Download Species functional redundancy, random extinctions and the stability

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Journal of
Ecology 2001
89, 118 –125
Species functional redundancy, random extinctions and
the stability of ecosystems
Blackwell Science, Ltd
CARLOS ROBERTO FONSECA and GISLENE GANADE*
Departamento de Zoologia, I. B., CP. 6109, Universidade Estadual de Campinas, Campinas, São Paulo,
CEP 13081-970, Brazil
Summary
1 The level of functional redundancy in natural communities is likely to modulate how
ecosystem stability is affected by local species extinction. Thus, extinction should have no
effect if all species have similar functions, but a major effect if each carries different functions.
2 We provide a probabilistic framework that, from any distribution of species number
across functional groups, generates specific predictions of how functional groups are
lost when species become randomly extinct within a given community. In particular, we
predict how many species can go extinct before a community loses its first functional
group, a useful index for conservation purposes.
3 We demonstrate that the probability of a whole functional group becoming extinct
from a given community increases with the number of recognized functional groups
(functional richness) but decreases with species richness and functional evenness (the
distribution of species across functional groups).
4 Application of this framework to one published data set for a South American plant
community suggested that, if local extinction is random, 75% of the species could be lost
before the disappearance of the first functional group.
5 However, if redundancy is to be used to determine conservation priorities, the
definition of functional groups must be carefully reviewed.
Key-words: community, conservation, functional evenness, functional group, species
richness
Journal of Ecology (2001) 89, 118–125
Introduction
The importance of species diversity in controlling the
stability of communities and ecosystems has been a
focus of long-term debate (MacArthur 1955; Elton
1958; May 1972; Ehrlich & Ehrlich 1981; Walker 1992;
Lawton & Brown 1993; Ehrlich & Walker 1998). It is
widely accepted that continued species extinction
invariably leads to irreversible degradation of ecosystem functions, including those involved in the maintenance of biogeochemical and hydrological cycles,
climate control, decomposition and soil formation,
pest control and pollination (Ehrlich & Ehrlich 1981).
However, because species may play equivalent roles
© 2001 British
Ecological Society
Correspondence and present address: C. R. Fonseca, Departamento de Biologia, CP. 275, Centro II, Universidade do Vale
do Rio dos Sinos, São Leopoldo, RS, CEP. 93022-000, Brazil
(e-mail [email protected]).
*Present address: Departamento de Biologia, CP. 275,
Centro II, Universidade do Vale do Rio dos Sinos, São
Leopoldo, RS, CEP. 93022-000, Brazil.
(i.e. are functionally redundant), some of them could
go locally extinct without a substantial loss in ecosystem function (Walker 1992; Lawton & Brown 1993).
The question is how much extinction can ecosystems
support before they become unstable?
Evaluating the degree of functional redundancy in
nature requires an agreed definition of functional
group. Here, we are mostly concerned with functional
classifications that group species in relation to their
effect on the functioning of communities and ecosystems (Walker 1992; Chapin et al. 1998; Walker et al.
1999), although other classifications are possible
(Gitay & Noble 1997; Walker et al. 1999). Classification of species in relation to how they respond to disturbance may enable prediction of species geographical
range shifts in response to climate change (Friedel et al.
1988; Smith et al. 1997). A hybrid definition, which
groups species based on both criteria described above,
has also been proposed (Díaz & Cabido 1997). Alternatively, species similarity in ecological strategy or
resource use may aid understanding of community
and evolutionary patterns (Grime 1979; Leishman &
118
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Functional
redundancy and
extinction
Westoby 1992; Westoby 1998) or species coexistence
(Root 1967; Pianka 1983; Simberloff & Dayan 1991;
Cornell & Hawkins 1993; Zak et al. 1994), respectively.
Current rates of local and global extinction
(Heywood & Watson 1995; May et al. 1995) will inevitably lead to communities being simplified in terms of
both species and function, and theoretical and empirical investigation of the relationship between species
and functional richness is thus increasingly important.
Theoretical studies, which have discussed how species
richness modulates individual ecosystem functions,
have predicted alternative outcomes (Vitousek &
Hooper 1993; Martinez 1996; Naeem 1998). These
have inspired empirical studies looking at the relationship between species richness and functions such as
carbon fixation (Naeem et al. 1994, 1995; Tilman et al.
1996), or at the effects of functional richness and composition, as well as species richness, on a small number
of major ecosystem functions (Hooper & Vitousek
1997; Tilman et al. 1997; Symstad et al. 1998; Hector
et al. 1999; Walker et al. 1999).
We examined how the stability of a natural ecosystem,
built upon a wide range of ecological functions, will be
affected by random species extinction. In particular, we
predicted how functional groups are lost when species
become randomly extinct from a given community and
demonstrate how this probability is influenced by
species richness, the number of functional groups
(henceforth functional richness) and the distribution
of species among functional groups (henceforth
functional evenness).
The species–function extinction curve
We began by asking how many functional groups
would be expected in a community when random
extinction events have reduced its species richness.
Assuming that the total number of species in the
community is S, the total number of functional groups
is F, and S i is the number of species in the functional
F

group i ∑ Si = S . If random extinction events reduce
 i =1

the species richness from S to s (S > s), then the
expected number of functional groups in a random
sample of s species [E(Fs)] will be given by:
F
E ( Fs ) = ∑
i =1
© 2001 British
Ecological Society,
Journal of Ecology,
89, 118 –125
 S – Si 
 s 
1 – -----------------S 
s 
eqn 1
where S  is the number of combinations of s species
s 
that can be chosen from a set of S species (S!/s!(S – s)!).
The mathematical solution of this estimate is analogous to that of the rarefaction method developed to
allow comparisons of species diversity among samples
with distinct sampling effort (Sanders 1968; reviewed
by Hulbert 1971). The large sample variance of this
estimate is that given by Heck et al. (1975) as
S –1
Var(Fs ) =  
s
F–1
2∑
F
∑
i =1 j= i +1
 S – Si 
 s 
S
–
S
i
- +
∑  s  1 – -----------------S 
i =1
s 
F
 S – Si   S – Sj 
 s  s 
–
–
S
S
S
i
j


 – ---------------------------------------s
S 
s 
eqn 2
where Var (Fs) is the variance of the expected number of
functional groups in a random sample of s species.
Some illustrative contrasts
We use equations (1) and (2) to compare four hypothetical communities showing independent variation in
species richness (100 or 50 species), functional richness
(20 or 10 functional groups) and functional evenness
(with either a similar or a different number of species
per functional group). Communities I and II differ in
species richness but functional richness and evenness
are held constant (Fig. 1a), whereas communities I and
III differ only in functional evenness (Fig. 1c) and communities I and IV differ only in functional richness
(Fig. 1e).
Because our model gives the expected number of
functional groups for any number of species extinctions, comparisons among communities can be based
on the whole curve relating species extinction to function losses. In addition, the curves allow us to ask how
many functional groups are lost for any number of species extinctions, and how many species losses will lead
to 10%, 50% or 90% of the functional groups being lost.
In the following examples we restrict our comparisons
of different communities to asking how many species
extinctions can be supported before a community suffers the extinction of the first functional group. We
believe that, for both ecologists and conservation biologists, this is a non-trivial question that is at the heart
of the redundancy controversy (Ehrlich & Ehrlich
1981; Walker 1992; Lawton & Brown 1993; Ehrlich &
Walker 1998).
   
Species-rich communities tend to have more functional
redundancy than species-poor communities, at least
when functional richness and functional evenness do
not vary dramatically among communities. Quantitative evidence that richer communities will be less
sensitive to extinction is given by comparison of the
species–function extinction curves for communities I
and II (Fig. 1b). In fact, the richer community I (100
species) is expected to support on average 80 random
extinctions (80% of the species) before losing the first
functional group, whereas community II (50 species)
loses its first functional group after only 32 species
(64%) have become extinct.
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C. R. Fonseca &
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Fig. 1 The effect of independently varying species richness, functional evenness and functional richness on species–function
extinction curves. Figures on the left show the frequency distribution of species number per functional group for two contrasting
communities, while their species–function extinction curves are shown, respectively, on the right. The expected number of
functional groups is represented by circles, while the lines enclose one standard deviation around the estimates. (a, b) The effect
of varying species richness (communities I and II with 100 and 50 species, respectively) while holding functional richness and
functional evenness constant. (c, d) The effect of varying functional evenness (communities I and III with even and uneven
distribution, respectively) while holding species richness and functional richness constant. (e, f ) The effect of varying functional
richness (communities I and IV with 10 and 20 functional groups, respectively) while holding species richness and functional
evenness constant.
© 2001 British
Ecological Society,
Journal of Ecology,
89, 118 –125
   
Communities exhibiting a more even distribution of
species number across functional groups will present
more functional redundancy than communities in which
species are distributed unevenly among functional
groups, others factors being equal. The quantitative
comparison shows that community III, with an uneven
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redundancy and
extinction
distribution of species across functional groups, is
able to withstand on average only 20 random species
extinctions (20%) before it loses the first functional
group, 60 fewer than observed for community I
(Fig. 1d).
   
Communities with fewer functional groups tend to
have more functional redundancy than functionally
rich communities. For example, community IV, with
twice the number of functional groups of community
I (20 and 10, respectively), is able to randomly lose
on average 56 species (56%) before losing the first
functional group, 24 fewer than in community I
(Fig. 1f ).
An empirical example
© 2001 British
Ecological Society,
Journal of Ecology,
89, 118 –125
Although, in nature, species richness, functional richness and functional evenness are unlikely to change
independent of each other, as in our hypothetical
examples, the species–function extinction equation
can be readily applied to any community in which the
distribution of species across functional groups is
known.
We therefore looked in the literature for empirical
studies that classify all species from a community into
functional groups based on their effect on the functioning of the ecosystem. Surprisingly, we were unable to
find any empirical study that conformed strictly to such
a definition, however, Díaz & Cabido (1997) used a
hybrid definition, considering plant functional groups
as sets of plants both exhibiting similar responses to
environmental conditions and having similar effects on
the dominant ecosystem processes. Despite the fact
that some of the conclusions therefore need to be
viewed more critically, we believe that this example
can help us to understand some of the advantages and
limitations of our approach.
In order to classify the 100 most abundant plant species along a steep climatic gradient in central-western
Argentina into functional groups, Díaz & Cabido
(1997) selected 24 key vegetative and regenerative
traits. These were chosen to reflect the ecosystem functions (e.g. nutrient cycling, water retention, productivity, carbon storage) most likely to be modified by
climatic change. Standard multivariate ordination and
classification techniques (DCA and ) were
applied to the species × traits matrix, and eight functional groups have been identified: (FT1) short graminoids; (FT2) tussock grasses and large forbs; (FT3)
short herbaceous and semi-woody erect, creeping or
rosette-like dicots; (FT4) saxicolous or epiphytic
rosettes; (FT5) trees; (FT6) evergreen shrubs and small
trees; (FT7) aphyllous or scale-leafed shrubs; and
(FT8) globular, cylindrical and columnar branched
stem-succulents of various sizes.
The distribution of species across functional groups
Fig. 2 (a) The frequency distribution of species number
per functional group for the 100 most abundant species
from central-western Argentina (Díaz & Cabido 1997). Functional group symbols are as follow: FT1, short graminoids;
FT2, tussock grasses and large forbs; FT3, short herbaceous
and semi-woody erect, creeping, or rosette-like dicots; FT4,
saxicolous or epiphytic rosettes; FT5, trees; FT6, evergreen
shrubs and small trees; FT7, aphyllous or scale-leafed shrubs;
FT8, globular, cylindrical, and columnar branched stemsucculents of various sizes. (b) The species–function
extinction curve. Conventions as in Fig. 1.
was relatively uneven (Fig. 2a), ranging from 29 species
in FT1 to four in FT4 and FT7. Our model predicted
that this community can support up to 75 random
extinctions (75% of the original species number) before
suffering the extinction of the first functional group
(Fig. 2b).
Discussion
The general analytical solution presented for the
relationship between functional richness and species
richness allows specific predictions about community
and/or ecosystem stability. Here we are concerned
with the extinction of whole functional groups within
communities, rather than the relationship between
function and species diversity within functional groups
(as in Vitousek & Hooper 1993). We have shown that
functional loss is more likely if communities are: (i)
species poor, (ii) functionally rich, and (iii) have species
distributed unevenly across functional groups.
Previous theoretical models have similarly suggested
that species redundancy is important for the functioning
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© 2001 British
Ecological Society,
Journal of Ecology,
89, 118 –125
and reliability of ecosystems (Naeem 1998) and our
model further highlights that system stability and reliability depend on how species redundancy is distributed across functional groups. We were unable to find
studies that classify whole communities into functional
groups on the basis of their effect on a wide range of
ecosystem processes (but see Walker et al. 1999). Data
on such distributions, and thus of how species richness,
functional richness and functional evenness are correlated with each other in nature, are thus fragmentary.
For example, although one might imagine that, at least
up to a given point, communities with more species
(e.g. tropical forests) will tend to contain more functional groups than species-poor communities (e.g.
boreal forests), this does not have to be the case.
There are several hypothetical ways in which species
richness and functional richness can be associated in
nature (Vitousek & Hooper 1993; Martinez 1996;
Naeem 1998). As case studies accumulate, it is possible
that there will be at least one empirical study to
corroborate most of the hypothetical patterns, and a
posteriori data analysis could then determine which
hypothesis received the strongest support. Our model,
however, allows us to make a priori quantitative
predictions of the relationship between species and
functional richness. The predicted species–function
extinction curve provides both a null hypothesis
against which observed data can be tested and the
best means available to predict future changes in
the absence of species- or functional group-specific
information.
The deviation around the species–function extinction curve, in addition to its statistical relevance, has a
very important biological meaning. As a rule, the variance in the expected number of functional groups
tends to be low at either low or high species extinction
levels, and to be high at intermediate species extinction
levels (see Figs 1 and 2). When species become extinct
at random, the first species to go extinct locally will, in
most cases, have no effect on the functioning of the
ecosystem, as their jobs will be taken by members of
the same functional group. Similarly, when species
extinction levels are high most redundant species will
already have disappeared, and the extinction of any
further species will be bound to produce an effect on
the functioning of the ecosystem, and variance around
our predictions will, therefore, be low. In contrast,
when species extinction levels are intermediate, our certainty about the system behaviour is very low. In some
cases, by chance, the community will retain at least one
representative of each functional group and the system
will continue to work, but if extinction events happen
to have an impact on functional groups with no redundancy, ecosystem stability will be affected. In other
words, if we lose one species we can confidently predict
what should happen to the ecosystem but, if a few
species are lost we can only guess. This unpredictability
pattern of species extinction on ecosystem function
was foreseen by Ehrlich & Ehrlich (1981).
  
By deriving species–function extinction curves for different communities one is able to compare them in
terms of functional redundancy. Although the curve
can be compared, we envisage that the number of random
extinctions the community supports (or the percentage
that could become extinct) before it suffers the extinction of the first functional group represents a useful
index of species redundancy across communities. Such
indicators could allow the detection of which set of
communities is more prone to functional extinction and
therefore requires more intensive conservation efforts.
A community that can lose up to 50% of its species
before experiencing a functional loss is certainly more
robust than a community that will lose the first functional group after 10% of its species become extinct.
The predictions of each species–function extinction
curve are, however, valid only within the scope and
definitions of the study concerned, and meaningful
comparisons between communities or data sets require
consistent definition and classification of species into
functional groups.
  
Our model was able to produce specific a priori predictions about the plant community of central-western
Argentina studied by Díaz & Cabido (1997), i.e. if local
extinction is random, 75% of the species could go
extinct before the disappearance of the first of the eight
recognized functional groups. However, the high
redundancy level thus suggested must be interpreted
with caution, as classification procedures of species
into functional groups strongly affect the estimated
levels of redundancy in natural communities.
    
 
One of the main assumptions of our model is that species can readily be classified into functional groups.
Species are, however, evolutionarily and ecologically
unique, and grouping into any functional classification
will inevitably ignore some biologically relevant
information. The exclusion of any species from a community is bound to have some effect, however marginal, on the functioning of the ecosystem. How much
information will be included in the classification system and how much we are willing to neglect will depend
on the aim and use in mind.
In any particular case, the definition of functional
groups involves five main steps: (i) deciding which type
of functional group is needed; (ii) selecting the criteria
for including species in the study (e.g. all species in
a forest patch); (iii) selecting which functions should
be considered (e.g. nitrogen and carbon fixation);
(iv) choosing morphological, physiological or ecological
traits which reflect such functions (e.g. N-fixation
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redundancy and
extinction
ability, wood volume); (v) choosing and applying
objective multivariate methods (e.g. cluster analysis)
to the species–trait matrix (S species × T traits) thus
produced. Choices to be made at each step will have
consequences for the model predictions.
Defining functional group
Our focus on classifications that group species in relation to their effect on ecosystem processes (Walker
1992) works well under relatively stable environmental
conditions. However, if the local environment drifts
due to external environmental pressure (e.g. global
change), heterogeneity can emerge within apparently
homogeneous functional groups, because species that
apparently do the same thing can respond quite differently to environmental pressures. Although Walker
et al. (1999) argue that this heterogeneity is good as it
increases the system’s resilience to environmental
changes, it may lead to redundancy levels being dangerously overestimated. Actual levels of functional
redundancy can be estimated more accurately when
functional group is defined as a set of species exhibiting
similar responses to environmental conditions and
having similar effects on the dominant ecosystem processes (Díaz & Cabido 1997).
Although most present-day global change research
is aimed at understanding shifts in species’ geographical
range (Smith et al. 1997), prediction of ecosystem-level
functions of the new, post-disturbance community
composition is also important and may be better
founded on Díaz & Cabido’s (1997) definition than
based strictly on the response of species to disturbance.
Species inclusion criteria
Most community studies have at least a taxonomic and
a spatial criterion for species inclusion, and the latter is
particularly relevant for the redundancy controversy.
Because communities are defined operationally as
the set of species in a given area at a given time, and
more area normally means more species (MacArthur
& Wilson 1967), it is inevitable that redundancy is scale
dependent. Local communities thus have less redundancy than regional, or larger scale, communities but the
spatial structure of vegetation means that, at the larger
scale, two species with similar function should be regarded
as redundant only if they co-occur. For example, all
trees were considered to be part of the same functional
group in Díaz & Cabido’s (1997) study, but two trees
should not be considered as functionally equivalent if
they occur in two different parts of the environmental
gradient.
Selecting the functions of interest
© 2001 British
Ecological Society,
Journal of Ecology,
89, 118 –125
If only a few functions are considered in the study, then
the level of functional redundancy will be very high; the
addition of more functions will increase the probability
of a species having a unique role, therefore decreasing
the redundancy level accordingly. If species redundancy is discussed only in terms of major ecosystem
processes, such as carbon fixation, nutrient cycles and
water retention, it is conceivable that a dozen plant species will be sufficient to fulfil all roles. For the functional group definition to become more complete and
useful, ‘dominant ecosystem processes’ should be
understood as including both: (i) the flow of energy and
materials (nutrients, water, atmospheric gases) in the
system; and (ii) community and population processes
normally found in an integral community (e.g. pollination, dispersal, herbivory).
Choosing the traits
After selecting the functions of interest, it is necessary
to find species traits that reflect them. This task is not
an easy one because the relationship between form and
function is hardly straightforward and is limited further by practical considerations of which traits can be
screened for a large set of species. Functional groups
built for different purposes therefore tend to be based
on a similar range of traits (see Leishman & Westoby
1992; Díaz & Cabido 1997).
Building a classification
The question of how to choose a single multivariate
method to classify species into groups among the range
of alternatives (e.g. cluster analysis, DCA, ) is
itself not trivial, but all suffer from a similar problem,
illustrated here for hierarchical arrangements of species into groups of decreasing similarity produced by
cluster analyses. At one extreme, all species could be
considered to be part of a single functional group,
whereas if enough traits are considered, each species
will constitute a ‘functional group’ by its own. It is
therefore up to the researcher and the methodology to
adopt an appropriate ‘cut-off’ level defining how much
trait variation we are willing to overlook in order to
give workable functional groups, and thus how much
dissimilarity will be allowed within each group. The literature suggests that high cut-off levels are frequently
accepted (e.g. Leishman & Westoby 1992; Boutin &
Keddy 1993; Golluscio & Sala 1993; Díaz & Cabido
1997), producing functional groups that can be easily
recognized (e.g. growth forms) but encompassing high
levels of trait variation (i.e. all trees are assumed to
function in the same way). By doing so, functional
redundancy inevitably emerges as very high, as in our
empirical example using the Díaz & Cabido (1997)
data set. Functional groups produced with lower cut-off
levels will increase the homogeneity of functional groups
and, consequently, define lower redundancy levels.
In summary, we would like to highlight that if conservation priorities or programmes of management or
ecosystem restoration are to be based on functional
redundancy, as proposed by Walker (1992), the best
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definition of functional group for the conservation aim
in question must be sought and, in order to be conservative, this may need to use as many functional
groups as possible.
  
Another main assumption of our model is that local
species extinction is considered to occur at random,
with the probability of extinction being equally distributed across species and functional groups. The basic
model could be further improved by the incorporation
of differential extinction probabilities across species
and functional groups. Empirical research is needed to
determine if and how: (i) extinction of whole functional
groups modifies the extinction probabilities of those
remaining because of interactions among different
functions; and (ii) the extinction of individual species
affects others in the same functional group due, for
instance, to compensatory effects (Naeem 1998).
Future theoretical work could include species-specific
information on differences in mating system, local
population density and geographical range that can
modulate species extinction and thus predict more
accurately the extinction rates of functional groups.
Such models would be of great value for conservation
programmes of functionally complex systems.
Acknowledgements
We thank Michelle Leishman, David Warton, Thomas
Lewinsohn, Lindsay Haddon and the BIOFORUM
discussion group for suggestions in earlier versions.
The authors were supported by CNPq, FAPERJ and
FAPESP (Brazil). This work is part of the BIOTA/
FAPESP – The Biodiversity Virtual Institute Program
(http://www.biotasp.org.br).
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