Wednesday, September 9, 2015

Predictable predator prey scaling - an ecological law?

Some ecologists react with skepticism about the idea of true laws in ecology. So when anything provides a strong and broad relationship between ecological variables, the response is often some combination of surprise, excitement, and disbelief. It’s not unexpected then that a new paper in Science - The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes – has received that reaction, and a fair amount of media coverage too.
Figure 1 from Hatton et al. 2015. "Predators include lion, hyena, and other large carnivores (20 to 140 kg), which compete for large herbivore prey from dik-dik to buffalo (5 to 500 kg). Each point is a protected area, across which the biomass pyramid becomes three times more bottom-heavy at higher biomass. This near ¾ scaling law is found to recur across ecosystems globally."
Ian Hatton and co-authors present robust evidence that across multiple ecosystems, predator biomass scales with prey biomass by a power law with an exponent of ~0.75. This suggests that ecosystems are typically bottom heavy, with decreasing amounts of predator biomass added as more prey biomass is added. The paper represents a huge amount of work (and is surprisingly long as Science papers typically go): the authors compiled a huge database from 2260 communities, representing multiple ecosystems (mammals, plants, protists, ectotherm, and more)(Figure below). Further, the same scaling relationship exists between community biomass and production, suggesting that production drops off as communities increase in density. This pattern appears consistently across each dataset.

Figure 5 from Hatton et al. 2015. "Similar scaling links trophic structure and production.
Each point is an ecosystem at a period in time (n = 2260 total from 1512 locations) along a biomass gradient. (A toP) An exponent k in bold (with 95% CI) is the least squares slope fit to all points n in each row of plots..."
Their analysis is classic macroecology, with all the strengths and weaknesses implicit. The focus is unapologetically on identifying general ecological patterns, with the benefit of large sample sizes, cross system analysis, and multiple or large spatial scales. It surpasses this focus only on patterns by exploring how this pattern might arise from simple predator-prey models. They demonstrate that, broadly, predator biomass can have the same scaling as prey production, which they show follows the 3/4 power law relationship. As for why prey production follows this rule, they acknowledge uncertainty as to the exact explanation, but suggest density dependence may be important.

Their finding is perhaps more remarkable because the scaling exponent has similarities to another possible law, metabolic scaling theory, particularly the ~0.75 exponent (or perhaps ~2/3, depending on who you talk to). It’s a bit difficult for me, particularly as someone biased towards believing in the complexities of nature, to explain how such a pattern could emerge from vastly different systems, different types of predators, and different abiotic conditions. The model they present is greatly 
Peter Yodzis' famous food web for
the Benguela ecosystem.
simplified, and ignores factors often incorporated into these models, such as migration between systems (and connectivity), non-equilibrium (such as disturbance), and prey refuges. There is variation in the scaling exponent, but it is not clear how to evaluate a large vs. small difference (for example, they found (section M1B) that different ways of including data produced variation of +/- 0.1 in the exponent. That sounds high, but it’s hard to evaluate). Trophic webs are typically considered complicated – there are parasites, disease, omnivores, cannibalism, changes between trophic levels with life stage. How do these seemingly relevant details appear to be meaningless?

There are multiple explanations to be explored. First, perhaps these consistent exponents represent a stable arrangement for such complex systems or consistency in patterns of density dependence. Consistent relationships sometimes are concluded to be statistical artefacts rather than actually driven by ecological processes (e.g. Taylor’s Law). Perhaps most interestingly, in such a general pattern, we can consider the values that don’t occur in natural systems. Macroecology is particularly good at highlighting the boundaries on relationships that are observed in natural systems, rather than always identifying predictable relationships. The biggest clues to understanding this pattern maybe in finding when (or if) systems diverge from the 0.75 scaling rule and why.

Ian A. Hatton, Kevin S. McCann, John M. Fryxell, T. Jonathan Davies, Matteo Smerlak, Anthony R. E. Sinclair, Michel Loreau. The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes. Science. Vol. 349 no. 6252. DOI: 10.1126/science.aac6284

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