, Volume 18, Issue 3, pp 343–354 | Cite as

From simple toxicological models to prediction of toxic effects in time

  • Francisco Sánchez-BayoEmail author


The ability to predict the effects of toxicants in organisms with reasonable accuracy depends to a great extent on the toxico-kinetic models used to describe such effects. Toxic effects of organic chemicals and heavy metals have been described adequately using a hyperbolic model that considers the concentration of the toxicant and the time of exposure only. Such a model relies on the median time to effect (ET50) of a chemical to estimate effects at any exposure time, but cannot make predictions for concentrations other than those tested experimentally. A complementary log-to-log model can calculate all ET50 values for a toxicant, thus enabling the hyperbolic model to predict any level of effect for any combination of concentrations and times of exposure. The parameter values used in both models are obtained from experimental bioassays where the time-to-effect of a toxicant is recorded regularly in addition to standard acute or chronic toxicity data. These models will facilitate the risk assessment of chemicals by (1) predicting effects under any combination of time and concentrations, and (2) reducing to a minimum the experimental efforts required to obtain comprehensive ecotoxicity data.


Modelling Risk assessment Exposure Time–dose relationship Insecticides 


  1. Bedaux JJM, Kooijman SALM (1994) Statistical analysis of bioassays based on hazard modelling. Environ Ecol Stat 1:303–314. doi: 10.1007/BF00469427 CrossRefGoogle Scholar
  2. Beketov MA, Liess M (2008) Acute and delayed effects of the neonicotinoid insecticide thiacloprid on seven freshwater arthropods. Environ Toxicol Chem 27:461–470. doi: 10.1897/07-322R.1 CrossRefGoogle Scholar
  3. Bliss CI (1937) The calculation of the time–mortality curve. Ann Appl Biol 24:815–852Google Scholar
  4. Bonnomet V, Duboudin C, Magaud H, Thybaud E, Vindimian E, Beauzamy B (2002) Modelling explicitly and mechanistically median lethal concentration as a function of time for risk assessment. Environ Toxicol Chem 21:2252–2259. doi:10.1897/1551-5028(2002)021<2252:MEAMML>2.0.CO;2CrossRefGoogle Scholar
  5. Breck JE (1988) Relationships among models for acute toxic effects: applications to fluctuating concentrations. Environ Toxicol Chem 7:775–778. doi: 10.1897/1552-8618(1988)7[775:RAMFAT]2.0.CO;2 CrossRefGoogle Scholar
  6. Brent RN, Herricks EE (1998) Postexposure effects of brief cadmium, zinc and phenol exposures on freshwater organisms. Environ Toxicol Chem 17:2091–2099. doi:10.1897/1551-5028(1998)017<2091:PEOBCZ>2.3.CO;2CrossRefGoogle Scholar
  7. Brisbin IL Jr (1990) Applications of a modified Richards sigmoid model to assess the uptake and effects of environmental contaminants upon birds. In: Kendall RJ, Larcher TE (eds) Wildlife toxicology and population modeling. Lewis Publishers, Boca Raton, pp 161–170Google Scholar
  8. Brown VM, Jordan DHM, Tiller BA (1969) The acute toxicity to rainbow trout of fluctuating concentrations and mixtures of ammonia, phenol and zinc. J Fish Biol 1:1–9. doi: 10.1111/j.1095-8649.1969.tb03837.x CrossRefGoogle Scholar
  9. Chaisuksant Y, Yu Q, Connell D (1997) Internal lethal concentrations of halobenzenes with fish (Gambusia affinis). Ecotoxicol Environ Saf 37:66–75. doi: 10.1006/eesa.1997.1524 CrossRefGoogle Scholar
  10. Connolly JP (1985) Predicting single-species toxicity in natural water systems. Environ Toxicol Chem 4:573–582. doi: 10.1897/1552-8618(1985)4[573:PSTINW]2.0.CO;2 CrossRefGoogle Scholar
  11. Daniels RE, Allan JD (1981) Life table evaluation of chronic exposure to a pesticide. Can J Fish Aquat Sci 38:485–494. doi: 10.1139/f81-070 CrossRefGoogle Scholar
  12. Dixon PM, Newman MC (1991) Analyzing toxicity data using statistical models for time-to-death: an introduction. In: Newman MC, McIntosh AW (eds) Metal ecotoxicology. Concepts and applications. Lewis Publishers, Chelsea, pp 207–242Google Scholar
  13. Forbes VE, Calow P, Sibly RM (2001) Are current species extrapolation models a good basis for ecological risk assessment? Environ Toxicol Chem 20:442–447. doi:10.1897/1551-5028(2001)020<0442:ACSEMA>2.0.CO;2CrossRefGoogle Scholar
  14. Grant A (1998) Population consequences of chronic toxicity: incorporating density dependence into the analysis of life table response experiments. Ecol Model 105:325–335. doi: 10.1016/S0304-3800(97)00176-2 CrossRefGoogle Scholar
  15. Hickie BE, McCarty LS, Dixon DG (1995) A residue-based toxicokinetic model for pulse–exposure toxicity in aquatic systems. Environ Toxicol Chem 14:2187–2197. doi: 10.1897/1552-8618(1995)14[2187:ARTMFP]2.0.CO;2 CrossRefGoogle Scholar
  16. Hoang TC, Tomasso JR, Klaine SJ (2007) An integrated model describing the toxic responses of Daphnia magna to pulsed exposures of three metals. Environ Toxicol Chem 26:132–138. doi: 10.1897/06-081R.1 CrossRefGoogle Scholar
  17. Kooijman SALM (1981) Parametric analyses of mortality rates in bioassays. Water Res 15:107–119. doi: 10.1016/0043-1354(81)90190-1 CrossRefGoogle Scholar
  18. Kooijman SALM (2000) Dynamic energy and mass budgets in biological systems. Cambridge University Press, CambridgeGoogle Scholar
  19. Kooijman SALM, Bedaux JJM (1996) The analysis of aquatic toxicity data. VU University Press, AmsterdamGoogle Scholar
  20. Kooijman SALM, Bedaux JJM, Slob W (1996) No-effect concentrations as a basis for ecological risk assessment. Risk Anal 16:445–447. doi: 10.1111/j.1539-6924.1996.tb01091.x CrossRefGoogle Scholar
  21. Mackay D, Puig H, McCarty LS (1992) An equation describing the time course and variability in uptake and toxicity of narcotic chemicals to fish. Environ Toxicol Chem 11:941–951. doi: 10.1897/1552-8618(1992)11[941:AEDTTC]2.0.CO;2 CrossRefGoogle Scholar
  22. Mancini JL (1983) A method for calculating effects on aquatic organisms of time varying concentrations. Water Res 17:1355–1362. doi: 10.1016/0043-1354(83)90264-6 CrossRefGoogle Scholar
  23. McCahon CP, Pascoe D (1990) Episodic pollution: causes, toxicological effects and ecological significance. Funct Ecol 4:375–383. doi: 10.2307/2389599 CrossRefGoogle Scholar
  24. McCarty LS, Mackay D (1993) Enhancing ecotoxicological modeling and assessment. Body residues and modes of toxic action. Environ Sci Technol 27:1719–1728. doi: 10.1021/es00046a001 CrossRefGoogle Scholar
  25. Mortimer MR, Connell DW (1994) Critical internal and aqueous lethal concentrations of chlorobenzenes with the crab Portunus pelagicus (L.). Ecotoxicol Environ Saf 28:298–312. doi: 10.1006/eesa.1994.1054 CrossRefGoogle Scholar
  26. Newman MC (1995) Quantitative methods in aquatic ecotoxicology. CRC Publishing, Boca RatonGoogle Scholar
  27. Newman MC, Aplin MS (1992) Enhancing toxicity data interpretation and prediction of ecological risk with survival time modeling: an illustration using sodium chloride toxicity to mosquitofish (Gambusia holbrooki). Aquat Toxicol 23:85–96. doi: 10.1016/0166-445X(92)90001-4 CrossRefGoogle Scholar
  28. Newman MC, McCloskey JT (1996) Time-to-event analyses of ecotoxicity data. Ecotoxicology 5:187–196. doi: 10.1007/BF00116339 CrossRefGoogle Scholar
  29. Organization for Economic Cooperation and Development (1993) OECD guidelines for testing of chemicals. Procedure 202—Daphnia sp., Acute immobilisation test and reproduction test. Paris, FranceGoogle Scholar
  30. Pascoe D, Shazili NAM (1986) Episodic pollution—a comparison of brief and continuous exposure of rainbow trout to cadmium. Ecotoxicol Environ Saf 12:189–198. doi: 10.1016/0147-6513(86)90010-2 CrossRefGoogle Scholar
  31. Peakall D (1992) Animal biomarkers as pollution indicators. Chapman & Hall, CornwallGoogle Scholar
  32. Péry ARR, Flammarion P, Vollat B, Bedaux JJM, Kooijman SALM, Garric J (2002) Using a biology-based model (DEBtox) to analyse bioassays in ecotoxicology: oportunities and recommendations. Environ Toxicol Chem 21:459–465. doi:10.1897/1551-5028(2002)021<0459:UABBMD>2.0.CO;2CrossRefGoogle Scholar
  33. Reinert KH, Giddings JM, Judd L (2002) Effects analysis of time-varying or repeated exposures in aquatic ecological risk assessment of agrochemicals. Environ Toxicol Chem 21:1977–1992. doi:10.1897/1551-5028(2002)021<1977:EAOTVO>2.0.CO;2CrossRefGoogle Scholar
  34. Sánchez-Bayo F (2006) Comparative acute toxicity of organic pollutants and reference values for crustaceans. I. Branchiopoda, Copepoda and Ostracoda. Environ Pollut 139:385–420. doi: 10.1016/j.envpol.2005.06.016 CrossRefGoogle Scholar
  35. Sánchez-Bayo F, Goka K (2006) Influence of light in acute toxicity bioassays of imidacloprid and zinc pyrithione to zooplankton crustaceans. Aquat Toxicol 78:262–271. doi: 10.1016/j.aquatox.2006.03.009 CrossRefGoogle Scholar
  36. Sánchez-Bayo F, Goka K (2007) Simplified models to analyse time- and dose-dependent responses of populations to toxicants. Ecotoxicology 16:511–523. doi: 10.1007/s10646-007-0158-9 CrossRefGoogle Scholar
  37. Sprague JB (1969) Measurement of pollutant toxicity to fish. I. Bioassay methods for acute toxicity. Water Res 3:793–821. doi: 10.1016/0043-1354(69)90050-5 CrossRefGoogle Scholar
  38. Suter-II GW, Rosen AE, Linder E, Parkhurst DF (1987) Endpoints for responses of fish to chronic exposures. Environ Toxicol Chem 6:793–809. doi: 10.1897/1552-8618(1987)6[793:EFROFT]2.0.CO;2 CrossRefGoogle Scholar
  39. Truhaut R (1977) Ecotoxicology: objectives, principles and perspectives. Ecotoxicol Environ Saf 1:151–173. doi: 10.1016/0147-6513(77)90033-1 CrossRefGoogle Scholar
  40. Walthall WK, Stark JD (1997) A comparison of acute mortality and population growth rate as endpoints of toxicological effect. Ecotoxicol Environ Saf 37:45–52. doi: 10.1006/eesa.1997.1521 CrossRefGoogle Scholar
  41. Widianarko B, Kuntoro FXS, Van Gestel CAM, Van Straalen NV (2001) Toxicokinetics and toxicity of zinc under time-varying exposure in the guppy (Poecilia reticulata). Environ Toxicol Chem 20:763–768. doi:10.1897/1551-5028(2001)020<0763:TATOZU>2.0.CO;2CrossRefGoogle Scholar
  42. Yu Q, Chaisuksant Y, Connell D (1999) A model for non-specific toxicity with aquatic organisms over relatively long periods of exposure time. Chemosphere 38:909–919. doi: 10.1016/S0045-6535(98)00220-3 CrossRefGoogle Scholar
  43. Zhao Y, Newman MC (2004) Shortcomings of the laboratory-derived median lethal concentration for predicting mortality in field populations: exposure duration and latent mortality. Environ Toxicol Chem 26:2147–2153. doi: 10.1897/03-557 CrossRefGoogle Scholar
  44. Zhao Y, Newman MC (2006) Effects of exposure duration and recovery time during pulsed exposures. Environ Toxicol Chem 25:1298–1304. doi: 10.1897/05-341R.1 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Environmental Sciences, Centre for EcotoxicologyUniversity of Technology-SydneyLidcombeAustralia

Personalised recommendations