Research Papers in Mathematical Biology

G.Ledder, R. Rebarber, T. Pendleton, A.N. Laubmeier, J. Weisbrod (2021), A discrete/continuous time resource competition model and its implications, J. Biol. Dyn. 15:sup1, S168-S189, DOI: 10.1080/17513758.2020.1862927.

This paper examines a model in which two consumers compete for resources, with each of the consumers reproducing at discrete times while the resource reproduces continuously.

G.Ledder, S.E. Russo, E.B. Muller, A. Peace, R.M. Nisbet (2020), Local control of resource allocation is sufficient to model optimal dynamics in syntrophic systems: a model for root:shoot allocation in plants, Theor. Ecol. 13, 481–501. DOI: 10.1007/s12080-020-00464-9.

This paper develops a model of plant resource allocation between roots and shoots that is based on local control of resources, similar to what happens in obligate syntrophy. Local control produces results that are optimal in several senses.

V. Couvreur, G.Ledder, S. Manzoni, D.A. Way, E.B. Muller, S.E. Russo (2018), Water transport through tall trees: A vertically explicit, analytical model of xylem hydraulic conductance in stems, Plant, Cell, Environ. 41, 1821–1839. DOI: 10.1007/s12080-020-00464-9.

We offer an innovative model for stem hydraulics that allows many of the properties of stems to be functions of path length from the base of the tree.

G.Ledder, D. Sylvester, R.R. Bouchat, J.A. Thiel (2018), Continuous and pulsed epidemiological models for onchocerciasis with implications for eradication strategy, Math. Biosci. Eng. 15, 841-862. DOI: 10.3934/mbe.2018038.

We offer an innovative model for stem hydraulics that allows many of the properties of stems to be functions of path length from the base of the tree.

G.Ledder (2017), Scaling for Dynamical Systems in Biology, Bull. Math. Biol. 79, 2747-2772.

Asymptotic methods are ubiquitous in models for physical science, but not often used in biological science. This is unfortunate, as many biological models have features that lend themselves to asymptotic methods. The first step in asymptotic analysis is scaling, which is not easy in biology. In this paper, I present some of the basic principles I use in scaling, using my onchocerciasis model as an example.

G. Ledder (2014), The basic dynamic energy budget model and some implications, Letters Biomath., 1, 221-233, DOI: 10.1080/23737867.2014.11414482.

This paper presents a simple introduction to DEB models, using standard mathematical notation rather than the specialized system favored by most DEB practitioners, but somewhat unintelligible to the uninitiated.

J.D. Logan, G. Ledder, W. Wolesensky (2009), Type II functional response for continuous, physiologically structured models, J. Theo. Biol., 259, 373-381, DOI: 10.1007/s00285-003-0263-1.

This paper generalizes the Holling type II functional response model to more complicated settings.

G. Ledder (2007), Forest defoliation scenarios, Math. Biosci. Eng., 4, 15-28.

This paper represents the "final word" on the spruce budworm model created by Ludwig, Jones, and Holling and previously analyzed by Brauer and Castillo-Chavez. Using asymptotic analysis, I identify various types of long-term behavior and link them to regions of the parameter space.

G. Ledder, J.D. Logan, A. Joern (2004), Dynamic energy budget models with size-dependent hazard rates, J. Math. Biol., 48, 605-622, DOI: 10.1007/s00285-003-0263-1.

It is often assumed in DEB models that the death rate of organisms is simply a Poisson process; that is, that longevity is exponentially distributed. In this paper, we see that a consequence of this fact is that the optimal time for transitioning from growth to reproduction occurs when the population is still large; that is, it is optimal for a significant fraction of individuals to mature, but at a small size. This is not typical in nature, where most species have life histories in which a vanishingly small fraction of offspring survive to adulthood, where they have long careers in reproduction. The way to resolve this anomaly is to posit a hazard rate that is a sharply decreasing function of size rather than the constant implied by the exponential distribution.