R. A. Fisher, apart from his fundamental contributions to statistical science, fostered many developments of theoretical evolutionary science. In commemoration of Fisher's birth centenary (1991), this paper highlights several of Fisher's interests in evolutionary processes. These include the "Fundamental Theorem of Natural Selection," studies on the phenomenon of an even sex ratio in natural populations, the "runaway process" of sexual selection and models of polygenic inheritance. Some historical discussions and perspectives on evolutionary science and the Fisher legacy are also presented.

Before the beginning of this century, statistics meant observed data and descriptive summary figures, such as means, variances, indices, etc., computed from data. With the introduction of the $\chi^2$ test for goodness of fit (specification) by Karl Pearson (1900) and the $t$ test by Gosset (Student, 1908) for drawing inference on the mean of a normal population, statistics started acquiring new meaning as a method of processing data to determine the amount of uncertainty in various generalizations we may make from observed data (sample) to the source of the data (population). The major steps that led to the establishment and recognition of statistics as a separate scientific discipline and an inevitable tool in improving natural knowledge were made by R. A. Fisher during the decade 1915-1925. Most of the concepts and methods introduced by Fisher are fundamental and continue to provide the framework for the discussion of statistical theory. Fisher's work is monumental, both in richness and variety of ideas, and provided the inspiration for phenomenal developments in statistical methodology for applications in all areas of human endeavor during the last 75 years. Some of Fisher's pioneering works have raised bitter controversies that still continue. These controversies have indeed helped in highlighting the intrinsic difficulties in inductive reasoning and seeking refinements in statistical methodology.

We review a wide variety of applications in different branches of sciences arising from the study of dynamical systems. The emergence of chaos and fractals from iterations of simple difference equations is discussed. Notions of phase space, contractive mapping, attractor, invariant density and the relevance of ergodic theory for studying dynamical systems are reviewed. Various concepts of dimensions and their relationships are studied, and their use in the measurement of chaotic phenomena is investigated. We discuss the implications of the growth of nonlinear science on paradigms of model building in the tradition of classical statistics. The role that statistical science can play in future developments of nonlinear science and its possible impact on the future development of statistical science itself are addressed.

The study of chaotic behavior has received substantial attention in many disciplines. Although often based on deterministic models, chaos is associated with complex, "random" behavior and forms of unpredictability. Mathematical models and definitions associated with chaos are reviewed. The relationship between the mathematics of chaos and probabilistic notions, including ergodic theory and uncertainty modeling, are emphasized. Popular data analytic methods appearing in the literature are discussed. A major goal of this article is to present some indications of how probability modelers and statisticians can contribute to analyses involving chaos.

The past decade has seen substantial research on exact inference for contingency tables, both in terms of developing new analyses and developing efficient algorithms for computations. Coupled with concomitant improvements in computer power, this research has resulted in a greater variety of exact procedures becoming feasible for practical use and a considerable increase in the size of data sets to which the procedures can be applied. For some basic analyses of contingency tables, it is unnecessary to use large-sample approximations to sampling distributions when their adequacy is in doubt. This article surveys the current theoretical and computational developments of exact methods for contingency tables. Primary attention is given to the exact conditional approach, which eliminates nuisance parameters by conditioning on their sufficient statistics. The presentation of various exact inferences is unified by expressing them in terms of parameters and their sufficient statistics in loglinear models. Exact approaches for many inferences are not yet addressed in the literature, particularly for multidimensional contingency tables, and this article also suggests additional research for the next decade that would make exact methods yet more widely applicable.