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 of prey.

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

• connectance,

• web asymmetry,

• links per species,

• number of compartments,

• compartment diversity,

• cluster coefficient, which will compute both the network-wide cluster coefficient as well as those for each level,

• nestedness,

• NODF,

• weighted nestedness,

• weighted NODF,

• ISA (or alternatively interaction strength asymmetry or
  dependence asymmetry),

• SA (or alternatively specialisation asymmetry),

• linkage density,

• weighted connectance,

• Fisher alpha,

• interaction evenness,

• Alatalo interaction evenness,

• Shannon diversity,

• H2;

and/or those invoked through grouplevel:

• number of species in the respective trophic level,

• mean number of links,

• mean number of shared partners,

• weighted cluster coefficient,

• degree distribution,

• togetherness,

• C score,

• V ratio,

• discrepancy,

• extinction slope,

• robustness,

• niche overlap,

• generality,

• vulnerability,

• fc (or alternatively functional complementarity).

Furthermore, there are some groups of indices that can be called:

• ALL calculates all indices (returning a list (since degree distribution fits are a table within this list and cannot be simplified)),

• ALLBUTDD (default) calculates all indices except degree distribution fits. This latter has the advantage that the output can be simplified to a vector;

• info returns more general information on the network;

• binary returns a best-of selection of indices based on a binary network;

• quantitative returns a best-of selection of indices based on quantitative networks;

• topology returns indices more abstractly describing network properties. Also CHECK details below!

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

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

Method to use for calculating interaction strength (= dependence) asymmetry; original by Bascompte is yielding artefact results based only on the asymmetry of the web (as shown by example in Blüthgen et al. 2007 analytically in Blüthgen 2010) and should hence be avoided; Bluethgen (default) excludes singletons and corrects for low number of interactions (range -1 to 1).

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

Specifies how species are removed from matrix: random, degree or abundance (partial matching). See second.extinct for details an option to predefine the sequence externally; idea from Memmott et al. (2004).

Number of replicates for the extinction sequence analysis.

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

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
dist = "jaccard".

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

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

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 Shannon uses ln. The choice of the base will not affect the results qualitatively, at most by a scaling factor. Note that for all these indices, we follow common practice and define 0 * log(0) = 0.

Shall all cells of the matrix be used to calculate the interaction evenness
(intereven = "prod")? Or, as given by Bersier et al. (2002) and Tylianakis et al. (2007), should only the realised links be used (intereven = "sum"; default)? Prod and sum refer to using the log of the product of matrix dimensions (i.e. all cells) or the log of the sum of non-zero cells (i.e. number of links) as denominator in the evenness formula. See last paragraph of the details-section for views on these two options!

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

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.

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

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 legacy=TRUE. This is only for the transition period until all papers in the making have been published (or binned). Index names and sometimes unclear focal level were downsides of the old implementation, which is now remedied. Thus, the use of legacy=TRUE and the direct call of .networklevel are strongly discouraged!

Realised 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)

Balance 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).

Mean number of links per species (qualitative): sum of links divided by number of species.

Compartments 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.

Shannon's diversity of compartment sizes (size = number of species from both levels); see Tylianakis et al. (2007).

The 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 https://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).

Nestedness 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.

Another index for nestedness, calling 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.

A 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!

Another 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.

(selected using index = "ISA") 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 ISAmethod = "Bluethgen") indicate higher dependence in the higher trophic level. See function specieslevel and its index interaction push/pull, which quantifies the balance of affecting and being effected by other species. Similarly, index strength quantifies the average effect of each species on all its partners.

(selected using index="SA") 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 (SAmethod="Bluethgen") or where d'-values are log-transformed (arguing that d'-values are indeed log-normally distributed: SAmethod="log"). 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.

Marginal 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.

Linkage density divided by number of species in the network (Bersier et al. 2002). This will respond to whether non-interacting species (e.g. unparasitised hosts) are included or not!

An alternative measure of interaction diversity (using fisherfit from vegan).

Shannon'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.

A different measure for web entry evenness, as proposed by Müller et al. (1999).

Shannon's diversity of interactions (i.e. network entries).

H2' 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.

in this level

for this level (same for both levels if weighted=FALSE).

Mean similarity in interaction pattern between species of the same level, calculated by default as Horn's index (dist="horn").

Mean number of co-occupancies across all species combinations.

Mean (normalised) number of checkerboard combinations across all species.

Variance-ratio of species numbers to individual numbers within species for that level.

Discrepancy as proposed by Brualdi & Sanderson (1999); see discrepancy for details.

See degreedistr for details and references.

Slope of the secondary extinction sequence in that level, following extermination of species in the other level.

Area below the “secondary extinction” curve; see robustness for details. Corresponds to “extinction slope”.

for a given level.

(Weighted) mean Shannon diversity of the number of interactions for the species of that level. Choose logbase=2 to change to a log2-based version.

(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.