Introduction

Variance components may play multiple roles (cf. Cox and Solomon 2003).First, magnitudes and relative magnitudes of the variances of random factorsmay have important scientific and management value in their own right. Forexample, variation in levels of invasive vegetation among and within lakesmay suggest causal agents that operate at both spatial scales – afinding that may be important for scientific and management reasons.

Second, variance components may also be of interest when they affectprecision of means and covariate coefficients. For example, variation in theeffect of water depth on the probability of aquatic plant presence in astudy of multiple lakes may vary by lake. This variation will affect theprecision of the average depth-presence association.

Third, variance component estimates may be used when designing studies,including monitoring programs. For example, to estimate the numbers of yearsand of samples per year required to meet long-term monitoring goals,investigators need estimates of within and among-year variances. Otherchapters in this volume (Chapters 7, 8, and 10) as well as extensiveexternal literature outline a framework for applying estimates of variancecomponents to the design of monitoring efforts. For example, a series ofpapers with an ecological monitoring theme examined the relative importanceof multiple sources of variation, including variation in means among sites,years, and site-years, for the purposes of temporal trend detection andestimation (Larsen et al. 2004, and referencestherein).