specieslevel: Calculate various indices for network properties at the species level

Description

Apart from the properties of the entire web, also its participants can be described specifically. Various simple numbers and indices are calculated and returned.

Usage

specieslevel(web, index="ALL", logbase="e", low.abun=NULL, high.abun=NULL)

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

index

Vector of indices to be calculated for each trophic level of the web; options are: species number for number of species, degree, ND for normalised degrees, dependence, in

logbase

Shall the various diversity indices 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, onl

low.abun

Optional vector of independent abundances of the lower trophic level to be passed on to dfun.

high.abun

Optional vector of independent abundances of the higher trophic level to be passed on to dfun.

Value

For both the higher trophic level and the higher trophic level a list with the following components:
number of speciesSic.
species degreeSum of interactions per species.
normalised degreeAs degree, but scaled by the number of possible partners; see ND.
dependenceWeb entry divided by column totals (for higher trophic level) or row totals (for lower trophic level). Expresses the proportion of interactions with each species, and sums to 1 for each.
strengthSum of dependencies of each species (proposed in Bascompte et al. 2006).
interaction push/pullDirection of interaction asymmetry: positive values indicate that a species affects the species of the other level it interacts with stronger then they affect it (pusher); negative values indicate that a species is, on average, on the receiving end of the stick (being pulled); formula based on Vazquez et al (2007), but push/pull is our own nomenclature. Values are highly correlated with species strengths (see below), but standardised to fall between -1 (being pulled) and 1 (pushing).
Pollination Service Index PSIfor the higher trophic level, and the equivalent Pollinator Support Index for the lower trophic level. Expresses the value of, say, a pollinator for all plant species as the sum (across all plant species) of the proportion of pollen deposited per visit. The more specialised the pollinator and the fewer pollinators the plants it pollinates, the higher is its value for the plant community. It is a really cool measure, but it's not easy to get one's head around it. Alternatively, one can see it as the inverse of redundancy of the species for the web: the higher the value, the less redundant.
node specialisation indexAnother measure of specialisation, based on the path length between any two higher-trophic level species. Species sharing hosts/prey have an FS-value of 1. See specific function nodespec for details, problems and reference.
betweennessA value describing the centrality of a species in the network by its position between other nodes; see BC and betweenness in sna.
closenessA value describing the centrality of a species in the network by its path lengths to other nodes; see CC and closeness in sna.
Fisher alphaFisher's alpha diversity for each species (see fisher.alpha in vegan for details).
Partner diversityShannon diversity (when using ) or per-species generality/vulnerability (when using ) of the interactions of each species. See also networklevel for the aggregated version of this index (i.e. averaged across all species in a trophic level).
effective partners to the power of partner.diversity: Bersier et al. (2002) interpret this as the effective number of partners, if each partner was equally common. Note that partner is a bit euphemistic when it comes to predator-prey or host-parasitoid networks.
dSpecialisation of each species based on its discrimination from random selection of partners. More specifically, it returns d', which is calculated based on the raw d, dmin and dmax for each species (see dfun. See Bl�thgen et al. (2006) for details.

encoding

latin1

Details

This function implements a variety of the many (and still procreating) indices describing species properties. Some are embaracingly simple (such as number of interacting species for each species). Others are variations on Shannon's diversity index applied to within species. Most indices are straightforward, one-line formulae; some, such as d', also require a re-arranging of the matrix. We (Dormann, Bl�thgen, Gruber) came up with a new one, called Pollination Service Index or psi, for which a few more details seem appropriate. PSI is comprised of three calculation steps: firstly, we calculate, for each pollinator species, the proportion to which it visits each plant species (or, phrased anthromorphically, the number to the question: To which proportion do I visit dandelion?). Secondly, we calculate the proportion to which a plant is visited by each bee species (Which proportion of my pollinators are red mason bees?). Multiplying, these two proportions gives the portion of own pollen for each plant species (because this depends both on a pollinators specialisation (step 1) and the plant's specific receptiveness (step 2). Finally, we sum the proportions own pollen delivered across all plant species. This value is the PSI-value. At its maximum, 1, it shows that all pollen delivered to exactly one plant species is derived from one monolectic pollinator. At its minimum, 0, it indicates that a pollinator is irrelevant to all plant species. Note that PSI is independent of the abundance of plants or pollinators: a bee been found only once on a plant species visited by no-one else receives a PSI of 1, even if in total 14 million visits were recorded. We envisage a penalty for the fact that a pollinator has to make two (more or less successive) visits to the same plant species: the first to take the pollen up, the second to pollinate the next. Thus, using 2 as an exponent in step 1 would simulate that a pollinator deposits all pollen at every second visit (or flies to their nest). That is certainly a too strong penalisation. At present we set the exponent to 1, because the step of controlling for pollen purity is already a major improvement. Also, we have no idea to which extent pollen gets mixed and/or lost during foraging flights, and the true exponent remains elusive.

References

Bascompte, J., Jordano, P. and Olesen, J. M. (2006) Asymmetric coevolutionary networks facilitate biodiversity maintenance. Science 312, 431--433 Bl�thgen, N., Menzel, F. and Bl�thgen, N. (2006) Measuring specialization in species interaction networks. BMC Ecology 6, 9 Mart�n Gonz�les, A.M., Dalsgaard, B. and Olesen, J.M. 2009. Centrality measures and the importance of generalist species in pollination networks. Ecological Complexity, in press (doi:10.1016/j.ecocom.2009.03.008) V�zquez, D. P., Meli�n, C. J., Williams, N. M., Bl�thgen N., Krasnov B. R. and Poulin, R. (2007) Species abundance and asymmetric interaction strength in ecological networks. Oikos 116, 1120--1127

Examples

Run this code

data(Safariland)
specieslevel(Safariland)
specieslevel(Safariland, index="ALLBUTD")[[2]]

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