Aster Models for Life History Analysis

Abstract

We present a new class of statistical models designed for life history analysis of plants and animals. They allow joint analysis of data on survival and reproduction over multiple years, allow for variables having different statistical distributions, and correctly account for the dependence of variables on earlier variables (for example, that a dead individual stays dead and cannot reproduce). We illustrate their utility with an analysis of data taken from an experimental study of Echinacea angustifolia sampled from remnant prairie populations in western Minnesota. Statistically, they are graphical models with some resemblance to generalized linear models and survival analysis. They have directed acyclic graphs with nodes having no more than one parent. The conditional distribution of each node given the parent is a one-parameter exponential family with the parent variable the sample size. The model may be heterogeneous, each node having a different exponential family. We show that the joint distribution is a flat exponential family and derive its canonical parameters, Fisher information, and other properties. These models are implemented in an R package "aster" available from CRAN.