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 prarie 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 oneparameter 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. This technical report consists of a draft paper about aster models supplemented by 5 appendicies on technical subjects.Appendix A (p. 19) gives details about "prediction" (what the predict.aster function does), although the technical details are about change-of-parameter formulas and their derivatives.Appendix B (p. 24) gives details about the one-parameter exponential families currently available as conditional distribution of variables given their parent variable in the aster package.Appendix C (p. 29) gives details about simulating a Poisson distribution conditional on being nonzero (the only non-trivial issue being getting efficient simulation for unconditional means close to zero).Appendix D (p. 31) gives details of the data analysis that is briefly described in the draft paper.Appendix E (p. 58) shows that steepness of conditional exponential families implies stepness of corresponding unconditional families, and the full unconditional family gets no new parameter points (that do not correspond to conditional parameter points). 2Chapter 1 Draft Paper IntroductionThis article introduces a class of statistical models that we call aster models. They were invented for life history analysis (LHA) of plants and animals, and are best introduced by example. Archetypal data for these models are about perennial plants censused at various times. For each individual planted, we record whether it is still alive, whether it has flowered, and how many flowers it has. These data are complicated, especially when recorded for several years, but when considered conditionally, simple models may suffice. We consider mortality status (dead or alive) to be Bernoulli given the preceding mortality status. Similarly for flowering status given mortality status. Given flowering, the number of flowers may have a Poisson distribution conditioned on be...

Quantitative genetic study of the adaptive process

“…Aster modeling has been developed to fill this methodological gap (Geyer et al, 2007;Shaw et al, 2008). Using a likelihood framework, aster explicitly models the components of fitness, including the dependence of later expressed components on earlier ones, for example, the number of offspring produced in a particular year on survival up to that year, on reproductive status and on the number of mates.…”

Introduction beyond a species range: a relationship between population origin, adaptive potential and plant performance

“…The performance of plants of different origins at Beer Sheva location was compared using aster modeling of individual and group lifetime fitness (Geyer et al, 2007;Shaw et al, 2008) as implemented in R (R Development Core Team, 2009). The life-history stages that we modeled, and their statistical distributions, for the first year assessment were early-season seed germination (Bernoulli), whether a plant reproduced or not (Bernoulli) and total seeds per plant (Poisson).…”

“…The RP values of plants of different origins in the introduction year were analyzed over plots by one-sample t-test. Similarly, the observed proportions of seeds of different origins in plots at 4 years after introduction were at first subtracted from those expected under no selective advantage (that is, equal for all accessions) and then analyzed over plots by one-sample t-test.The performance of plants of different origins at Beer Sheva location was compared using aster modeling of individual and group lifetime fitness (Geyer et al, 2007;Shaw et al, 2008) as implemented in R (R Development Core Team, 2009). The life-history stages that we modeled, and their statistical distributions, for the first year assessment were early-season seed germination (Bernoulli), whether a plant reproduced or not (Bernoulli) and total seeds per plant (Poisson).…”

The genetic and ecological basis of diversification

“…Further laboratory work could use manipulative experiments to confirm the putative selective agents and the traits under selection. More detailed measurements of field performance at each life history stage could dissect how natural selection reduces fitness across ontogeny and provide better estimates of lifetime fitness using Aster models (Geyer et al 2007;). More replicate populations from the heterogeneous landscape could be included to provide a more robust regression between environment or phenotype, and field performance.…”