Quantitative undergraduate ecology education and the "rule-of-five"

Background/Question/Methods

A host of national reports over the past two decades have noted the growing importance of quantitative approaches in biology and encouraged the development of undergraduate curricula which incorporate quantitative methods. The major formal quantitative education that undergraduates receive is through mathematics, statistics and computer science courses that are generally only loosely linked to the diverse quantitative conceptual foundations that are necessary in biology. Calculus still reigns as often the only mathematical component of undergraduate ecology requirements, despite the fact that comprehension of much of the theoretical underpinnings of ecology requires understanding of probability and discrete mathematics such as lineear algebra and discrete dynamical systems. Basic concepts such as equilibrium and stability are typically not even mentioned in these calculus-oriented courses. The growing number of math courses designed specifically for biology undergraduates, and the variety of texts and other materials to support them, have had limited impact, and these courses are calculus-focused. There is also very little connection to observation and data even in the math courses specifically designed for biology students, so students see these courses as divorced in context from their laboratory and field-oriented biology courses.

Results/Conclusions

As a supplement to quantitative education initiatives such as those fostered by projects such as Vision and Change, colleagues and I have developed a pedagogy and text based upon the "rule-of-five" which utilizes a mixture of approaches (symbolic, graphical, numerical, verbal analogy, and data) to relate key concepts while accounting for the diverse learning styles of students. This assists in learning and reinforcing key concepts throughout entry-level quantitative courses and undergraduate ecology courses. I will demonstrate how data on photosynthetic rates is used to build a large portion of standard calculus concepts, how landscape change based on images from Google Earth is used to encourage hypothesis formulation and testing and allows students to derive themselves the basic rules of matrix multiplication, and to discover the relationship between eigenvectors and landscape equilibrium. The stochastic aspects of bird watching are used to illustrate key concepts of uncertainty including the notion of "bad luck" in waiting-time situations. Throughout, the availability of computational tools such as R allow students to more readily apply quantitative methods to data, while building comprehension of basic coding that goes beyond the use of a "black-box".