechanisms determining ecosystem processes (Hodgson et al. 1999).
This seems unlikely for the legume/non-legume trait
that was selected as important by our analyses. Nevertheless and in general, inclusion of soft traits will
reduce the ability of these analyses to identify the functionally important differences among species (hard
traits). An alternate perspective is that soft traits may
855
still be useful for identifying important axes of differentiation if suites of traits (soft and hard) always go
together (Hodgson et al. 1999).
Each of these properties of the analyses highlights
the importance of selecting candidate traits that are
known or at least probable determinants of ecosystem
functioning. Although we have shown that the analyses
can identify a functionally important trait from a set
of less important traits, more careful selection of candidate traits may have produced better performing measures of functional diversity.
Alternate explanations of results and
sources of error
The results of experimental manipulations of biodiversity have attracted multiple explanations. For example, the contribution of resource use complementarity and the selection probability effect have both
been implicated (Naeem et al. 1996, Hector et al. 1999,
Emmerson et al. 2001, Cardinale et al. 2002). Our analyses of plots that vary in species richness (A and B)
are open to similar alternate explanations. Here, both
FAD and FD are correlated with variation in species
richness, so that any of the hidden effects mentioned
by Huston (1997) could operate. Our analyses C and
D are immune to these effects, however, since there is
no variation in species richness. These analyses showed
a significant explanatory power of either FAD or FD
with four candidate traits (see Discussion: Analyzing
biodiversity-ecosystem functioning experiments using
FAD and FD for discussion of this) so that there is
some evidence of functional diversity effects in the
absence of variation in species richness. Furthermore,
the traits contributing were similar to those that contribute in analyses A and B, suggesting that these results were not due only to hidden treatments (Huston
1997).
The candidate traits measured from the BIODEPTH
monoculture plots (Table 1) were measured at several
European locations. We calculated a regional average
for each species across locations, and used this in the
candidate trait matrix. This approach allowed us to analyze all sites simultaneously using FAD and FD. Trait
values differed across Europe, due to changes in the
local environment, such that perhaps use of local trait
values (rather than regional averages) would result in
more powerful measures of FAD and FD. This hypothesis remains to be tested.
Concluding remarks
A trade-off exists among different measures of biodiversity (Tilman and Lehman 2002). At one extreme
are measures such as species richness that incorporate
little or no information about individual species and
are, therefore, relatively easy to obtain. Since they incorporate little information they may explain less and
predict relatively poorly. At the other extreme are measures that incorporate more detailed information about
OWEN L. PETCHEY ET AL.
856
individual species, such as PD (phylogenetic diversity
[Faith 1992]), FAD and FD, and these are relatively
harder to obtain (also see Clarke and Warwick 1998).
Our results suggest that the additional biological information they contain allows for better explanation
and possibly prediction.
Some of the variance in ecosystem functioning cannot be accounted for by any of the functional diversity
measures used here. For example, none of the discussed
measures of functional diversity incorporate the abundances of species. That is, there is no functional equivalent of Shannon or Simpson’s diversity (though see
Clarke and Warwick 1999). Other examples are given
by facilitative interactions among species (Bertness and
Hacker 1994) that impact ecosystem functioning (Cardinale et al. 2002) and ecosystem engineers (Jones et
al. 1994); some aspects of each may be difficult to
include in measures of functional diversity. Including
aspects of trophic structure in measures of functional
diversity could also be a great challenge. Nevertheless,
we believe that the rigorous quantitative approach we
have taken to assessing the relative performance of
different measures of functional diversity will force a
more rigorous and quantitative examination of the
functional traits of species and resource axes along
which species separate.
ACKNOWLEDGMENTS
O. L. Petchey is a Natural Environment Research Council
Fellow. Adrian Tate and Mike Pettipher facilitated bootstrap
simulations at Manchester University. We are grateful to all
of the BIODEPTH project participants. Joe Fargione, Tad
Fukami, David Hooper, Michel Loreau, Henry Stevens, David
Wardle, and an anonymous referee provided comments that
improved the ms. We are extremely grateful for the access to
trait information provided by Phil Grime, John Hodgson, Ken
Thompson, Peter Wilson, and Roberta Ceriani.
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