How long is too long?

This past weekend was our departmental retreat, where we all head out to a big old house for a whole day of short talks and good food. We also invite our prospective students to come so we can show off how awesome our department is. This year I gave a talk on some recent work I have been doing on trophic chain length. So I thought I would write up a little bit about what I talked about/what I hope to write about. Unfortunately, even though I am a fan of open science I think I am going to wait to discuss methods and results until I have the paper ready to submit at least.

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Trophic chains are representations of energy flow from a basal species to a higher level consumer. Based on energy flow, we can assign different organisms to a specific trophic level. As a general rule a species trophic level is 1+the highest trophic level it consumes. Thus one way we can characterize a community is by the number of trophic levels. There is an interesting pattern that has been found in the number of trophic levels that are most often observed in nature. In fact, it is rare to see more than 3 or for trophic levels in a community.

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A slide I used to illustrate the energy efficiency idea.

One of the original hypotheses for this apparent constraint on the number of trophic levels in a community is based on the amount of energy available to top predators. This idea was developed by ecologists such as Elton and Lindeman and was based on the idea that energy moves up a trophic chain with low efficiency. A commonly accepted value is 10% efficiency, meaning that approximately 90% of the energy in prey is lost to the consumer.

With such a low efficiency of transfer, there should be relatively little energy available to the top of the chain. Larry Slobodkin once wrote of a hypothetical species occupying a trophic level greater than 20 that would require the resources of an entire continent to support it. Since its conception however, several flaws have been noted in the energetic efficiency hypothesis. Namely, given a 10% efficiency, we would expect to see 1 trophic level added for every 10-fold increase in energy at the base of the chain. Empirical evidence does not support this prediction as far as I can tell. Ecologists have observed  variation in productivity (a proxy for energy) of about 3-5 orders of magnitude, but the apparent constraint on the number of trophic levels is still observed (it is still 3-4 levels).

There are a number of other hypotheses that have been proposed as alternative arguments for why trophic chains are so short (why chains are only 3-4 levels high). What comes to mind are the productive-space hypothesis (most recently championed by Post), and another on adaptive foraging (proposed by Kondoh). I have some problems with the productive-space hypothesis, however, primarily that there is conflicting evidence in the literature. Of the four studies I have looked at that examine the productive-space hypothesis two found support, and two failed to find support. Post argues that the reason for this is in the manner in which productive-space is defined. It can either be the product of the size of the environment and productivity, or it can be measured with productivity and size being separate gradients. There is a simpler explanation out there, in my opinion, proposed by Pimm and Lawton in 1977.

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From Pimm and Lawton 1977, a figure to illustrate their sample communities.

In their paper, “Number of trophic levels in ecological communities,” Pimm and Lawton proposed and tested the dynamic constraints hypothesis. Their idea was that longer chains are dynamically unstable, and as such have a greater risk of extinction. They tested their idea by sampling Jacobian matrices for four species communities organized into varying numbers of trophic levels (see figure to the right). They drew sample values from two uniform distributions. For the impact of the predator on the prey they sampled from (0,10), and (-0.1,0) for the impact of prey on the predator. For each of these sampled matrices they determined whether or not the system was locally stable. For those that were locally stable, they also assessed the resilience (the time it takes to return to equilibrium following a perturbation). I think their results are relatively interesting.

Pimm and Lawton found that while the number of trophic levels had no impact on the stability of their communities (although omnivory did), there was an impact of the number of levels on resilience. Specifically, as the number of trophic levels increased the median amount of time it takes to return to equilibrium increases as well.

Cut to 20 years later and Bob Sterner and colleagues decided to take a second look at what Pimm and Lawton did. Their paper asserts that Pimm and Lawton confounded two main effects, that of the number of trophic levels and the number of self-damping terms. The problem they found was that when Pimm and Lawton decreased the number of trophic levels in their sample systems they did not control for the number of self-damping terms (essentially the number of levels with density dependence). Their chains with fewer trophic levels also had more density dependence terms. Sterner et al. examined food chains of 2-8 levels with a variety of organizations. They found that the number of density dependence terms has an impact on stability, the more levels with density dependence the more stable the system. Furthermore, when controlling for these terms, Sterner et al. found no effect of the number of levels on stability.

This seems like pretty damning evidence against the hypothesis of dynamic constraints. But there are a few things missing in both of these studies that may provide more meaningful support, but I will talk about that later.

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