In the summer of 1993, twenty-six graduate and postdoctoral stu dents and fourteen lecturers converged on Cornell University for a summer school devoted to structured-population models. This school was one of a series to address concepts cutting across the traditional boundaries separating terrestrial, marine, and freshwa ter ecology. Earlier schools resulted in the books Patch Dynamics (S. A. Levin, T. M. Powell & J. H. Steele, eds., Springer-Verlag, Berlin, 1993) and Ecological Time Series (T. M. Powell & J. H. Steele, eds., Chapman and Hall, New York, 1995); a book on food webs is in preparation. Models of population structure (differences among individuals due to age, size, developmental stage, spatial location, or genotype) have an important place in studies of all three kinds of ecosystem. In choosing the participants and lecturers for the school, we se lected for diversity-biologists who knew some mathematics and mathematicians who knew some biology, field biologists sobered by encounters with messy data and theoreticians intoxicated by the elegance of the underlying mathematics, people concerned with long-term evolutionary problems and people concerned with the acute crises of conservation biology. For four weeks, these perspec tives swirled in discussions that started in the lecture hall and carried on into the sweltering Ithaca night. Diversity mayor may not increase stability, but it surely makes things interesting.

In this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution.

Populations living in natural environments experience fluctuations in environmental conditions that drive variability in demographic rates. This dissertation develops new and existing mathematical methods for studying environmental stochasticity and uses these tools to investigate the role of environmental stochasticity in driving observed population dynamics and plant life history evolution. In the first two chapters I develop new approaches to a classic method in population biology, the life table response experiment (LTRE). Whereas existing methods used time-averaged demographic rates and deterministic sensitivities to decompose observed differences in population growth rates, this new method allows estimation of the contributions to those differences made by variances in demographic rates as well as by mean rate values. I use this stochastic LTRE to show how differential variability in the vital rates of Anthyllis vulneraria (kidney vetch) contribute to differences in the population growth rates of nine populations growing in southwest Belgium; we also show how the effects of demographic rate variability depend on soil depth, where the greater moisture retention of deeper soils buffers populations against the otherwise negative effects of demographic variability. The second chapter provides a different approach to LTRE that uses an iterated two-factor decomposition of the small noise approximation of the stochastic population growth rate to quantify contributions to that growth rate made by: (i) mean vital rates, (ii) temporal variability in vital rates, (iii) elasticities of the population growth rate to individual vital rates, and (iv) correlations between vital rates across the study period. Contributions of elasticities tell us about differences in local selection pressures acting on distinct populations and contributions of correlations tell us about differences in the phenotypic tradeoffs associated with vital rates. I use this new method to show how these differences drive dynamics in two species: Anthyllis vulneraria (the same populations studied in the first chapter) and Cypripedium calceolus (lady's slipper orchid). In Anthyllis vulneraria, variability in large adult fertility and seedling survival made the largest contributions; there were also effects of differences in elasticities of large adult fertility and survival, as well as differences in the correlations between rapid growth and survival in seedlings (a survival cost of rapid early development), between large adult fertility and survival (a survival cost of reproduction) and between large adult fertility and seedling survival. In Cypripedium calceolus, population growth rates were driven most by differences in the elasticities to the probabilities of adult stasis vs. entering dormancy, as well as by differences in the variability and tradeoffs associated with adult dormancy; correlation played a role through differences in the survival payoff of dormancy vs. the complimentary fertility cost of dormancy in terms of lost opportunity for reproduction. The third and final chapter investigates the role of fire disturbance in driving the life histories and population-level dynamics of five woody plant species growing in the Brazilian cerrado, a savannah-forest mosaic in which woody vegetation cover is primarily mediated by fire disturbance. This study presents a set of diagnostics that use demographic responses to recurring disturbance to categorize species along a continuum of adaptation: on one end we find 'resistant' species that must weather disturbance in order to attain large sizes that are buffered against fire-induced mortality; on the other end we find 'resilient' species that are relatively indifferent to disturbance and harness transient opportunities afforded by early post-fire successional habitats in order to take advantage of increased nutrient availability and reduced competition. Each of these chapters uses stochastic demographic analysis to extend theory describing the dynamics of populations in variable environments; together, these studies present a variegated perspective on the role of environmental stochasticity that provides new methods and novel perspectives that should be useful in the study of population biology and life history evolution.

DEVELOPING MATRICES AND USING DATA PROCESSING TO CREATE POPULATION MODELS.

This book provides a review of methods for obtaining and analysing data from stage-structured biological populations. The topics covered are sam pling designs (Chapter 2), the estimation of parameters by maximum likelihood (Chapter 3), the analysis of sample counts of the numbers cif individuals in different stages at different times (Chapters 4 and 5), the analysis of data using Leslie matrix types of model (Chapter 6) and key factor analysis (Chapter 7). There is also some discussion of the approaches to modelling and estimation that have been used in five studies of particular populations (Chapter 8). There is a large literature on the modelling of biological populations, and a multitude of different approaches have been used in this area. The various approaches can be classified in different ways (Southwood, 1978, ch. 12), but for the purposes of this book it is convenient to think of the three categories mathematical, statistical and predictive modelling. Mathematical modelling is concerned largely with developing models that capture the most important qualitative features of population dynamics. In this case, the models that are developed do not have to be compared with data from natural populations. As representations of idealized systems, they can be quite informative in showing the effects of changing parameters, indicating what factors are most important in promoting stability, and so on.