This document describes a new method for estimating functional diversity at taxon and community levels using intraspecific trait data. The key aspects of the new method are: 1) It considers intraspecific trait variability, which is important for traits like body size that show great variation within species. 2) It uses fuzzy coding of trait data that includes intraspecific variability from aquatic trait databases. 3) It performs dimensionality reduction via PCA on the fuzzy coded trait matrix to build a functional space, then projects randomized trait categories for each taxon into this space to represent potential functional variability.

1. A new method for estimating
functional components at taxon and
community levels using intraspecific
trait data
Cayetano
Gu#érrez-­‐Cánovas1,2,
David
Sánchez-­‐Fernández2,
Josefa
Velasco2,
Andrés
Millán2
&
Núria
Bonada4
1:
3:
4:
2:

2. Why a new method to estimate functional diversity?
• Biodiversity
is
a
mul?-­‐facet
concept
• Ecological
studies
tradi?onally
focused
on
the
taxonomic
components
• Func?onal
features
related
with
environmental
filtering,
evolu#on
and
ecosystem
func#oning
• Recent
methodological
advances
allowed
for
calcula?ng
func?onal
components
from
mul?ple
traits
at
community
level

3. Key
papers:
Villéger
et
al.
(2008)
Ecology
Laliberté
&
Legendre,
(2010)
Ecology
Mouillot
et
al.
(2013)
Trends
Eco
Ev
R
packages:
ade4,
FD
(dbFD),
ca#,
Estimation of functional components: the mean-trait approach

4. Why a new method to estimate functional diversity?
• Community
func?onal
components
are
calculated
using
the
mean
trait
data
of
each
taxon
Taxon
Trait
a
Trait
b
Sp
1
1.2
Gills
Sp
2
2.3
Tegument
Sp
3
2.4
Tegument
Sp
4
10.2
Aerial
Sp
5
45.5
Tegument
Sp
6
0.2
Gills
• However,
some
traits
show
a
great
intraspecific
variability
as
body
size,
number
of
genera?ons
or
diet
• Considering
intraspecific
trait
varia?on
may
improve
the
accuracy
of
the
func?onal
component
es?ma?on

5. Taxon
a1
a2
a3
a4
a5
a6
a7
b1
b2
G1
0.0
0.4
0.4
0.2
0.0
0.0
0.0
1.0
0.0
G2
0.0
0.0
0.0
0.0
0.4
0.4
0.2
0.0
1.0
G3
0.0
0.2
0.4
0.4
0.0
0.0
0.0
0.5
0.5
G4
0.2
0.2
0.2
0.2
0.2
0.0
0.0
0.5
0.5
G5
0.2
0.2
0.2
0.2
0.2
0.0
0.0
0.3
0.7
G6
0.2
0.2
0.2
0.2
0.2
0.0
0.0
0.1
0.9
Taxa x traits matrix (Fuzzy coding)
Rows: taxa (usually, genus of aquatic organisms)
Columns: categories of biological traits a and b
Aquatic trait databases:
fuzzy coding data includes intraspecific variability

6. Dimensionality
reduc#on
(PCA):
building
a
Func#onal
Space
Limita#ons:
Taxon-­‐level
metrics
Low-­‐richness
communi?es
(<
3
taxa)
Func?onal
redundancy
(poten?al
informa?on
loss)
Taxon
1
Taxon
2
Taxon
3
Taxon
4
Taxon
5
Taxon
6
Trait
1
Trait
2

7. Why a new method to estimate functional diversity?
Goal:
To
develop
a
set
of
indexes
able
to
work
with
fuzzy
coding
data
to
produce
taxon
and
community
level
func?onal
indexes
based
on
intra-­‐specific
trait
data
Addi#onal
aims:
• Showcase
of
new
features
• To
compare
the
new
method
with
popular
approaches
based
on
mean-­‐trait
values

8. (a)
building
a
Func#onal
Space
(PCA)
Taxon
1
Taxon
2
Taxon
3
Taxon
4
Taxon
5
Taxon
6
Trait
category
1
Trait
category
2
How?
Performing
a
PCA
on
the
raw
fuzzy
coded
matrix
to
retain
the
relevant
func?onal
axis

9. a1
a2
a3
a4
a5
a6
a7
b1
b2
G1
0
0
1
0
0
0
0
1
0
G2
0
0
0
0
0
0
1
0
1
G3
0
1
0
0
0
0
0
0
1
G4
0
1
0
0
0
0
0
1
0
G5
0
1
0
0
0
0
0
1
0
G6
0
0
0
1
0
0
0
0
1
a1
a2
a3
a4
a5
a6
a7
b1
b2
G1
0
1
0
0
0
0
0
1
0
G2
0
0
0
0
0
1
0
0
1
G3
0
0
0
1
0
0
0
0
1
G4
0
0
1
0
0
0
0
0
1
G5
1
0
0
0
0
0
0
0
1
G6
0
1
0
0
0
0
0
1
0
a1
a2
a3
a4
a5
a6
a7
b1
b2
G1
0
1
0
0
0
0
0
1
0
G2
0
0
0
0
1
0
0
0
1
G3
0
1
0
0
0
0
0
0
1
G4
0
1
0
0
0
0
0
1
0
G5
1
0
0
0
0
0
0
0
1
G6
1
0
0
0
0
0
0
0
1
a1
a2
a3
a4
a5
a6
a7
b1
b2
G1
0
1
0
0
0
0
0
1
0
G2
0
0
0
0
0
1
0
0
1
G3
0
0
0
1
0
0
0
1
0
G4
1
0
0
0
0
0
0
1
0
G5
0
0
0
0
1
0
0
1
0
G6
0
0
0
0
1
0
0
0
1
(b)
Randomising
trait
categories

10. (c)
Projec#ng
the
randomised
trait
categories
onto
the
func#onal
space
Taxon
1
Taxon
2
Taxon
3
Taxon
4
Taxon
5
Taxon
6
The
clouds
of
points
of
each
taxon
represents
the
suite
of
poten#al
func#onal
variability
based
on
the
probability
of
each
trait
category
to
be
present
in
a
random
individual
belonging
to
that
taxon

11. (d)
Mean
Taxon
func#onal
richness
(tRic)
Taxon
1
Taxon
2
Taxon
3
Taxon
4
Taxon
5
Taxon
6
f
e
d
c
a b
tRic =
niche_ areai
i=a
n
∑
n

12. Taxon
1
Taxon
2
Taxon
3
Taxon
4
Taxon
5
Taxon
6
c
ab
bc
FSim =
2×overlapping_areaij
niche_areai + niche_areaji=a, j=b
n
∑
number _of _ pairs
(e)
Func#onal
similarity
(FSim)
b
a
d
cd

13. (f)
Func#onal
richness
(FRic)
Taxon
1
Taxon
2
Taxon
3
Taxon
4
Taxon
5
Taxon
6
Area
filled
by
the
convex
hull

14. (g)
Func#onal
dispersion
(FDis)
Taxon
1
Taxon
2
Taxon
3
Taxon
4
Taxon
5
Taxon
6
FDis =
dist(i, j)
i=a, j=b
n
∑
n
dist(x,y) = x − xc( )
2
+ y − yc( )
2

15. (h)
Func#onal
redundancy
(FR)
Taxon
1
Taxon
2
Taxon
3
Taxon
4
Taxon
5
Taxon
6
c
a
b
FR = overlaping_ areaij
i=a, j=b
n
∑

16. Func%ontal*axis*1*
Func%ontal*axis*2*
Func%ontal*axis*1*
Func%ontal*axis*2*
Func%ontal*axis*1*
Func%ontal*axis*2*
Func%ontal*axis*1*
Func%ontal*axis*2*
Func%ontal*axis*1*
Func%ontal*axis*2*
(d)$Taxon*func%onal*
richness*
(e)$Func%onal*similarity*
between*taxa*
(f)$Func%onal*
richness*
(g)$Func%onal*
dispersion*
(h)$Func%onal*
redundancy*
Func%ontal*axis*1*
Func%ontal*axis*2*
Trait*categories*
0.2$
c1$ c2$ c3$
0.8$ 0.0$T1$
0.2$0.8$ 0.0$T2$
0.3$0.3$ 0.4$T3$
Taxa*
1$
c1$ c2$ c3$
0$ 0$T1$
0$ 1$ 0$T2$
0$ 0$ 1$T3$
0$
c1$ c2$ c3$
1$ 0$T1$
0$ 1$ 0$T2$
0$ 1$ 0$T3$
1$
c1$ c2$ c3$
0$ 0$T1$
0$ 1$ 0$T2$
1$ 0$ 0$T3$
1$
c1$ c2$ c3$
0$ 0$T1$
1$ 0$ 0$T2$
0$ 0$ 1$T3$
0$
c1$ c2$ c3$
1$ 0$T1$
0$ 1$ 0$T2$
0$ 1$ 0$T3$
1$
c1$ c2$ c3$
0$ 0$T1$
1$ 0$ 0$T2$
0$ 0$ 1$T3$
(a)$Defining*a*
reduced*func%onal*
space*(PCA)*
(b)$Randomising*matrices*
(c)$Projec%ng*randomised*trait*
combina%ons*into*func%onal*
space*

17. Let’s see some applications:
Ecological
niche
drivers
Do
more
func+onally
generalised
organisms
occupy
a
wider
ecological
niche?
Rela#onship
between
ecological
and
func#onal
niche
widths
(Taxon
func#onal
richness)
of
stream
invertebrates,
based
on
intraspecific
biological
and
ecological
traits
(Source:
Tachet
et
al.,
2002)

18. 20 30 40 50
02040
Bryozoa
Functional niche
Ecologicalniche
20 40 60 80 100
02040
Turbellaria
Functional niche
Ecologicalniche
50 100 150
02040
Oligochaeta
Functional niche
Ecologicalniche
40 80 120
02040
Hirudinea
Functional niche
Ecologicalniche
50 100 150 200
02040
Gastropoda
Functional niche
Ecologicalniche
50 100 150 200 250
02040
Bivalvia
Functional niche
Ecologicalniche
40 60 80 100
02040
Crustacea
Functional niche
Ecologicalniche
50 150 250
02040
Ephemeroptera
Functional niche
Ecologicalniche
50 150 250
02040
Plecoptera
Functional niche
Ecologicalniche
50 100 150 200
02040
Odonata
Functional niche
Ecologicalniche
50 150 250
02040
Heteroptera
Functional niche
Ecologicalniche
50 70 90
02040
Lepidoptera
Functional nicheEcologicalniche
50 100 150 200 250
02040
Coleoptera
Functional niche
Ecologicalniche
0 100 200 300
02040
Trichoptera
Functional niche
Ecologicalniche
50 150 250
02040 Diptera
Functional niche
Ecologicalniche
R2=0.18
R2=0.41
R2=0.50
R2=0.18
R2=0.25 R2=0.20
Ecological and functional niche sizes

19. Let’s see some applications:
Community
assembly
Do
organisms
that
share
common
biological
features
occupy
similar
ecological
niches?
Rela#onship
between
the
rela#ve
overlap
in
ecological
and
func#onal
niches
(Func#onal
similarity)
of
stream
invertebrates,
based
on
intraspecific
biological
and
ecological
traits
(Source:
Tachet
et
al.,
2002)

20. 0.0 0.2 0.4 0.6
0.00.40.8
Bryozoa
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8
0.00.40.8
Turbellaria
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8
0.00.40.8
Oligochaeta
Functional overlap
Ecologicaloverlap
0.3 0.4 0.5 0.6 0.7 0.8
0.00.40.8
Hirudinea
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8
0.00.40.8
Gastropoda
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6
0.00.40.8
Bivalvia
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8
0.00.40.8
Crustacea
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8
0.00.40.8
Ephemeroptera
Functional overlap
Ecologicaloverlap
0.2 0.4 0.6 0.8
0.00.40.8
Plecoptera
Functional overlap
Ecologicaloverlap0.0 0.2 0.4 0.6 0.8
0.00.40.8
Odonata
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8
0.00.40.8
Heteroptera
Functional overlap
Ecologicaloverlap
0.55 0.65 0.75
0.00.40.8
Lepidoptera
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8 1.0
0.00.40.8
Coleoptera
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8
0.00.40.8
Trichoptera
Functional overlap
Ecologicaloverlap
0.0 0.2 0.4 0.6 0.8
0.00.40.8
Diptera
Functional overlap
Ecologicaloverlap
R2=0.27 R2=0.07
R2=0.04 R2=0.22
R2=0.20
R2=0.04 R2=0.12 R2=0.10
Pairwise ecological and functional niche overlap

21. Let’s see some applications:
Responses
to
environmental
change
Do
community
func+onal
features
show
non-­‐
random
responses
along
stress
gradients?
Changes
in
the
func#onal
features
of
stream
insects
(EPT
+
OCH)
along
gradients
of
stress
(salinity
and
land-­‐use):
Comparing
intra-­‐
specific
trait
data
vs
mean-­‐trait
data

22. 6 8 10 12
51015
F.Richness
6 8 10 12
0.00.40.8
0 1 2 3 4
51015
0 1 2 3 4
0.00.40.8
6 8 10 12
2.02.53.03.54.0
F.Dispersion
6 8 10 12
0.01.02.03.0
0 1 2 3 4
2.02.53.03.54.0
0 1 2 3 4
0.01.02.03.0
6 8 10 12
12345678
log(Conductivity)
log(F.Redundancy)
6 8 10 12
1.01.52.02.5
log(Conductivity)
0 1 2 3 4
12345678
log(Land−use intensity+1)
0 1 2 3 4
1.01.52.02.5
log(Land−use intensity+1)
R2=0.65
R2=0.14
R2=0.29
R2=0.27R2=0.53
R2=0.74
R2=0.17R2=0.13
R2=0.15
R2=0.13
R2=0.17R2=0.72
Salinity
dbFD
dbFD
Novel
method
Novel
method
Land
use
β0
***
β1
***
β0
***
β1
***
β0
***
β1
***
β0
***
β1
***
β0
***
β1
***
β0
***
Β1
ns
β0
***
β1
**
β0
***
β1
**
β0
*
β1
**
β0
***
β1
***
β0
***
β1
**
β0
***
Β1
ns

23. • The novel method provides additional features able to
test fundamental ecological hypotheses
• Multiple functional axes (different responses /
functions)
• The new method performed better in 4 out 6
comparisons (explained variance)
• Novel method showed a better performance against
null models (all cases vs. 4 out 6)
• This novel method may provide additional indexes in
the same multidimensional space and a useful
approach to analyse patterns of aquatic biodiversity
Conclusions

24. Thanks for your attention!
Gu?errezCanovasC@cardiff.ac.uk
@tano_gc