Structural network models
Structure of ecological networks is non-random. Network architecture can have a strong effect on important ecosystem properties (Mougi and Kondoh 2012, Thébault and Fontaine 2010). Many of the structural features of food-webs can be simulated using small number of simple rules. Despite this simplicity these models can often accurately reproduce some of the second order characteristics of empirical food-webs (Stouffer et al. 2005). These characteristics of phenomenological stochastic models allow for their wide applications e.g. to simulate biomass dynamics using dynamical models or study extinction cascades.
Mougi, A. and Kondoh, M. (2012) ‘Diversity of Interaction Types and
Ecological Community Stability’, Science, 337(6092), pp. 349–351. doi: 10.1126/science.1220529.
Thébault, E. and Fontaine, C. (2010) ‘Stability of Ecological Communities
and the Architecture of Mutualistic and Trophic Networks’, Science, 329(5993), pp. 853–856. doi: 10.1126/science.1188321.
Stouffer, D. B. et al. (2005) ‘Quantitative Patterns in the Structure
of Model and Empirical Food Webs’, Ecology, 86(5), pp. 1301–1311. doi: 10.1890/04-0957.
Many models with various interactions assignment algorithms have been proposed. EcologicalNetworks
provides functions to generate random ecological networks of the UnipartiteNetwork
type. Listed below are those most often used in ecological studies.
Cascade model
This model uses one abstract trophic trait. For any given consumer links can be randomly assigned to a resource species with the trait value smaller than that of a consumer.
EcologicalNetworks.cascademodel
— Functioncascademodel(S::Int64, Co::Float64)
Return matrix of the type UnipartiteNetwork
randomly assembled according to the cascade model for a given nuber of S
and connectivity Co
.
See also: nichemodel
, mpnmodel
, nestedhierarchymodel
References
Cohen, J.E., Newman, C.M., 1985. A stochastic theory of community food webs I. Models and aggregated data. Proceedings of the Royal Society of London. Series B. Biological Sciences 224, 421–448. https://doi.org/10.1098/rspb.1985.0042
cascademodel(N::T) where {T <: UnipartiteNetwork}
Applied to a UnipartiteNetwork
return its randomized version.
References
Cohen, J.E., Newman, C.M., 1985. A stochastic theory of community food webs I. Models and aggregated data. Proceedings of the Royal Society of London. Series B. Biological Sciences 224, 421–448. https://doi.org/10.1098/rspb.1985.0042
cascademodel(S::Int64, L::Int64)
Number of links can be specified instead of connectance.
References
Cohen, J.E., Newman, C.M., 1985. A stochastic theory of community food webs I. Models and aggregated data. Proceedings of the Royal Society of London. Series B. Biological Sciences 224, 421–448. https://doi.org/10.1098/rspb.1985.0042
cascademodel(parameters::Tuple)
Parameters tuple can also be provided in the form (S::Int64, Co::Float64) or (S::Int64, L::Int64).
References
Cohen, J.E., Newman, C.M., 1985. A stochastic theory of community food webs I. Models and aggregated data. Proceedings of the Royal Society of London. Series B. Biological Sciences 224, 421–448. https://doi.org/10.1098/rspb.1985.0042
Niche model
Niche model extended cascade model by introducing ranges for each consumer. In this model consumers can predate on resources which trait values are within the predators' 'niche' range.
EcologicalNetworks.nichemodel
— Functionnichemodel(S::Int64, L::Int64)
Return UnipartiteNetwork
where resources are assign to consumers according to niche model for a network of S
species and L
links.
References
Williams, R., Martinez, N., 2000. Simple rules yield complex food webs. Nature 404, 180–183.
nichemodel(N::T) where {T <: UnipartiteNetwork}
Applied to empirical UnipartiteNetwork
return its randomized version.
References
Williams, R., Martinez, N., 2000. Simple rules yield complex food webs. Nature 404, 180–183.
nichemodel(S::Int64, C::Float64)
References
Williams, R., Martinez, N., 2000. Simple rules yield complex food webs. Nature 404, 180–183.
nichemodel(parameters::Tuple)
Parameters tuple can also be provided in the form (Species::Int64, Co::Float64) or (Species::Int64, Int::Int64).
References
Williams, R., Martinez, N., 2000. Simple rules yield complex food webs. Nature 404, 180–183.
Nested hierarchy model
In order to reproduce more faithfully properties of complex and multidimensional natural nested hierarchy model tries to use simple rules to incorporate also the phylogenetic similarity in resource composition of predators.
EcologicalNetworks.nestedhierarchymodel
— Functionnestedhierarchymodel(S::Int64, L::Int64)
Return UnipartiteNetwork
where resources are assigned to consumers according to the nested hierarchy model for S
species and L
.
References
Cattin, M.-F., Bersier, L.-F., Banašek-Richter, C., Baltensperger, R., Gabriel, J.-P., 2004. Phylogenetic constraints and adaptation explain food-web structure. Nature 427, 835–839. https://doi.org/10.1038/nature02327
nestedhierarchymodel(S::Int64, Co::Float64)
Connectance can be provided instead of number of links.
References
Cattin, M.-F., Bersier, L.-F., Banašek-Richter, C., Baltensperger, R., Gabriel, J.-P., 2004. Phylogenetic constraints and adaptation explain food-web structure. Nature 427, 835–839. https://doi.org/10.1038/nature02327
nestedhierarchymodel(N::T) {T <: UnipartiteNetwork}
Applied to empirical UnipartiteNetwork
return its randomized version.
References
Cattin, M.-F., Bersier, L.-F., Banašek-Richter, C., Baltensperger, R., Gabriel, J.-P., 2004. Phylogenetic constraints and adaptation explain food-web structure. Nature 427, 835–839. https://doi.org/10.1038/nature02327
nestedhierarchymodel(parameters::Tuple)
Parameters tuple can also be provided in the form (Species::Int64, Co::Float64) or (Species::Int64, Int::Int64).
References
Cattin, M.-F., Bersier, L.-F., Banašek-Richter, C., Baltensperger, R., Gabriel, J.-P., 2004. Phylogenetic constraints and adaptation explain food-web structure. Nature 427, 835–839. https://doi.org/10.1038/nature02327
Minimum potential niche model
This model attempts to explicitly simulate forbidden links in empirical food webs.
EcologicalNetworks.mpnmodel
— Functionmpnmodel(S::Int64, Co::Float64, forbidden::Float64)
Return UnipartiteNetwork
with links assigned according to minimum potential niche model for given number of S
, connectivity Co
and probability of forbidden
link occurence.
References
Allesina, S., Alonso, D., Pascual, M., 2008. A General Model for Food Web Structure. Science 320, 658–661. https://doi.org/10.1126/science.1156269
mpnmodel(N::T) where {T<: UnipartiteNetwork}
Applied to UnipartiteNetwork
return its randomized version.
References
Allesina, S., Alonso, D., Pascual, M., 2008. A General Model for Food Web Structure. Science 320, 658–661. https://doi.org/10.1126/science.1156269
mpnmodel(parameters::Tuple)
Parameters tuple can also be provided in the form (S::Int64, Co::Float64, forbidden::Float64).
References
Allesina, S., Alonso, D., Pascual, M., 2008. A General Model for Food Web Structure. Science 320, 658–661. https://doi.org/10.1126/science.1156269
mpnmodel(mpnmodel(S::Int64, L::Int64, forbidden::Float64))
Average number of links can be specified instead of connectance.
References
Allesina, S., Alonso, D., Pascual, M., 2008. A General Model for Food Web Structure. Science 320, 658–661. https://doi.org/10.1126/science.1156269