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ResearchCite this article: Allhoff KT, Drossel B.
2016Biodiversity and ecosystem functioning
in evolving food webs. Phil. Trans. R. Soc. B
371: 20150281.http://dx.doi.org/10.1098/rstb.2015.0281
Accepted: 8 February 2016
One contribution of 17 to a theme issue
Biodiversity and ecosystem functioning
in dynamic landscapes.
Subject Areas:evolution, computational biology, ecology,
environmental science, systems biology,
theoretical biology
Keywords:food web evolution models, ecosystem
services, global change, evolutionary
emergence, community assembly,
bioenergetics approach
Author for correspondence:K. T. Allhoff
e-mail: [email protected]
& 2016 The Author(s) Published by the Royal Society. All
rights reserved.
Electronic supplementary material is available
at http://dx.doi.org/10.1098/rstb.2015.0281 or
via http://rstb.royalsocietypublishing.org.
Biodiversity and ecosystem functioningin evolving food webs
K. T. Allhoff1,2 and B. Drossel1
1Institute for Condensed Matter Physics, Technische Universitat
Darmstadt, Darmstadt, Germany2Institute of Ecology and
Environmental Sciences, Universite Pierre et Marie Curie, Paris,
France
KTA, 0000-0003-0164-7618
We use computer simulations in order to study the interplay
between biodi-versity and ecosystem functioning (BEF) during both
the formation andthe ongoing evolution of large food webs. A
species in our model is character-ized by its own body mass, its
preferred prey body mass and the width of itspotential prey body
mass spectrum. On an ecological time scale, populationdynamics
determines which species are viable and which ones go extinct.On an
evolutionary time scale, new species emerge as modifications of
existingones. The network structure thus emerges and evolves in a
self-organizedmanner. We analyse the relation between functional
diversity and five com-munity level measures of ecosystem
functioning. These are the metabolicloss of the predator community,
the total biomasses of the basal and the pred-ator community, and
the consumption rates on the basal community andwithin the predator
community. Clear BEF relations are observed during theinitial
build-up of the networks, or when parameters are varied,
causingbottom-up or top-down effects. However, ecosystem
functioning measuresfluctuate only very little during long-term
evolution under constant environ-mental conditions, despite changes
in functional diversity. This resultsupports the hypothesis that
trophic cascades are weaker in more complexfood webs.
1. IntroductionDuring the past decades, the relation between
biodiversity and ecosystem func-tioning (BEF) has been intensely
investigated (for reviews, see [15]). TheseBEF studies are
motivated by the need to understand the mechanisms that med-iate
the functioning of diverse ecosystems and to predict the
consequences ofrapid changes in biodiversity owing to current
extinction events [6,7]. Duffyet al. [2] emphasized the importance
of taking into account processes that occurboth within and among
trophic levels, because trophic processes between levelsaffect
ecosystem functioning as much as facilitation and competition
withintrophic levels. The authors point out that many earlier BEF
studies focusedinstead on rather simple systems, as for example on
a single trophic level ofrandomly assembled species, but not on
complex multi-trophic communitieswith a coevolutionary history.
While these studies provided first insights intoBEF relations, they
are far from providing a complete picture. An overview ofnew
approaches dealing with multi-trophic and non-equilibrium
biodiversity,with larger spatial or temporal scales and with
different types of ecosystems,can be found in the introductory
chapter of this theme issue [8].
Here, we follow the suggestion of Loreau [9] that evolutionary
food webmodels provide an excellent tool to study BEF-related
questions. Such modelsinclude evolutionary changes in species
composition in addition to populationdynamics [1012]. The network
structure is not static, but evolves in a coevolu-tionary manner
via the dynamical interplay between population dynamics andthe
introduction of new species or morphs. It is thus possible to
investigate thetime-dependent behaviour of the functioning of large
food webs, both duringthe initial build-up of a network and during
the ongoing species turnoveron larger time scales. Such a long-term
perspective may lead to surprises thatsignificantly differ from
short-term experiments, as shown by Reich et al. [13].
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2s3
log10( f3)log10(m)
FCR
Figp
XCC
R
3
1 2
0log10(m3)log10(m2)log10(m1)log10(m0 = 1) = 0
Figure 1. Model illustration using four species. Species 3
(black triangle) is characterized by its body mass m3, the centre
of its feeding range f3 and the width of itsfeeding range s3. The
Gaussian function (black curve) describes its attack rate kernel
N3j on potential prey species. Here, species 3 feeds on species 2
and 1 (greytriangles) with a high-respiration low attack rate.
Species 1 and 2 are consumers of the external resource, represented
as species 0 with a body mass m0 1 (whitetriangle). Also
illustrated is the corresponding network graph with the five
measures of ecosystem functioning. After [19].
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Well-known examples of evolutionary food web modelsare the
webworld model [14,15] and the matching model[16,17]. An
individual-based approach was recently takenby Takahashi et al.
[18], who found abrupt communitytransitions and cyclic evolutionary
dynamics in complexfood webs. These three models use abstract trait
vectors tocharacterize the ecological niche of a species. By
contrast,the model by Allhoff et al. [19] used here is based on
bodymasses. It is related to the model by Loeuille & Loreau
[20],and its later modifications [2123]. The species in ourmodel
differ concerning their body masses (as in [20]), butalso
concerning their preferred prey body masses and thewidths of their
potential prey body mass spectrum. Thisreflects different possible
feeding strategies and results inmore realistic and less static
food web structures [19].
We investigate the relationship between the functionaldiversity
of the evolving networks and five community levelmeasures of
ecosystem functioning. These are the metabolicloss of the predator
community, the total biomasses of thebasal and the predator
community, and the consumptionrates on the basal community and
within the predator commu-nity. Theoretical [2426] and empirical
[27] food web studiessuggest a large variety of different BEF
relations, owing tobottom-up or top-down effects. Other studies
suggest a satur-ation of BEF relations owing to the dampening of
trophiccascades in complex and diverse communities [2833]. Atthe
beginning of our simulations, when the networks are stillrelatively
small, each species addition or extinction causesmajor changes in
the network structure and hence in the abilityof the consumer guild
to exploit the resource. We thereforeexpect all measures of
ecosystem functioning (except forresource biomass) to be positively
correlated with biodiversity.However, we expect the ecosystem
functioning to saturateduring the ongoing fluctuations in the
network structurelong after this initial build-up, when a complex
multi-trophiccommunity has formed, where the function performed by
aspecies that goes extinct can be retained by others.
We also analyse the impact of two model parameters on theBEF
relations, which are both well known to respond to promi-nent
drivers of global change: the respiration and mortality
rateincreases owing to an increased temperature in a climatechange
scenario [34,35], and the carrying capacity may eitherincrease
owing to nutrient enrichment or decrease with anincreasing
temperature [36]. Both parameters are assumed tohave a significant
impact on the resulting network structures.We expect that an
increased carrying capacity leads tobottom-up effects that enable
the emergence of a more diverseconsumer community, whereas an
increased respiration andmortality rate leads to biomass loss in
the consumer guild
and hence to a release of the resource owing to
decreasedtop-down control.
2. ModelThe model includes fast ecological processes
(populationdynamics) which determine for a given species
compositionthe population sizes, biomass flows, and whether a
species isviable in the environment created by the other species.
Addition-ally, slow evolutionary processes (speciation or invasion
events)add new species to the system that are similar to existing
ones,leading to an ever-changing network structure. A species i
ischaracterized by its body mass, mi, the centre of its
feedingrange, fi and the width of its feeding range, si. These
traits deter-mine the feeding interactions in the community and
thereby thepopulation dynamics, as illustrated in figure 1.
(a) Population dynamicsThe population dynamics follows the
multi-species generaliz-ation of the bioenergetics approach by
Yodzis & Innes [37,38].The rates of change of the biomass
densities Bi of the populationsare given by
_B0 G0B0 X
jconsumersg j0Bj 2:1
for the external resource (species 0 with body mass m0 1);and
by
_Bi X
jresourcesejgijBi
Xjconsumers
g jiBj xiBi 2:2
for consumer species. The coefficient G0 r(1 2 B0/K)describes
the logistic growth of the external resource, with agrowth rate r
and a carrying capacity K. The time scale of thesystem is defined
by setting r 1. The efficiency ej is prey-dependent and equals
either 0.45 for feeding on the resourceor 0.85 for preying on other
consumer species. gij is the mass-specific rate with which species
i consumes species j, andxi x0m0:25i is a combined, mass-specific
rate that describesis losses owing to respiration and mortality.
The carryingcapacity K (in the same units as biomass density) and
the con-stant of the respiration and mortality rate x0 (in units of
kg
0.25
per year) are model parameters that are varied in this study.The
mass-specific consumption rate is described via a
BeddingtondeAngelis functional response [39]:
gij 1
mi
aijBj1
Pkres: hiaikBk
Plcomp: cilBl
: 2:3
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The per capita rate of successful attacks of predator i on prey
j,aij, is based on a Gaussian feeding kernel Nij,
aij m0:75i Nij m0:75i1
siffiffiffiffiffiffi2pp exp
log10 fi log10 mj2
2s2i
" #:
2:4
The parameter hi 0:398m0:75i in equation (2.3) is thehandling
time of species i for one unit of prey biomass, andcil quantifies
interference competition among predators iand l. It depends on
their similarity, as measured by theoverlap Iil
NijNljd(log10mj) of their feeding kernels, via
cil cfoodIilIii
for i = l: 2:5
We assume that interference competition is higher within
aspecies than between different species, e.g. owing to
territorialor mating behaviour. We therefore introduce an
intraspecificcompetition parameter cintra and set cii cfood cintra.
The influ-ence of these competition parameters has been discussed
in aprevious article [19]. Here, we use fixed values: cfood 0.8and
cintra 0.6.
1
(b) Speciation eventsEach simulation starts with a single
ancestor specieswith body mass m1 100 and optimal feeding
parametersf1 1 and s1 1. The initial biomass densities are B0 K 100
for the resource and B1 m1e 2 102 for the ances-tor species. The
parameter e 2 104 is the extinctionthreshold, i.e. the minimum
population density requiredto survive.
A speciation event occurs every 104 time units. Then,
eachspecies with a population size below the extinction thresholdis
removed from the system, and one of the remaining species(but not
the external resource) is chosen randomly as parentspecies i for a
mutant species j. The logarithm of themutants body mass, log10(mj),
is chosen randomly from theinterval [log10(0.5 mi), log10(2 mi)],
meaning that the bodymasses of parent and mutant species differ at
most by afactor of 2. The mutants initial biomass density is set
toBj mje and is taken from the parent species. The logarithmof the
mutants feeding centre, log10fj, is drawn randomlyfrom the interval
[log10(mj) 2 3.5), (log10(mj) 2 0.5)], meaningthat the preferred
prey body mass is 31000 times smallerthan the consumers body mass,
consistent with the resultsfrom Brose et al. [40]. The width of the
feeding range sj isdrawn randomly from the interval [0.5, 1.5].
Several vari-ations of these rules, most of them with only minor
impactson the resulting network structures, were discussed in
aprevious article [19].
3. MethodsTwo species with similar feeding traits (e.g. species
1 and 2 infigure 1) have a similar function in the food web and are
poten-tially redundant: one of them can retain their function when
theother one goes extinct. Large extinction events may thus
changethe systems diversity (measured as the number of species
S)with little impact on its functioning. To account for this, weuse
the following measure of functional diversity (taken fromthe work
of Schneider et al. (Schneider FD, Brose U, Rall BC,Guill C. 2014
The dynamics of predator diversity and ecosystem
functioning in complex food webs, unpublished data)):
FD 11
max( N1j, N2j, . . . , NSjdlog10mj: 3:1
It represents the area below the envelope of all Gaussian
feedingkernels Nij, with 1 i S. Note that the area below each
feedingkernel is normalized to 1, so that two species with little
(much)overlap in their feeding kernels have a functional
diversityclose to 2 (1). Consequently, the little network
illustrated infigure 1 has a functional diversity slightly above 2.
FD is thus ameasure of complementarity in the feeding preferences
androughly corresponds to the number of trophic levels.
Alternativedefinitions of functional diversities can be found in
[41].A measure of link overlap that additionally includes the
overlapin predator links and that is applicable to discrete trophic
layerswas introduced by Poisot et al. [26].
We analyse the relationship between FD and five measuresof
ecosystem functioning:
(1) The total biomass density of all consumer species,C
PSi1 Bi:
(2) The total biomass density of the resource species R B0.(3)
The total energetic loss of the system owing to the respiration
and mortality of the consumers,XC
PSi1 xiBi:
(4) The total consumption rate on the resource,FCR
PSi1 0:45 gi0Bi:
(5) The intraguild consumption rate,Figp
PSi1
PSj1 0:85 gijBi
:
We analyse the development of these measures during the
initialbuild-up of the networks and during the ongoing species
turnoverlater on. For each value of the respiration and mortality
rate, x00.3, 0.5, 0.7, 0.9, we performed 60 simulations (with a
fixed value ofthe carrying capacity K 100). Simulations with
identical parametervalues differ concerning the set of random
numbers and concerningtheir runtime (Tend 5 108, 1 108, 2.5 107, 1
107, 5 106,1 106). For comparison, the generation time of the
initial ances-tor species with body size m1 100 is of the order of
1/x11000.25/0.314 10 time units. The measures of ecosystem
functioningare evaluated after every single, 10th or 50th mutation
event, depen-dent on the runtime. In addition to these 240
simulations, weperformed another 40 simulations with a runtime of
Tend 5 . 108and a fixed value of x0 0.3, but with different values
of the carryingcapacity, K 50, 100, 150, 200. K and x0 both respond
to promi-nent drivers of global change, as highlighted in
Introduction. Theirvariation thus reflects different environmental
conditions.
4. Results(a) Time seriesExamples of the initial build-up
(columns 2 and 4) and of thelong-term behaviour (columns 1 and 3)
of the evolving net-works are shown in figure 2. After a short
period of strongdiversification, we observe a fairly layer-like
structure. With alow respiration and mortality rate, x0 0.3, we
obtain networkswith approximately three body mass clusters around
1, 2.5 and4. Note that the species in one body mass cluster can
differ intheir feeding preferences and hence belong to different
trophiclevels. Higher respiration and mortality rates represent
anincreased biomass loss, so that the emergence of
higher-levelspecies is hampered. With x0 0.9, only two body
massclusters can emerge. The ongoing species turnover is due
tonewly emerging mutants that are better adapted to availableprey
species or experience less predation pressure, and
thereforedisplace other species with similar feeding
preferences.
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time9 105 0 1.5 108 3 108
time4.5 108 0 3 105 6 105
time9 105
0 1.5 108 3 108 4.5 108 0 3 105 6 105 9 105 0 1.5 108 3 108 4.5
108 0 3 105 6 105 9 105
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108 0 3 105 6 105 9 105
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108 0 3 105 6 105 9 105
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1
10
2040
resourceconsumers
6080
100
510152025
totaltr. Pos. >2.530
3540
5.5
4.5
3.5
2.5
Figure 2. Four exemplary simulation runs with different run
times and different values of the respiration and mortality rate
x0. Shown is the evolution of bodymasses and flow-based trophic
positions, and the time series of the measures that are defined in
the Methods section. A detailed analysis of various
networkproperties can be found in [19].
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Comparing the two long-term simulations, we find thatboth
parameter sets lead to food webs with a similarnumber of species.
Their network structure and the measuresof ecosystem functioning,
however, differ significantly. Thisconfirms the expectation that
functional diversity is a betterpredictor of ecosystem functioning
than the pure number ofspecies. For comparison, the same analysis
as in the follow-ing, but with the species number instead of the
functionaldiversity, is presented in the electronic
supplementarymaterial.
Functional diversity (figure 2, line 4) increases at the
begin-ning of the simulations. Later, it fluctuates around a
constantvalue in case of x0 0.3 or it shows a step-like behaviour
incase of x0 0.9. This step-like behaviour represents a
changing
number of trophic levels: the species with body masses around3
occurring in the middle of the simulation run feed on theexternal
resource, so that both body mass clusters form asingle trophic
level. The two body mass clusters that emergeat the end of the
simulation represent two distinct trophiclayers, as also reflected
in the increased values of functionaldiversity and intraguild
predation.
In general, the measures of ecosystem functioning (lines 5and 6)
remain surprisingly stable after the initial build-up,despite the
ongoing changes in the trophic structure. Notethat at population
equilibria we find
0 X
_Bi FCR XC 1 ej
ejFigp: 4:1
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functional diversity
3.0 3.5 4.0 4.5 1.0 1.5 2.0 2.5
functional diversity
3.0 3.5 4.0 4.5 1.0 1.5 2.0 2.5
functional diversity
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200
406080
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1 1082 1083 1084 1085 108
4.0 4.5
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
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1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Figure 3. The relationship between biodiversity and ecosystem
functioning during the evolutionary history of the food webs with
different values of the respiration andmortality rate x0. The
carrying capacity is set to K 100. Different colours indicate
different times: black represents data from networks shortly after
the simulation start,whereas light blue represents data from fully
developed networks after 1.5 108 time units. (Online version in
colour.)
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The last term (describing efficiency losses owing to
intraguildpredation) is by far the smallest, so that the predation
on theresource FCR and the total metabolic loss XC are of the
sameorder of magnitude.
(b) Biodiversity and ecosystem functioning duringthe initial
build-up of the networks
Figure 3 shows BEF relations during the evolutionary history
ofthe networks, with early and later stages coded in black or
lightblue. For a low respiration and mortality rate, (x0 0.3,
column1), the number of species and functional diversity
increaseduring the initial period of diversification. The more
diversethe consumer guild becomes, the more biomass is
accumu-lated, which can be observed as an increasing value of
thetotal consumer biomass C. This leads to a decreasing
resource
biomass R, owing to an increased predation pressure FCR onthe
resource. We also observe an increasing intraguild preda-tion Figp,
owing to the emergence of higher trophic levels,and an increasing
total metabolic loss XC. If we focus on thedata points long after
the initial build-up (in light blue), wefind that the measures of
ecosystem functioning remain sur-prisingly stable, even though
functional diversity fluctuatesbetween 2.5 and 4.5, representing
networks with differentnumbers of trophic levels.
The comparison of the different columns reveals thestrong impact
of the respiration and mortality rate x0. Thedata clouds shift to
the left with increasing values of x0,reflecting flatter network
structures with fewer trophiclevels and hence lower values of
functional diversity. How-ever, all datasets result in networks of
similar speciesnumbers, again highlighting the importance of
functional
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Figure 4. The relationship between biodiversity and ecosystem
functioning during the ongoing species turnover after the initial
build-up of the emerging food webs.Only those data points that
emerged from the simulations with the longest runtime, tend 5 108,
are shown, so that the initial build-up plays only a minor role.The
colours represent four different values of the respiration and
mortality rate: red (in the background) x0 0.3, green x0 0.5, blue
x0 0.7, pink (in theforeground) x0 0.9. The carrying capacity is
set to K 100. (Online version in colour.)
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diversity. In the last column, we observe two clusters of
datapoints that reflect the existence or absence of a second
trophiclevel above the resource, as explained in 4a.
(c) The influence of environmental conditions onbiodiversity and
ecosystem functioning relations
The different colours in figure 4 represent different values
ofthe respiration and mortality rate x0. In the first panel,
weobserve again that the resulting networks differ strongly intheir
functional diversity, but not so much in species number.Looking at
the other panels, we observe the same qualitativetrends as in
figure 3 with data from the initial build-up. Thisis due to a
top-down effect: increasing values of x0 lead toless biomass flow
into higher trophic levels and hence to flatternetwork structures
with lower functional diversities and smal-ler amounts of consumer
biomass, and therefore to a reducedpredation pressure on the
resource.
However, this is not a universal pattern. Figure 5shows data
that were generated with different values of thecarrying capacity
K. Here, we observe a bottom-up effect:higher values of the
carrying capacity correspond to moreresource biomass and therefore
to a larger amount of availableenergy for the system. This enables
the emergence of largernetworks (in terms of both number of species
and functionaldiversity) and explains the increase in consumer
biomassand in the rates of biomass flow. A similar (but weaker)
effect can be obtained by increasing the growth rate r of
theresource, as shown in the electronic supplementary material.
5. DiscussionAs Loreau [9] highlighted, evolutionary food web
models canprovide major contributions to the BEF debate.
Communitiesgenerated with such models emerge from individual
levelprocesses and share a coevolutionary history, instead ofbeing
randomly put together or suffering from random, arti-ficial
extinction events. In our study, we analyse BEF relations(i) during
the initial build-up of our networks and (ii) duringongoing changes
in the species composition after that. Theformer reveals that an
increasing functional diversity(which corresponds to an increasing
trophic complexity inthe consumer guild) correlates with an
increasing total consu-mer biomass, a decreasing resource biomass,
and increasingbiomass flows into, within and out of the consumer
guild(figure 3). This can be explained with a top-down argument:the
larger the network, the more biomass can be accumulatedand the
higher is the predation pressure on the resource.A similar pattern
has been found in a meta-analysis of exper-imental studies [42].
The authors show that the average effectof a decreasing species
richness is to reduce the abundance orbiomass of the focal trophic
group, leading to less completedepletion of resources used by that
group.
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Figure 5. As in figure 4, but with different values of the
carrying capacity: red (in the background) K 200, green K 150, blue
K 100, pink (in theforeground) K 50. The respiration and mortality
rate is set to x0 0.3. (Online version in colour.)
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Our results are also consistent with a study by Schneideret al.
(Schneider FD, Brose U, Rall BC, Guill C. 2014 Thedynamics of
predator diversity and ecosystem functioningin complex food webs,
unpublished data), who investigatedthe same measures of ecosystem
functioning in a non-evolvingfood web model. The authors reject a
long-established hypo-thesis, which suggests the release of the
basal communityfrom feeding pressure with growing functional
diversityowing to an increased intraguild predation within the
consumercommunity [2,3,30,43]. Schneider et al. showed that such
anincrease of functional diversity indeed leads to an
increasedintraguild predation in the consumer community, but not
toan increase of the total biomass of the basal community. Adiverse
predator community might simultaneously be moreexploitative but
less efficient than a species-poor community.
However, the described BEF relations are not valid over thewhole
simulation time. Our measures of ecosystem functioningbecome almost
constant after the initial build-up of the net-works, although
functional diversity continues to varysignificantly, reflecting
ongoing changes in the trophic struc-ture (figure 3). A saturation
of ecosystem functioning isknown from leaf breakdown by stream
fungi [44] and fromother single trophic layer systems. Saturation
was also pre-dicted by the early hypothesis of the redundancy model
[45].It is nevertheless surprising in our model context,
becausethere is theoretical evidence that ecosystem properties
greatlydepend on the functional biodiversity and in particular
onthe trophic structure [2426]. In addition, empirical
studiessuggest diverse BEF relations based on bottom-up or top-down
effects in multi-trophic communities. For example,
Gamfeldt et al. [27] studied a controlled marine microbialsystem
and found that increasing consumer richness leads toreduced prey
and increased consumer biomass, whereas anincreased prey richness
leads to enhanced energy transferinto higher trophic levels, and
thus to increased biomasses ofconsumers and prey.
One possible explanation for the discrepancy betweenthese
diverse results and our observed saturation might bethe use of
different approaches to generate communities withdifferent
biodiversities. Random extinction events, as com-monly used, might
be too simple: Fung et al. [46] analysed amarine food web under
harvesting and showed that therelation between total biomass
production and the proportionof remaining fish species strongly
depends on the algorithm ofspecies deletion. The need to study more
realistic scenarios ofextinction was also highlighted in the
reviews by Duffy et al.[2] and Cardinale et al. [3]. But no matter
what algorithm isused, most studies assume that species loss is
irreversible, with-out taking into account that empty niches might
be refilled viaevolution or immigration. In our model, many
extinctionevents take place because one existing species is
replacedby a similar but slightly better-adapted new species. In
thisparticular case, intact functioning is indeed no surprise.
However, we observe intact functioning even if occasion-ally a
whole trophic level disappears, supporting thehypothesis that
trophic cascades are weaker in more complexfood webs [2830]. Duffy
predicted that the addition of anew top predator to a diverse,
multi-trophic system influencesspecies abundances in the trophic
level directly below, but thisinfluence does not necessarily
cascade down to even lower
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levels (see fig. 4 in [31]), because formerly rare
predator-resist-ant species might be released from competition, so
that theirfeeding compensates for loss of formerly dominant
speciesthat are now eaten by the new predator. This hypothesis
wassupported in a meta-analysis by Schmitz et al. [32]. Finke
&Denno [33] analysed a coastal marsh community and foundthat
adding more and more predators can further dampentrophic cascades
owing to increased intraguild predation.These processes can only
occur in communities that are suffi-ciently complex and diverse. We
assume that this is givenafter, but not during, the initial
build-up of our networks.
Another reason why we do not find such strong anddiverse BEF
relations as observed in previous studies couldbe the fact that
ecosystems in different study sites experienceand adapt to
different environmental conditions [47]. This isequivalent to
combining in our model simulations performedwith different
respiration and mortality rates or carryingcapacities. Both
parameters are well known to respond toenvironmental conditions
[3436].
By varying the respiration and mortality rate x0, we foundthe
same BEF relations as during the initial build-up of the net-works
(figure 4). Again, this can be explained with a top-downargument:
higher values of the respiration rate increase the bio-mass loss of
the system, which directly leads to a decreasedtotal amount of
consumer biomass, which then leads to andecreased predation
pressure on the resource. Moreover, thedecreased consumer biomass
hampers the emergence ofhigher-level species, which goes hand in
hand with lowervalues of functional diversity. These trends become
moreobvious when considering functional diversity instead of
thenumber of species, as has been observed already by manyother
researchers (see [48] and references therein).
In contrast, varying the carrying capacity leads to positiveBEF
relations both for the resource biomass and for the
consumer biomass (figure 5). This can be explained with
abottom-up argument: an increased value of the carryingcapacity K
directly corresponds to an increased resource bio-mass and
therefore to a larger amount of energy that isavailable to the
consumer guild. Thus, larger networks witha higher functional
diversity and with a larger amount of con-sumer biomass can emerge.
A similar bottom-up effect wasfound in a dataset from the Cedar
Creek Ecosystem ScienceReserve (see [5] for more information about
this studysystem): Haddad et al. showed that the species
richnessand abundance in higher trophic levels (predatory and
parasi-toid anthropods) is strongly and positively related to
thespecies richness in lower trophic levels (plants) [49].
Inaddition, Scherber et al. reported that plant diversity hasstrong
bottom-up effects in multi-trophic networks [50].
To conclude, within a single food web model, we foundinstances
of positive, negative or no correlations between func-tional
diversity and ecosystem functioning measures. Thediversity of our
results highlights the fact that there is noglobal answer to the
question of how biodiversity interactswith ecosystem functioning,
because different mechanisms areinvolved and each of them affects
BEF relations in different ways.
Authors contributions. Both authors designed the study and
analysed theresults. K.T.A. performed the simulations and wrote the
manuscriptdraft. Both authors reviewed the manuscript.Competing
interests. We declare we have no competing interests.Funding. This
work was supported by the DFG research unit 1748(contract no.
Dr300/13) and by the ANR ARSENIC
project(ANR-14-CE02-0012).Acknowledgements. We thank Florian
Schneider, Christian Guill, BjornRall, Elisa Thebault and Nicolas
Loeuille for useful discussionsand/or comments on early versions of
the manuscript.
References
1. Hooper DU et al. 2005 Effects of biodiversity on
ecosystemfunctioning: a consensus of current knowledge.
Ecol.Monogr. 75, 3 35. (doi:10.1890/04-0922)
2. Duffy JE, Cardinale BJ, France KE, McIntyre PB,Thebault E,
Loreau M. 2007 The functional role ofbiodiversity in ecosystems:
incorporating trophiccomplexity. Ecol. Lett. 10, 522 538.
(doi:10.1111/j.1461-0248.2007.01037.x)
3. Cardinale B, Duffy E, Srivastava D, Loreau M,Thomas M,
Emmerson M. 2009 Towards a food webperspective on biodiversity and
ecosystemfunctioning. Studies 60, 20.
(doi:10.1093/acprof:oso/9780199547951.003.0008)
4. Reiss J, Bridle JR, Montoya JM, Woodward G. 2009Emerging
horizons in biodiversity and ecosystemfunctioning research. Trends
Ecol. Evol. 24,505 514. (doi:10.1016/j.tree.2009.03.018)
5. Tilman D, Isbell F, Cowles JM. 2014 Biodiversity andecosystem
functioning. Annu. Rev. Ecol. Evol. Syst.45, 471 493.
(doi:10.1146/annurev-ecolsys-120213-091917)
6. Barnosky AD et al. 2011 Has the earths sixth massextinction
already arrived? Nature 471, 51 57.(doi:10.1038/nature09678)
7. Mooney H et al. 2009 Biodiversity, climatechange, and
ecosystem services. Curr. Opin.Environ. Sustain. 1, 46 54.
(doi:10.1016/j.cosust.2009.07.006)
8. Brose U, Hillebrand H. 2016 Biodiversity andecosystem
functioning in dynamic landscapes. Phil.Trans. R. Soc. B 371,
20150267. (doi:10.1098/rstb.2015.0267)
9. Loreau M. 2010 Linking biodiversity and ecosystems:towards a
unifying ecological theory. Phil.Trans. R. Soc. B 365, 49 60.
(doi:10.1098/rstb.2009.0155)
10. Drossel B, McKane AJ. 2005 Modelling food webs.In Handbook
of graphs and networks: from thegenome to the internet, ch. 10.
Weinheim, Germany:Wiley-VCH.
11. Fussmann GF, Loreau M, Abrams PA. 2007Eco-evolutionary
dynamics of communities andecosystems. Funct. Ecol. 21, 465 477.
(doi:10.1111/j.1365-2435.2007.01275.x)
12. Brannstrom A, Johansson J, Loeuille N, Kristensen N,Troost
TA, Lambers RHR, Dieckmann U. 2012Modelling the ecology and
evolution ofcommunities: a review of past achievements,
current efforts, and future promises. Evol. Ecol. Res.14, 601
625.
13. Reich PB, Tilman D, Isbell F, Mueller K, Hobbie SE,Flynn
DFB, Eisenhauer N. 2012 Impacts ofbiodiversity loss escalate
through time asredundancy fades. Science 336, 589
592.(doi:10.1126/science.1217909)
14. Drossel B, Higgs PG, McKane AJ. 2001 The influenceof
predator prey population dynamics on the long-term evolution of
food web structure. J. Theor. Biol.208, 91 107.
(doi:10.1006/jtbi.2000.2203)
15. Drossel B, McKane AJ, Quince C. 2004 The impactof nonlinear
functional responses on the long-term evolution of food web
structure. J. Theor.Biol. 229, 539 548.
(doi:10.1016/j.jtbi.2004.04.033)
16. Rossberg AG, Matsuda H, Amemiya T, Itoh K. 2006Food webs:
experts consuming families of experts.J. Theor. Biol. 241, 552 563.
(doi:10.1016/j.jtbi.2005.12.021)
17. Rossberg AG, Ishii R, Amemiya T, Itoh K. 2008 Thetop-down
mechanism for body-mass abundancescaling. Ecology 89, 567 580.
(doi:10.1890/07-0124.1)
http://dx.doi.org/10.1890/04-0922http://dx.doi.org/10.1111/j.1461-0248.2007.01037.xhttp://dx.doi.org/10.1111/j.1461-0248.2007.01037.xhttp://dx.doi.org/10.1093/acprof:oso/9780199547951.003.0008http://dx.doi.org/10.1093/acprof:oso/9780199547951.003.0008http://dx.doi.org/10.1016/j.tree.2009.03.018http://dx.doi.org/10.1146/annurev-ecolsys-120213-091917http://dx.doi.org/10.1146/annurev-ecolsys-120213-091917http://dx.doi.org/10.1038/nature09678http://dx.doi.org/10.1016/j.cosust.2009.07.006http://dx.doi.org/10.1016/j.cosust.2009.07.006http://dx.doi.org/10.1098/rstb.2015.0267http://dx.doi.org/10.1098/rstb.2015.0267http://dx.doi.org/10.1098/rstb.2009.0155http://dx.doi.org/10.1098/rstb.2009.0155http://dx.doi.org/10.1111/j.1365-2435.2007.01275.xhttp://dx.doi.org/10.1111/j.1365-2435.2007.01275.xhttp://dx.doi.org/10.1126/science.1217909http://dx.doi.org/10.1006/jtbi.2000.2203http://dx.doi.org/10.1016/j.jtbi.2004.04.033http://dx.doi.org/10.1016/j.jtbi.2004.04.033http://dx.doi.org/10.1016/j.jtbi.2005.12.021http://dx.doi.org/10.1016/j.jtbi.2005.12.021http://dx.doi.org/10.1890/07-0124.1http://dx.doi.org/10.1890/07-0124.1http://rstb.royalsocietypublishing.org/
-
rstb.royalsocietypublishing.orgPhil.Trans.R.Soc.B
371:20150281
9
on July 17,
2018http://rstb.royalsocietypublishing.org/Downloaded from
18. Takahashi D, Brannstrom A, Mazzucco R, YamauchiA, Dieckmann
U. 2013 Abrupt communitytransitions and cyclic evolutionary
dynamics incomplex food webs. J. Theor. Biol. 337, 181
189.(doi:10.1016/j.jtbi.2013.08.003)
19. Allhoff KT, Ritterskamp D, Rall BC, Drossel B, Guill C.2015
Evolutionary food web model based on bodymasses gives realistic
networks with permanentspecies turnover. Nat. Sci. Rep. 5, 10955.
(doi:10.1038/srep10955)
20. Loeuille N, Loreau M. 2005 Evolutionary emergenceof
size-structured food webs. Proc. Natl Acad.Sci. USA 102, 5761 5766.
(doi:10.1073/pnas.0408424102)
21. Brannstrom A, Loeuille N, Loreau M, Dieckmann U.2011
Emergence and maintenance of biodiversity inan evolutionary
food-web model. Theor. Ecol. 4,467 478.
(doi:10.1007/s12080-010-0089-6)
22. Ingram T, Harmon LJ, Shurin JB. 2009 Nicheevolution, trophic
structure, and species turnover inmodel food webs. Am. Nat. 174, 56
67. (doi:10.1086/599301)
23. Allhoff KT, Drossel B. 2013 When do evolutionaryfood web
models generate complex networks?J. Theor. Biol. 334, 122 129.
(doi:10.1016/j.jtbi.2013.06.008)
24. Thebault E, Loreau M. 2003 Food-web constraintson
biodiversity ecosystem functioningrelationships. Proc. Natl Acad.
Sci. USA 100, 14949 14 954. (doi:10.1073/pnas.2434847100)
25. Thebault E, Huber V, Loreau M. 2007 Cascadingextinctions and
ecosystem functioning: contrastingeffects of diversity depending on
food webstructure. Oikos 116, 163 173.
(doi:10.1111/j.2006.0030-1299.15007.x)
26. Poisot T, Mouquet N, Gravel D. 2013 Trophiccomplementarity
drives the biodiversity ecosystemfunctioning relationship in food
webs. Ecol. Lett. 16,853 861. (doi:10.1111/ele.12118)
27. Gamfeldt L, Hillebrand H, Jonsson PR. 2005 Speciesrichness
changes across two trophic levelssimultaneously affect prey and
consumer biomass.Ecol. Lett. 8, 696 703.
(doi:10.1111/j.1461-0248.2005.00765.x)
28. Berlow EL, Dunne JA, Martinez ND, Stark PB,Williams RJ,
Brose U. 2009 Simple prediction ofinteraction strengths in complex
food webs. Proc.
Natl Acad. Sci. USA 106, 187 191.
(doi:10.1073/pnas.0806823106)
29. Shurin JB, Borer ET, Seabloom EW, Anderson K,Blanchette CA,
Broitman B, Cooper SD, Halpern BS.2002 A cross-ecosystem comparison
of the strengthof trophic cascades. Ecol. Lett. 5, 785 791.
(doi:10.1046/j.1461-0248.2002.00381.x)
30. Strong DR. 1992 Are trophic cascades all wet?Differentiation
and donor-control in specioseecosystems. Ecology 73, 747 754.
(doi:10.2307/1940154)
31. Duffy JE. 2002 Biodiversity and ecosystem function:the
consumer connection. Oikos 99, 201
219.(doi:10.1034/j.1600-0706.2002.990201.x)
32. Schmitz OJ, Hamback PA, Beckerman AP. 2000Trophic cascades
in terrestrial systems: a review ofthe effects of carnivore
removals on plants. Am. Nat.155, 141 153. (doi:10.1086/303311)
33. Finke DL, Denno RF. 2004 Predator diversitydampens trophic
cascades. Nature 429, 407 410.(doi:10.1038/nature02554)
34. Brown JH, Gillooly JF, Allen AP, Savage VM, WestGB. 2004
Toward a metabolic theory of ecology.Ecology 85, 1771 1789.
(doi:10.1890/03-9000)
35. Rall BC, Vuvic-Pestic O, Ehnes RB, Emmerson M,Brose U. 2010
Temperature, predator preyinteraction strength and population
stability. Glob.Change Biol. 16, 2145 2157.
(doi:10.1111/j.1365-2486.2009.02124.x)
36. Binzer A, Guill C, Brose U, Rall BC. 2012 Thedynamics of
food chains under climate change andnutrient enrichment. Phil.
Trans. R. Soc. B 367,2935 2944. (doi:10.1098/rstb.2012.0230)
37. Yodzis P, Innes S. 1992 Body size and consumer resource
dynamics. Am. Nat. 139, 1151 1175.(doi:10.1086/285380)
38. Brose U, Williams RJ, Martinez ND. 2006 Allometricscaling
enhances stability in complex food webs.Ecol. Lett. 9, 1228 1236.
(doi:10.1111/j.1461-0248.2006.00978.x)
39. Skalski GT, Gilliam JF. 2001 Functional responseswith
predator interference: viable alternatives to theHolling type II
model. Ecology 82, 3083
3092.(doi:10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2)
40. Brose U et al. 2006 Consumer resource body sizerelationships
in natural food webs. Ecology 87,
2411 2417.
(doi:10.1890/0012-9658(2006)87[2411:CBRINF]2.0.CO;2)
41. Petchey OL, OGorman EJ, Flynn DFB. 2009A functional guide to
functional diversity measures. InBiodiversity, ecosystem
functioning, and humanwellbeing: an ecological and economic
perspective (edsS Naeem, DE Bunker, A Hector, M Loreau, C
Perrings),pp. 49 60. Oxford, UK: Oxford University Press.
42. Cardinale BJ, Srivastava DS, Duffy JE, Wright JP,Downing AL,
Sankaran M, Jouseau C. 2006 Effects ofbiodiversity on the
functioning of trophic groupsand ecosystems. Nature 443, 989 992.
(doi:10.1038/nature05202)
43. Finke DL, Denno RF. 2005 Predator diversity and
thefunctioning of ecosystems: the role of intraguildpredation in
dampening trophic cascades. Ecol. Lett. 8,1299 1306.
(doi:10.1111/j.1461-0248.2005.00832.x)
44. Dang CK, Chauvet E, Gessner MO. 2005 Magnitudeand
variability of process rates in fungal diversity litter
decomposition relationships. Ecol. Lett. 8,1129 1137.
(doi:10.1111/j.1461-0248.2005.00815.x)
45. Naeem S, Loreau M, Inchausti P. 2002 Biodiversityand
ecosystem functioning: the emergence of asynthetic ecological
framework. In Biodiversity andecosystem functioning: synthesis and
perspectives(eds M Loreau, S Naeem, P Inchausti), pp. 3 11.Oxford,
UK: Oxford University Press.
46. Fung T, Farnsworth KD, Reid DG, Rossberg AG. 2015Impact of
biodiversity loss on production in complexmarine food webs
mitigated by prey-release. Nat.Commun. 6, 6657.
(doi:10.1038/ncomms7657)
47. Partel M, Laanisto L, Zobel M. 2007 Contrastingplant
productivity diversity relationships acrosslatitude: the role of
evolutionary history. Ecology88, 1091 1097.
(doi:10.1890/06-0997)
48. Hooper DU et al. 2002 Species diversity, functionaldiversity
and ecosystem functioning. Biodivers.Ecosyst. Funct. Synth.
Perspect. 17, 195 208.
49. Haddad NM, Crutsinger GM, Gross K, Haarstad J,Knops JMH,
Tilman D. 2009 Plant species lossdecreases arthropod diversity and
shifts trophicstructure. Ecol. Lett. 12, 1029 1039.
(doi:10.1111/j.1461-0248.2009.01356.x)
50. Scherber C et al. 2010 Bottom-up effects of plantdiversity
on multitrophic interactions in abiodiversity experiment. Nature
468, 553 556.(doi:10.1038/nature09492)
http://dx.doi.org/10.1016/j.jtbi.2013.08.003http://dx.doi.org/10.1038/srep10955http://dx.doi.org/10.1038/srep10955http://dx.doi.org/10.1073/pnas.0408424102http://dx.doi.org/10.1073/pnas.0408424102http://dx.doi.org/10.1007/s12080-010-0089-6http://dx.doi.org/10.1086/599301http://dx.doi.org/10.1086/599301http://dx.doi.org/10.1016/j.jtbi.2013.06.008http://dx.doi.org/10.1016/j.jtbi.2013.06.008http://dx.doi.org/10.1073/pnas.2434847100http://dx.doi.org/10.1111/j.2006.0030-1299.15007.xhttp://dx.doi.org/10.1111/j.2006.0030-1299.15007.xhttp://dx.doi.org/10.1111/ele.12118http://dx.doi.org/10.1111/j.1461-0248.2005.00765.xhttp://dx.doi.org/10.1111/j.1461-0248.2005.00765.xhttp://dx.doi.org/10.1073/pnas.0806823106http://dx.doi.org/10.1073/pnas.0806823106http://dx.doi.org/10.1046/j.1461-0248.2002.00381.xhttp://dx.doi.org/10.1046/j.1461-0248.2002.00381.xhttp://dx.doi.org/10.2307/1940154http://dx.doi.org/10.2307/1940154http://dx.doi.org/10.1034/j.1600-0706.2002.990201.xhttp://dx.doi.org/10.1086/303311http://dx.doi.org/10.1038/nature02554http://dx.doi.org/10.1890/03-9000http://dx.doi.org/10.1111/j.1365-2486.2009.02124.xhttp://dx.doi.org/10.1111/j.1365-2486.2009.02124.xhttp://dx.doi.org/10.1098/rstb.2012.0230http://dx.doi.org/10.1086/285380http://dx.doi.org/10.1111/j.1461-0248.2006.00978.xhttp://dx.doi.org/10.1111/j.1461-0248.2006.00978.xhttp://dx.doi.org/10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2http://dx.doi.org/10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2http://dx.doi.org/10.1890/0012-9658(2006)87[2411:CBRINF]2.0.CO;2http://dx.doi.org/10.1890/0012-9658(2006)87[2411:CBRINF]2.0.CO;2http://dx.doi.org/10.1038/nature05202http://dx.doi.org/10.1038/nature05202http://dx.doi.org/10.1111/j.1461-0248.2005.00832.xhttp://dx.doi.org/10.1111/j.1461-0248.2005.00815.xhttp://dx.doi.org/10.1038/ncomms7657http://dx.doi.org/10.1890/06-0997http://dx.doi.org/10.1111/j.1461-0248.2009.01356.xhttp://dx.doi.org/10.1111/j.1461-0248.2009.01356.xhttp://dx.doi.org/10.1038/nature09492http://rstb.royalsocietypublishing.org/
Biodiversity and ecosystem functioning in evolving food
websIntroductionModelPopulation dynamicsSpeciation events
MethodsResultsTime seriesBiodiversity and ecosystem functioning
during the initial build-up of the networksThe influence of
environmental conditions on biodiversity and ecosystem functioning
relations
DiscussionAuthors contributionsCompeting
interestsFundingAcknowledgementsReferences