bipartite (version 2.05)

grouplevel: Analysis of bipartite webs at the level of each of the two levels (groups) of the network

Description

Calculates a variety of indices and values for each group of a bipartite network (one.grouplevel is the actual function to do the computations and is not intended to be called by the user)

Usage

grouplevel(web, index="ALLBUTDD", level="both", weighted=TRUE, empty.web=FALSE, 
dist="horn", CCfun=mean, logbase="e", normalise=TRUE,  extinctmethod="r", 
nrep=100, fcdist="euclidean", fcweighted=TRUE)

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 of

index

One or more of the following (exact match only!):

• number of speciesin the respective trophic level,
• mean number of links,
• mean number of shared partners,
• cluste

level

For which of the two groups (levels) should these indices be computed? Options are lower, higher and both (default). Although groupwise can be employed on its own, it typical

weighted

logical; for those indices which are simply averaged across species to yield the group-level index (e.g. niche overlap), should this averaging take into account the number of observations for a species? Defaults to TRUE. The

empty.web

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

dist

Distance metric to be used to calculate niche overlap; defaults to Horn's index, which is the recommendation of Krebs (1989); for other options see vegdist in vegan.

CCfun

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

logbase

Shall various indices (partner diversity, generality/vulnerability) 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 affec

normalise

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

extinctmethod

Specifies how species are removed from matrix: random or abundance (partial matching), where abundance removes species in the order of increasing abundance (i.e. rarest first); see Memmott et al. (2004).

nrep

Number of replicates for the extinction sequence analysis.

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.

Value

• The suffixes LL and HL refer to lower and higher level, respectively. If values for both levels are requested, those for the higher level are given first, followed immediately by those for the lower level. Depending on the selected indices, some or all of the below (returned as vector if degree distribution was not requested, otherwise as list):
• mean number of species
  sic, possibly weighted (if weighted=TRUE; the weighted mean is not something typically reported, but it seems a very plausible way to embrace the uncertainty introduced by species with very few interactions).
• mean number of links
  sic (sum of links for each species, averaged over all species in that level), possibly weighted (if weighted=TRUE).
• mean number of shared partners
  Based on the distance matrix between species, counting the number of species in the other level that both interact with; based on Roberts & Stone (1990) and Stone & Roberts (1992), i.e. for pollinators will yield mean number of plants shared by any two pollinators (Cannot be weighted.)
• cluster coefficient
  The cluster coefficient for a level is the (weighted) average cluster coefficients of its members. The cluster coefficient for each species, in turn, is simply the number of realised links divided 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. If you want to use Tore Opsahl's adaptation to two-modes, please see the next index, based on his function clustering_tm in tnet. To my knowledge, so far every study has used the wrong one, i.e. the one presented here as cluster coefficient.
• weighted cluster coefficient
  When asking for weighted cluster coefficient, this version will automatically use interactions as weights unless the data are binary. The computation is based on clustering_tm in tnet. See there (and more on Tore Opsahl's webpages) for help.
• niche overlap
  Mean similarity in interaction pattern between species of that level, calculated by default as Horn's index (use dist to change this.). Values near 0 indicate no common use of niches, 1 indicates perfect niche overlap.
• togetherness
  Mean number of co-occupancies across all species-combinations; the whole matrix is scanned for submatrices of the form (0,0,1,1), representing perfect matches of co-presences and co-absences. These are counted for each pairwise species combination, and averaged (without weighting). Since the number of species differs between the levels, the same number of co-occupancies will lead to different togetherness-values for the two levels. Based on Stone & Roberts (1992).
• C score
  (Normalised) mean number of checkerboard combinations across all species of the level. Values close to 1 indicate that there is evidence for disaggregation, e.g. through competition. Value close to 0 indicate aggregation of species (i.e. no repelling forces between species). Since the number of species differs between the levels, the same number of checkerboard patterns will lead to different C-scores for the two levels. See Stone and Roberts (1990) for details.
• V ratio
  Variance-ratio of species numbers to interaction numbers within species of a level. Values larger than 1 indicate positive aggregation, values between 0 and 1 indicate disaggregation of species. See Schluter (1984) for details.
• discrepancy
  Discrepancy as proposed by Brualdi & Sanderson (1999); see discrepancy for details.
• degree distribution
  Coefficients and fits for three different functions to a level's degree distributions: exponential, power law and truncated power law. See degreedistr for details and references.
• extinction slope
  Slope of the secondary extinction sequence in one level, following extermination of species in the other level; extinction slope.HL refers to the robustness of the higher level to extinctions in the lower level (and vice versa); see slope.bipartite and second.extinct for details.
• robustness
  Calculates the area below the secondary extinction curve; robustness.HL refers to the robustness of the higher level to extinctions in the lower level (and vice versa); see robustness for details. Corresponds to extinction slope.
• functional complementarity
  Functional complementarity for a given level. This measure of niche complementarity (as described by Devoto et al. 2012), is computed as the total branch length of a functional dendrogram based on qualitative differences of interactions of one level with the other. Thus, the functional aspect of functional complementarity refers to the function of sharing interactions. Should be highly correlated with niche overlap, only binary.
• 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.

encoding

UTF-8

Details

This function implements a variety of the many (and still procreating) indices describing network topography at the group level.Note that Bersier et al. (2002) have three levels of values for some of their indices: qualitative (i.e. based on binary networks), quantitative (based on networks with information on the number of interactions observed for each link), and weighted-quantitative (where each species is given a weight according to the number of interactions it has). At present, we implement a mixture of qualitative, quantitative and weighted-quantitative indices and offer the option weighted to compute the weighted-quantitative version of some of them (mean number of links, mean number of shared partners, cluster coefficient, partner diversity, generality / vulnerability). For all others, the mechanics behind the index do not allow a weighted mean to be computed (e.g. the distance-matrix between all species combinations used to compute niche.overlap). All indices in this function work with real as well as integer values. Extinction slope works on a repeated random sequence of species extinctions (within one trophic level), and calculates the number of secondary extinctions (in the other level). These values are then averaged (over the nrep runs) and plotted against the number of species exterminated. The proportion still recent (on the y-axis) regressed against the proportion exterminated (on the x-axis) is hence standardised to values between 0 and 1 each. Through this plot, a hyperbolic regression is fitted, and the slope of this regression line is returned as an index of extinction sensitivity. The larger the slope, the later the extinction takes its toll on the other trophic level, and hence the higher the redundancy in the trophic level under consideration. Using plot.it=F also returns the graphs (set history to recording in the plotting window). Changing the extinctionmethod to abundance will always result in the same sequence (by increasing abundance) and hence does not require replication. Most indices are straightforward, one-line formulae; some, such as betweenness, also require a re-arranging of the matrix; and one, secondary extinction slope, internally requires iterative runs, making the function relatively slow. If you are not interested in the secondary extinction slopes, simply set nrep=1 to make it much faster.

References

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 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 Gotelli, N. J., and G. R. Graves. 1996 Null Models in Ecology. Smithsonian Institution Press, Washington D.C. Jost, L. 2006. Entropy and diversity. Oikos 113, 363-–375. doi: 10.1111/j.2006.0030-1299.14714.x 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 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

See Also

This function can (and typically will) be called, with all its arguments, by networklevel. Several indices have their own function as implementation: second.extinct, degreedistr, C.score and V.ratio

Examples

data(Safariland)
grouplevel(Safariland)
grouplevel(Safariland, level="lower", weighted=FALSE) #excludes degree distribution fits