After a long hiatus, I am returning to a blog I started during my Master’s program.  In the time since then, I (like most marine scientists) have spent a lot of time thinking about environmental effects on marine populations.  In summary, we know that marine populations vary on annual, decadal, and 100+ year cycles — tonnero fisheries for Mediterranean tuna have shown fluctuations over >1000 years!  However, we know from Ram Myers that correlations between the environment and fish demographics often break down.  What’s a marine scientist to do?

Well, there’s an emerging consensus in other branches of ecology about how to estimate environmental effects.  In an illuminating review, Frederiksen et al. (here) claim that its important to use random-effect models when testing environmental effects:

there are potential pitfalls when assessing the statistical significance and biological importance of environmental covariates (detailed review in Grosbois et al. 2008). Briefly, when between-year variation in a given parameter is pronounced (which is often the case in even moderately large data sets), both standard likelihood ratio tests and AIC-based model selection (Burnham & Anderson 2002) are biased. Two approaches exist to deal with this problem: analysis of deviance (Skalski, Hoffmann & Smith 1993), which provides an anova-like partitioning of the total between-year variation into a component explained by the covariate and residual variation, and mixed models with random year effects (Loison et al. 2002). Analysis of deviance has recently been shown to give a robust approximation to the more sophisticated approaches in the mixed model framework (Lebreton, Choquet & Gimenez 2012). Proper statistical assessment of the importance of environmental covariates is critical for achieving robust inference.

This mirrors my own thoughts: when estimating an environmental effect, you are essentially speculating that the environment causes variability in some demographic rate (e.g., larval survival in fish recruitment).  Thus, you must begin by including stochastic variability, and this can be done easily and generically by using random effects (i.e. using a state-space model).  You can then see if this stochastic variability is explained by the environmental effect.  However, including an environmental effect in a deterministic model (i.e., without already including random effects) is obviously strange — it specifies that a demographic effect varies environmentally, but that we know exactly the shape and nature of this effect.

A second branch of research supports this view.  In short, researchers have shown that model mis-specification causes problems during the interpretation of model results.  For example, a deterministic model of a population (i.e. models without random effects for some demographic process) will generally have serial autocorrelation (e.g., where residuals are consistently above or below model predictions).  And in this case, estimates will have standard errors that are too small (see discussions here and here), so statistical tests of environmental effects will pass tests of statistical significance too often.

Anyway, this discussion came up recently during questions after a quantitative talk and I welcome thoughts and discussion.