Mark Kot

Associate Professor of Applied Mathematics

Education

Research

My research is at the interface between applied mathematics and ecology and evolutionary biology. I model the dynamics of biological populations, use mathematics to shed light on the abundance and distribution of biological populations, and use biology to motivate interesting mathematical problems.

In recent years, my research has centered on integrodifference equations. These are discrete-time, continuous-space models for the growth and spread of biological populations. Integrodifference equations readily incorporate a range of dispersal mechanisms. They appear to be both more flexible and more realistic than simple reaction-diffusion models. Integrodifference equations are extremely useful for modeling biological invasions.

In addition to my long-standing interest in integrodifference equations, I am also interested in understanding how simple ecological models can give rise to complex or chaotic dynamics and in a broad range of other ecological and evolutionary models and analyses.

Publications

• Kot, M. 2001.
  Elements of Mathematical Ecology.
  Cambridge University Press, Cambridge, UK, x + 453 pp.
  (2nd corrected printing in 2003)

Published Papers

• Zhou, Y. and Kot, M. 2011. Discrete-time growth-dispersal models with shifting species ranges.
  Theoretical Ecology, 4, 13-25.

• Seo, G. and Kot, M. 2009. The dynamics of a simple laissez-faire model with two predators.
  Mathematical Biosciences and Engineering, 6, 145-172.

• Kot, M. and Neubert, M. G. 2008. Saddle-point approximations, integrodifference equations, and Invasions.
  Bulletin of Mathematical Biology, 70, 1790-1826.

• Seo, G. and Kot, M. 2008
  A comparison of two predator-prey models with Holling's type I functional response.
  Mathematical Biosciences, 212, 161-179.

• Toth, D. and Kot, M. 2006.
  Limit cycles in a chemostat model for a single species with age structure.
  Mathematical Biosciences, 202, 194-217.

• Kot, M. 2005.
  Torus bubbling in a discrete-time predator-prey model.
  Journal of Difference Equations and Applications, 11, 431-441.
  erratum

• Kot, M., Medlock, J., Reluga, T., and Walton, D. B. 2004.
  Stochasticity, invasions, and branching random walks.
  Theoretical Population Biology, 66, 175-184.

• Medlock, J. and Kot, M. 2003.
  Spreading disease: integro-differential equations old and new.
  Mathematical Biosciences, 184, 201-222.

• Kot, M., Silverman, E., and Berg, C. A. 2003.
  Zipf's law and the diversity of biology newsgroups.
  Scientometrics, 56, 247-257.

• Kot, M. 2002.
  Do invading organisms do the wave?
  Canadian Applied Mathematics Quarterly, 10, 139-170.

• Wang, M.-H., Kot, M., and Neubert, M. G. 2002.
  Integrodifference equations, Allee effects, and invasions.
  Journal of Mathematical Biology, 44, 150-168.

• Silverman, E. D., Kot, M. and Thompson, E. 2001.
  Testing a simple stochastic model for the dynamics of waterfowl aggregations.
  Oecologia, 128, 608-617.

• Wang, M.-H. and Kot, M. 2001.
  Speeds of invasion in a model with strong or weak Allee effects.
  Mathematical Biosciences, 171, 83-97.

• Neubert, M. G., Kot, M., and Lewis, M. A. 2000.
  Invasion speeds in fluctuating environments.
  Proceedings of the Royal Society of London B, 267, 1603-1610.
  (Errata: 267, 2568-2569).

• Silverman, E. and Kot, M. 2000.
  Rate estimation for a simple movement model.
  Bulletin of Mathematical Biology, 62, 351-375.

• Kot, M., Lewis, M., and van den Driessche, P. 1996.
  Dispersal data and the spread of invading organisms.
  Ecology, 77, 2027-2042.

• King, A. A., Schaffer, W. M., Gordon, C., Treat, J., Kot, M. 1996.
  Weakly dissipative predator-prey systems.
  Bulletin of Mathematical Biology, 58, 835-859.

• Gittleman, J. L., Anderson, C. G., Kot, M. and Luh, H.-K. 1996.
  Comparative tests of evolutionary lability and rates using molecular phylogenies.
  In, New Uses for New Phylogenies
  (P. H. Harvey, A. J. Leigh Brown, J. Maynard Smith, and S. Nee, eds.),
  pages 289-307. Oxford University Press, Oxford.

• Gittleman, J. L., Anderson, C. G., Kot, M., Luh, H.-K. 1996.
  Phylogenetic lability and rates of evolution: A comparison of behavioral, morphological, and life history traits.
  In, Phylogenies and the Comparative Method in Animal Behavior (E. P. Martins, ed.),
  pp. 166-205. Oxford University Press, Oxford.

• Neubert, M. G., Kot, M., and Lewis, M. A. 1995.
  Dispersal and pattern formation in a discrete-time predator-prey model.
  Theoretical Population Biology, 48, 7-43.

• Edwards, S. and Kot, M. 1995.
  Comparative methods at the species level: geographic variation in morphology and group size in Grey-crowned Babblers (Pomatostomus temporalis).
  Evolution, 49, 1134-1146.

• Funasaki, E. and Kot, M. 1993.
  Invasion and chaos in a pulsed mass-action chemostat.
  Theoretical Population Biology, B44, 203-224.

• Neubert, M. and Kot, M. 1992.
  Subcriticality and population collapse in some simple discrete-time predator-prey models.
  Mathematical Biosciences, 110, 45-66.

• Kot, M., Sayler, G. S., and Schultz, T. W. 1992.
  Complex dynamics in a model microbial system.
  Bulletin of Mathematical Biology, 54, 619-648.

• Kot, M. 1992.
  Discrete-time travelling waves: ecological examples.
  Journal of Mathematical Biology, 30, 413-436.

• Gittleman, J. L. and Kot, M. 1990.
  Adaptation: statistics and a null model for estimating phylogenetic effects.
  Systematic Zoology, 39, 227-241.

• Stafford, S. A., Kot, M., and Roth, J. R. 1990.
  Investigation of the nonlinear behavior of a partially ionized, turbulent plasma in a magnetic field.
  Journal of Applied Physics, 68, 488-499.

• Bingham, S. and Kot, M. 1989.
  Multidimensional trees, range searching, and a correlation dimension algorithm of reduced complexity.
  Physics Letters A, 140, 327-330.

• Kot, M. 1989.
  Diffusion-driven period-doubling bifurcations.
  BioSystems, 22, 279-287.

• Kot, M., Schaffer, W. M., Truty, G. L., Graser, D. J., and Olsen, L. F. 1988.
  Changing criteria for imposing order.
  Ecological Modelling, 43, 75-110.

• Kot, M. and Schaffer, W. M. 1986.
  Discrete-time growth-dispersal models.
  Mathematical Biosciences, 80, 109-136.

• Schaffer, W. M., Ellner, S., and Kot, M. 1986.
  Effects of noise on some dynamical models in ecology.
  Journal of Mathematical Biology, 24, 479-523.

• Schaffer, W. M. and Kot, M. 1986.
  Differential systems in ecology and epidemiology.
  In Chaos, A. V. Holden (Ed.), pp. 158-178.
  Princeton University Press, Princeton.

• Schaffer, W. M. and Kot, M. 1986.
  Chaos in ecological systems: the coals that Newcastle forgot.
  Trends in Ecology and Evolution, 1, 58-63.

• Schaffer, W. M. and Kot, M. 1985.
  Nearly one-dimensional dynamics in an epidemic.
  Journal of Theoretical Biology, 112, 403-427.

• Schaffer, W. M. and Kot, M. 1985.
  Do strange attractors govern ecological systems?
  Bioscience, 35, 342-350.

• Kot, M. and Schaffer, W. M. 1984.
  The effects of seasonality on discrete models of population growth.
  Theoretical Population Biology, 26, 340-360.

Courses

I have taught a variety of undergraduate and graduate courses at the University of Washington.
These courses include:

Amath 351

Amath 351 is:

• Introduction to Differential Equations and Applications

Please see

Amath 353

Amath 353 is:

• Fourier Analysis and Partial Differential Equations

Please see

Amath 383

Amath 383 is:

• Introduction to Continuous Mathematical Modeling

Please see

Amath 401

Amath 401 is:

• Vector Calculus and Complex Variables

Amath 402

Amath 402 is:

• Methods for Ordinary Differential Equations

Please see

Amath 422

Amath 422 is:

• Introduction to Mathematical Biology

Amath 423

Amath 423 is:

• Mathematical Biology: Stochastic Models

Please see

Amath 501

Amath 501 is:

• Vector Calculus and Complex Variables

Amath 504

AMath 504 is:

• Mathematical Biology II

Amath 507

Amath 507 is:

• Calculus of Variations

Amath 521

Amath 521 is:

• Mathematical Ecology

Please see

Amath 522

Amath 522 is:

• Introduction to Mathematical Biology

Amath 535

Amath 535 is:

• Mathematical Ecology

Amath 536

Amath 536 is:

• Spatial Models in Ecology & Epidemiology

Lab

Members

Members

Postdoctoral Research Associates:

• Melanie Harsch

Graduate Students:

• Austin Phillips

• Scott Rinnan

• Joy (Ying) Zhou

Alumni

Stuart Bingham

Links

Interesting links:

Programs

Graduate students can work with me through either one of two graduate programs:

Meetings

Here are some scientific meetings that I recently enjoyed or that I will soon attend: