Trying to fit a square peg into a round hole

This is a quick review of a paper discussing a relatively new technique in food web comparisons across multiple ecosystems using stable isotopes. Layman et al. (2007) report a new methodology for quantitatively characterizing community-wide aspects of trophic structure.

The authors review six community-wide metrics reflecting important aspects of trophic structure based on δ¹³C - δ¹⁵N bi-plots. The metrics discussed revolve around a "Convex Hull" that is formed by joining all peripheral isotopic signatures in a δ¹³C - δ¹⁵N bi-plot. An example of this is illustrated in Fig.1 below.

Fig.1 Stable isotope bi-plots based on species collected from a Bahamian tidal creek. Each point on the graph represents the mean value of 2–9 individuals of that particular species with error bars around the mean omitted for simplicity. Calculation of community-wide metrics was based on the distribution of species in niche space: diamonds, fish; squares, crustaceans; triangles, mollusks; and circles, other invertebrate taxa. Solid symbols are used to illustrate how individual species' niches, and dispersion of those niches, affect values of the community-wide metrics. The convex hull used to calculate the TA metric is represented by the dotted line.

The six metrics include: δ¹⁵N range,  δ¹³C range, Total area, Mean distance to centroid, Mean nearest neighbour distance and Standard deviation of nearest neighbour distance.

1) δ¹⁵N range - Distance between the two species with the most enriched and most depleted δ¹⁵N values. This is one representation of vertical structure within a food web.

2) δ¹³C range - Distance between the two species with the most enriched and most depleted δ¹³C values. This provides insight into basal carbon sources for the food web. Increased values would be expected in food webs in which there are multiple basal resources with varying δ¹³C values.

3) Total area - Convex hull area encompassed by all species in δ¹³C - δ¹⁵N bi-plot space. This represents a measure of the total amount of niche space occupied, a proxy for the total extent of trophic diversity within a food web.

4) Mean distance to centroid - Calculated taking the average δ¹³C and δ¹⁵N values for the entire food web (centroid), and determining the distance from individual isotope signals to the centroid. This metric provides a measure of the average degree of trophic diversity within a food web.

5) Mean nearest neighbour distance - Just as it sounds, this is the mean of the Euclidean distances to each species' nearest neighbour in bi-plot space. This is a measure of the overall density of species packing.

6) Standard deviation of nearest neighbour distance - This is a measure of the evenness of species packing in bi-plot space that is less influenced than nearest neighbour distance by sample size

Here is an illustrated example provided by the authors that really helps in understanding these metrics.


Fig. 2. Conceptual models (B-D) of different ways food web structure can be altered through the addition of three new species to an existing tidal creek food web (A). Symbols are consistent with Fig. 1, and solid symbols represent a new species added in each scenario. The ways  community-metrics will vary under each scenario are depicted below each graph.

 I was really excited when I read this paper. It gave me another perspective when answering my thesis questions. I think this method is would be a perfect match for determining community shifts (or lack thereof) after the insertion of a new species into the food web. Changes in these convex hulls will provide insight to the community response to the invading species.

This article is a great read. There are some set-backs and limitations with this technique, but it is fairly new in food web ecology field. Enjoy!

Reference:
Layman, C.A., Arrington, D.A., Montana, C.G., and Post, D.M. (2007) Can stable isotope ratios provide for community-wide measures of trophic structure? Ecology 88(1): 42-48.