On the use of biomass size spectra linear adjustments to design ecosystem indicators


  • Paúl Gómez-Canchong COPAS Sur-Austral, Centro de Investigación Oceanográfica en el Pacífico Sur-oriental, Universidad de Concepción - Departamento de Oceanografía, Universidad de Concepción
  • José M. Blanco Grupo de Investigación en Ecología Marina y Limnología (GEML), Departamento de Ecología, Universidad de Málaga
  • Renato A. Quiñones COPAS Sur-Austral, Centro de Investigación Oceanográfica en el Pacífico Sur-oriental, Universidad de Concepción - Departamento de Oceanografía, Universidad de Concepción




biomass size spectrum, Pareto distribution, bioenergetic model, linear biomass hypothesis, complex food webs, ecosystem management


Biomass size spectra describe the structure of aquatic communities ataxonomically. The slope (b) of the normalized biomass size spectrum (NBSS) is often used as an indicator of the impact of perturbations, such as pollution or overfishing. The NBSS intercept (a), has generally been ignored on the basis of a correlation between the NBSS slope and intercept, although this correlation has not been shown to be universal. We assessed whether the NBSS parameters are correlated using: (i) theoretical analysis, (ii) virtual communities randomly generated based only on statistical considerations, and (iii) virtual food webs changing over time following a dynamic bioenergetic model. We also analyzed whether the parameters of the Pareto distribution are correlated or not, using approaches (i) and (ii). We found that when communities change over time there is no single relationship between the two NBSS parameters, due to a dependence on the variation in total community abundance (N). We conclude that to characterize any aquatic system at least two parameters are necessary from the NBSS triad N, a, b. In the case of the Pareto distribution, both NPareto and bPareto are necessary.


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Bartkiw S., Boldt J., Livingston P., Walters G., Hoff G. 2007. Indicators of size diversity in the eastern Bering Sea. Copenhagen Denmark Ices 2007/E: 21.

Beddington J.R. 1975. Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol. 44: 331-340. http://dx.doi.org/10.2307/3866

Benoit E., Rochet M.J. 2004. A continuous model of biomass size spectra governed by predation and the effects of fishing on them. J. Theor. Biol. 226: 9-21. http://dx.doi.org/10.1016/S0022-5193(03)00290-X

Berlow E.L., Dunne J.A., Martinez N.D., Stark P.B., Williams R.J., Brose U. 2009. Simple prediction of interaction strengths in complex food webs. Proc. Natl. Acad. Sci. U.S.A. 106: 187-191. http://dx.doi.org/10.1073/pnas.0806823106 PMid:19114659 PMCid:PMC2629248

Bianchi G., Gislason H., Graham K., Hill L., Jin X., Koranteng K., Manickchand-Heileman S., Payá I., Sainsbury K., Sanchez F., Zwanenburg K. 2000. Impact of fishing on size composition and diversity of demersal fish communities. ICES J. Mar. Sci. 57: 558-571. http://dx.doi.org/10.1006/jmsc.2000.0727

Binduo X., Xianshi S. 2005. Variations in fish community structure during winter in the southern Yellow Sea over the period 1985–2002. Fish. Res. 71: 79-91. http://dx.doi.org/10.1016/j.fishres.2004.07.011

Blanchard J.L., Jennings S., Law R., Castle M.D., McCloghrie P., Rochet M.J., Benoit E. 2009. How does abundance scale with body size in coupled size-structured food webs? J. Anim. Ecol. 78: 270-280. http://dx.doi.org/10.1111/j.1365-2656.2008.01466.x PMid:19120607

Blanchard J.L., Law R., Castle M.D., Jennings S. 2011. Coupled energy pathways and the resilience of size-structured food webs. Theor. Ecol. 4(3): 289-300. http://dx.doi.org/10.1007/s12080-010-0078-9

Blanco J.M., Echevarría F., García C. 1994. Dealing with size spectra: some conceptual and mathematical problems. Sci. Mar. 58: 17-29.

Blumenshine S.C., Lodge D.M., Hodgson J.R. 2000. Gradient of fish predation alters body size distributions of lake benthos. Ecology 81(2): 374-386.

Borgmann U. 1983. Effect of somatic growth and reproduction on biomass transfer up pelagic food web as calculated from particle-size-conversion efficiency. Can. J. Fish. Aquat. Sci. 44: 136-140. http://dx.doi.org/10.1139/f87-316

Borgmann U. 1985. Predicting the effect of toxic substances on pelagic ecosystems. Sci. Total Environ. 44: 111-121. http://dx.doi.org/10.1016/0048-9697(85)90115-9

Borgmann U. 1987. Models on the shape of, and biomass flow up, the biomass size-spectrum. Can. J. Fish. Aquat. Sci. 44(suppl. 2): 136-140. http://dx.doi.org/10.1139/f87-316

Borgmann U., Whittle D.M. 1983. Particle-size-conversion efficiency and contaminant concentrations in Lake Ontario biota. Can. J. Fish. Aquat. Sci. 40: 328-336. http://dx.doi.org/10.1139/f83-048

Boudreau P.R., Dickie L.M., Kerr S. 1991. Body-size spectra of production and biomass as system-level indicators of ecological dynamics. J. Theor. Biol. 152: 329-339. http://dx.doi.org/10.1016/S0022-5193(05)80198-5

Boudreau P.R., Dickie L.M. 1992. Biomass spectra of aquatic ecosystems in relation to fisheries yield. Can. J. Fish. Aquat. Sci. 49: 1528-1538. http://dx.doi.org/10.1139/f92-169

Brose U., Berlow E.L., Martinez N.D. 2005. Scaling up keystone effects from simple to complex ecological networks. Ecol. Lett. 8: 1317-1325. http://dx.doi.org/10.1111/j.1461-0248.2005.00838.x

Brose U., Williams R.J., Martinez N.D. 2006. Allometric scaling enhances stability in complex food webs. Ecol. Lett. 9: 1228-1236. http://dx.doi.org/10.1111/j.1461-0248.2006.00978.x PMid:17040325

Brown J.H., Gillooly J.F., Allen A.P., Savage V.M., West G.B. 2004. Toward a metabolic theory of ecology. Ecology 85: 1771-1789. http://dx.doi.org/10.1890/03-9000

Brucet S., Boix D., López-Flores R., Badosa A., Moreno-Amich R., Quintana X.D. 2006. Size and species diversity of zooplankton communities in fluctuant Mediterranean salt marshes. Estuar. Coast. Shelf Sci. 67: 424-432. http://dx.doi.org/10.1016/j.ecss.2005.11.016

Camacho J., Sole R.V. 2001. Scaling in ecological size spectra. Europhys. Lett. 55(6): 774-780. http://dx.doi.org/10.1209/epl/i2001-00347-0

Capitán J.A., Delius G.W. 2010. Scale-invariant model of marine population dynamics. Physical Review E 81: 061901. http://dx.doi.org/10.1103/PhysRevE.81.061901 PMid:20866434

Choi J.S., Mazumder A., Hansell R.I.C. 1999. Measuring perturbation in a complicated, thermodynamic world. Ecol. Model. 117: 143-158. http://dx.doi.org/10.1016/S0304-3800(99)00042-3

Clauset A., Shalizi C.R., Newman M.E.J. 2009. Power-law distributions in empirical data. SIAM Rev. 51: 661-703. http://dx.doi.org/10.1137/070710111

Cousins S.H. 1985. Ecologists build pyramids again. New Scient. 106: 50-54.

Cury P., Shannon L., Shin Y. 2003. The functioning of marine ecosystems: a fisheries perspective. In: Sinclair M., Valdimarsson G. (eds), Responsible fisheries in the marine ecosystem. FAO, Rome, pp. 103-123. http://dx.doi.org/10.1079/9780851996332.0103

Daan N., Gislason H., Pope J.G., Rice J.C. 2005. Changes in the North Sea fish community: evidence of indirect effects of fishing? ICES J. Mar. Sci. 62: 177-188. http://dx.doi.org/10.1016/j.icesjms.2004.08.020

de Bruyn A.M.H., Marcogliese D.J., Rasmussen J.B. 2002. Altered body size distributions in a large river fish community enriched by sewage. Can. J. Fish. Aquat. Sci. 59: 818-828.

DeAngelis D.L., Goldstein R.A., O'Neill R.V. 1975. A model for trophic interactions. Ecology 56: 881-892. http://dx.doi.org/10.2307/1936298

Dickie L.M., Kerr S.R., Boudreau P.R. 1987. Size-dependent processes underlying regularities in ecosystem structure. Ecol. Monogr. 57: 233-250. http://dx.doi.org/10.2307/2937082

Dimech, M., Camilleri, M.,Hiddink, J.G., Kaiser M.J., Ragonese S., Schembri P.J. 2008. Differences in demersal community structure and body-size spectra within and outside the Maltese Fishery Management Zone. Sci. Mar. 72(4): 669-682. http://dx.doi.org/10.3989/scimar.2008.72n4669

Drgas A., Radziejewska T., Warzocha J. 1998. Biomass size Spectra of near-shore shallow-water benthic communities in the Gulf of Gdansk (Southern Baltic Sea). Mar. Ecol. 19(3): 209-228. http://dx.doi.org/10.1111/j.1439-0485.1998.tb00463.x

Echevarría F., Carrillo P., Jimenez F., Sanchez-Castillo P., Cruz Pizarro L., Rodriguez J. 1990. The size-abundance distribution and taxonomic composition of plankton in an oligotrophic, high mountain lake (La Caldera, Sierra Nevada, Spain). J. Plankton Res. 12(2): 415-422. http://dx.doi.org/10.1093/plankt/12.2.415

Finlay K., Beisner B.E., Patoine A., Pinel-Alloul B. 2007. Regional ecosystem variability drives the relative importance of bottomup and top-down factors of zooplankton size spectra. Can. J. Fish. Aquat. Sci. 64: 516-529. http://dx.doi.org/10.1139/f07-028

Gaedke U. 1993. Ecosystem analysis based on biomass-size distributions: a case study of a plankton community in a large lake. Limnol. Oceanogr. 38: 112-127. http://dx.doi.org/10.4319/lo.1993.38.1.0112

Garcia S.M., Kolding J., Rice J., Rochet M.J., Zhou S., Arimoto T., Beyer J.E., Borges L., Bundy A., Dunn D., Fulton E.A., Hall M., Heino M., Law R., Makino M., Rijnsdorp A.D., Simard F., Smith A.D.M. 2012. Reconsidering the consequences of selective fisheries. Science 335(6072): 1045-1047. http://dx.doi.org/10.1126/science.1214594 PMid:22383833

Gislason H., Rice J. 1998. Modelling the response of size and diversity spectra of fish assemblages to changes in exploitation. ICES J. Mar. Sci. 55: 362-370. http://dx.doi.org/10.1006/jmsc.1997.0323

Gobert B. 1994. Size structures of demersal catches in a multispecies multigear tropical fishery. Fish. Res. 19:87-104. http://dx.doi.org/10.1016/0165-7836(94)90016-7

Gómez-Canchong P., Qui-ones R.A., Brose U. 2013. Robustness of normalized biomass size-structure across ecological networks. Theor. Ecol. 6: 45-56. http://dx.doi.org/10.1007/s12080-011-0156-7

Gómez-Canchong P., Qui-ones R.A., Manjarrés L.M. 2011. Size structure of a heavily fished benthic/demersal community by shrimp trawling in the Colombian Caribbean Sea. Lat. Am. J. Aquat. Res. 39(1): 43-55.

Jennings S., Dinmore T.A., Duplisea D.E., Warr K.J., Lancaster J.E. 2001. Trawling disturbance can modify benthic production processes. J. Anim. Ecol. 70: 459-475. http://dx.doi.org/10.1046/j.1365-2656.2001.00504.x

Jennings S., Dulvy N.K. 2005. Reference points and reference directions for size-based indicators of community structure. ICES J. Mar. Sci. 62: 397-404. http://dx.doi.org/10.1016/j.icesjms.2004.07.030

Jennings S., Kaiser M.J. 1998. The effects of fishing on marine ecosystems. Adv. Mar. Biol. 34: 201-352. http://dx.doi.org/10.1016/S0065-2881(08)60212-6

Kerr S.R., Dickie L.M. 2001. Biomass Spectrum. Columbia University Press.

Law R., Plank M.J., James A., Blanchard J.L. 2009. Size spectra dynamics from stochastic predation and growth of individuals. Ecology 90(3): 802-811. http://dx.doi.org/10.1890/07-1900.1 PMid:19341149

Lundvall D., Svanbäck R., Persson L., Byström P. 1999. Size-dependent predation in piscivores: interactions between predator foraging and prey avoidance abilities. Can. J. Fish. Aquat. Sci. 56: 1285-1292.

Macpherson E., Gordoa A., García-Rubies A. 2002. Biomass size spectra in littoral fishes in protected and unprotected areas in the NW Mediterranean. Estuar. Coast. Shelf Sci. 55: 777-788. http://dx.doi.org/10.1006/ecss.2001.0939

Macpherson E., Gordoa A. 1996. Biomass spectra in benthic fish assemblages in the Benguela system. Mar. Ecol. Prog. Ser. 138: 27-32. http://dx.doi.org/10.3354/meps138027

Makarieva A.M., Gorshkov V.G., Li B.L. 2004. Body size, energy consumption and allometric scaling: a new dimension in the diversity-stability debate. Ecol. Complex. 1: 139-175. http://dx.doi.org/10.1016/j.ecocom.2004.02.003

Mara-ón E., Cerme-o P., Rodríguez J., Zubkov M.V., Harris R.P. 2007. Scaling of phytoplankton photosynthesis and cell size in the ocean. Limnol. Oceanogr. 52(5): 2120-2198.tr>

McAbendroth L., Ramsay P.M., Foggo A., Rundle S.D., Bilton D.T. 2005. Does macrophyte fractal complexity drive invertebrate diversity, biomass and body size distributions? Oikos 111: 279-290. http://dx.doi.org/10.1111/j.0030-1299.2005.13804.x

MoloneyC.L., Field J.G. 1985. Use of particle-size data to predict potential pelagic-fish yields of some southern African areas. S. Afr. J. Mar. Sci. 3: 119-128. http://dx.doi.org/10.2989/025776185784461144

Murawski S.A., Idoine J.S. 1992. Multispecies size composition: A conservative property of exploited fishery systems? J. Northw. Atl. Fish. Sci. 14: 79-85. http://dx.doi.org/10.2960/J.v14.a5

Odum E.P. 1971. Fundamentals of Ecology. Third ed. Saunders, Philadelphia.

Pareto V. 1897. Cours d'economie politique. In: Busino G. (ed.) 1964. OEuvres complètes, Busino, vol. 1, Genève.

Pauly D., Christensen V. 1995. Primary production required to sustain global fisheries. Nature (374): 255-257. http://dx.doi.org/10.1038/374255a0

Peterson I., Wroblewski J.S. 1984. Mortality rate of fishes in the pelagic ecosystem. Can. J. Fish. Aquat. Sci. 41: 1117-1120. http://dx.doi.org/10.1139/f84-131

Platt T. 1985. Structure of the marine ecosystem: Its allometric basis. In: Ulanowicz R.E., Platt T. (eds), Ecosystem theory for biological oceanography. Can. Bull. Fish. Aquat. Sci. 213: 55-64.

Platt T., Denman K. 1977. Organization in the pelagic ecosystem. Helgol. Wiss. Meresunter. 30: 575-581. http://dx.doi.org/10.1007/BF02207862

Platt T., Denman K. 1978. The structure of the pelagic marine ecosystems. Rapp. Proc.-Verb. Reun. Cons. Perm. Int. Explor. Mer. 173: 60-65.

Pope J.D., Stokes T.K., Murawski S.A., Idoine S.I. 1987. A comparison of fish size composition in the North Sea and on Georges Bank. In: Wolff W., Soeder C.J., Drepper F.R. (eds), Ecodynamics, Contributions to Theoretical Ecology. Springer-Verlag, Berlin, pp. 146-152.

Quintana X.D., Comín F.A., Moreno-Amich R. 2002. Biomass-size spectra in aquatic communities in shallow fluctuating Mediterranean salt marshes (Empordà wetlands, NE Spain). J. Plankton Res. 24: 1149-1161. http://dx.doi.org/10.1093/plankt/24.11.1149

Quintana X.D., Brucet S., Boix D., López-Flores R., Gascón S., Badosa A., Sala J., Moreno-Amich R., Egozcue J.J. 2008. A nonparametric method for the measurement of size diversity with emphasis on data standarization. Limnol Oceanogr: Meth 6: 75-86. http://dx.doi.org/10.4319/lom.2008.6.75

Quiñones R.A. 1994. A comment on the use of allometry in the study of pelagic ecosystem processes. Sci. Mar. 58: 11-16. Qui-ones R.A., Platt T., Rodríguez J. 2003. Patterns of biomass size spectra from oligotrophic waters of the Northwest Atlantic. Prog. Oceanogr. 57: 405-427.

Quiroga E., Qui-ones R.A., Palma M., Sellanes J., Gallardo V.A., Gerdes D., Rowe G. 2005. Biomass size-spectra of macrobenthic communities in the oxygen minimum zone off Chile. Estuar. Coast. Shelf Sci. 62: 217-231. http://dx.doi.org/10.1016/j.ecss.2004.08.020

Real L.A. 1977. Kinetics of functional response. Am. Nat. 111: 289-300. http://dx.doi.org/10.1086/283161

Rice J., Gislason H. 1996. Patterns of change in the size spectra of numbers and diversity of the North Sea fish assemblage, as reflected in surveys and models. ICES J. Mar. Sci. 53: 1214-1225. http://dx.doi.org/10.1006/jmsc.1996.0146

Robson B.J., Barmuta L.A., Fairweather P.G. 2005. Methodological and conceptual issues in the search for a relationship between animal body-size distributions and benthic habitat architecture. Mar. Freshw. Res. 56: 1-11. http://dx.doi.org/10.1071/MF04210

Rochet M.J., Benoît E. 2011. Fishing destabilizes the biomass flow in the marine size spectrum. Proc. R. Soc. B http://www.ncbi.nlm.nih.gov/pubmed/21632631.

Rodriguez J. 1994. Some comments on the size based structural analysis of the pelagic ecosystem. Sci. Mar. 58: 1-10.

Rodriguez J., Mullin M. 1986. Relation between biomass and body weight of plankton in a steady state oceanic ecosystem. Limnol. Oceanogr. 31(2): 361-370. http://dx.doi.org/10.4319/lo.1986.31.2.0361

San Martin E., Harris R.P., Irigoien X. 2006. Latitudinal variation in plankton size spectra in the Atlantic Ocean. Deep-Sea Res. Part II 53: 1560-1572. http://dx.doi.org/10.1016/j.dsr2.2006.05.006

Schwinghamer P. 1985. Observations on size-structure and pelagic coupling of some shelf and abyssal benthic communities. In: Gibbs P.E. (ed.). Proceedings of the 19th European Marine Biology Symposium, September 1984, pp. 347-360.

Sheldon R.W., Prakash A., Sutcliffe Jr W.H. 1972. The size distribution of particles in the ocean. Limnol. Oceanogr. 17: 327-340. http://dx.doi.org/10.4319/lo.1972.17.3.0327

Sheldon R.W., Sutcliffe Jr W.H., Prakash A. 1977. Structure of pelagic food chain and relationships between plankton and fish production. J. Fish. Res. Board Can. 34: 2334-2353. http://dx.doi.org/10.1139/f77-314

Shin Y.J., Cury P. 2004. Using an individual-based model of fish assemblages to study the response of size spectra to changes in fishing. Can. J. Fish. Aquat. Sci. 61: 414-431. http://dx.doi.org/10.1139/f03-154

Shin Y.J., Rochet M.J., Jennings S., Field J.G., Gislason H. 2005. Using size-based indicators to evaluate the ecosystem effects of fishing. ICES J. Mar.Sci. 62: 384-396. http://dx.doi.org/10.1016/j.icesjms.2005.01.004

Silvert W., Platt T. 1978. Energy flux in the pelagic ecosystem: a time dependent equation. Limnol. Oceanogr. 18: 813-816. http://dx.doi.org/10.4319/lo.1978.23.4.0813

Silvert W., Platt T. 1980. Dynamic energy-flow model of the particle size-distribution in pelagic ecosystems. In: Kerfoot W.C. (ed.), Evolution and ecology of zooplankton communities. The University Press of New England, Hanover, New Hampshire, pp. 754-763.

Skalsk, G.T., Gillia, J.F, 2001. Functional responses with predator interference: viable alternatives to the Holling type II model. Ecology 82: 3083-3092. http://dx.doi.org/10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2

Sprules W.G., Goyke A.P. 1994. Size-Based Strudure and Production in the Pelagia of Lakes Ontario and Michigan. Can. J. Fish. Aquat. Sci. 51: 2603-2611. http://dx.doi.org/10.1139/f94-260

Sprules W.G., Munawar M. 1986. Plankton size spectra in relation to ecosystem productivity, size and perturbation. Can. J. Fish. Aquat. Sci. 43: 1789-1794. http://dx.doi.org/10.1139/f86-222

Thiebaux M.L., Dickie L.M. 1992. Models of aquatic biomass size spectra and the common structure of their solutions. J. Theor. Biol. 159: 147-161. http://dx.doi.org/10.1016/S0022-5193(05)80699-X

Thiebaux M.L., Dickie L.M. 1993. Structure of the body-size spectrum of the biomass in aquatic ecosystems: A consequence of allometry in predator-prey interactions. Can. J. Fish. Aquat. Sci. 50:1308-1317. http://dx.doi.org/10.1139/f93-148

Thomann R.V. 1979. An analysis of PCB in Lake Ontario using a size-dependent food chain model. In: Scavia D., Robertson A. (eds), Perspectives on Lake Ecosystem Modelling. Ann. Arbor Sci. 293-320.

Thomann R.V. 1981. Equilibrium model of fate of microcontaminants in diverse aquatic food chains. Can. J. Fish. Aquat. Sci. 38: 280-296. http://dx.doi.org/10.1139/f81-040

Vidondo B., Prairie Y., Blanco J.M., Duarte C.M. 1997. Some aspects of the analysis of size spectra in aquatic ecology. Limnol. Oceanogr. 42(1): 184-192. http://dx.doi.org/10.4319/lo.1997.42.1.0184

Wang H., Morrison W., Singh A., Weiss H. 2009. Modeling inverted biomass pyramids and refuges in ecosystems. Ecol. Model. 220: 1376-1382. http://dx.doi.org/10.1016/j.ecolmodel.2009.03.005

Warwick R.M., Collins N.R., Gee J.M., George C.L. 1986. Species size distributions of benthic and pelagic Metazoa: Evidence for interaction. Mar. Ecol. Prog. Ser. 34: 63-68. http://dx.doi.org/10.3354/meps034063

White E.P., Ernest S.K.M., Kerkhoff A.J., Enquist B.J. 2007 Relationships between body size and abundance in ecology. Trends Ecol. Evol. 22: 323-330. http://dx.doi.org/10.1016/j.tree.2007.03.007 PMid:17399851

Williams R.J. Martinez N.D. 2000. Simple rules yield complex webs. Nature 404: 180-183. http://dx.doi.org/10.1038/35004572 PMid:10724169

Williams R.J., Martinez N.D. 2004. Stabilization of chaotic and non permanent food web dynamics. Eur. Phys. J. B. 38: 297-303. http://dx.doi.org/10.1140/epjb/e2004-00122-1

Yodzis P., Innes S. 1992. Body size and consumer-resource dynamics. Am. Nat. 139: 1151-1175. http://dx.doi.org/10.1086/285380

Yvon-Durocher G., Montoya J.M., Trimmer M., Woodward G. 2011. Warming alters the size spectrum and shifts the distribution of biomass in freshwater ecosystems. Glob. Chang. Biol. 17: 1681-1694. http://dx.doi.org/10.1111/j.1365-2486.2010.02321.x

Zhou M. 2006. What determines the slope of a plankton biomass spectrum? J. Plankton Res. 28(5): 437-448. http://dx.doi.org/10.1093/plankt/fbi119




How to Cite

Gómez-Canchong P, Blanco JM, Quiñones RA. On the use of biomass size spectra linear adjustments to design ecosystem indicators. Sci. mar. [Internet]. 2013Jun.30 [cited 2024Apr.13];77(2):257-68. Available from: https://scientiamarina.revistas.csic.es/index.php/scientiamarina/article/view/1451