Advertisement

Static ecological system measures

A holistic analysis of compartmental systems
  • Huseyin CoskunEmail author
ORIGINAL PAPER

Abstract

A new mathematical method for the static analysis of ecological systems has recently been developed by the author and was presented in a separate article. Based on this methodology, multiple new ecological system measures and indices of matrix, vector, and scalar types are systematically introduced in the present paper. These mathematical system analysis tools are quantitative ecological indicators that monitor the flow distribution and storage organization, quantify the direct, indirect, acyclic, cycling, and transfer (diact) effects and utilities of one compartment—directly or indirectly—on another, and determine the residence times and compartmental activity levels. Major flow- and stock-related concepts and quantities of the current static network analyses are also integrated with the proposed measures and indices within this novel and unifying mathematical framework. This comprehensive framework enables a holistic view and analysis of static ecological systems. A quantitative technique for the classification and characterization of interspecific interactions and the determination of their strength within food webs is also developed. The proposed methodology allows for both input- and output-oriented analyses of ecological networks. The holistic perspective of the proposed methodology is extended further from the input-oriented to the output-oriented analysis. The proposed system measures and indices, thus, extract detailed information about ecosystems’s characteristics, as well as their functions, properties, behaviors, and various other system attributes that are potentially hidden in and even obscured by data.

Keywords

Complex systems theory Ecological network analysis Compartmental systems System and subsystem partitioning Subsystem scaling diact flows and storages diact effect measures and indices diact utility measures and indices diact residence times Food webs Interspecific interactions Input-output economics Epidemiology Infectious diseases Toxicology Pharmacokinetics Neural networks Chemical and biological systems Control theory Information theory Information diffusion Social networks Computer networks Malware propagation Traffic flow 

Notes

Acknowledgements

The author would like to thank Hasan Coskun for useful discussions and his helpful comments that improved the manuscript.

References

  1. Allen T, Giampietro M (2014) Holons, creaons, genons, environs, in hierarchy theory: where we have gone. Ecol Model 293:31–41. ISSN 03043800.  https://doi.org/10.1016/j.ecolmodel.2014.06.017 CrossRefGoogle Scholar
  2. Bailey R, Allen JK, Bras B (2004) Applying ecological input-output flow analysis to material flows in industrial systems part i: tracing flows. J Ind Ecol 8(1–2):45–68.  https://doi.org/10.1162/1088198041269346  https://doi.org/10.1162/1088198041269346 Google Scholar
  3. Belgrano A, Scharler UM, Dunne J, Ulanowicz RE (2005) Aquatic food webs: an ecosystem approach. Oxford University Press, OxfordCrossRefGoogle Scholar
  4. Borrett SR, Lau MK (2014) Enar: an R package for ecosystem network analysis. Methods Ecol Evol 5 (11):1206–1213.  https://doi.org/10.1111/2041-210x.12282 CrossRefGoogle Scholar
  5. Borrett SR, Whipple SJ, Patten BC, Christian RR (2006) Indirect effects and distributed control in ecosystems: temporal variation of indirect effects in a seven-compartment model of nitrogen flow in the Neuse River Estuary, USA—time series analysis. Ecol Model 194(1):178–188.  https://doi.org/10.1016/j.ecolmodel.2005.10.011 CrossRefGoogle Scholar
  6. Borrett SR, Freeze MA, Salas AK (2011) Equivalence of the realized input and output oriented indirect effects metrics in ecological network analysis. Ecol Model 222(13):2142–2148. ISSN 03043800.  https://doi.org/10.1016/j.ecolmodel.2011.04.003 CrossRefGoogle Scholar
  7. Christensen V, Pauly D (1992) ECOPATH II-a software for balancing steady-state ecosystem models and calculating network characteristics. Ecol Model 61(3):169–185CrossRefGoogle Scholar
  8. Christian RR, Thomas CR (2000) Neuse River Estuary modeling and monitoring project stage 1: network analysis for evaluating the consequences of nitrogen loading. Technical Report UNC-WRRI-2000-325-f, Biology Department East Carolina UniversityGoogle Scholar
  9. Christian RR, Boyer JN, Stanley DW (1991) Multi-year distribution patterns of nutrients within the Neuse River Estuary, North Carolina. Mar Ecol Prog Ser 71:259–274CrossRefGoogle Scholar
  10. Coskun H (2018a) Dynamic ecological system analysis. Preprint.  https://doi.org/10.31219/osf.io/35xkb
  11. Coskun H (2018b) Dynamic ecological system measures. Preprint.  https://doi.org/10.31219/osf.io/j2pd3
  12. Coskun H (2018c) Nonlinear decomposition principle and fundamental matrix solutions for dynamic compartmental systems. Preprint.  https://doi.org/10.31219/osf.io/cyrzf
  13. DeAngelis DL (1980) Energy flow, nutrient cycling, and ecosystem resilience. Ecol 61(4):764–771CrossRefGoogle Scholar
  14. Fath BD (2007) Network mutualism: positive community-level relations in ecosystems. Ecol Model 208(1):56–67.  https://doi.org/10.1016/j.ecolmodel.2007.04.021 CrossRefGoogle Scholar
  15. Fath BD, Borrett SR (2006) A Matlab® function for network environ analysis. Environ Model Softw 21 (3):375–405. ISSN 13648152.  https://doi.org/10.1016/j.envsoft.2004.11.007 CrossRefGoogle Scholar
  16. Fath BD, Patten BC (1998) Network synergism: emergence of positive relations in ecological systems. Ecol Model 107(2–3):127–143. ISSN 03043800.  https://doi.org/10.1016/S0304-3800(97)00213-5 CrossRefGoogle Scholar
  17. Fath BD, Patten BC (1999) Review of network the foundations of environ analysis. Ecosystems 2(2):167–179CrossRefGoogle Scholar
  18. Finn J (1976) Measures of structure and functioning derived from analysis of flows. J Theor Biol 56(23):363–380CrossRefGoogle Scholar
  19. Finn JT (1980) Flow analysis of models of the Hubbard Brook ecosystem. Ecology 61(3):562–571. ISSN 00129658CrossRefGoogle Scholar
  20. Hannon B (1973) The structure of ecosystems. J Theor Biol 41(3):535–546CrossRefGoogle Scholar
  21. Higashi M, Patten BC (1989) Dominance of indirect causality in ecosystems. Am Nat 133(2):288–302CrossRefGoogle Scholar
  22. Hirata H, Ulanowicz RE (1985) Information theoretical analysis of the aggregation and hierarchical structure of ecologial networks. J Theor Biol 116(1635):321–341CrossRefGoogle Scholar
  23. Holt RD (1997) Community modules. In: Gange AC, Brown VK (eds) Multitrophic interactions in terrestrial ecosystems, 36th symposium. British Ecological Society, Blackwell Science, pp 333–349Google Scholar
  24. Holt RD (1977) Predation, apparent competition, and the structure of prey communities. Theor Popul Biol 12(2):197–229. ISSN 10960325.  https://doi.org/10.1016/0040-5809(77)90042-9 CrossRefGoogle Scholar
  25. Kazanci C (2009) Network calculations II: a user’s manual for EcoNet. In: Handbook of ecological modelling and informatics. WIT Press Ltd, pp 325–350.  https://doi.org/10.2495/978-1-84564-207-5/18 CrossRefGoogle Scholar
  26. Leontief WW (1936) Quantitative input and output relations in the economic systems of the United States. Rev Econ Stat 18(3):105–125CrossRefGoogle Scholar
  27. Leontief WW (1986) Input-output economics. Oxford University Press on Demand, New YorkGoogle Scholar
  28. Lindeman RL (1942) The trophic-dynamic aspect of ecology. Ecol 23(4):399–417CrossRefGoogle Scholar
  29. Loehle C (1990) Indirect effects: a critique and alternate methods. Ecology 71(6):2382–2386.  https://doi.org/10.2307/1938651. 2018/12/19CrossRefGoogle Scholar
  30. Ma Q, Kazanci C (2013) Analysis of indirect effects within ecosystem models using pathway-based methodology. Ecol Model 252(1):238–245. ISSN 03043800.  https://doi.org/10.1016/j.ecolmodel.2012.05.002  https://doi.org/10.1016/j.ecolmodel.2012.05.002 CrossRefGoogle Scholar
  31. Ma Q, Kazanci C (2014) How much of the storage in the ecosystem is due to cycling? J Theor Biol 357:134–142.  https://doi.org/10.1016/j.jtbi.2014.05.014  https://doi.org/10.1016/j.jtbi.2014.05.014 CrossRefGoogle Scholar
  32. Matis JH, Patten BC (1981) Environ analysis of linear compartmental systems: the static, time invariant case. Stat Ecol 48:527–565Google Scholar
  33. Menge BA (1995) Indirect effects in marine rocky intertidal interaction webs: patterns and importance. Ecol Monogr 65(1):21–74.  https://doi.org/10.2307/2937158. 2018/12/20CrossRefGoogle Scholar
  34. Menge AB (1997) Detection of direct versus indirect effects: were experiments long enough? Am Nat 149 (5):801–823CrossRefGoogle Scholar
  35. Paine RT (1966) Food web complexity and species diversity. Am Nat 100(910):65–75CrossRefGoogle Scholar
  36. Patten BC (1978) Systems approach to the concept of environment. Ohio J Sci 78(4):206–222Google Scholar
  37. Patten BC (1985a) Energy cycling length of food chains, and direct versus indirect effects in ecosystems. Can Bull Fish Aquat Sci 213:119–138Google Scholar
  38. Patten BC (1985b) Energy cycling in the ecosystem. Ecol Model 28(1–2):1–71. ISSN 03043800.  https://doi.org/10.1016/0304-3800(85)90013-4  https://doi.org/10.1016/0304-3800(85)90013-4 CrossRefGoogle Scholar
  39. Patten BC (1990) Environ theory and indirect effects: a reply to loehle. Ecology 71(6):2386–2393.  https://doi.org/10.2307/1938652. 2018/12/19CrossRefGoogle Scholar
  40. Patten BC (1991) Network ecology: indirect determination of the life-environment relationship in ecosystems. In: Higashi M, Burns TP (eds) Theoretical studies of ecosystems: the network perspective. Cambridge University Press, Cambridge, pp 288–351Google Scholar
  41. Patten BC (1992) Energy, emergy and environs. Ecol Model 62(1–3):29–69. ISSN 03043800.  https://doi.org/10.1016/0304-3800(92)90081-O  https://doi.org/10.1016/0304-3800(92)90081-O CrossRefGoogle Scholar
  42. Patten BC, Higashi M (1984) Modified cycling index for ecological applications. Ecol Model 25(1–3):69–83CrossRefGoogle Scholar
  43. Patten BC, Whipple SJ (2011) Ecological utility analysis determination of interaction types between organisms in ecosystems, vol 2, WIT Press.  https://doi.org/10.2495/ECO-V2-N2-88-96 CrossRefGoogle Scholar
  44. Patten BC, Bosserman RW, Finn JT, Cale WG (1976) Propagation of cause in ecosystems. Systems Analysis and Simulation in Ecology 4:457–579CrossRefGoogle Scholar
  45. Pilette R (1989) Evaluating direct and indirect effects in ecosystems. Am Nat 133(2):303–307. ISSN 00030147, 15375323. http://www.jstor.org/stable/2462307 CrossRefGoogle Scholar
  46. Rasmussen M, Hastings A, Smith MJ, Agusto FB, Chen-Charpentier BM, Hoffman FM, Jiang J, Todd-Brown KEO, Wang Y, Wang Y-P, Luo Y (2016) Transit times and mean ages for nonautonomous and autonomous compartmental systems. J Math Biol 73(6):1379–1398. ISSN 1432-1416.  https://doi.org/10.1007/s00285-016-0990-8  https://doi.org/10.1007/s00285-016-0990-8 CrossRefGoogle Scholar
  47. Schramski JR, Gattie DK, Patten BC, Borrett SR, Fath BD, Whipple SJ (2007) Indirect effects and distributed control in ecosystems: distributed control in the environ networks of a seven-compartment model of nitrogen flow in the Neuse River Estuary, USA-Time series analysis. Ecol Model 206(1–2):18–30. ISSN 03043800.  https://doi.org/10.1016/j.ecolmodel.2007.03.023 CrossRefGoogle Scholar
  48. Schramski JR, Kazanci C, Tollner EW (2011) Network environ theory, simulation, and EcoNet®, 2.0. Environ Model Softw 26(4):419–428. ISSN 13648152.  https://doi.org/10.1016/j.envsoft.2010.10.003 CrossRefGoogle Scholar
  49. Strauss SY (1991) Indirect effects in community ecology: their definition, study and importance. Trends Ecol Evol (Personal edition) 6(7):206–210. ISSN 01695347.  https://doi.org/10.1016/0169-5347(91)90023-Q  https://doi.org/10.1016/0169-5347(91)90023-Q CrossRefGoogle Scholar
  50. Tilly LJ (1968) The structure and dynamics of Cone Spring. Ecol Monogr 38(2):169–197CrossRefGoogle Scholar
  51. Tuominen LK, Whipple SJ, Patten BC, Karatas ZY, Kazanci C (2014) Contribution of throughflows to the ecological interpretation of integral network utility. Ecol Model 293:187–201. ISSN 03043800.  https://doi.org/10.1016/j.ecolmodel.2014.01.027 CrossRefGoogle Scholar
  52. Ulanowicz RE (1972) Mass and energy flow in closed ecosystems. J Theor Biol 34(2):239–253. ISSN 10958541.  https://doi.org/10.1016/0022-5193(72)90158-0  https://doi.org/10.1016/0022-5193(72)90158-0 CrossRefGoogle Scholar
  53. Ulanowicz RE (2004) Quantitative methods for ecological network analysis. Comput Biol Chem 28(5–6):321–339. ISSN 14769271.  https://doi.org/10.1016/j.compbiolchem.2004.09.001 CrossRefGoogle Scholar
  54. Ulanowicz RE, Kay JJ (1991) A package for the analysis of ecosystem flow networks. ISSN 02669838Google Scholar
  55. Ulanowicz RE, Puccia CJ (1990) Mixed trophic impacts in ecosystems. Coenoses 5(1):7–16Google Scholar
  56. Ulanowicz RE, Holt RD, Barfield M (2013) Limits on ecosystem trophic complexity: insights from ecological network analysis. Ecol Lett 17(2):127–136.  https://doi.org/10.1111/ele.12216 CrossRefPubMedGoogle Scholar
  57. Whipple SJ, Patten BC, Borrett SR (2014) Indirect effects and distributed control in ecosystems: comparative network environ analysis of a seven-compartment model of nitrogen storage in the Neuse River Estuary, USA: time series analysis. Ecol Model 293:161–186CrossRefGoogle Scholar
  58. Wootton JT (1993) Indirect effects and habitat use in an intertidal community: interaction chains and interaction modifications. Am Nat 141(1):71–89.  https://doi.org/10.1086/285461. 2018/12/20CrossRefGoogle Scholar
  59. Wootton JT (1994) The nature and consequences of indirect effects in ecological communities. Annu Rev Ecol Syst 25(1): 443–466.  https://doi.org/10.1146/annurev.es.25.110194.002303. 2018/12/20CrossRefGoogle Scholar
  60. Wootton JT (2002) Indirect effects in complex ecosystems: recent progress and future challenges. J Sea Res 48(2):157–172. ISSN 13851101.  https://doi.org/10.1016/S1385-1101(02)00149-1 CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GeorgiaAthensUSA

Personalised recommendations