Food web measures

distance_to_producer(N::UnipartiteNetwork; f=maximum)

Returns the distance from a primary producert of every species in the food web. Primary producers have a trophic level of 1, after that, it's complicated (see e.g. Williams & Martinez 2004, Thompson et al. 2007).

Post (2002) notes that the trophic level can be obtained from the maximum, mean, or minimum distance to a producer. Given that consumers may be connected to more than one producer, one might argue that the mode of this distribution is also relevant.

In favor of the minimum, one can argue that most energy transfer should happen along short chains; but imagining a consumer atop a chain of length 5, also connected directly to a producer, the minimum would give it a trophic level of 2, hiding its position at the top of the food web.

In favor of the maximum, one can argue that the higher chains give a better idea of how far energy coming from the bottom of the food web can go. This is a strong indication of how vertically diverse it is.

In this package, the keyword f defaults to maximum. Using any other function, as long as it accepts an array (of chain distances) and return a scalar, will work; minimum and Statistics.mean are natural alternatives, as is StatsBase.mode or Statistics.median.

The chain length from any species to any producer is taken as the shortest possible path between these two species, as identified by the Dijkstra algorithm.

trophic_level(N::UnipartiteNetwork; kwargs...)

Returns the fractional trophic level (after Odum & Heald 1975) of species in a binary unipartite network. The trophic level is calculated after Pauly & Christensen (1995), specifically as TLᵢ = 1 + ∑ⱼ(TLⱼ×DCᵢⱼ)/∑ⱼ(DCᵢⱼ), wherein TLᵢ is the trophic level of species i, and DCᵢⱼ is the proportion of species j in the diet of species i. Note that this function is calculated on a network where the diagonal (i.e. self loops) are removed.

This function uses a pseudo-inverse to solve the linear system described above iff the determinant of the diet matrix is 0 (it is non-invertible). Otherwise, it will use an exact inverse.

omnivory(N::T) where {T <: UnipartiteNetwork}

Returns a vector of length richness(N) with an index of consumption across trophic levels. Note we explicitly assume that diet contribution is spread evenly across prey species, in proportion to their degree. Omnivory is measured based on the output of trophic_level.

References

• Christensen, Villy, and Daniel Pauly. "ECOPATH II—a software for balancing steady-state ecosystem models and calculating network characteristics." Ecological modelling 61, no. 3-4 (1992): 169-185.