Agent-Based Modeling and Simulation in Mathematics and Biology Education.

With advances in computing, agent-based models (ABMs) have become a feasible and appealing tool to study biological systems. ABMs are seeing increased incorporation into both the biology and mathematics classrooms as powerful modeling tools to study processes involving substantial amounts of stochasticity, nonlinear interactions, and/or heterogeneous spatial structures. Here we present a brief synopsis of the agent-based modeling approach with an emphasis on its use to simulate biological systems, and provide a discussion of its role and limitations in both the biology and mathematics classrooms.

Mathematics and evolutionary biology make bioinformatics education comprehensible.

The patterns of variation within a molecular sequence data set result from the interplay between population genetic, molecular evolutionary and macroevolutionary processes-the standard purview of evolutionary biologists. Elucidating these patterns, particularly for large data sets, requires an understanding of the structure, assumptions and limitations of the algorithms used by bioinformatics software-the domain of mathematicians and computer scientists. As a result, bioinformatics often suffers a 'two-culture' problem because of the lack of broad overlapping expertise between these two groups.

Bioinformatics education dissemination with an evolutionary problem solving perspective.

Bioinformatics is central to biology education in the 21st century. With the generation of terabytes of data per day, the application of computer-based tools to stored and distributed data is fundamentally changing research and its application to problems in medicine, agriculture, conservation and forensics. In light of this 'information revolution,' undergraduate biology curricula must be redesigned to prepare the next generation of informed citizens as well as those who will pursue careers in the life sciences.

Mathematical manipulative models: in defense of "beanbag biology".

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations.

Selection in context: patterns of natural selection in the glycoprotein 120 region of human immunodeficiency virus 1 within infected individuals.

Evolution of the HIV-1 V3 loop was monitored in 15 subjects over a period of 5 years at approximately 6-month intervals. Putative recombination was detected in many of the sequences. Evolutionary trees were estimated from the nonrecombinant viral sequences found in each individual.