Skip to main content
SpringerLink
Log in

Matrix Population Models as Relevant Modeling Tools in Ecotoxicology

  • Chapter
  • First Online:
Ecotoxicology Modeling

Part of the book series: Emerging Topics in Ecotoxicology ((ETEP,volume 2))

Abstract

Nowadays, one of the big challenge in ecotoxicology is to understand how individually measured effects can be used as predictive indices at the population level. A particular interesting aspect is to evaluate how individual measures of fitness and survival under various toxic conditions can be used to estimate the asymptotic population growth rate known as one of the most robust endpoint in population risk assessment. Among others, matrix population models are now widely recognized as a convenient mathematical formalism dedicated to the characterization of the population demographic health. They offer the advantage of simplicity, not only in the modeling process of underlying biological phenomena, but also in the sensitivity analyses and the simulation running. On the basis of different biological systems among aquatic animal species (from fish to zooplankton), we illustrate the use of matrix population models to quantify environmental stress effects of toxic type. We also show how critical demographic parameters for the population dynamics can be highlighted by sensitivity analyses. The first example will focus on coupled effects of food amount and exposure concentration on chironomid population dynamics in laboratory. The second example will exemplify the use of energy-based models coupled with matrix population ones to properly describe toxic effects on daphnid populations. Last, we will show how to introduce a spatial dimension in Leslie type models to describe space-specific aspects of contaminant induced population dynamics alteration with the case of brown trout population modeling at the river network scale.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Truhaut R (1977) Ecotoxicology: Objectives, principles and perspectives. Ecotoxicol Environ Safety 1: 151–173

    Article  CAS  Google Scholar 

  2. Levin SA, Harwell MA, Kelly JR, Kimball KD (1989) Ecotoxicology: Problems and approaches. Springer, New York

    Google Scholar 

  3. Emlen JM, Springman KR (2007) Developing methods to assess and predict the population level effects of environmental contaminants. Integr Environ Assess Manag 3: 157–165

    Article  CAS  Google Scholar 

  4. Forbes VE, Calow P (1998) Is the per capita rate of increase a good measure of population-level effects in ecotoxicology? Environ Toxicol Chem 18: 1544–1556

    Article  Google Scholar 

  5. Forbes VE, Calow P (2002) Population growth rate as a basis for ecological risk assessment of toxic chemicals. Philos Trans R Soc London Ser B 357: 1299–1306

    Article  Google Scholar 

  6. Stark JD, Banks JE (2003) Population-level effects of pesticides and other toxicants on arthropods. Ann Rev Entomol 48: 505–519

    Article  CAS  Google Scholar 

  7. Mooij WM, Hülsmann S, Vijverberg J, Veen A, Lammens EHRR (2003) Modeling Daphnia population dynamics and demography under natural conditions. Hydrobiologia 491: 19–34

    Article  Google Scholar 

  8. Hülsmann S, Mehner T, Worischka S, Plewa M (1999) Is the difference in population dynamics of Daphnia galeata in littoral and pelagic areas of a long-term biomanipulated reservoir affected by age-0 fish predation? Hydrobiologia 408–409: 57–63

    Article  Google Scholar 

  9. Nisbet RM, Gurney WSC, Murdoch WW, Mccauley E (1989) Structured population-models – A tool for linking effects at individual and population-level. Biol J Linn Soc 37: 79–99

    Article  Google Scholar 

  10. Lotka AJ (1939) A contribution to the theory of self-renewing aggregates, with special reference to industrial replacement. Ann Math Stat 10: 1–25

    Article  Google Scholar 

  11. Breitholtz M, Wollenberger L, Dinan L (2003) Effects of four synthetic musks on the life cycle of the harpacticoid copepod Nitocra spinipes. Aquat Toxicol 63: 103–118

    Article  CAS  Google Scholar 

  12. Leslie PH (1945) On the use of matrices in certain population mathematics. Biometrika 33: 184–212

    Article  Google Scholar 

  13. Leslie PH (1948) Some further notes on the use of matrices in poulation mathematics. Biometrika 35: 213–245

    Google Scholar 

  14. Caswell H (2001) Matrix population models – Construction, analysis, and interpretation. Sinauer Associates, Sunderlands, MA

    Google Scholar 

  15. Caswell H (1996) Demography meets ecotoxicology: Untangling the population level effects of toxic substances. In: MC Newmann, CH Jagoe (Eds), Ecotoxicology: A hierarchical treatment. Lewis Publishers, Boca Raton, FL

    Google Scholar 

  16. Caswell H (1996) Analysis of life table response experiments.2. Alternative parameterizations for size- and stage-structured models. Ecol Model 88: 73–82

    Article  Google Scholar 

  17. Levin L, Caswell H, Bridges T, DiBacca C, Cabrera D, Plaia G (1996) Demographic responses of estuarine polychaetes to pollutants: Life table response experiments. Ecol Appl 6: 1295–1313

    Article  Google Scholar 

  18. Lopes C, Péry ARR, Chaumot A, Charles S (2005) Ecotoxicology and population dynamics: Using DEBtox models in a Leslie modeling approach. Ecol Model 188: 30–40

    Article  CAS  Google Scholar 

  19. Smit MGD, Kater BJ, Jak RG, van den Heuvel-Greve MJ (2006) Translating bioassay results to field population responses using a Leslie-matrix model for the marine amphipod Corophium volutator. Ecol Model 196: 515–526

    Article  CAS  Google Scholar 

  20. Klok C, Holmstrup M, Damgaardt C (2007) Extending a combined dynamic energy budget matrix population model with a bayesian approach to assess variation in the intrinsic rate of population increase. An example in the earthworm Dendrobaena octaedra. Environ Toxicol Chem 26: 2383–2388

    Article  CAS  Google Scholar 

  21. Billoir E, Péry ARR, Charles S (2007) Integrating the lethal and sublethal effects of toxic compounds into the population dynamics of Daphnia magna: A combination of the DEBtox and matrix population models. Ecol Model 203: 204–214

    Article  CAS  Google Scholar 

  22. Ducrot V, Péry ARR, Mons R, Charles S, Garric J (2007) Dynamic engergy budgets as a basis to model population-level effects of zinc-spiked sediments in the gastropod Valvata piscinalis. Environ Toxicol Chem 26: 1774–1783

    Article  CAS  Google Scholar 

  23. Lebreton J-D, Gonzales-Davila G (1993) An introduction to models of subdivided populations. J Biol Syst 1: 389–423

    Article  Google Scholar 

  24. Chaumot A, Charles S, Flammarion P, Auger P (2003) Ecotoxicology and spatial modeling in population dynamics: An illustration with brown trout. Environ Toxicol Chem 22: 958–969

    Article  CAS  Google Scholar 

  25. Lefkovitch LP (1965) The study of population growth in organisms grouped by stages. Biometrics 21: 1–18

    Article  Google Scholar 

  26. Cull P, Vogt A (1973) Mathematical analysis of the asymptotic behavior of the Leslie population matrix model. Bull Math Biol 35: 645–661

    CAS  Google Scholar 

  27. Lebreton JD (1996) Demographic models for subdivided populations: The renewal equation approach. Theor Popul Biol 49: 291–313

    Article  Google Scholar 

  28. Rogers A (1966) The multiregional matrix growth operator and the stable interregional age structure. Demography 3: 537–544

    Article  CAS  Google Scholar 

  29. Rogers A (1985) Regional population projection models. Sage Publications, Beverly Hills, CA

    Google Scholar 

  30. Levin SA (1989) Applied mathematical ecology. Springer-Verlag, Berlin

    Google Scholar 

  31. Hanski I, Gilpin ME (1997) Metapopulation dynamics: Ecology, genetics and evolution. Academic Press, San Diego

    Google Scholar 

  32. Isnard P, Flammarion P, Roman G, Babut M, Bastien P, Bintein S, Essermeant L, Ferard JF, Gallotti-Schmitt S, Saouter E, Saroli M, Thiebaud H, Tomassone R, Vindimian E (2001) Statistical analysis of regulatory ecotoxicity tests. Chemosphere 45: 659–669

    Article  CAS  Google Scholar 

  33. Kooijman SALM, Bedaux JJM (1996) The analysis of aquatic toxicity data. VU University Press, Amsterdam

    Google Scholar 

  34. Kooijman SALM (2000) Dynamic energy and mass budgets in biological systems. Cambridge University Press, Great Britain

    Book  Google Scholar 

  35. Billoir E, da Silva Ferrão-Filho A, Delignette-Muller ML, Charles S (2009) DEBtox theory and matrix population models as helpful tools in understanding the interaction between toxic cyanobacteria and zooplankton. J Theor Biol 258: 380–388

    Article  Google Scholar 

  36. Billoir E, Delignette-Muller ML, Péry ARR, Geffard O, Charles S (2008) Statistical cautions when estimating DEBtox parameters. J Theor Biol 254: 55–64

    Article  CAS  Google Scholar 

  37. Billoir E, Delignette-Muller ML, Péry ARR, Charles S (2008) On the use of Bayesian inference to estimate DEBtox parameters. Environ Sci Technol 42: 8978–8984

    Article  CAS  Google Scholar 

  38. Charles S, Ferreol M, Chaumot A, Péry ARR (2004) Food availability effect on population dynamics of the midge Chironomus riparius: A Leslie modeling approach. Ecol Model 175: 217–229

    Article  Google Scholar 

  39. Charles S, Mallet J-P, Persat H (2006) Population dynamics of grayling: Modelling temperature and discharge effects. Math Model Nat Phenom 1: 33–48

    Article  Google Scholar 

  40. Caswell H (1978) A general formula for the sensitivity of population growth rate to changes in life history parameters. Theor Popul Biol 14: 215–230

    Article  CAS  Google Scholar 

  41. Caswell H (2000) Prospective and retrospective perturbation analyses: Their roles in conservation biology. Ecology 81: 619–627

    Article  Google Scholar 

  42. De Kroon H, Van Groenendael J, Ehrlen J (2000) Elasticities: A review of methods and model limitations. Ecology 81: 607–618

    Article  Google Scholar 

  43. Yearsley JM, Fletcher D, Hunter C (2003) Sensitivity analysis of equilibrium population size in a density-dependent model for Short-tailed Shearwaters. Ecol Model 163: 119–129

    Article  Google Scholar 

  44. Caswell H, Takada T (2004) Elasticity analysis of density-dependent matrix population models: The invasion exponent and its substitutes. Theor Popul Biol 65: 401–411

    Article  Google Scholar 

  45. Goddeeris BR, Vermeulen AC, De Geest E, Jacobs H, Baert B, Ollevier F (2001) Diapause induction in the third and fourth instar of Chironomus riparius (Diptera) from Belgian lowland brooks. Arch Hydrobiol 150: 307–327

    Google Scholar 

  46. Marking LL, Chandler JH (1981) Toxicity of 6 bird control chemicals to aquatic organisms. Bull Environ Contam Toxicol 26: 705–716

    Article  CAS  Google Scholar 

  47. Péry ARR, Ducrot V, Mons R, Miege C, Gahou J, Gorini D, Garric J (2003) Survival tests with Chironomus riparius exposed to spiked sediments can profit from DEBtox model. Water Res 37: 2691–2699

    Article  Google Scholar 

  48. Péry ARR, Mons R, Ducrot V, Garric J (2004) Effects of methiocarb on Chironomus riparius survival and growth with and without tube-building. Bull Environ Contam Toxicol 72: 358–364

    Article  Google Scholar 

  49. Armitage PD, Cranston PS, Pinder LCV (1995) The Chironomidae: Biology and ecology of non-biting midges. Chapman and Hall, London, UK

    Google Scholar 

  50. OECD (1998) OECD guidelines for testing of chemicals. Daphnia magna reproduction test. Organization for Economic Co-operation and Development, Paris

    Google Scholar 

  51. ISO (2000) 10706. Water quality – Determination of long term toxicity of substances to Daphnia magna Straus (Cladocera, Crustacea). International Organization for Standardization, Geneva, Switzerland

    Google Scholar 

  52. Anderson BG (1944) The toxicity threshold of various substances found in industrial wastes as determined by the use of Daphnia magna. Sewage Work J 16: 156–165

    Google Scholar 

  53. Koivisto S (1995) Is Daphnia magna an ecologically representative zooplankton species in toxicity tests? Environ Pollut 90: 263–267

    Article  CAS  Google Scholar 

  54. Adema DMM (1978) Daphnia magna as a test animal in acute and chronic toxicity tests. Hydrobiologia 59: 125–134

    Article  CAS  Google Scholar 

  55. Gilks WR, Richardson S, Spiegelhalter DJ (1996) Markov Chain Monte Carlo in practice. Chapman and Hall, New York

    Google Scholar 

  56. Nogueira AJA, Baird DJ, Soares AMVM (2004) Testing physiologically-based resource allocation rules in laboratory experiments with Daphnia magna Straus. Ann Limnol 40: 257–267

    Article  Google Scholar 

  57. Oli MK (2004) The fast-slow continuum and mammalian life-history patterns: An empirical evaluation. Basic Appl Ecol 5: 449–463

    Article  Google Scholar 

  58. Ares J (2003) Time and space issues in ecotoxicology: Population models, landscape pattern analysis, and long-range environmental chemistry. Environ Toxicol Chem 22: 945–957

    Article  CAS  Google Scholar 

  59. Chaumot A, Charles S, Flammarion P, Garric J, Auger P (2002) Using aggregation methods to assess toxicant effects on population dynamics in spatial systems. Ecol Appl 12: 1771–1784

    Article  Google Scholar 

  60. Chaumot A, Charles S, Flammarion P, Auger P (2003) Do migratory or demographic disruptions rule the population impact of pollution in spatial networks? Theor Popul Biol 64: 473–480

    Article  CAS  Google Scholar 

  61. Chaumot A, Charles S (2006) Pollution, stochasticity and spatial heterogeneity in the dynamics of an age-structured population of brown trout living in a river network. In: R Akcakaya (Editor), Population-level ecotoxicological risk assessment: Case studies. Oxford University Press, New York

    Google Scholar 

  62. Baglinière JL, Maisse G, Lebail PY, Nihouarn A (1989) Population dynamics of brown trout, Salmo trutta L., in a tributary in Brittany (France): Spawning and juveniles. J Fish Biol 34: 97–110

    Article  Google Scholar 

  63. Ovidio M (1999) Annual activity cycle of adult brown trout (Salmo trutta L.): A radio-telemetry study in a small stream of the Belgian Ardenne. Bull Fr Peche Pisc: 1–18

    Google Scholar 

  64. Spromberg JA, John BM, Landis WG (1998) Metapopulation dynamics: indirect effects and multiple distinct outcomes in ecological risk assessment. Environ Toxicol Chem 17: 1640–1649

    Article  CAS  Google Scholar 

  65. Hansen F, Forbes VE, Forbes TL (1999) Using elasticity analysis of demographic models to link toxicant effects on individuals to the population level: an example. Funct Ecol 13: 157–162

    Article  Google Scholar 

  66. Sherratt JA (1993) The amplitude of periodic plane waves depends on initial conditions in a variety of lambda - Omega systems. Nonlinearity 6: 1055–1066

    Article  Google Scholar 

  67. Akçakaya HR (1994) RAMAS metapop: Viability analysis for stage-structured metapopulations. Version 1.0. Setauket, New York

    Google Scholar 

  68. Tuljapurkar S, Caswell H (1997) Structured-population models in marine, terrestrial, and freshwater systems. Springer, Berlin

    Google Scholar 

  69. Van den Brink P, Baveco H, Verboom J, Heimbach F (2007) An individual-based approach to model spatial population dynamics of invertebrates in aquatic ecosystems after pesticide contamination. Environ Toxicol Chem 26: 2226–2236

    Article  Google Scholar 

  70. Van Kirk RW, Hill SL (2007) Demographic model predicts trout population response to selenium based on individual-level toxicity. Ecol Model 206: 407–420

    Article  Google Scholar 

  71. Grimm V (1999) Ten years of individual-based modelling in ecology: what have we learned and what could we learn in the future? Ecol Model 115: 129–148

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Biométrie et Biologie Evolutive, Université de Lyon, F-69000, Lyon; Université Lyon 1; CNRS UMR5558, F-69622, Villeurbanne, France

    Sandrine Charles, Elise Billoir & Christelle Lopes

  2. CEMAGREF, F-69000, Lyon, UR “Biologie des Ecosystèmes Aquatiques”, Laboratoire d’ècotoxicologie, 3bis quai Chauveau, CP 220, F-69336, Lyon Cedex 9, France

    Arnaud Chaumot

Authors
  1. Sandrine Charles
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elise Billoir
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christelle Lopes
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arnaud Chaumot
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sandrine Charles .

Editor information

Editors and Affiliations

  1. l'Information Scientifique (CTIS), Centre de Traitement de, chemin de la Graviere 3, Rillieux La Pape, 69140, France

    James Devillers

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Charles, S., Billoir, E., Lopes, C., Chaumot, A. (2009). Matrix Population Models as Relevant Modeling Tools in Ecotoxicology. In: Devillers, J. (eds) Ecotoxicology Modeling. Emerging Topics in Ecotoxicology, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-0197-2_10

Download citation

Publish with us

Policies and ethics

Search

Navigation