Functions that compute different measures of trophic level.
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PreyAveragedTrophicLevel(community, include.isolated=TRUE) FlowBasedTrophicLevel(community, weight.by, include.isolated=TRUE) ShortestTrophicLevel(community, include.isolated=TRUE) ShortWeightedTrophicLevel(community, include.isolated=TRUE) LongestTrophicLevel(community, include.isolated=TRUE) LongWeightedTrophicLevel(community, include.isolated=TRUE) ChainAveragedTrophicLevel(community, include.isolated=TRUE) TrophicHeight(community, include.isolated=TRUE) TrophicLevels(community, weight.by=NULL, include.isolated=TRUE)
an object of class
the name of a node property, either first-class or computed,
by which to weight flow-based trophic level. Must satisfy the criteria
Trophic level is a measure of a node's ‘distance’ from the primary
producers in the community and hence indicates how many steps matter, and hence
energy, has been through to reach that node. Each function (with the exception
TrophicLevels) returns a vector containing a different measure of
trophic level. These functions follow the definitions of Williams and Martinez
PreyAveragedTrophicLevel returns 1 plus the mean trophic level of the
node's resources, using the matrix inversion method of Levine (1980) that is
very fast and accounts for flow through loops. If this matrix inversion fails
then there is an important problem with the network topology and the function
will return a vector containing all
NAs. For a food web to be
energetically feasible, every node must be connected to a basal node. When the
inversion fails it is because there is at least one node that has no connection
to a basal node.
FlowBasedTrophicLevel also implements the matrix
inversion technique and uses the
weight.by node property to provide an
estimate of energy flow through each trophic link.
ChainAveragedTrophicLevel compute trophic level by
examining the position of each node in every food chain in which it appears.
ShortestTrophicLevel returns 1 plus the shortest chain length from a
node to a basal species.
ShortWeightedTrophicLevel returns the average
LongestTrophicLevel is the longest chain length from each node to a
LongWeightedTrophicLevel is the average of
ChainAveragedTrophicLevel is 1 plus the average chain length of all
paths from each node to a basal species. These five functions each
enumerate every unique food chain (using
TrophicChainsStats), which can
be lengthy for complex food webs. If more than one of these five measures of
trophic level is required, it will be faster to use the
convenience function, which enumerates unique food chains only once and returns
a matrix containing every measure of trophic level in columns ‘ShortestTL’,
‘ShortWeightedTL’, ‘LongestTL’, ‘LongWeightedTL’, ‘ChainAveragedTL’,
‘PreyAveragedTL’ and, if
weight.by is given, ‘FlowBasedTL’.
Jonsson et al (2005) defined ‘trophic height’ to be the same as
Williams and Martinez' (2004) chain-averaged trophic level so
TrophicHeight is a synonym for
All methods will return a vector containing all
NAs if no nodes are basal
i.e., all nodes are cannibalistic or ‘community’ has no trophic links.
Either a vector of length
NumberOfNodes or a
Lawrence Hudson and Rich Williams
Jonsson, T. and Cohen, J. E. and Carpenter, S. R. (2005) Food webs, body size, and species abundance in ecological community description. Advances in Ecological Research 36, 1–84.
Levine, S (1980) Several measures of trophic structure applicable to complex food webs. Journal of Theoretical Biology 83, 195–207.
Williams, R. J. and Martinez, N. D. (2004) Limits to Trophic Levels and Omnivory in Complex Food Webs: Theory and Data. American Naturalist 163, 63, 458–468.
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