Carleton College, BA; University of Minnesota, MS, PhD
I study how disturbances and intrinsic recovery processes balance or fail to balance in a dynamical system, based on its transient behavior. Motivated by applications to environmental change and resilience, I also develop new mathematical theory when existing tools do not suffice. My interests span from abstract mathematics to interdisciplinary collaborations.
On the abstract side of the spectrum, I leverage disturbances themselves to illuminate the robustness and structure of a dynamical system. My doctoral work on attractor intensity with Dick McGehee integrated control theory and Conley theory to put a number on how wrong an ordinary differential equation (ODE) model can be while still providing useful information about the long-term behavior of a system. Current directions include extending intensity theory from attractors to general isolated invariant sets and relating changes in reachable sets to Morse decompositions.
Midway between theory and application, I helped develop flow-kick models to quantify resilience of ecosystem structure and function to discrete, repeated perturbations. This work revealed connections to continuous disturbance models in the limit of arbitrarily small kicks and recovery times. I am now focused on the dynamic implications of selecting a discrete versus continuous disturbance model: which structures (fixed points, isolated invariant sets, bifurcations) do we maintain, lose, or gain when we go discrete?
My interdisciplinary projects have centered on collaborations with ecologists at Cedar Creek Ecosystem Science Reserve. My collaborators and I used mathematical models to test which verbally plausible mechanisms might explain the observed lack of recovery in grassland biodiversity following nutrient pollution. In addition, I advise student modeling projects that complement the RESCUE field experiment at Cedar Creek, testing the conditions under which seed additions maintain biodiversity in plant communities following habitat loss.
Meyer K, Broda J, Brettin A, Sànchez Muñiz M, Gorman S, Isbell F, Hobbie SE, Zeeman ML, McGehee R (2023) Nitrogen-induced hysteresis in grassland biodiversity: a theoretical test of litter-mediated mechanisms. The American Naturalist 201(6):E153-67.
Meyer K and McGehee R (2022) Intensity—A metric approach to quantifying attractor robustness in ODEs. SIAM Journal on Applied Dynamical Systems 21(2):
Meyer K (2019) Extinction debt repayment via timely habitat restoration. Theoretical Ecology 12(3):297-305.
Meyer K, Hoyer-Leitzel A, Iams S, Klasky I, Lee V, Ligtenberg S, Bussman E, and Zeeman ML (2018) Quantifying resilience to recurrent ecosystem disturbances using flow-kick dynamics. Nature Sustainability 1(11):671-678.
Zeeman ML, Meyer K, Bussmann E, Hoyer-Leitzel A, Iams S, Klasky I, Lee V, and Ligtenberg S (2018) Resilience of socially valued properties of natural systems to repeated disturbance: a framework to support value-laden management decisions. Natural Resource Modeling, e12170
Guswa AJ, Hamel P, and Meyer K (2018) Curve number approach to estimate monthly and annual runoff and baseflow. Journal of Hydrologic Engineering 23(2): doi 10.1061
Meyer K (2016) A mathematical review of resilience in ecology. Natural Resource Modeling 29(3):339-352.
Saito TT, Lui DY, Kim HM, Meyer K, and Colaiacovo MP (2013) Interplay between structure-specific endonucleases for crossover control during Caenorhabditis elegans meiosis. PLOS Genetics 9(7): e1003586.
Saito TT, Mohideen F, Meyer K, Harper WJ, and Colaiacovo MP (2012) SLX-1 is required for maintaining genomic integrity and promoting meiotic noncrossovers in the Caenorhabditis elegans germline. PLOS Genetics 8(8): e1002888.