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. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education

Oceanographic barriers, divergence, and admixture : phylogeography and taxonomy of two putative subspecies of short-finned pilot whale

Funding:Commander, U.S. Pacific Fleet Environmental Readiness Division and NMFS Pacific Islands Fisheries Science Center; NMFS West Coast Region; Scripps Institution of Oceanography Edna Bailey Sussman Research Fellowship; and Woods Hole Oceanographic Institution.Genomic phylogeography plays an important role in describing evolutionary processes and their geographic, ecological, or cultural drivers. These drivers are often poorly understood in marine environments, which have fewer obvious barriers to mixing than terrestrial environments. Taxonomic uncertainty of some taxa (e.g., cetaceans), due to the difficulty in obtaining morphological data, can hamper our understanding of these processes. One such taxon, the short‐finned pilot whale, is recognized as a single global species but includes at least two distinct morphological forms described from stranding and drive hunting in Japan, the “Naisa” and “Shiho” forms. Using samples (n = 735) collected throughout their global range, we examine phylogeographic patterns of divergence by comparing mitogenomes and nuclear SNP loci. Our results suggest three types within the species: an Atlantic Ocean type, a western/central Pacific and Indian Ocean (Naisa) type, and an eastern Pacific Ocean and northern Japan (Shiho) type. mtDNA control region differentiation indicates these three types form two subspecies, separated by the East Pacific Barrier: Shiho short‐finned pilot whale, in the eastern Pacific Ocean and northern Japan, and Naisa short‐finned pilot whale, throughout the remainder of the species' distribution. Our data further indicate two diverging populations within the Naisa subspecies, in the Atlantic Ocean and western/central Pacific and Indian Oceans, separated by the Benguela Barrier off South Africa. This study reveals a process of divergence and speciation within a globally‐distributed, mobile marine predator, and indicates the importance of the East Pacific Barrier to this evolutionary process.PostprintPeer reviewe