networklevel | R Documentation |
Calculates a variety of indices and values for a bipartite network
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", effective=FALSE, legacy=FALSE)
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 of prey. |
index |
One or more of the following (exact match only!). First the group of “pure” network indices, then those computed for each level.
and/or those invoked through
Furthermore, there are some groups of indices that can be called:
|
level |
For which level should the level-specific indices be computed: both (default), lower or higher? |
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 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). |
SAmethod |
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). |
extinctmethod |
Specifies how species are removed from matrix: random, degree or abundance (partial matching). See |
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 median, because cluster coefficients are strongly skewed. |
dist |
Distance metric to be used to calculate niche overlap. Any of vegan's |
normalise |
Logical; shall the C-score and togetherness metrics be normalised to a range of 0 to 1? Defaults to |
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 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. |
intereven |
Shall all cells of the matrix be used to calculate the interaction evenness |
H2_integer |
Logical; indicates whether values in web are integers. Passed on to |
fcweighted |
Logical; when computing “functional complementarity” sensu function |
fcdist |
Distance measure to be used to compute functional complementarity through |
effective |
logical; should interaction evenness, Alatalo evenness, H2' and diversity be expressed as “effective” diversity? For Jost (2010, page 210) this seems to be the better decomposition of an index into a diversity and an evenness component. On a downside, H2' is then no longer ranged in [0,1], and “diversity” becomes the same as “vulnerability” and “generality”. For these reasons, and backward compatibility, the default is |
legacy |
Logical; should the old (pre-2.00) version of |
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 H2_integer=FALSE 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.
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):
connectance |
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) |
web asymmetry |
Balance between numbers in the two levels: positive values indicate more higher-trophic level species, negative more lower-trophic level species; implemented as |
links per species |
Mean number of links per species (qualitative): sum of links divided by number of species. |
number of compartments |
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 |
compartment diversity |
Shannon's diversity of compartment sizes (size = number of species from both levels); see Tylianakis et al. (2007). |
cluster coefficient |
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 |
Nestedness temperature of the matrix (0 means cold, i.e. high nestedness, 100 means hot, i.e. chaos). |
NODF |
Another index for nestedness, calling |
weighted nestedness |
A nestedness version that considers interaction frequencies (and is hence weighted), proposed by Galeano et al. (2007) and implemented in |
weighted NODF |
Another quantitative (=weighted) index for nestedness, building on NODF (see |
interaction strength asymmetry |
(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 |
specialisation asymmetry |
(selected by using index="SA"). Asymmetry (higher vs. lower trophic level) of specialisation now based on d' (see |
linkage density |
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 connectance |
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! |
Fisher's alpha |
An alternative measure of interaction diversity (using |
interaction evenness |
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 |
Alatalo interaction evenness |
A different measure for web entry evenness, as proposed by Müller et al. (1999). |
Shannon diversity |
Shannon's diversity of interactions (i.e. network entries). |
H2 |
H2' is a network-level measure of specialisation. It ranges between 0 (no specialisation) and 1 (complete specialisation). More specifically, H2' is a measure of discrimination, i.e. calculated in comparison to no specialisation (see |
others now to come: |
all other indices are returned as output from |
number of species |
|
mean number of shared partners |
in this level |
cluster coefficient |
for this level (same for both levels if weighted=FALSE). |
weighted cluster coefficient |
|
niche overlap |
Mean similarity in interaction pattern between species of the same level, calculated by default as Horn's index (dist="horn"). |
togetherness |
Mean number of co-occupancies across all species combinations. |
C score |
Mean (normalised) number of checkerboard combinations across all species. |
V ratio |
Variance-ratio of species numbers to individual numbers within species for that level. |
discrepancy |
Discrepancy as proposed by Brualdi & Sanderson (1999); see also |
degree distribution |
See |
extinction slope |
Slope of the secondary extinction sequence in that level, following extermination of species in the other level. |
robustness |
Area below the “secondary extinction” curve; see |
functional complementarity |
for a given level. |
partner diversity |
(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. |
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. |
Sum or Prod: How to calculate interaction evenness? I shall first put down my argument for “prod” and then Jason Tylianakis' arguments for “sum”.
Carsten: “I do not want to defend a position I cannot hold against the flood of qualified criticism, and shall be happy to change the default to option “sum” (i.e. Jason's proposal). Nevertheless, I shall make a very brief attempt to defend my (and Nico's point of view). Imagine a completely different situation: I have “counted” birds in a landscape. From a more meticulous colleague I know that there are 27 bird species breeding at the moment, but on that two mornings that I went out, I could only hear 15. Now I want to calculate the Shannon diversity (and evenness) of birds in that landscape. The “normal” (in the sense of established) approach to use the data from my 15 species. But hold on: I KNOW there are more species out there. I don't know how many (i.e. there may be more than the 27 my colleague has found), but there are at least 27. If I only use the data from my 15 species, I will get a higher evenness value than when I also include the 12 zeros. My conclusion would be: I don't want to overestimate evenness only because I couldn't look long enough, thus I use all 27 values.”
Jason: “I would disagree because what you “know” is based on your meticulous colleague's ‘sampling’, which will also have its limits. If all you wanted was to know the total number of species there (assuming none have gone extinct), then what you propose is fine. However, the problem comes when you want to compare sites, and then sampling effort should be standardised. In most cases we know we don't have a full representation of the diversity (or food web) of an area, but we know for a given spatial or temporal sampling scale that one site differs from another in certain ways, and to me that is the most important. Anyway, it is all a question of scale and the precise question being asked. So what about making it an option in bipartite that you can either choose to divide by the realised links (give our 2007 paper as a ref, so people know it's comparable to that) or divide by the number of potential links, if that's the question people want to ask?” There you go: it's your choice!
NA values: All error and warning messages are (or at least should be) suppressed! If your web returns and NA for some of the indices, this can be because the index cannot be computed. For example, if the web is full (i.e. no 0-cells), extinction slopes cannot be fitted (singularity of gradient). Check if you can expect the index to be computable! If it is, and networklevel doesn't do it, let me know.
Reducing computation time: Some indices require rather long computation times on large webs. If you want to increase the speed by omitting some indices, here a rough guide: Ask only for the indices you are interested in! Otherwise, here is the sequence of most time-consuming indices:
The slowest function is related to extinction slopes and robustness. Excluding both makes the function faster.
weighted cluster coefficient is also very time consuming (an exhaustive search for 4-loops in the one-mode projection of the network). Omitting it can dramatically boost speed.
Degree distributions are somewhat time consuming.
Fisher's alpha is computed iteratively and hence time consuming.
Nestedness and weighted nestedness are not the fastest of routines.
Number (and diversity) of compartments calls a recursive and hence relatively slow algorithm.
H2 and specialisation asymmetry require an iterative, heuristic search algorithm. Finally, excluding discrepancy can also moderately decrease computation time.
Does the species sequence in the data matter?
Obviously, it shouldn't, and for most indices it doesn't. However, particularly indices based on binary representation of web will have ties, where several species have the number of links. In this case, it does matter how the matrix is sorted before simulating extinctions or computing discrepancy. There is no (known) foolproof way to get this sequence "right" (see also "Details" of help for nesteddisc
). Re-running the same code with a shuffled network may thus yield (slightly) different values for (weighted) nestedness, togetherness, discrepancy, extinction slopes and robustness. (Thanks to Valentin Stefan for making us explicitly addressing this issue!)
Carsten F. Dormann carsten.dormann@biom.uni-freiburg.de
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Some functions are implemented separately: H2fun
, second.extinct
, degreedistr
, C.score
and V.ratio
## Not run:
data(Safariland)
networklevel(Safariland)
networklevel(Safariland, index="ALLBUTDD") #excludes degree distribution fits
## End(Not run)
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