, Volume 20, Issue 6, pp 1268–1276 | Cite as

A comparison of simple and complex population models to reduce uncertainty in ecological risk assessments of chemicals: example with three species of Daphnia

  • Niklas HansonEmail author
  • John D. Stark


Ecological risk assessments (ERA) are mostly based on effects on survival (S) and fertility (F) of individuals. However, the protection goals are most often defined on the population or community levels. It has been argued that population models can be a useful link between the individual and the population in ERA. However, for population models to be efficiently and routinely used in ERA, the level of model complexity that is needed has to be clearly determined. In the present study, complex age classified matrix population models and simple 2-stage models were developed for three species of Daphnia. The population growth rate (λ) from the simple 2-stage model correlated strongly to the results of the complex matrix model, which included density dependence and temporary reductions in S and F. This shows that the information that can be provided by more complex models also can be relatively well predicted with the simpler model. The output of the complex matrix population models were also compared to the reductions in S that were used in the models. This was done because acute mortality is the most commonly used estimate of toxic effects. The results showed that λ from the 2-stage model correlated stronger to the endpoints of the matrix model than S did in all cases except for pulsed exposures, where S and λ correlated equally well.


Population modeling 2-stage model Leslie matrix Individual-to-population extrapolation Population growth rate 



We thank Grace and Oriki Jack for their help with this study. Niklas Hansons participation was financed by the Swedish Research Council.


  1. Akçakaya HR, Stark JD, Bridges TS (eds) (2008) Demographic toxicity: methods in ecological risk assessment. Oxford University Press, New YorkGoogle Scholar
  2. Barnthouse LW (2004) Quantifying population recovery rates for ecological risk assessment. Environ Toxicol Chem 23(2):500–508CrossRefGoogle Scholar
  3. Bartell S, Campbell K, Lovelock C, Nair S, Shaw J (2000) Characterizing aquatic ecological risks from pesticides using diquat dibromide. Case Study III: Ecological process models. Environ Toxicol Chem 19:1441–1453CrossRefGoogle Scholar
  4. Boersma M, Vijverberg J (1994) Resource depression in Daphnia-Galeata, Daphnia-Cucullata and their interspecific hybrid-life-history consequences. J Plankton Res 16(12):1741–1758CrossRefGoogle Scholar
  5. Bradley MC, Baird DJ, Calow P (1991) Mechanisms of energy allocation to reproduction in the cladoceran Daphnia-Magna Straus. Biol J Linn Soc 44(4):325–333CrossRefGoogle Scholar
  6. Calow P, Forbes VE (2003) Does ecotoxicology inform ecological risk assessment? Environ Sci Technol 37(7):146A–151ACrossRefGoogle Scholar
  7. Calow P, Sibly RM, Forbes V (1997) Risk assessment on the basis of simplified life-history scenarios. Environ Toxicol Chem 16(9):1983–1989CrossRefGoogle Scholar
  8. Caswell H (2001) Matrix population models, 2nd edn. Sinauer associates, Imc. Publishers, SunderlandGoogle Scholar
  9. Ferson S, Ginzburg LR, Goldstein RA (1996) Inferring ecological risk from toxicity bioassays. Water Air Soil Pollut 90(1–2):71–82CrossRefGoogle Scholar
  10. Forbes VE, Calow P (1999) Is the per capita rate of increase a good measure of population-level effects in ecotoxicology? Environ Toxicol Chem 18(7):1544–1556CrossRefGoogle Scholar
  11. Forbes VE, Calow P (2002a) Extrapolation in ecological risk assessment: balancing pragmatism and precaution in chemical controls legislation. Bioscience 52(3):249CrossRefGoogle Scholar
  12. Forbes VE, Calow P (2002b) Population growth rate as a basis for ecological risk assessment of toxic chemicals. Philos Trans R Soc Lond B Biol Sci 357(1425):1299–1306CrossRefGoogle Scholar
  13. Forbes VE, Calow P, Sibly RM (2001a) Are current species extrapolation models a good basis for ecological risk assessment? Environ Toxicol Chem 20(2):442–447CrossRefGoogle Scholar
  14. Forbes VE, Sibly RM, Calow P (2001b) Toxicant impacts on density-limited populations: a critical review of theory, practice, and results. Ecol Appl 11(4):1249–1257CrossRefGoogle Scholar
  15. Forbes VE, Calow P, Sibly RM (2008) The extrapolation problem and how population modeling can help. Environ Toxicol Chem 27(10):1987–1994CrossRefGoogle Scholar
  16. Galic N, Hommen U, Boveco JM, van den Brink PJ (2010) Potential application of population models in the European ecological risk assessment of chemicals II: review of models and their potential to address environmental protection aims. Integr Environ Assess Manag 6(3):338–360CrossRefGoogle Scholar
  17. Gliwicz ZM, Wrzosek D (2008) Predation-mediated coexistence of large- and small-bodied Daphnia at different food levels. Am Nat 172(3):358–374CrossRefGoogle Scholar
  18. Hommen U, Baveco J, Galic N, van den Brink PJ (2010) Potential application of ecological models in the European environmental risk assessment of chemicals I: review of protection goals in EU directives and regulations. Integr Environ Assess Manag 6(3):325–337CrossRefGoogle Scholar
  19. Hovenkamp W (1990) Instar-specific mortalities of coexisting Daphnia species in relation to food and invertebrate predation. J Plankton Res 12(3):483–495CrossRefGoogle Scholar
  20. Levin SA, Goodyear CP (1980) Analysis of an age-structured fishery model. J Math Biol 9(3):245–274CrossRefGoogle Scholar
  21. Ricker W (1975) Computation and interpretation of biological statistics of fish populations. Fish res bd Canada bull 191. Department of the environment, fisheries and marine service, OttawaGoogle Scholar
  22. Stark JD (2005) How closely do acute lethal concentration estimates predict effects of toxicants on populations? Integr Environ Assess Manag 1(2):109–113CrossRefGoogle Scholar
  23. Stark JD, Banken JAO (1999) Importance of population structure at the time of toxicant exposure. Ecotoxicol Environ Saf 42(3):282–287CrossRefGoogle Scholar
  24. Stark JD, Vargas RI (2003) Demographic changes in Daphnia pulex (Leydig) after exposure to the insecticides spinosad and diazinon. Ecotoxicol Environ Saf 56(3):334–338CrossRefGoogle Scholar
  25. Stark JD, Sugayama RL, Kovaleski A (2007) Why demographic and modeling approaches should be adopted for estimating the effects of pesticides on biocontrol agents. Biocontrol 52(3):365–374CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Puyallup Research and Extension CenterWashington State UniversityPuyallupUSA

Personalised recommendations