Research Article

The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes

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Science  04 Sep 2015:
Vol. 349, Issue 6252, aac6284
DOI: 10.1126/science.aac6284

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  1. African large-mammal communities are highly structured.

    In lush savanna, there are three times more prey per predator than in dry desert, a pattern that is unexpected and systematic. [Photo: Amaury Laporte]

  2. Fig. 1 African predator-prey communities exhibit systematic changes in ecosystem structure.

    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.

  3. Fig. 2 The predator-prey power law exponent k describes relative changes in pyramid shape.

    The slope k (from logC = k logB + logc) identifies how the predator-prey ratio changes along a biomass gradient. Top-heavy and bottom-heavy refer to relative tendencies at higher biomass.

  4. Fig. 3 Emergent trophic structure in African savanna.

    Large mammal abundance is aggregated across systems to show size structure and trophic structure. Trophic structure follows a regular pattern that is not evident from lower-level structure. These data are also shown in Fig. 1 and Fig. 5, A and B. Further details are in section M2. (A) African large mammals vary greatly in density, estimated for 38 species in 23 protected areas at different times. (B) Size structure of predator and prey communities is nearly constant across the biomass gradient. Populations from (A) are aggregated into their respective predator and prey communities, so that each point is an ecosystem. Mean body mass averages over all individuals in each community (both slopes are k = 0.03 and are not significant). Relative frequencies of different size classes are also near constant, as shown by histograms (bars sum to 1). (C) Carnivore-to-herbivore biomass ratios show significant declines at greater prey biomass (P value < 10−9). Data are as in Fig. 1 but show the predator/prey ratio, which changes threefold across the biomass gradient.

  5. Fig. 4 A predator-prey model (C, B) with two functions (P, Q).

    Different models are specified based on the functions for prey production P(B) and prey consumption by predators, Q(B,C). Predator production, gQ, depends on the growth efficiency g in converting consumption into offspring. Predator loss is mC, where m is mortality rate.

  6. Fig. 5 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 to P) An exponent k in bold (with 95% CI) is the least squares slope fit to all points n in each row of plots. Further details are in section M3 and table S1.

  7. Fig. 6 Individual production to body mass exhibits near ¾ scaling across taxa.

    Maximum individual production includes somatic growth and offspring production. Each point is an individual, representing 1098 species over 127 taxonomic orders. Further details are in section M4 and table S3.

  8. Fig. 7 Ecosystem and individual growth patterns are similar.

    Least squares exponents k (and 95% CI) for production-mass across ecosystems (from Fig. 5) and individuals (from Fig. 6) are often near k = ¾. Each exponent estimate is for n > 100 data points. Seagrass data (n = 104; Fig. 5M) were excluded. Further details are in section M4.

  9. Fig. 8 Mean body mass is poorly correlated to community biomass except in plankton.

    Points are mostly the same as those in Fig. 5. Mean body mass averages over all individuals in a community. The slopes k in (A) to (D) are not significant (N.S; all R2 < 0.05), but plankton size structure varies positively with biomass (E and F). Mammal systems (A and B) include data from Fig. 3B. Further details are in section M5 and table S4.

  10. Fig. 9 African savanna ecosystem characteristics.

    These data are shown in Fig. 1, but here abundance in different time periods are averaged to give equal weight to each protected area (k = 0.75 ; 95% CI = 0.66, 0.83; n = 23). We excluded migrant biomass in Serengeti and Masai Mara, which include the largest three outliers above the line (ser and mas). Mega-herbivores were excluded as prey in all but the Savuti region of Chobe NP (sav), where lions prey on elephants (116). When excluded from Savuti, the point becomes a notable outlier (savElx). The largest outlier below the line is Katavi NP (kat), where previous research has reported relatively few predators (118). Tarangire (tar) is not averaged due to large biomass fluctuations. Black circles are the ecosystems in which time series data are shown in Fig. 10D.

  11. Fig. 10 African mammal biomass, numerical density relations, and population time series.

    (A) This relation duplicates Fig. 9 (colored according to rainfall) to allow comparisons to the pyramid of numbers (B) and prey biomass including mega-herbivores (C). Note that Savuti is excluded and Tarangire is not averaged for reasons outlined in Fig. 9. (B) Predator-prey total numerical density shows a similar pattern because of the near invariance of mean body mass with community biomass (Fig. 3B). The lower exponent is driven largely by two areas of Kruger NP (sab and nwa; orange triangles) with high densities of impala. The exponent for all ecosystem time periods, omitting sab and nwa, is k = 0.70 (n = 42; R2 = 0.90). (C) Predator to total herbivore biomass, including all the prey in (A) plus all mega-herbivores (giraffe to elephant). The exponent for all ecosystem-time periods is k = 0.70 (n = 44; R2 = 0.67). (D) Population biomass time series for dominant species in each of four protected areas with complete ecosystem censuses. Replicate years used in Fig. 1 are labeled in color and chosen on the basis of available census data for all species. Total prey biomass has a consistently lower coefficient of variation (standard deviation divided by mean; CV) than the population biomass it comprises for all but two populations in Serengeti (ser), where data are sparse. The CV for total prey biomass is as follows (with min. and max. CV for the six dominant herbivore populations): kru—0.196 (0.20, 0.40); hlu—0.29 (0.32, 0.69); ser—0.30 (0.20, 0.53); ngo—0.16 (0.19, 0.73).

  12. Fig. 11 Published cross-system meta-analyses contributing to regressions in Fig. 5.

    (A to L) These plots each derive from a single source and show similar scaling to combined plots in Fig. 5 (table S2).

  13. Fig. 12 A near-constant fraction of primary production is transferred to herbivores and decomposers.

    Data show near-linear (k = 1) scaling in the fraction of primary production (A) transferred to herbivore consumption and (B) recycled to decomposers, across global productivity gradients. This suggests few systematic changes in the ratios of flux rates. These data and regressions are reported in Cebrian and Cebrian and Lartigue (36, 37), combining 196 original published sources. Further details are available in the original studies (36, 37) and table S5.

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