• antagonistic;
  • cumulative impacts;
  • multivariable;
  • non-additive;
  • synergistic

It is often recognized, but seldom addressed, that a quantitative assessment of the cumulative effects, both additive and non-additive, of multiple stressors on fish survival would provide a more realistic representation of the factors that influence fish migration. This review presents a compilation of analytical methods applied to a well-studied fish migration, a more general review of quantitative multivariable methods, and a synthesis on how to apply new analytical techniques in fish migration studies. A compilation of adult migration papers from Fraser River sockeye salmon Oncorhynchus nerka revealed a limited number of multivariable methods being applied and the sub-optimal reliance on univariable methods for multivariable problems. The literature review of fisheries science, general biology and medicine identified a large number of alternative methods for dealing with cumulative effects, with a limited number of techniques being used in fish migration studies. An evaluation of the different methods revealed that certain classes of multivariable analyses will probably prove useful in future assessments of cumulative effects on fish migration. This overview and evaluation of quantitative methods gathered from the disparate fields should serve as a primer for anyone seeking to quantify cumulative effects on fish migration survival.