networklevel: Analysis of bipartite webs at the level of the entire network

Description

Calculates a variety of indices and values for a bipartite network

Usage

networklevel(web, index="ALLBUTDD", level="both", weighted=TRUE, 
   ISAmethod="Bluethgen",  SAmethod = "Bluethgen", extinctmethod = "r", 
   nrep = 100, CCfun=median, dist="horn", normalise=TRUE, empty.web=TRUE, 
   logbase="e", intereven="prod", H2_integer=TRUE, fcweighted=TRUE, 
   fcdist="euclidean", legacy=FALSE)

Arguments

web

Web is a matrix representing the interactions observed between higher trophic level species (columns) and lower trophic level species (rows). Usually this will be number of pollinators on each species of plants or number of parasitoids on each species o

index

One or more of the following (exact match only!). First the group of pure network indices, then those computed for each level.

level

For which level should the level-specific indices be computed: (default), or ?

weighted

Logical; should the weighted average be computed for indices that are averaged across species (at the group level)? Defaults to TRUE.

ISAmethod

Method to use for calculating interaction strength (= dependence) asymmetry; original by is yielding artefact results based only on the asymmetry of the web (as shown by example in Blüthgen et al. 2007 analytically in Blüthgen 2

SAmethod

How to aggregate d'-based specialisation values: mean of log-transformed dependencies () or Blüthgen's marginal totals-weighted mean (default); see Blüthgen et al. (2007).

extinctmethod

Specifies how species are removed from matrix: , or (partial matching). See second.extinct for details an option to predefine

nrep

Number of replicates for the extinction sequence analysis.

CCfun

Method to use when calculating the clustering coefficient. Originally proposed as mean of cluster coefficients for each species. Defaults to , because cluster coefficients are strongly skewed.

dist

Distance metric to be used to calculate niche overlap. Any of vegan's vegdist-metrics can be used; defaults to Horn's index, which is the recommendation of Krebs (1989). Binary percent niche overlap would be computed with

normalise

Logical; shall the C-score and togetherness metrics be normalised to a range of 0 to 1? Defaults to TRUE.

empty.web

Shall the empty columns and rows be deleted? Defaults to TRUE.

logbase

Shall the various diversity indices (linkage density, partner diversity, generality/vulnerability, interaction evenness) be calculated to the base of e (default) or 2? Log2 is the proposal for generality and vulnerability by Bersier et al. (2002), while S

intereven

Shall all cells of the matrix be used to calculate the interaction evenness ()? Or, as given by Bersier et al. (2002) and Tylianakis et al. (2007), should only the realised links be used (

H2_integer

Logical; indicates whether values in web are integers. Passed on to H2fun; see there for details.

fcweighted

Logical; when computing ``functional complementarity'' sensu function fc, should the weights of the matrix be used. Defaults to TRUE, but original paper (Devoto et al. 2012) is based on FALSE.

fcdist

Distance measure to be used to compute functional complementarity through fc; any measure accepted by dist is acceptable.

legacy

Logical; should the old (pre-2.00) version of networklevel be used? To be backward compatible, the old networklevel-function is still available (.networklevel) and can be called by setting

Value

The suffixes LL and HL refer to lower and higher level, respectively Depending on the selected indices, some or all of the below (returned as vector if degree distribution was not requested, otherwise as list):
connectanceRealised proportion of possible links (Dunne et al. 2002): sum of links divided by number of cells in the matrix (= number of higher times number of lower trophic level species). This is the standardised number of species combinations often used in co-occurrence analyses (Gotelli & Graves 1996)
web asymmetryBalance between numbers in the two levels: positive values indicate more higher-trophic level species, negative more lower-trophic level species; implemented as (ncol(web)-nrow(web))/sum(dim(web)); web asymmetry is a null model for what one might expect in dependence asymmetry: see Blüthgen et al. (2007).
links per speciesMean number of links per species (qualitative): sum of links divided by number of species.
number of compartmentsCompartments are sub-sets of the web which are not connected (through either higher or lower trophic level) to another compartment. Mathematically, they are Jordan blocks, but this implementation is rule-based (and fast). They are also nicely visualised in the visweb function.
compartment diversityShannon's diversity of compartment sizes (size = number of species from both levels); see Tylianakis et al. (2007).
cluster coefficientThe cluster coefficient for a network is the average cluster coefficients of its members, i.e. simply the number of realised links devided by the number of possible links. Introduced by Watts & Strogatz (1998) and described in Wikipedia under http://en.wikipedia.org/w/index.php?title=Clustering_coefficient. The cluster coefficient can be computed both for the entire network, as well as for each level (for the latter indicated by suffix HL or LL).
nestednessNestedness temperature of the matrix (0 means cold, i.e. high nestedness, 100 means hot, i.e. chaos). For details see nestedness and Rodriguez-Girones & Santamaría (2002). Notice that the function nestedness does not calculate any null model, simply because it is too computer-intensive. networklevel calls nestedtemp! If you are interested in the different null models, please use the function nestedness or nestedtemp in vegan directly.
weighted nestednessA nestedness version that considers interaction frequencies (and is hence weighted), proposed by Galeano et al. (2007) and implemented in wine. It ranges between 1 (perfect nestedness) and 0 (perfect chaos). Note that this is the OPPOSITE interpretation of nestedness temperature!
weighted NODFAnother quantitative (=weighted) index for nestedness, building on NODF (see nestednodf in vegan). High values indicate nestedness. According to the analysis of Almeida-Neto et al. (2008, 2010), NODF is more consistent and better than usual measures of nestedness.
interaction strength asymmetry(selected using ) Explaining dependence asymmetry is also a measure of specialisation, across both trophic levels. Proposed by Bascompte et al. (2006) and critised and alterations proposed by Blüthgen et al. (2007). The latter also show that dependence asymmetry can be almost entirely explained by web asymmetry (see above). Positive values (only possible of ) indicate higher dependence in the higher trophic level. See function specieslevel and its index , which quantifies the balance of affecting and being effected by other species. Similarly, index quantifies the average effect of each species on all its partners.
specialisation asymmetry(selected using ) Asymmetry (higher vs. lower trophic level) of specialisation now based on d' (see dfun), which is insensitive to the dimensions of the web. Again, two options of calculation are available: the one proposed by Blüthgen et al. (2007), where they weight the specialisation value for each species by its abundance () or where d'-values are log-transformed (arguing that d'-values are indeed log-normally distributed: ). Since the mean d-value for the lower trophic level is subtracted from that of the higher, positive values indicate a higher specialisation of the higher trophic level.
linkage densityMarginal totals-weighted diversity of interactions per species (quantitative). Actually, this is computed as the average of vulnerability and generality (Bersier et al. 2002). Does not respond to setting weighted=FALSE.
weighted connectanceLinkage density divided by number of species in the network (Tylianakis et al. 2007). This will respond to whether non-interacting species (e.g. unparasitised hosts) are included or not!
Fisher's alphaAn alternative measure of interaction diversity (using fisherfit from vegan).
interaction evennessShannon's evenness for the web entries. Note that the two options are rather different. By definition, IE = H/Hmax; H = -sum(p.i.mat*log(p.i.mat)), where p.i.mat = matrix/sum(entries in matrix). This means, when calculating H, do we treat all possible links as species, and the interactions (cell values) as measure of their abundance? By definition, Hmax = ln(N). The key question is: What is the right value for N? Since we treat the matrix cells as species, it is (clearly?) the number of matrix cells, i.e. number of higher trophic level species x number of lower trophic level species. We think this logic justifies our default "prod". However, others argue in favour of N=number of links. Please see note for our discussion on this point.
Alatalo interaction evennessA different measure for web entry evenness, as proposed by Müller et al. (1999).
Shannon diversityShannon's diversity of interactions (i.e. network entries).
H2H2' is a network-level measure of specialisation. It ranges between 0 (no specialisation) and 1 (complete specialisation). H2' is a measure of discrimination, i.e. calculated in comparison of no specialisation (see H2fun for details. To avoid confusion of keys (apostrophe vs. accent), we call the H2' only H2 here.
others now to come: all other indices are returned as output from grouplevel. Please see there for details, we here only provide minimal listing.
number of species
mean number of shared partnersin this level
cluster coefficientfor this level (same for both levels if ).
weighted cluster coefficient
niche overlapMean similarity in interaction pattern between species of the same level, calculated by default as Horn's index ().
togethernessMean number of co-occupancies across all species combinations.
C scoreMean (normalised) number of checkerboard combinations across all species.
V ratioVariance-ratio of species numbers to individual numbers within species for that level.
discrepancyDiscrepancy as proposed by Brualdi & Sanderson (1999); see discrepancy for details.
degree distributionSee degreedistr for details and references.
extinction slopeSlope of the secondary extinction sequence in that level, following extermination of species in the other level.
robustnessArea below the secondary extinction curve; see robustness for details. Corresponds to extinction slope.
functional complementarityfor a given level.
partner diversity(Weighted) mean Shannon diversity of the number of interactions for the species of that level. Choose to change to a log2-based version.
generality/vulnerability(Weighted) mean effective number of LL species per HL species (generality; HL species per LL species for vulnerability), weighted by their marginal totals (row sums); see Tylianakis et al. (2007) and Bersier et al. (2002). This is identical to exp(partner diversity, i.e., simply the Jost (2006)-recommended version of diversity.

encoding

UTF-8

Details

For explanations of any of the indices computed for a level (i.e. those with HL and/or LL suffix), please see grouplevel for details. This function implements a variety of the many (and still procreating) indices describing network topography. Some are embarrassingly simple and mere descriptors of a network's outer appearance (such as number of species in each trophic level or the number of links (= non-zero cells) in the web). Others are variations on Shannon's diversity index applied to within column or within rows. Only extinction slope is newly implemented here, and hence described in a bit more detail. Currently, you cannot get the qualitative version of quantitative indices such as vulnerability! Integers or continuous values - what are the quantities in quantitative webs? Some web metrics expect in their typical formulation that the entries in the web-matrix are integers - e.g. H2' is defined relative to minimum and maximum based on marginal totals. Blüthgen et al. (2006) use an algorithm assuming values can only be integers. If your quantities are not constrained to be integers, multiplication and rounding may or may not give consistent results, depending on rounding errors and the factor applied. Multiplication with high numbers such as 10 000 seems to be OK. For H2' a simplified calculation applicable to continuous numbers is available (by declaring option in H2fun). Note that values of H2' based on integers are not directly comparable to H2' based on continuous values (for sparse webs, H2'_continuous is much higher than H2'_integer). We tentatively think that other indices are hardly affected by non-integer values or by multiplication and rounding. Please let us know your experience.

References

Almeida-Neto, M., Loyola, R.D., Ulrich, W., Guimaraes, P., Guimaraes, Jr., P.R. 2008. A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement. Oikos 117, 1227--1239 Almeida-Neto, M. & Ulrich, W. (2011) A straightforward computational approach for measuring nestedness using quantitative matrices. Environmental Modelling & Software 26, 173--178 Bascompte, J., Jordano, P. and Olesen, J. M. 2006 Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science 312, 431--433 Bersier, L. F., Banasek-Richter, C. and Cattin, M. F. (2002) Quantitative descriptors of food-web matrices. Ecology 83, 2394--2407 Blüthgen, N. (2010) Why network analysis is often disconnected from community ecology: A critique and an ecologist's guide. Basic and Applied Ecology 11, 185--195 Blüthgen, N., Menzel, F., Hovestadt, T., Fiala, B. and Blüthgen N. 2007 Specialization, constraints and conflicting interests in mutualistic networks. Current Biology 17, 1--6 Burgos, E., H. Ceva, R.P.J. Perazzo, M. Devoto, D. Medan, M. Zimmermann, and A. Maria Delbue (2007) Why nestedness in mutualistic networks? Journal of Theoretical Biology 249, 307--313 Corso G, de Araújo AIL, de Almeida AM (2008) A new nestedness estimator in community networks. arXiv 0803.0007v1 [physics.bio-ph] Devoto M., Bailey S., Craze P., and Memmott J. (2012) Understanding and planning ecological restoration of plant-pollinator networks. Ecology Letters 15, 319--328. http://dx.doi.org/10.1111/j.1461-0248.2012.01740.x Dormann, C.F., Fründ, J., Blüthgen, N., and Gruber, B. (2009) Indices, graphs and null models: analysing bipartite ecological networks. The Open Ecology Journal 2, 7--24. Dunne, J. A., R. J. Williams, and N. D. Martinez. 2002 Food-web structure and network theory: the role of connectance and size. Proceedings of the National Academy of Science USA 99, 12917--12922 Galeano, J., Pastor, J.M. and Iriondo, J.M. (2008) Weighted-Interaction Nestedness Estimator (WINE): A new estimator to calculate over frequency matrices. arXiv 0808.3397v1 [physics.bio-ph] Gotelli, N. J., and G. R. Graves. 1996 Null Models in Ecology. Smithsonian Institution Press, Washington D.C. Krebs, C. J. 1989. Ecological Methodology. Harper Collins, New York. Memmott, J., Waser, N. M. and Price M. V. 2004 Tolerance of pollination networks to species extinctions. Proceedings of the Royal Society B 271, 2605--2611 Müller, C. B., Adriaanse, I. C. T., Belshaw, R. and Godfray, H. C. J. 1999 The structure of an aphid-parasitoid community. Journal of Animal Ecology 68, 346--370 Roberts, A. and Stone, L. 1990 Island-sharing by archipelago species. Oecologia 83, 560--567 Rodríguez-Girónes M.A., and Santamaría L. 2006. A new algorithm to calculate the nestedness temperature of presence-absence matrices. Journal of Biogeography 33, 924--935 Schluter, D. (1984) A variance test for detecting species associations, with some example applications. Ecology 65, 998-1005. Stone, L. and Roberts, A. (1990) The checkerboard score and species distributions. Oecologia 85, 74--79. Stone, L. and Roberts, A. (1992) Competitive exclusion, or species aggregation? An aid in deciding. Oecologia 91, 419--424 Tylianakis, J. M., Tscharntke, T. and Lewis, O.T. (2007) Habitat modification alters the structure of tropical host-parasitoid food webs. Nature 445, 202--205 Watts, D. J. and Strogatz, S. (1998) Collective dynamics of small-world networks. Nature 393, 440--442

Examples

Run this code

data(Safariland)
networklevel(Safariland)
networklevel(Safariland, index="ALLBUTDD") #excludes degree distribution fits

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