Models of Invasive Species : Spatial, Genetic and Socio-Environmental Systems.

Fellowship : October 2022 to june 2023

Discipline(s) : Mathematics

Pays : USA


Judith Miler’s fellow seminar was held on monday 5 decembre 2022 :

What mathematical models can tell us about invasive species

Mathematics is playing a more and more prominent role in meeting ecological challenges, including the control of invasive species. 

We present an introduction to mathematical modeling, including a historical example from epidemiology and recent work of the presenter and collaborators on the invasion of North America by the cabbage white butterfly Pieris rapae. We then outline challenges in mathematical modeling of invasive species control, particularly in landscapes divided into patches controlled by different owners or managers.


Suggestions for the week :

Film :

1) Journeys of Women in Mathematics (short documentary) This film was created by the IMU Committee for Women in Mathematics. Filmed and edited by Micro-Documentaries. Made possible by a grant from the Simons Foundation. Copyright 2018 International Mathematical Union

2) Hidden Figures (Hollywood feature based on true story)

It is an adaptation of Margot Lee Shetterly’s book of the same name, featuring African-American female calculators Katherine Johnson, Dorothy Vaughan and Mary Jackson who contributed to the National Aeronautics and Space Administration (NASA) aeronautics and space programs. The film shows how Katherine Johnson came to calculate the trajectories of the Mercury program and the Apollo 11 mission to the Moon in 1969,1 how Dorothy Vaughan became head of the computer calculations department, and Mary Jackson the first African-American female aeronautical engineer. 

Lecture :

God in Search of Man by Abraham Joshua Heschel 

Abraham Joshua Heschel was one of the most revered religious leaders of the 20th century, and God in Search of Man and its companion volume, Man Is Not Alone, two of his most important books, are classics of modern Jewish theology. God in Search of Man combines scholarship with lucidity, reverence, and compassion as Dr. Heschel discusses not man’s search for God but God’s for man--the notion of a Chosen People, an idea which, he writes, "signifies not a quality inherent in the people but a relationship between the people and God." It is an extraordinary description of the nature of Biblical thought, and how that thought becomes faith.

Image : 

Sainte-Chapelle made of Lego 

Research project: Models of Invasive Species: Spatial, Genetic and Socio-Environmental Systems.

The spread of invasive species worldwide is accelerating due to human-mediated dispersal and climate change. It is well established that invasive species have highly detrimental effects on the ecosystems to which they are introduced and take a high economic toll both because of this ecosystem degradation and because of direct effects on agriculture and industries relying on natural resources. My project comprises three parts, which together use mathematical models to shed light on the population dynamics, genetics, and susceptibility to control measures of invasive species. One part will yield rigorous mathematical analysis of an influential model; one part will result in a rare empirical test of the same model; and one part will build on techniques from economics and sociology to build a model of stakeholder willingness to participate in invasive species control. This interdisciplinary research will provide both insight into the processes that drive the spread of an invasive species and practical guidance for managers charged with slowing, halting or reversing such spread.


I completed my A.B. in Mathematics at Harvard in 1989 and my Ph.D at the University of Michigan in 1994. My adviser was Michael Weinstein, now of Columbia University. After postdocs at the Courant Institute of Mathematical Sciences/New York University and Simon Fraser University, I arrived at Georgetown University in 1997. My early work concerned partial differential equations of mathematical physics, but at Georgetown I seized the opportunity to get to know my colleagues in Biology. Through patient listening and many discussions, I published my first interdisciplinary work on a popular, but often abused, statistical test for the action of natural selection. I eventually moved on to harmonize my interest in dynamical systems with evolutionary biology by working on the evolutionary ecology of invasive species. I have recently become interested in the social science of gaining cooperation and collaboration to stop the spread of biological invaders, a microcosm of efforts to remedy the worst effects of climate change.


Refereed journal articles:
F. Shirani, and J.R. Miller, Competition, Trait Variance Dynamics, and the Evolution of a
Species’ Range. Bulletin of Mathematical Biology 84 (2022): 1-52.
J.R. Miller, Invasion waves and pinning in the Kirkpatrick–Barton model of evolutionary range
dynamics. Journal of Mathematical Biology (2019)
H. Zeng and J.R. Miller, Range limits in spatially explicit models of quantitative traits. Journal of
Mathematical Biology 68 (2014), 207–234.
J.R. Miller and H. Zeng, Multidimensional stability of planar traveling waves for an
integrodifference model. Discrete and Continuous Dynamical Systems B 18 (2013), 741–751.
J.R. Miller and H. Zeng, Stability of traveling waves for systems of nonlinear integral recursions
in spatial population biology. Discrete and Continuous Dynamical Systems B 16 (2011),
E. Andjel, J.R. Miller, and E. Pardoux, Survival of a single mutant in one dimension. Electronic
Journal of Probability 15 (2010), 386–408.
J.R. Miller, Survival of mutations arising during invasions. Evolutionary Applications 3 (2010),
J.R. Miller, B.P. Wood, and M.B. Hamilton, Fst and Qst under neutrality. Genetics 180 (2008),
S. Rottenstreich, J.R., Miller, and M.B. Hamilton, Dynamics of Fst for the island model,
Theoretical Population Biology 72 (2007), 485-503.
S. Rottenstreich, J.R. Miller, and M.B. Hamilton, Steady State of Homozygosity and Gst for the
Island Model, Theoretical Population Biology 72 (2007), 231-244.
B.P. Wood and J.R. Miller, Linked selected and neutral loci in heterogeneous environments,
Journal of Mathematical Biology 53 (2006), 939–975.
J.R. Miller and M. O’Leary, A diffusion model in population genetics with dynamic fitness,
Journal of Differential Equations 225 (2006), 465-512.
J.R. Miller, M.C. Pugh and M.B. Hamilton, A finite locus effect diffusion model for the evolution
of a quantitative trait, Journal of Mathematical Biology 52 (2006), 761-787
J.R. Miller and D. Hawthorne, Durability of marker-quantitative trait loci haplotypes in
structured populations, Genetics 171 (2005), 1353-1364.
H. Fan, S. Jin and J.R. Miller, Wave patterns, stability and slow motions in inviscid and viscous
hyperbolic equations with stiff reaction terms, Journal of Differential Equations 189 (2003), 267-
M.B. Hamilton and J.R. Miller, Comparing relative rates of pollen and seed gene flow in the
island model using nuclear and organelle measures of population structure, Genetics 162
(2002), 1897-1909.
A. Iosevich and J.R. Miller, Dispersive effects in a modified Kuramoto-Sivashinsky equation,
Communications in Partial Differential Equations, 27 (2002), pp 2423-2448.
J.R. Miller, M. O’Leary and M. Schonbek, Nonexistence of singular pseudo-self-similar
solutions to the Navier-Stokes system. Mathematische Annalen 319 (2001), pp 809-815.
J. Goodman and J.R. Miller, Long-time Behavior of Scalar Viscous Shock Fronts
in Two Dimensions. Journal of Dynamics and Differential Equations, 11 (1999), no.2, 255-277.
J.R. Miller, Spectral Properties and Time Decay for an Airy Operator with Potential.
Journal of Differential Equations 141 (1997), 102-121.
J.R. Miller and M.I. Weinstein, Asymptotic stability of solitary waves for the Regularized Long
Wave equation. Communications on Pure and Applied Mathematics 49 (1996), 399-441.
Refereed proceedings:
J.R. Miller, Stability properties of solitary waves in a complex modified KdV System.
Mathematics and Computers in Simulation 55 (2001), 557-565.
J.R. Miller, The dispersive regime in a modified Kuramoto-Sivashinsky system, in: Proceedings
of the Fifth International Conference on Mathematical and Numerical Aspects of Wave
Propagation, Santiago de Compostela, Spain, July 10-14, 2000. Philadelphia: Society for
Industrial and Applied Mathematics, 2000, pp. 350-353.