There Is No Need To Be Normal: Generalized Linear Models of Natural Variation

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 distributio...