Both ecological field studies and attempts to extrapolate from laboratory experiments to natural populations generally encounter the high degree of natural variability and chaotic behavior that typify natural ecosystems. Regardless of this variability and non-normal distribution, most statistical models of natural systems use normal error which assumes independence between the variance and mean. However, environmental data are often random or clustered and are better described by probability distributions which have more realistic variance to mean relationships. Until recently statistical software packages modeled only with normal error and researchers had to assume approximate normality on the original or transformed scale of measurement and had to live with the consequences of often incorrectly assuming independence between the variance and mean. Recent developments in statistical software allow researchers to use generalized linear models (GLMs) and analysis can now proceed with probability distributions from the exponential family which more realistically describe natural conditions: binomial (even distribution with variance less than mean), Poisson (random distribution with variance equal mean), negative binomial (clustered distribution with variance greater than mean). GLMs fit parameters on the original scale of measurement and eliminate the need for obfuscating transformations, reduce bias for proportions with unequal sample size, and provide realistic estimates of variance which can increase power of tests. Because GLMs permit modeling according to the non-normal behavior of natural systems and obviate the need for normality assumptions, they will likely become a widely used tool for analyzing toxicity data. To demonstrate the broad-scale utility of GLMs, we present several examples where the use of GLMs improved the statistical power of field and laboratory studies to document the rapid ecological recovery of Prince William Sound following the Exxon Valdez oil spill.