The lifetime fitnesses of individuals comprising a population determine its numerical dynamics, and genetic variation in fitness results in evolutionary change. The dual importance of individual fitness is well understood, but empirical fitness records generally generally violate the assumptions of standard statistical approaches. This problem has plagued comprehensive study of fitness and impeded empirical study of the link between numerical and genetic dynamics of populations. Recently developed aster models address this problem by explicitly modeling the dependence of later expressed components of fitness (e.g. fecundity) on those expressed earlier (e.g. survival to reproduce). Moreover, aster models employ different sampling distributions for components of fitness, as appropriate (e.g. binomial for survival over a given interval and Poisson for fecundity). The analysis is conducted by maximum likelihood, and the resulting compound distributions for lifetime fitness closely approximate the observed data. We illustrate the breadth of aster's utility with three examples demonstrating estimation of the finite rate of increase, comparison of mean fitness among genotypic groups, and phenotypic selection analysis. Aster models offer a unified approach to address the breadth of questions in evolution and ecology for which life history data are gathered.

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...

I investigated reproduction in a three-year study of Echinacea angustifolia, purple coneflower, growing in a fragmented prairie landscape. I quantified the local abundance of flowering conspecifics at individual-based spatial scales and at a population-based spatial scale. Regression analyses revealed that pollen limitation increased while seed set and fecundity decreased with isolation of individual plants. Isolation, defined as the distance to the k(th) nearest flowering conspecific, was a good predictor of pollen limitation, for all nearest neighbors considered (k = 1-33), but the strength of the relationship, as quantified by R2, peaked at intermediate scales (k = 2-18). The relationship of isolation to seed set and fecundity was similarly strongest at intermediate scales (k = 3-4). The scale dependence of individual density effects on reproduction (density of flowering plants within x meters) resembled that of isolation. Analyses at a population-based scale showed that pollen limitation declined significantly with population size. Seed set and fecundity also declined with population size, but significantly so only in 1998. Whether quantifying local abundance with population- or individual-based measures, reproductive failure due to pollen limitation is a consistent consequence of Echinacea scarcity. However, individual-based measures of local abundance predicted pollen limitation from a wider sample of plants with a simpler model than did population size. Specifically, the largest site, a nature preserve, is composed of plants with intermediate individual isolation and, as predicted, intermediate pollen limitation, but its large population size poorly predicted population mean pollen limitation.

Pollen limitation of plant reproduction occurs in many plant species, particularly those in fragmented habitat; however, causes of pollen limitation are often unknown. We investigated the relationship between pollen limitation and pollinator visitation in the purple coneflower, Echinacea angustifolia (Asteraceae), which grows in the extremely fragmented tall grass prairie of North America. Previous investigations showed that pollen limitation of E. angustifolia increases with plant isolation and decreases with population size. We observed insect visitation to E. angustifolia over two flowering seasons and estimated pollen limitation of observed plants, using seed set as a proxy measure in 2004 and persistence of receptive style rows in 2005. We analyzed spatial patterns of bee visitation and pollination at two spatial scales: individual isolation, as measured by the distance to their kth nearest flowering neighbors (k = 1 - 15), and population size. Our results indicate that E. angustifolia is pollinated by over 26 species of native bees, with 70-75% of visits by halictid bees. Surprisingly, in both years, bee visitation increased with isolation of individual plants and did not vary significantly with population size. As expected, plant isolation increased pollen limitation and lowered seed set. There was no effect of population size on seed set in 2004, and pollen limitation decreased nonsignificantly with population size in 2005. We conclude that pollen receipt limits reproduction in E. angustifolia, but pollinator visitation does not. Remarkably, isolated plants simultaneously have increased rates of pollinator visitation by pollinators and decreased reproduction. We discuss alternative explanations of pollen limitation that are consistent with this apparent discrepancy, including a decline in the availability of compatible conspecific pollen with increased plant isolation.

Community genetics synthesizes community ecology and population genetics and yields fresh insights into the interplay between evolutionary and ecological processes. A community genetics framework proves especially valuable when strong selection on traits results from or impinges on interspecific interactions, an increasingly common phenomenon as more communities are subject to direct management or anthropogenic disturbances. We draw illustrations of this perspective from our ongoing studies of three representative communities, two managed and one natural, that have recently undergone large perturbations. The studied communities are: (1) insect pests of crop plants genetically engineered to produce insecticidal toxins; (2) insect‐pollinated plants in habitats severely fragmented by agriculture and urbanization; and (3) a pathogen and its crop host now grown extensively outside their native ranges. We demonstrate the value of integrating genetic and ecological processes to gain a full understanding of community dynamics, particularly in nonequilibrium systems that are subject to strong selection. Corresponding Editor: A. A. Agrawal