Grand Valley State University
Annis Water Resources Institute 740 West Shoreline Drive Muskegon, MI 49441
Office: 133 Lake Michigan Center
Phone: 616-331-3987 Fax: 616-331-3864 E-mail: email@example.com
BIO/NRM/CMB 480/580: Techniques for Modeling Biological Systems (Fall semester, 3 credits). Theories based on mathematical models have long been of fundamental importance in various subdisciplines of the biological sciences. In population biology, this importance dates back at least as far as the 1700s with, for example, Euler's work in mathematical demography and Malthus's work on population regulation. In the early to mid 20th century, there was a great flowering of mathematical approaches in many areas of biology, including ecology, population genetics, fisheries and wildlife management, biophysics, epidemiology, physiology, and biochemistry. More recently, mathematical models have become important in new areas, such as developmental biology, bioinformatics, and systems biology.
Despite the rapidly increasing importance of mathematical theories in the biological sciences, biology students often are not required to learn the mathematical and computational skills needed to understand, assess, apply, or develop mathematical models. The main purpose of this course is to partially fill this gap by providing biology students with a set of basic mathematical, computational, and computer graphics skills that will allow them to understand and critically evaluate several of the most common types of models in the biological literature, and to develop new models of their own.
The main types of models covered in this course are difference equations, matrix models, and ordinary differential equations. No prior knowledge of any of these topics is assumed. As background, the course begins by refreshing students' memories of various topics in elementary mathematics, including the basic rules of algebra and various standard mathematical functions (power functions, exponential functions, etc.). The course also provides students with an introduction to the required parts of elementary calculus, tailored to biology students and with no prior knowledge assumed.
Each modeling technique studied is illustrated by readings from the literature. Applications to various branches of modern biology are illustrated with worked examples. Specific applications examined during the course each year will be selected based on interests of the students but may include, for example, topics in animal behavior, population and community ecology, population genetics, fisheries and wildlife management, ecotoxicology, epidemiology, cell and organism physiology, biochemistry, regulation of genes and metabolism, and statistical topics such as least-squares parameter estimation.
This is not a mathematics or computer programming course. Emphasis is placed on how to apply the various techniques to biological problems rather than on mathematics or programming per se.
Research Interests and Approach
My three main research interests at the present time are methods of estimating components of lake metabolism based on free-water dissolved-oxygen (DO) dynamics, evolutionary ecology of invasive aquatic plants, and turbulent transport of suspended particles (e.g., fine particulate organic matter, microorganisms, and invertebrate larvae) in streams.
Exchange of carbon between the biosphere and atmosphere is dominated by rates of photosynthetic CO2 uptake and respiratory CO2 release by aquatic and terrestrial ecosystems worldwide. Obtaining accurate estimates of these rates is therefore important. In lakes, the most common estimation method is based on a model of DO dynamics and a corresponding time series of DO concentrations measured in the well-mixed layer of water at the lake surface. O2 production and consumption are inferred from changes in DO concentration, then converted to estimates of carbon uptake and release using photosynthetic and respiratory quotients. The traditional method of this type uses a simple accounting procedure to estimate daily gross primary production (GPP), total respiration (R), and net production (NP), but it assumes that the time series of measured DO concentrations contains no error, and its estimates of R and GPP hinge on a subjectively assumed value for daytime respiration. In collaboration with Dr. Bopi Biddanda of AWRI and several of our graduate students, I have developed several new alternative methods for estimating GPP, R, and NP that resolve these problems and facilitate assessment of model adequacy. We are applying these new methods to high-frequency time-series data acquired by AWRI's Muskegon Lake Buoy Observatory and are also working on practical ways to modify the mechanistic model of DO dynamics that underlies the estimating methods to improve their performance.
My work on the evolutionary ecology of invasive aquatic plants is a collaborative effort with Dr. Ryan Thum of AWRI. We are exploring both purely ecological models and ecological models that include evolution of quantitative and categorical traits in finite populations coupled by migration. Our main focus currently is on populations of Northern watermilfoil (indigenous) and Eurasian watermilfoil (exotic) in Michigan and Wisconsin. Eurasian watermilfoil is highly invasive in these states, threatening indigenous populations of Northern watermilfoil and creating extremely dense nuisance growths that require management. Among other things, we are interested in the role of hybridization in both the evolution of invasiveness and the evolution of herbicide resistance.
My work on turbulent transport of suspended particles centers on a stochastic diffusion model called the Local Exchange Model, which I developed to describe the random-like dynamics of individual particles suspended in a turbulent fluid. The model can be applied to the transport of molecules, seston, microorganisms, and invertebrates in aquatic systems characterized by turbulent flowing water (e.g., streams, estuaries, and marine systems), and to a variety of other turbulent transport problems, as well.
A complete theory of particle transport in turbulent aquatic systems can be decomposed into at least four problems: (1) The entrainment problem how does a particle on the bottom (or other solid surface) become entrained into the water column? (2) The travel-time problem how long does a suspended particle take to hit the bottom for the first time, following release from a given initial elevation? (3) The travel-distance problem how far does a suspended particle travel before hitting the bottom for the first time, following release from a given initial elevation? And (4) the settlement problem what determines whether a particle settles on the bottom when it hits, rather than bouncing off and immediately returning to the water column? Thus far, I have derived equations governing the probability distribution and moments of the hitting time, hitting distance, settling time, and settling distance (the hitting time and distance are the travel time and distance at which a suspended particle hits the bottom for the first time; the settling time and distance are the travel time and distance at which a suspended particle settles for the first time). I have applied these theoretical results to empirical settling-distance distributions for 14C-labeled natural FPOM in streams, and I am currently applying them to data for additional types and sizes of particles in streams and flumes.
McNair, J. N., Sesselmann, M. R., Gereaux, L. C., Weinke, A. D., Kendall, S. T., and Biddanda, B. A. 2014. Alternative methods for estimating components of lake metabolism using process-based models of dissolved-oxygen dynamics. Fundamental and Applied Limnology (in press).
Ruetz, C. R. III, Harris, B. S., McNair, J. N., and Homola, J. J. 2014. Removal and mark-recapture methods for estimating abundance: empirical and simulation results for Mottled Sculpin in streams. North American Journal of Fisheries Management (in press).
McNair, J. N., Gereaux, L. C., Weinke, A. D., Sesselmann, M. R., Kendall, S. T., and Biddanda, B. A. 2013. New methods for estimating components of lake metabolism based on free-water dissolved-oxygen dynamics. Ecological Modelling 263: 251–263.
Sisson, A.J., Wampler, P.J., Rediske, R.R., McNair, J.N., and Frobish, D. 2013. Long-term field performance of the Biosand Filter in the Artibonite Valley, Haiti. American Journal of Tropical Medicine and Hygiene 88: 862–867.
Homola, J.J., Scribner, K.T., Elliott, R.F., Donofrio, M.C., Kanefsky, J., Smith, K.M., and McNair, J.N. 2012. Genetically-derived estimates of contemporary natural straying rates and historical gene flow among Lake Michigan lake sturgeon populations. Transactions of the American Fisheries Society 141: 1374–1388.
McNair, J.N., and Newbold, J.D. 2012. Turbulent particle transport in streams: Can exponential settling be reconciled with fluid mechanics? Journal of Theoretical Biology 300: 62–80.
McNair, J.N., Sunkara, A., and Frobish, D. 2012. How to analyze seed germination data using statistical time-to-event analysis: nonparametric and semiparametric methods. Seed Science Research 22: 77–95.
McNair, J.N. 2009. Two new methods for predicting effects of landcover-related stressors on stream biotic integrity at the catchment scale. Proceedings of the Academy of Natural Sciences of Philadelphia 158: 61–88.
Sieg, A.E., O'Connor, M.P., McNair, J.N., Grant, B.W., Agosta, S.J., and Dunham, A.E. 2009. Mammalian metabolic allometry: do intraspecific variation, phylogeny, and regression models matter? American Naturalist 174: 720–733.
Araujo, A. and McNair, J.N. 2007. Individual- and population-level effects of antimicrobials on the rotifers, Brachionus calyciflorus and B. plicatilis. Hydrobiologia 593: 185–199.
Johnson, T.E., McNair, J.N., Srivastava, P., and Hart, D.D. 2007. Stream ecosystem responses to spatially variable landcover: a model for developing riparian restoration strategies. Freshwater Biology 52: 680–695.
O'Connor, M.P., Agosta, S.J., Hansen , F., Kemp, S.J., Sieg, A.E., McNair, J.N. and Dunham, A.E. 2007. Phylogeny, regression, and the allometry of physiological traits. American Naturalist 170: 431–442.
O'Connor, M.P., Agosta, S.J., Hansen , F., Kemp, S.J., Sieg, A.E., Wallace, B.P., McNair, J.N. and Dunham, A.E. 2007. Size, selection, and physiology: Reconsidering the mechanistic basis of the metabolic theory of ecology. Oikos 116: 1058–1072.
McNair, J.N. 2006. Probabilistic settling in the Local Exchange Model of turbulent particle transport. Journal of Theoretical Biology 241: 420–437.
Srivastava, P., McNair, J.N., and Johnson, T.E. 2006. Comparison of process-based and artificial neural network approaches for streamflow modeling in an agricultural watershed. Journal of the American Water Resources Association 42: 545–563.
Fingerut, J.T., Hart, D.D. and McNair, J.N. 2006. Silk use enhances benthic invertebrate settlement. Oecologia 150: 202–212.
Bram, M.R. and McNair, J.N. 2004. Seed germinability and its seasonal onset in three populations of Japanese knotweed. Weed Science 52: 759–767.
McNair, J.N., and Newbold, J.D. 2001. Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-distance problem for the Local Exchange Model. Journal of Theoretical Biology 209: 351–369.
McNair, J.N. 2000. Turbulent transport of suspended particles and dispersing benthic organisms: the hitting-time distribution for the Local Exchange Model. Journal of Theoretical Biology 202: 231–246.
Goulden, C.E., Moeller, R.E., McNair, J.N., and Place, A.R. 1999. Lipid dietary dependencies in zooplankton. Pages 91–108 in: Arts, M.T. and Wainman, B.C. (Eds.) Lipids in Freshwater Ecosystems. New York: Springer-Verlag.
McNair, J.N., Boraas, M.E., and Seale, D.B. 1998. Size-structure dynamics of the rotifer chemostat: a simple physiologically structured model. Hydrobiologia 387/388: 469–476.
Boraas, M.E., Seale, D.B., Boxhorn, J.E., and McNair, J.N. 1998. Rotifer size distribution changes during transient phases in open cultures. Hydrobiologia 387/388: 477–482.
McNair, J.N., Newbold, J.D., and Hart, D.D. 1997. Turbulent transport of suspended particles and dispersing benthic organisms: how long to hit bottom? Journal of Theoretical Biology 188: 29–52.
McNair, J.N. 1995. Ontogenetic patterns of density-dependent mortality: contrasting stability effects in populations with adult dominance. Journal of Theoretical Biology 175: 207–230.
McNair, J.N., Goulden, C.E., and Ziegenfuss, M.C. 1995. Is there a place for ecotoxicology? Setac News 15: 18–21.
McNair, J.N. and Goulden, C.E. 1991. The dynamics of age-structured populations with a gestation period: density-independent growth and egg ratio methods for estimating the birth rate. Theoretical Population Biology 39: 1–29.
McNair, J.N. 1989. Stability effects of a juvenile period in age-structured populations. Journal of Theoretical Biology 137: 397–422.