Download Social and landscape effects on food webs: a

Journal of Complex Networks (2013) 1, 160–182
doi:10.1093/comnet/cnt013
Advance Access publication on 25 September 2013
Social and landscape effects on food webs: a multi-level network
simulation model
M. Scotti, F. Ciocchetta and F. Jordán∗
The Microsoft Research - University of Trento Centre for Computational and Systems Biology, Piazza
Manifattura 1, 38068 Rovereto (TN), Italy
∗
Corresponding author: [email protected]
Edited by: Jennifer Dunne
[Received on 31 January 2013; accepted on 13 August 2013]
One source of complexity in ecological systems is the hierarchical organization of parallel biological
processes. Our ‘horizontal’ knowledge describing different levels is quite massive, but the understanding of their vertical interactions is very poor. We present a toy model linking social networks, food
webs and a landscape graph. Horizontal processes refer to population, community and metacommunity
dynamics, while vertical processes connect the three organizational levels. The model is stochastic and
individual-based. We parametrized it by using reasonable empirical values found in the literature. Sensitivity analysis shows how the parameters describing the dynamics of a particular species (e.g., probability
of social tie formation with conspecific individuals, or migration rate) can affect metapopulation size and
spatial heterogeneity of all food web species. Changing the values of various parameters at any of the
three levels have commensurable effects on the population size of all species. In contrast to the general
intuition, community dynamics do not dominate population biology; social and landscape processes can
trigger greater effects than food web interactions. More rapidly changing social relationships lead to a
decrease in social network cohesion, thus impairing the feeding efficiency of consumers. In food webs,
trophic specialization provides an advantage when it contributes to avoid competition, being detrimental otherwise. Highest migration rates result in a more heterogeneous metapopulation distribution of the
generalist consumer, indirectly supporting its specialist competitor. We discuss conceptual and methodological aspects of the model, demonstrating the importance of an integrative view. We also emphasize
the relevance of vertical connections, suggesting how such a modelling framework could support conservation biology. Further studies should focus on methods to approximate external pressures with changes
in model parameters, thus allowing to characterize possible impacts on ecological systems.
Keywords: social network; food web; landscape graph; hierarchy; stochastic simulation; individual-based
modelling.
1. Introduction
The hierarchical organization of biological systems is well known, both below and above the level of
the individual organism. Still, because of the multi-disciplinary and integrative nature of the problem,
not too many studies focus explicitly on linking different organizational levels [1–3].
From a network perspective, it is clear that the structure of the social network formed by interactions among the individuals can be related to group dynamics and ecology of the population [4–6]. For
example, Lusseau [4] suggests that a heterogeneous interaction network structure increases the relative
importance of a few individuals in the group. Social structure can be related to communication among
c The authors 2013. Published by Oxford University Press. All rights reserved.
SOCIAL AND LANDSCAPE EFFECTS ON FOOD WEBS
161
the individuals over large distances: in case of elephants, the spatial dynamics of the population is also
related to the fine structure of the social network, at several levels [5]. Barton et al. [7] have shown
that social group coherence is related to predation pressure: the fragmentation of the social network of
baboon groups can increase if the density of predators is lower.
Also, interspecific interactions have effects on spatial community dynamics (see [8] for butterflies,
[9] for pitcher plants and [10] for beetles). In butterfly associated metacommunities, van Nouhuys and
Hanski [8] present the competition/dispersal trade-off and several other multi-species interactions linking the community and the landscape level. For pitcher plant metacommunities, it was shown how
different migration abilities cause species sorting and, thus, generate differences between local pitcher
plant communities [9]. A systematic study on beetle metacommunities has shown that low dispersal
rates are associated with more stable local communities [10].
Changes at landscape level can have fundamental effects on local communities and populations
[11–15]. The famous example of coyotes and shrub-living birds [13] demonstrated how habitat fragmentation results in small isolated patches where top-predators can be locally absent, triggering mesopredator release and finally the local extinction of lower-level species (birds, in this case). Isolation is
an extreme case but it can be considered as changing the migration rate to zero.
These vertical, intra-level effects tie together different organizational levels and integrate the myriads of horizontal interactions into a single multi-layer ecosystem.
The interplay of horizontal and vertical effects is an essential property of living systems and
modelling this can shed more light on better understanding the diversity and vulnerability of natural
ecosystems (and food web assembly [16]). For example, the trade-off between competition ability and
mobility [17], the local extinction–recolonization dynamics [18] or extinction following inbreeding [19]
are well-known evolutionary phenomena. Since there can be massive individual-level variability in the
frequency of inter-specific interactions (e.g., trophic habits differ between individuals, see Bolnick et al.
[20]), taking an individual-based modelling approach is quite reasonable here. It is increasingly recognized that variability itself has a great conservation value [21], since it is of extreme importance for
adaptability and evolvability. Especially in the case of small populations, focusing on mean population
values there is the risk to lose essential information on variability.
In this paper, (a) we present an individual-based, stochastic, dynamical modelling framework, where
social networks of conspecific individuals represent the building blocks of food webs that are spatially
linked in a landscape graph (resulting in a metacommunity; see Box 1). We model network dynamics
at all of these three levels. Then, (b) we simulate the behaviour of this hierarchical network model and
perform sensitivity analysis on it. Based on this, (c) we study the dynamics of the metapopulations of
each species in the food web and present their sensitivity to changing population, community and metacommunity parameters of a particular species. Since the model is very complicated and characterized
by a large number of parameters, we deliberately narrow our interest to the local perturbation of one
particular parameter set. Finally, (d) we discuss the advantages and caveats of this framework and argue
for its importance in future conservation science.
2. Methods
2.1
The model
We constructed a hierarchical model where population, community and metacommunity dynamics are
simulated (Fig. 1). Population demography is regulated by birth and death rates. Conspecific individuals can be linked to each other to form a social network. The social networks of various species are
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Box 1 . Glossary
Primary producers: species that do not feed on other species (e.g., most of the plants).
Consumers: species feeding on other species (e.g., animals and carnivorous plants).
Top-predators: species that no other species feeds on (i.e., species at the top of the trophic chain).
Social network: a network of individuals as nodes, where edges are social relationships (e.g., interactions oriented towards food search and processing, or responsible for mechanisms of group vigilance/predator avoidance).
Food web: a network where nodes stand for species (or trophic components), and edges represent
predator–prey (trophic) interactions.
Landscape graph: a network of habitat patches as nodes, with edges representing the ecological
corridors that link the patches.
Local population: conspecific individuals coexisting in a habitat patch (i.e., a discrete area of habitat).
Local community: coexisting local populations in a habitat patch. These local populations belong
to different species that interact in a single habitat patch.
Metapopulation: a set of local populations belonging to a species and linked by the regular dispersal
of individuals between them.
Metacommunity: a set of local communities linked by the regular dispersal of individuals of several
species between them.
Local extinction: the disappearance of a local population from a habitat patch.
Global extinction: the disappearance of a species from all habitat patches it inhabited previously.
Network topology: the neighbourhood relationships describing what is connected to what, independently of all other kinds of information. It illustrates the structure of the network, showing how the
nodes are connected with each other.
Complete graph: a network where each node is linked to all other nodes.
dynamical: ties can be formed and broken. Besides creating and removing social ties, individuals are
involved in food web interactions (i.e., trophic relationships with individuals belonging to other species).
We consider food webs composed of five species: the top-predator E consumes specialist (C) and generalist (D) prey that feed on a single (A) or two (A and B) primary producers, respectively. This food
web topology has been well-studied earlier [22]. The five habitat patches in the fully connected (i.e.,
complete) landscape graph contain these food webs of fixed topology. Possible resources are defined,
for each consumer, by the fixed topology of the food web. However, the number of individuals and
the strength of interspecific interactions do differ and are dynamical. Migration rates that regulate the
mobility of individuals among the five patches are determined for each species.
Demographic parameters contribute to change the population size in the five patches, thus affecting trophic relationships and spatial dynamics. Structural properties of the social network influence
food web dynamics: more dense social networks provide a positive feedback at community-level by
SOCIAL AND LANDSCAPE EFFECTS ON FOOD WEBS
163
Fig. 1. The hierarchical structure of the model. Every population is composed of a social network of individuals (shown for
species D). In each patch, the local community consists of five species: A and B are primary producers, C and D are primary
consumers and E is top-predator. Five patches constitute the fully connected landscape graph.
both increasing the efficiency of the predators in capturing prey, and enhancing the predator avoidance.
Trophic relationships shape the population size leading to prey death and, in certain cases, predator
reproduction. Migration rates mould population size in each patch and spatial distribution of species at
landscape-level.
2.1.1
Structure
2.1.1.1 Population level: demographic properties and social network interactions.
Species i
is characterized by the initi initial number of individuals. For each species, initial population size
(popi,t = initi , at time t = 0) is spatially homogeneous in all five patches and differs only between
species. Population dynamics is governed by (spatially homogeneous) birth (bi ) and death (di ) rates,
but can also be affected by community-level interactions (i.e., trophic relationships in the food
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webs that lead to prey death/resource removal, and can also trigger predator/consumer reproduction)
and landscape-level dynamics (i.e., migration determines the population size of species in the five
patches).
If i is a primary producer (species A and B in Fig. 1), the reproduction rate at time t + 1(rrPPi,t+1 )
is obtained by multiplying a constant birth rate (bi ) with the population size at time t(popPPi,t ) (1).
Reproduction rates of consumers (species C, D and E in Fig. 1) are always associated to feeding events
(i.e., a consumer can either ‘eat’, or ‘eat and reproduce’). The reproduction rate of consumer i at time
t + 1(rrCi,t+1 ) is computed as the product of a constant ‘eat and reproduce’ rate (erji ) with the population
size of the consumer i at time t (popCi,t ), the population size of the resource j at time t (popRj,t ) and the
ratio of the social network densities of consumer i and prey j at time t(Di,t /Dj,t ) (2).
rrPPi,t+1 = popPPi,t · bi ,
rrCi,t+1 = popCi,t · popRj,t · erji ·
(1)
Di,t
.
Dj,t
(2)
The mortality of the individuals of species j is a function of either predation or internal mechanisms
(e.g., aging). At time t + 1, the mortality of the individuals belonging to species j and eaten by the
predator i (mortj,t+1 ) is related to the population size of consumer i (popCi,t ) and resource j (popRj,t )
at time t, regulated by a constant predation rate (either ‘eat’ = eji or ‘eat and reproduce’ = erji ) and
modulated by the ratio of the social network densities involving the individuals that belong to consumer
i (Di,t ) and resource j (Dj,t ) (3a), (3b). Otherwise, internal mortality of primary producers i at time t + 1
(mortPPi,t+1 ) is computed as the product of a constant death rate (di = bi /1000) by the square of the
population size of species i at time t (popPPi,t ) (4). When i is a consumer, its internal mortality (i.e., not
related to any feeding interaction) at time t + 1 (mortCi,t+1 ) is linearly proportional to population size
at time t (popCi,t ; death rate = dCi ) (5). Death by predation and other causes do not concurrently apply
and represent two separate events.
mortj,t+1 = popCi,t · popRj,t · eji ·
Di,t
,
Dj,t
mortj,t+1 = popCi,t · popRj,t · erji ·
Di,t
,
Dj,t
(3a)
(3b)
2
mortPPi,t+1 = popPPi,t
, ·di ,
(4)
mortCi,t+1 = popCi,t · dCi .
(5)
Conspecific individuals of species i can establish social connections with each other. Social connections
of population i are dynamically added with a social tie formation rate pi (that stands for the probability
of adding a non-existing link to the social network) and decrease by rate qi (probability of removing an
existing link from the social network). For the population of species i, the effective rates of formation
(linkFi,t+1 ) and removal (linkRi,t+1 ) of social connections at time t + 1 depend on the number of missing
(non_linksi,t ) (6) and existing(linksi,t ) (7) social links at time t, respectively.
linkFi,t+1 = pi · non_linksi,t ,
(6)
linkRi,t+1 = qi · linksi,t .
(7)
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165
At time t, the social network density of the individuals of species i (Di,t ) is computed as the ratio between
existing links (2 linksi,t ; we doubled the number of links because, in presence of an undirected graph,
each social interaction corresponds to two non-zero entries in the adjacency matrix) and all possible
social connections (popi,t · (popi,t − 1); self-loops are not allowed) (8). We also added a constant value
to the denominator (0.001) to avoid a division by zero (see Supplementary Materials S1).
Di,t =
2 · linksi,t
.
[popi,t · (popi,t − 1) + 0.001]
(8)
In stochastic simulations, some variance can be observed when comparing the social network densities
(related to the same population) during different runs, even if we used the same constant values for
social link formation and removal (pi = qi ). The social network needs not to be a connected graph
(isolated individuals can exist); its density drives population dynamics and affects trophic interactions
(see equations (2–3b)).
2.1.1.2 Community level: trophic interactions in the food web.
In the food web, we considered the
direction of trophic links, and dynamical effects can spread in both bottom-up and top-down directions.
Food web connectance (C) in a community composed of S species is computed as the ratio between
existing trophic links (l) and all of the possible trophic interactions in the food web (S 2 ; i.e., also selfloops are allowed) (9). Food web connectance is preserved in all landscape patches and equals 0.2
(as we considered directed trophic links that leave the prey and enter the predators); it represents the
architecture of all the food web links that dynamically govern predator–prey interactions.
C=
5
l
=
= 0.2.
S 2 52
(9)
Food web links are characterized by well-defined base rates of interaction. We denoted these values
by the names of species involved in the trophic relationship (e.g., eij stands for the rate of the feeding
interaction involving the consumer j and the resource i, in absence of reproduction).
At time t, the population sizes of consumer j (popCj,t ) and resource i (popRi,t ) influence the probability of a trophic interaction involving the two species. This probability can simply regulate trophic
activities that satisfy the energetic needs of the consumer (eatj,t+1 ) (10a) or also cause its reproduction
(eat_reprj,t+1 ) (10b). These events are positively and linearly regulated by the social network density of
j (Dj,t ), while a linear negative relationship exists with the social network density of i (Di,t ). Constant
base rates regulate in a positive and linear way the ‘eat’ (eij ) and ‘eat and reproduce’ (erij ) dynamics.
eatj,t+1 = popCj,t · popRi,t · eij ·
Dj,t
,
Di,t
eat_reprj,t+1 = popCj,t · popRi,t · erij ·
Dj,t
.
Di,t
(10a)
(10b)
Both of these equations also serve to quantify the probability of prey i death following a feeding event;
see analogies with equations (3a) and (3b). Equation (10b) also refers to reproduction rates of predator
j; see equation (2).
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2.1.1.3 Metacommunity level: migration rates in a complete landscape graph.
Each species i
forms a metapopulation, where the migration rate is mi (for simplicity, migration rates are spatially
homogeneous). The words ‘migration’ and ‘dispersal’ can be used interchangeably, but in the text we
always refer to ‘migration’. The landscape graph is a complete graph for each species, thus, we modelled
metacommunities from a mass effect perspective (i.e., we focused on the immigration and emigration
dynamics of local populations, and not on landscape graph topology) [23–25]. At time t + 1, effective migration rate of species i (mri,t+1 ) is proportional to a constant migration rate parameter (mi ) and
changes according to the population size at time t (popi,t ) (11). All events that dynamically modify the
population size of the species in the five patches contribute to affect the intensity of migration rates
(e.g., reproduction and mortality rates at population level, and strength of feeding relationships in the
food web community).
(11)
mri,t+1 = popi,t · mi .
2.1.2 Dynamics Simulations were carried out with BlenX, a programming language that is based on
the process calculus Beta-binders [26]. BlenX language is stochastic and the programme is executed
with the Gillespie SSA algorithm [27]. In BlenX, individuals are represented by boxes. These boxes are
composed of a set of interfaces/binders (i.e., binding sites) that allow interactions between individuals
(e.g., the interfaces contribute to establish social interactions with conspecific individuals, or define prey
preference/affinity). Boxes also have an internal programme that drives the behaviour of each individual
(e.g., it includes instructions for birth/mortality rates, or defines the probability of migration).
The BlenX code is composed of three files (see Supplementary Materials S1): the first defines the
model (.PROG); the second declares the functions (.FUNC); the third summarizes the types (.TYPES).
The .PROG file is made up of the header info (they indicate the number of steps that the simulator
will schedule and execute, and specify a delta parameter to record events only at a certain frequency),
a list of declarations (which summarizes: boxes—e.g., species individuals; interaction capabilities—
e.g., they define predator–prey interactions or determine the formation of new social connections with
conspecific individuals; internal control mechanisms—e.g., reproduction following the feeding activity), events (statements that have to be executed with a specified rate and/or when some conditions
are satisfied—e.g., ‘spontaneous’ reproduction of the primary producers), the keyword run and a list
of starting individuals (where the initial population size of each species in the five patches is set). The
.FUNC file holds the constant definitions (e.g., feeding preferences of a predator for its prey) and quantifies rate functions (i.e., interaction rates or probability of events that are computed with a function,
instead of being simply defined by a constant value—e.g., the migration rate of a species is given by the
product of the population density in a patch with the constant migration rate parameter). The .TYPES
file stores all the binder identifiers that can be used, and the affinities between binders associated with
a particular identifier (e.g., it summarizes that species D can feed on A and B, by also declaring feeding preferences—i.e., affinities—that characterize each trophic interaction). Affinities can be defined by
simple constant values or more complex functions. They govern the dynamical evolution of the model
by affecting interactions between individuals (that are characterized by specific binder identifiers) and
do not require to know the exact address of the interacting individuals.
Three main advantages are related to the use of BlenX: (a) it permits avoiding any global policy on
the usage of names in order to make individuals interact; (b) it relaxes the style of interaction of exact
name pairing; (c) it allows composability (i.e., models can be built in a modular way), with interaction information listed in a separate file (.TYPES) that can be edited or modified without altering the
programme (.PROG file).
SOCIAL AND LANDSCAPE EFFECTS ON FOOD WEBS
167
In BlenX, we implemented an individual-based description [28–30] of the hierarchical system. This
allows performing stochastic simulations based on simple kinetic laws between the boxes representing
the organisms [31]. In the model, primary producers have a net positive reproduction rate (given by the
positive difference between birth and death rates), and they are assumed to reproduce autonomously (1).
Animals have a net negative reproduction rate, but they can reproduce with some rate after eating (i.e.,
they have a fixed death rate that is independent from trophic interactions, while reproduction is constrained by the occurrence of feeding activity). In absence of trophic interactions, the population size
of primary producers would continuously increase (i.e., they are not limited by resource availability),
while consumers would go to extinction. Feeding interactions contribute to keep the equilibrium where
primary producers do not exponentially grow, and consumers do not go extinct. Social tie formation
and interspecific (trophic) interactions are described as affinities between boxes, while migration is represented by changes in internal states of the boxes. We adopted simple kinetic rules to describe trophic
interactions. A trophic interaction is always proportional to the population size of prey and predators.
It leads to the death of the prey and, possibly, to the reproduction of the predator (see equations (10a)
and (10b)). We did not consider other functional responses (e.g., Holling types II and III) or asymmetric
feeding interactions (e.g., we did not model small herbivores that damage large and modular plants by
reducing their mass, without leading to death).
2.2
The simulations
For simulating the dynamics of the hierarchical system, we needed a parameter set that allowed all
populations in the five patches to persist. First, we gathered empirical values from literature for the
parameters that are essential to describe the dynamics. This dataset served to construct a preliminary
‘base model’. Then, we evolved the parameters of the ‘base model’ set through particle swarm optimization (PSO) [32]. We assembled a ‘reference model’ with all populations at equilibrium (i.e., no species
go to extinction or continuously grow during simulation runs). Finally, we used the ‘reference model’ to
carry out sensitivity analysis (with a focus on the generalist species D). We aimed at understanding the
impact of population-, community- and metacommunity-level parameters on metapopulation size and
spatial heterogeneity.
2.2.1 Parameter search All parameters we used vary in nature among different species and in different ecosystems. There is no straightforward way to build a ‘universal’ model based on typical parameter
values for social link formation, predation and migration. Apart of variability and lack of data, the available datasets often describe different systems; there is no hope to find all necessary information about a
single, particular three-level hierarchical system. Data at different levels of the model typically describe
different kinds of systems: most social network data represent vertebrates or insects [4], most food webs
describe wet ecosystems [33] and most landscape ecological studies focus on some particular organisms
like carabids [34].
Data from literature include details concerning population size in landscape patches, social network
interactions (i.e., density of the network and probability of social tie formation), food web structure
(i.e., connectance) and dynamics (strength of trophic interactions), and landscape graph architecture
(density of the networks) and dynamics (migration rates). These values served to assemble the ‘base
model’ which was completed with arbitrary birth and death rates (see Table 1 for numerical values and
references). In certain cases, the values in the ‘base model’ correspond to what is in the literature (i.e.,
food web connectance equals 0.2—see equation (9)—and fits well with a realistic range). Migration
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Table 1 The values of the parameters found in literature and used in the ‘reference model’. Population level (demography) : for each species we listed the initial population size (init) in the five patches;
birth (b) and death (d) rates were arbitrary chosen and consumers (i.e., species C, D and E) cannot
reproduce in absence of feeding activity; death rates of consumers correspond to their base birth rates
(see Supplementary Materials S1). Population level (social networks): we set a constant rate of social
tie formation and removal (p = q); density of the social networks (DS ) dynamically changes during
simulations and this is why no values are indicated for the ‘reference model’. Community level (food
web): feeding rates can either simply determine prey death (i.e., eAC , eAD , eBD , eCE , eDE ) or be also
responsible for the consumer reproduction (i.e., erAC , erAD , erBD , erCE , erDE ); food web connectance
(C) does not affect system dynamics, but defines the architecture of the five food web interactions. Metacommunity level (landscape graph): migration rates in the ‘reference model’ (m) are representative of
the literature values; the density of the landscape graph (DL ) equals 1 (i.e., the landscape graph is a
complete network). Food web connectance and network densities (for social network and landscape
graph) are dimensionless. All the other parameters are expressed as probabilities, except the initial
population size (which indicates the number of individuals)
Literature
Parameter Value Reference
Population level (demography)
init
14
[35]
21
[36]
94
[37]
127
[38]
b
d
Population level (social network)
p (and q)
0.77
[37]
Ds
0.15
[39]
0.37
[36]
Community level (food web)
e
0.001
[40]
0.008
[41]
0.01
[42]
0.52
[43]
C
0.1
0.11
0.17
‘Reference model’
Species A
Species B
Species C
Species D
Species E
250
249
253
245
252
0.2722
0.0003
202
203
195
196
198
0.1199
0.0001
150
145
153
148
154
170
180
190
170
170
60
56
53
54
56
0.0449
0.2369
0.0810
0.1
0.1
0.1
0.1
0.1
eAC
0.0003
erAC
0.0008
eAD
5.6020E−05
eBD
2.8988E−06
erAD
0.0003
erBD
0.0006
eCE
0.0003
eDE
1.7335E−05
erCE
6.9924E−05
erDE
0.0004
[44,45]
[33]
[46]
(continued)
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Table 1 Continued
Literature
Parameter
Value
Reference Species A
Metacommunity level (landscape graph)
m
0.5
[47]
0.001
0.01
[48]
0.15
[49]
0.23
[50]
DL
0.18
[51]
0.0027
[52]
‘Reference model’
Species B
0.001
Species C
0.03
Species D
0.01
Species E
0.08
rates found in the literature range from 0.01 to 0.5; we used values in this range (0.01–0.08) for species
at higher trophic levels (i.e., species C, D and E) but values smaller by an order of magnitude (0.001)
for the lower trophic level species. The reason is that most literature data describe lower migration rates
for species at lower trophic levels [53,54].
Since we aimed to perform sensitivity analysis in a close to equilibrium state, we needed to refine
our initial parameter set (without this, several components can go extinct or increase exponentially,
making sensitivity analysis meaningless and impossible). We applied an evolutionary approach based
on PSO [32] to evolve the parameter set of the ‘base model’. Once a proper fitness function is defined
(i.e., a stable behaviour of the system), the PSO algorithm iteratively selects the most promising regions
in the parameter space until convergence criteria are met. Every parameter guess is evaluated using the
fitness function on the results of stochastic simulations. By using this evolved parameter set we defined a
‘reference model’ (see Table 1). Simulation outcomes of the ‘reference model’ are much more consistent
than before and ready for meaningful sensitivity analysis. Such a hierarchical dynamical model can
hardly be created by using much less parameters. However, because of the high number of parameters,
the parameter space is huge and it is clearly impossible to systematically map it. One option is to
sample it in a mathematically defined way (which is ‘biologically blind’). Another option is to map the
neighbourhood of biological datasets (which is technically probably less elegant). The latter approach
could be favoured by biologists, but because of the general lack of data, it is still simply impossible. We
chose a hybrid approach: we tried to define biologically meaningful values and performed a standard
screening of parameters. Although our main objective was relying on a single parameter set that allowed
populations to persist, we also aimed at selecting this set in the most realistic way (this is why we started
with real parameters from the literature, and then evolved the parameter set through PSO).
2.2.2 Sensitivity analysis. To carry out sensitivity analysis we focused on the dynamics of species D.
We aimed at analysing the sensitivity of all species to changing six parameters that govern the dynamics
of D at the three hierarchical levels. At population-level, we modified the initial number of individuals
(i.e., initial population size: initD ), the death rate (dD ; see equation (5)) and the probability of social
tie formation and removal (pD and qD ; see equations (6) and (7)). At community-level we analysed the
consequences of generalist vs. specialist trophic activities (ratio of D consumption rates, with respect
to species B and A: eBD /eAD ; see equation (10a)), and impacts related to changes in predation losses
to predator E (eDE ; see equation (10a)). To test the relevance of metacommunity-level dynamics we
checked different migration rates (mD ; see equation (11)). We modified the parameters of the ‘reference
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M. SCOTTI ET AL.
model’ to perform sensitivity analysis. We always tested 15 alternative values to explore the surrounding
of the 6 ‘reference model’ parameters (i.e., the average of the scanned parameter values was close
to the parameter value in the ‘reference model’, except for the social tie formation and the feeding
preferences of D; often, we used the ‘reference model’ value as the barycentre of the scanned ones; see
Supplementary Materials S2).
For each parameter value we ran 100 simulations (i.e., a set of 15 values required 1500 simulation
runs, for testing the sensitivity to a specific parameter). We sampled the time-series after 60 steps.
Based on the chosen parameter values, this simulation time corresponds to the time-scale of 2 months.
To evaluate the results of the simulations, only the population size in the second-half of the time series
was used (i.e., after a supposed transient phase). Average population size and coefficient of variation
(CV; i.e., the ratio between standard deviation and the mean) were computed for each species in the five
patches, using the data extracted from the 100 simulations (i.e., they were measured over the second-half
of the time series; see Fig. 2(a)). This strategy is the best as it avoids too volatile results (e.g., by using
only the last point of the time series, the results could be strongly affected by the initial conditions) and
minimizes risks of transient dynamics (i.e., possible limit associated to the analysis of the entire time
series).
Using the average and the CV over the second-half of the 100 time series, we ended with two
sequences of 25 values (Fig. 2(b)). They describe the sensitivity analysis outcomes for a scanned value
of a specific parameter. To summarize sensitivity analysis of each parameter we created two matrices
(one for the average values and the other for the CVs) of 15 rows (one for each value scanned) and
25 columns (showing results for five species in five patches). Response variables were finally extracted
from the matrices obtained for the six parameters through simulations (i.e., six matrices describing
average values and six matrices summarizing CVs). In case of average values, response variables are
classified as metapopulation size and spatial heterogeneity (Fig. 2(c)). Metapopulation size refers to
the row sum of the five average population sizes in the five patches, while the spatial heterogeneity
quantifies the row CV of the five average population sizes in the five patches. We also measured sum
and spatial heterogeneity (i.e., CV) of the intra-patch variability.
3. Results
We measured fluctuations in metapopulation size and spatial heterogeneity of five species distributed
among five habitat patches. To quantify the effects of population, community and metacommunityrelated mechanisms we performed sensitivity analysis on parameters describing the behaviour of species
D. For each species in the five patches, we computed average and CV of the population size, over the
second-half of the simulated time series (see Supplementary Materials S3). We found that food web
processes have the weakest effects on metapopulation size and spatial distribution of species, while
parameters regulating population and metacommunity dynamics are of at least comparable magnitude.
In Fig. 3, we illustrate how the metapopulation size of D (scenario ‘MS’, Fig. 2(c)) is modulated by
changes in: frequency of social tie formation and removal (population-level); degree of feeding specialization (community-level); intensity of inter-patch migration (metacommunity-level). Highest rates of
social tie formation generate less cohesive social networks, resulting in smallest metapopulation size.
Species D feeds on species A and B; it is the only consumer of B, while it competes with species
C for A (Fig. 1). We explored a gradient of feeding solutions ranging between the specialization on
either A or B. All the simulated feeding strategies have a weak impact on the average metapopulation size of species D (i.e., they are responsible for changes in the range of ∼3%), showing a weaker
effect than the probability of social tie formation (for which a drop from more than 26 individuals to
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Fig. 2. Sensitivity analysis. We evaluated the effects of six parameters that describe species D dynamics at three hierarchical
levels (population, community and metacommunity). (a) For each parameter we checked 15 values by running 100 simulations
per value (i.e., altogether we performed 1500 simulations for each parameter). (b) Consequences on the population size of the
five species in the five patches were measured as average or CV over the second-half of the 100 time series simulated for each
value. For each parameter, we obtained two matrices composed of 25 columns (five species in five patches) and 15 rows (one
for each checked value). (c) Metapopulation size refers to the sum of the five average population sizes in the five patches and
spatial heterogeneity quantifies the CV of the five average population sizes in the five patches. We also estimated the sum of the
intra-patch variability (row-sum of the five CVs in the five patches) and the spatial heterogeneity of the intra-patch variability
(CV of the five CVs in the five patches).
<16 is observed when moving from PD = 0.1 to PD = 0.3). Strict specialization on A is detrimental,
while largest metapopulation sizes correspond to diets more specialized on B. Generalist trophic habits
(i.e., at intermediate values of the x-axis) often lead to a large metapopulation size, although a minimum is observed when the feeding preference of D for A equals 70% (eBD /eAD = 0.3/0.7 = 0.429).
An optimum range of migration rates allows better persistence of species D, while too intense interpatch movements impair the metapopulation size. The peak in the metapopulation size is in the range
of biologically realistic values (0.01 mD 0.5). Effects of changes in other parameters describing
demography and community-level dynamics of species D are shown in Supplementary Materials S4.
Initial local populations determine small impacts on the metapopulation size of D. A sharp decrease in
the metapopulation size of D corresponds to highest mortality rates; this intuitive pattern contributed to
validate the soundness of the model structure. Low predation rates of the top-predator E are associated
to largest metapopulation sizes of D.
Besides characterizing the impacts on metapopulation size, we quantified the consequences on spatial heterogeneity (see Fig. 4 that refers to scenario ‘SH’ of Fig. 2(c)). In case of social tie formation and removal, spatial distribution displays a rather regular pattern that is independent of the social
network density (i.e., on average, we observed differences accounting for 10% of the metapopulation
size); exceptions correspond to PD = 0.3 and PD = 1.0. Highest spatial variability is found with trophic
specialization, while a more predictable spatial distribution matches the generalist trophic behaviours.
Migration rates below the threshold of mD = 0.5 correspond to spatially homogeneous distributions;
beyond this limit, the populations are unevenly distributed among the five habitat patches. Supplementary Materials S5 includes plots on spatial heterogeneity controlled by demographic and communitylevel parameters. Lowest heterogeneity is observed with highest death rates. A more heterogeneous
metapopulation distribution (i.e., spatial specialization) is related to intermediate sizes of initial local
populations and highest predation rates of E. In Supplementary Materials S6 and S7, we show total
intra-patch variability and spatial heterogeneity of the intra-patch variability (see scenarios ‘IPV’ and
‘SHIPV’, Fig. 2(c)).
We also investigated the consequences on the metapopulation size of different food web species
(see Fig. 5). More rapidly changing social relationships impair the feeding activity of D, with an advantage for the primary producer B; this triggers a (bottom-up) cascade effect (starting from D), ending with
smallest metapopulation size for the top-predator E. Specialization on the primary producer A (which
is a resource shared with C) and more generalist trophic behaviours have detrimental effects for species
D. A direct positive mechanism regulates metapopulation size of B, while indirect effects prevail in the
dynamics of top-predator E (which preferentially prey on C; prey C over-competes with D when this
latter is more generalist; see Supplementary Materials S8). Highest migration rates determine a sharp
decrease in the metapopulation size of D; a cascade effect depletes top-predator E metapopulation size,
while species C over-competes and increases (i.e., apparent competition).
173
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35
26
27.6
30
20
27.5
# ind
22
# ind
# ind
24
27.4
10
27.3
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.05 0.1 0.2
probability of social tie formation
20
15
18
16
25
0.5
1
2
5
10
0.0
20
0.2
ratio of consumption rates B/A
0.4
0.6
0.8
1.0
1.2
migration rate
Fig. 3. Sensitivity of the metapopulation size of species D to parameters describing its dynamics at three hierarchical levels. For
the ratio of consumption rates B/A, the x-axis is in log scale.
0.15
0.20
3.0
0.14
2.5
0.13
0.15
0.10
0.05
0.12
2.0
0.11
1.5
0.10
1.0
0.09
0.5
0.08
0.2
0.4
0.6
0.8
1.0
1.2
probability of social tie formation
1.4
0.0
0.05 0.1 0.2 0.5 1 2
5 10
ratio of consumption rates B/A
20
0.0
0.2
0.4
0.6
0.8
1.0
1.2
migration rate
Fig. 4. Spatial heterogeneity of species D in response to changes in the dynamics at three hierarchical levels. The x-axis in the
plot illustrating the ratio of consumption rates B/A is in log scale.
4. Discussion
The multi-level network simulation model illustrates the vertical (inter-level) relationships in the system. We constructed the model starting from real data that refer to different ecological systems, with the
objective of studying how changes in a particular hierarchical level can affect the others (e.g., changed
social network cohesion influencing metapopulation size and spatial distribution).
Social network theory has been recently suggested as a promising approach in behavioural ecology
[55]. Group living can involve cooperative hunting [56] and information transfer about the location of
high-value food sources [57]. Animal sociality can result in vigilance with information transfer (e.g.,
via alarm calls or predator inspection), thus enhancing predator avoidance and increasing foraging efficiency [58].
In our hierarchical model, populations characterized by more intense social tie dynamics are endangered because, on average, display lowest social network densities (i.e., less cohesive networks). Given
the structure of the model (see equations (10a) and (10b)), sparse social networks reduce the efficiency
of consumer feeding activity (thus simulating possible consequences of less cohesive social structures
on food search and processing) and impair predator avoidance (by mimicking how less cohesive social
networks can weaken mechanisms of group vigilance, group defence and confusion effect [59]). A
decrease in the metapopulation size of D emerges in presence of more intense social dynamics (Fig. 3);
in these conditions, a concurrent level of variability is preserved in spatial distribution (Fig. 4). More
intense social relationships result in sparse social networks, without triggering clear changes in spatial
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27.3
4830
4795
27.2
4810
4790
# ind (C)
# ind (B)
# ind (B)
4820
4785
27.0
4800
4780
4790
26.9
4775
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.05 0.1 0.2
probability of social tie formation (D)
0.5
1
2
5
10
20
0.0
0.4
0.6
0.8
1.0
1.2
migration rate (D)
35
27.6
30
22
20
# ind (D)
# ind (D)
24
# ind (D)
0.2
ratio of consumption rates B/A (D)
26
27.5
27.4
10
27.3
16
0.2
0.4
0.6
0.8
1.0
1.2
0.05 0.1 0.2
1.4
probability of social tie formation (D)
25
20
15
18
0.5
1
2
5
10
20
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.0
1.2
migration rate (D)
ratio of consumption rates B/A (D)
27.0
26
28
26
# ind (E)
22
# ind (E)
26.5
24
# ind (E)
27.1
26.0
22
20
25.5
20
24
18
25.0
16
18
0.2
0.4
0.6
0.8
1.0
1.2
probability of social tie formation (D)
1.4
0.05 0.1 0.2
0.5
1
2
5
10
ratio of consumption rates B/A (D)
20
0.0
0.2
0.4
0.6
0.8
migration rate (D)
Fig. 5. Metacommunity-level sensitivity to changes in species D dynamics (at three hierarchical levels). Impacts are measured as
consequences on metapopulation size; x-axes in the plots relative to feeding preferences of D are in log scale.
distribution. Also Pacala et al. [57] observed that high interaction rates can cause social groups to pursue unprofitable tasks. This finding is in agreement with our modelling outcome, although Pacala et al.
mainly focused on the effects of social group size on social interactions and information exchange.
They pointed out how the adaptability of larger groups to changing environment is likely to be more
efficient as per capita rates of social interaction can increase with group size. However, they also showed
that more intense social relationships can be detrimental for large groups (with population size larger
than 100 individuals) as individuals become more involved in conspecific interactions at the expense of
adapting to environmental conditions. The effects of such an unbalanced activity are more pronounced
for large groups than for a small one (i.e., with population size smaller than 100). We found many similarities with our results where the initial population size of species D (in each patch) is well above 100
individuals (see Table 1), and the increase of tie formation and removal rates leads to a sharp decline of
the metapopulation size (Fig. 3). Moreover, our simulations stabilized the population size of species D
SOCIAL AND LANDSCAPE EFFECTS ON FOOD WEBS
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below an average value of 10 individuals per patch. This happened in presence of very intense social
relationships and is consistent with the findings of Pacala and colleagues. Given the same level of
social activity, Pacala et al. described groups with 10 individuals as more stable than larger ones; their
findings could justify the fact that our model reached a new equilibrium with smaller population size
when individuals pertaining to species D were involved in more frequent social relationships.
To better understand whether less cohesive social networks of species D have more effect on the
impairment of foraging efficiency or predator avoidance, we studied the metapopulation size of other
species in the system (Fig. 5). The primary producer B benefits from the decreased feeding activity
of its unique consumer D. D feeds with less efficiency on B and decreases its metapopulation size.
This outcome is in agreement with the idea that individuals involved in too intense social relationships
tend to undermine their adaptation to environmental conditions [57], thus failing to efficiently feed on
resources. This generates a bottom-up effect that determines the concurrent drop in the metapopulation
size of the top-predator E. The top-predator cannot offset this trend by simply feeding on D with more
efficiency (i.e., this could be the consequence of the fact that it preserves its social network topology,
thus being favoured by less cohesive social structures of D). Top-predator survival is therefore limited
by the availability of the resources, rather than receiving an advantage by highest prey vulnerability.
We observed a bottom-up regulation that, on the top-predator E, has analogous consequences to what
is observed for pelagic fish in marine ecosystems [60]. The structure of our model includes the chance
that such a kind of mechanism also originates from species social behaviour (and can be of comparable
magnitude to other demographic-, community- and metacommunity-level effects; e.g., sensitivity to
death rates and migration rates; see Fig. 3 and Supplementary Materials S4), rather than being solely
regulated by food availability.
Trophic specialization of D generates two contrasting results when considering the effects on
metapopulation size (Fig. 3). However, both of the cases are characterized by higher levels of spatial heterogeneity if compared with scenarios based on more generalist behaviours (Fig. 4). In the toy
model as in real ecosystems, specialists tend to specialize on a specific habitat patch, while generalists
use a greater diversity of habitat patches [61,62].
Several studies have been dedicated to a better understanding of the ecological traits that exacerbate
the vulnerability of species to extinction. Within this framework, specialization and small population
size are both believed to enhance the risk of extinction [63]. Our results confirm that specialization
is the most dangerous strategy for species persistence, but only when D exclusively feeds on A (i.e.,
when it competes with C; see Fig. 3). This finding is in agreement with the literature suggesting that
specialization is associated with highest risks of extinction [63,64]. However, specialization on B shows
opposite and partially contra-intuitive effects: it contributes to raise the metapopulation size of both
D and B, also sustaining the growth of the top-predator E (Fig. 5). The model illustrates how being
specialized can be an efficient strategy under certain conditions (i.e., D avoids to compete with C). The
positive feedback received by E is a consequence of the increased metapopulation size of D. A possible
justification for the concurrent raise of B can be related to the structure of the social relationships
of D. Larger metapopulations of D are not accompanied by a proportional increase in the number of
social connections. Lower social network density found for the scenario of extreme specialization on
B partially reduces the feeding efficiency of D. This complex pattern involves the spread of social
network effects beyond the population-level dynamics and further demonstrates the relevance of the
hierarchical approach. Although dietary specialization is mainly associated to highest risk of extinction,
the dynamics simulated by our model is not unrealistic. For example, the persistence of specialized
groups, at the expense of species implementing more generalist strategies, is described for ants in a
fragmented landscape [65].
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The specificity of the evolved parameter set (i.e., the fact that the model reacts with extreme sensitivity to small changes in certain parameter values; see in Table 1 the initial predation rates among
the five species in the ‘reference model’) can suggest we are close to a local minimum. Therefore, the
predation rates adopted in our model can show the extremes of the system, failing to be fully representative of its ‘average’ behaviour. This hypothesis is further corroborated by the fact that the sensitivity
analysis carried out for the community-level parameters (ratio of D consumption rates and predation
losses to predator E; see Figs 3 and 4, and Supplementary Materials S4 and S5) does provide less robust
patterns than in the cases of population- and metacommunity-level parameters. This can be due to the
fact that small changes in the predation rates push the system away from the equilibrium found with
PSO. However, small changes (in absolute terms) observed with sensitivity analysis of communitylevel parameters could also stand for a highly representative configuration, despite the specificity of the
evolved parameter set (i.e., they activate much less penetrant consequences on metapopulation size and
spatial heterogeneity than population- and metacommunity-level parameters).
Understanding the evolution of migration rates and the wide diversity exhibited by animals and
plants are major subjects of study in theoretical ecology. Concrete applications can involve the investigation of the mechanisms that lead to changes in the migration rates [66] and a better quantification
of the extinction risks [67]. Many publications claimed for an optimum migration rate that emerges as
a trade-off between energy consumed for migration and advantages associated to it (e.g., benefits can
involve rescuing a metapopulation from extinction in a deteriorating landscape, or minimizing the predation risks) [66,67]. Other researchers showed how discontinuous areas (i.e., habitat fragmentation)
threaten species persistence; in this case, extinction rates fall sharply when migration is increased from
zero, but stabilize at highest migration rates [68]. Nonetheless, high migration rates can be as detrimental as low migration rates, for the fate of the metapopulation [69].
In our model, five landscape patches were connected in a complete graph (i.e., there are no effects
of topological fragmentation). We simply modulated the intensity of migration for species D, thus mimicking possible consequences of fragmentation through a gradient of migration rates. For each scenario,
we simulated homogeneous migration rates in the whole landscape graph. We observed how largest
metapopulation sizes correspond to low-intermediate migration rates (Fig. 3). Highest migration rates
do not contribute to synchronize the populations that are dispersed in the five patches (i.e., there is
highest spatial heterogeneity; see Fig. 4), and also decrease the metapopulation size. Our results corroborate previous findings: an increase in the migration rate is not automatically associated to more
persistent metapopulations [69]. The asynchrony generated by our simulations does not correspond
to a concurrent raise in the metapopulation size. A possible explanation for the weak positive impact
of migration on metapopulation size could be due to population density dependence [70]. Ives et al.
[70] adopted a stochastic framework for investigating the effects of migration on population density.
They concluded that the effect of migration on the population size is enhanced by (a) weak density
dependence, (b) high environmental variability regulating population growth rates and (c) lack of synchrony between the populations in the habitat patches. In our model, we considered constant birth
and death rates. Reproduction and mortality rates of consumers change as a function of their population size. They are also affected by the social networks of resources and consumers, but we did not
explicitly consider the role of environmental variability (see equation (2)). Asynchrony emerges with
highest migration rates (Fig. 4) but, contrary to what showed by Ives et al. [70], it is not enough for
raising the metapopulation size. Therefore, we argue that intra-population competition (i.e., density
dependence) can be responsible for the decrease of the metapopulation size. Another possible explanation of the discrepancies between our study and the findings of Ives et al. can depend on the structure of the model. As observed with the sensitivity analysis of social tie formation rates, the feeding
SOCIAL AND LANDSCAPE EFFECTS ON FOOD WEBS
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activity of D is highly compromised by low social network densities (see the small metapopulation
size in Fig. 3). More heterogeneous spatial distributions (as the ones obtained with high migration
rates) lead, in some patches, to extremely incohesive social structures. These result in less efficient
consumers and smaller population size if compared with scenarios with low-intermediate migration
rates.
Highest migration rates caused a more heterogeneous metapopulation distribution of the generalist
consumer, indirectly supporting its specialist competitor (Fig. 5). This is because of the apparent competition mechanism regulating the coexistence of the two consumer species (C and D) that are both
preyed upon by the same top-predator (E) [71]. The simulation framework was essential to capture such
a kind of behaviour. Based on feeding preferences (Table 1), we would conclude that species C represents the preferential prey of the top-predator, thus being the ideal candidate for establishing an apparent
competition control. Changes in migration rates of species D generate a different scenario. The more
heterogeneous spatial distribution found for species D in presence of highest migration rates is also
associated to less cohesive social structures. Given the architecture of the model (see equations (10a)
and (10b)), species D becomes a more appealing food for the top-predator E. A decrease in the population size of D is therefore associated to a concurrent negative effect on the top-predator population size,
relaxing the feeding pressure on the other consumer (i.e., species C).
5. Conclusions
We showed that, within the context of our modelling framework (model structure, parameter set and
sensitivity analysis), changes at the bottom level (social dynamics) can impact the top level (metapopulation structure). Changes in food web dynamics caused the weakest effects, and this contra-intuitive
finding illustrates the possibly similarly important role of population and landscape-level mechanisms,
as well as the need for considering vertical mechanisms.
We found that rapidly changing social relationships generated less cohesive social networks and
determined less effective consumption patterns. Other authors suggested that too intense social relationships can be detrimental of the population status, leading to lowest probability of success [57]. We also
observed that less cohesive social groups were more affected in their feeding activity, rather than being
more vulnerable to the predator attacks.
In our toy model, feeding specialization is an advantage when allows escaping competition, while
it becomes detrimental in case competition is sharpened. Although some authors showed the possible
advantages associated to a specialized feeding strategy [65], risks of extinctions are usually thought to
be dampened by generalist trophic behaviours [63,64]. We noticed how highest spatial heterogeneity is
associated to more specialized diets. Dietary specialization can provide a competitive advantage but this
tends to be localized in specific habitat patches (i.e., it results in spatial specialization) [61,62], while
generalist species are more homogeneously persistent.
An increase in the migration rates is not monotonically associated to a raise of the metapopulation
size. By simulating the consequences of a range of migration rates we found an optimum (i.e., a peak
in the metapopulation size) in correspondence of realistic values. We observed that highest migration
rates can be as harmful as the lowest ones [69]. Other researchers showed how asynchrony enhances
metapopulation size [70], but our simulations identified an opposite pattern (i.e., highest migration rates
are associated to population asynchrony but lead to a decrease of the metapopulation size). Different
criteria in model construction (e.g., the lack of environmental variability) can explain this discrepancy. Changes in migration rates also contributed to emphasize the presence of an apparent competition
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mechanism. This provided an example of how indirect vertical effects can modulate community composition (i.e., different migration rates determine a change in the social structure of populations in habitat
patches, thus affecting predator avoidance and feeding efficiency). Although these results depend on
the architecture of the model, we argue that it is not unrealistic the presence of a link connecting the
migration-dependent frequency of social relationships to population stability [55].
The presented model is, on one hand, over-simplified (e.g., sociality is represented only as the density of the social network) and, on the other hand, extremely complicated (many parameters). It was
constructed using different data sources and did not aim at providing suggestions on how to manage
a real system. Our main objective was illustrating possible interdependencies between the population,
community and metacommunity levels, and quantifying their relative importance. Other details could
be included and different equations adopted to better describe ecological processes involving the three
layers. The presented version of the model is more like a framework that helps to understand how ecological effects can spread between hierarchical levels. Potential future extensions include exploring a
larger region of the parameter space (with as much as possible real parameters). Also, the effects of
landscape topology can be easily studied by structuring the landscape graph [34,72–74]. Importantly,
we can add local instead of global determination for some parameters: for example, rates p and m
can depend on food web position of species. On the other side, increased global determination can be
explored by adding direct links between social networks and the landscape graph [75]. Modelling also
vertical effects can contribute to better understanding the direct and indirect determination in ecosystems [76–78]. However, the large number of parameters and the need for real data (see a rare example
for metacommunity data in [79]) are clear disadvantages.
Several studies aim to serve decision-making but most of them are of structural and static nature
[80]. Our modelling framework will offer the possibility for integrating multiple sources of information for strategic conservation management. If a particular population is in extinction risk, the reason
can be related to its internal structure (e.g., demography, sex-ratio, social structure), to its interspecific
interactions (predators, parasites, competitors, scarcity of food) or to its spatial behaviour (source-sink
structure, mobility, migration). Our integrative model, if realistically parametrized, can show the best
way to manage multi-level systems: sensitivity analysis can indicate the critical parameters and suggest
how to approach the problem, if able to quantify the strength of external pressures. Being able to connect changes in the values of some parameters to the magnitude of external pressures would give the
chance of measuring these pressures in the simulations. This is just a hypothetical approach we did not
implement in the manuscript. For example, if we consider a target species, pollution can decrease the
initial population size, increase the death rate or reduce social dynamics, while habitat fragmentation
can result in poor migration ability. The multi-level network simulation model can be an interesting and
promising application for conservation practice on the long term.
6. Supplementary data
Supplementary data are available at Journal of Complex Networks online.
Acknowledgments
We are grateful to Michele Forlin, Davide Prandi and Wei-Chung Liu for technical help and collaboration. Bianca Baldacci is kindly acknowledged for the graphic design contribution. We also thank the
three anonymous referees who gave very important and useful comments on the manuscript.
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