Modeling pattern in collections of parameters

Wildlife management is increasingly guided by analyses of large and complex datasets. The description of such datasets often requires a large number o f parameters, among which certain patterns might be discernible. For exampl e, one may consider a long-term study producing estimates of annual surviva l rates; of interest is the question whether these rates have declined thro ugh time. Several statistical methods exist for examining pattern in collec tions of parameters. Here, I argue for the superiority of "random effects m odels" in which parameters are regarded as random variables, with distribut ions governed by "hyperparameters" describing the patterns of interest. Unf ortunately, implementation of random effects models is sometimes difficult. Ultrastructural models, in which the postulated pattern is built into die parameter structure of the original data analysis, are approximations to ra ndom effects models. However, this approximation is not completely satisfac tory: failure to account for natural variation among parameters can lead to overstatement of the evidence for pattern among parameters. I describe qua si-likelihood methods that can be used to improve the approximation of rand om effects models by ultrastructural models.