How mathematics and statistics related to Biology?
This report emphasizes the benefits that the fields of mathematics and statistics can bring to biology, but there are reciprocal benefits as well. Biological questions have historically opened up new areas in mathematics and statistics. For example, in addition to his invention of a whole new field of statistics (analysis of variance) for interpreting the results of biological experiments, Sir Ronald Fisher as well opened up new areas of mathematical analysis through his interest in travelling waves of invasion of novel genes. The following sections explore quantitative biology from a mathematical, rather than a biological, point of view, although the emphasis is still chiefly on solutions to biological rather than mathematical problems.
Many of the problems addressed below are the same as those in the biological examples given above, but organized by mathematical themes rather than biological problems. The ubiquity of stochastic, nonlinear, spatially extended systems in biologically has always been known, but these systems have been so intractable in the past that most mathematical results that were obtained were too hard to apply to real systems. The combination of advances in mathematics, computation, and statistics, and the new synergies of these fields, is now permitting quantitative biologists to tackle these problems rather than focusing only on those issues of biological systems that can be understood along with deterministic, linear, homogeneous models.