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Parvinen K.,University of Turku | Seppanen A.,University of Turku | Nagy J.D.,Scottsdale Community College | Nagy J.D.,Arizona State University
Bulletin of Mathematical Biology | Year: 2012

The question of how dispersal behavior is adaptive and how it responds to changes in selection pressure is more relevant than ever, as anthropogenic habitat alteration and climate change accelerate around the world. In metapopulation models where local populations are large, and thus local population size is measured in densities, density-dependent dispersal is expected to evolve to a single-threshold strategy, in which individuals stay in patches with local population density smaller than a threshold value and move immediately away from patches with local population density larger than the threshold. Fragmentation tends to convert continuous populations into metapopulations and also to decrease local population sizes. Therefore we analyze a metapopulation model, where each patch can support only a relatively small local population and thus experience demographic stochasticity. We investigated the evolution of density-dependent dispersal, emigration and immigration, in two scenarios: adult and natal dispersal. We show that density-dependent emigration can also evolve to a nonmonotone, "triple-threshold" strategy. This interesting phenomenon results from an interplay between the direct and indirect benefits of dispersal and the costs of dispersal. We also found that, compared to juveniles, dispersing adults may benefit more from density-dependent vs. density-independent dispersal strategies. © 2012 Society for Mathematical Biology.


Van Zwieten D.A.J.,TU Eindhoven | Rooda J.E.,TU Eindhoven | Armbruster D.,TU Eindhoven | Armbruster D.,Arizona State University | Nagy J.D.,Scottsdale Community College
European Physical Journal B | Year: 2011

We extend discrete event models (DEM) of substrate-enzyme reactions to include regulatory feedback and reversible reactions. Steady state as well as transient systems are modeled and validated against ordinary differential equation (ODE) models. The approach is exemplified in a model of the first steps of glycolysis with the most common regulatory mechanisms. We find that in glycolysis, feedback and reversibility together act as a significant damper on the stochastic variations of the intermediate products as well as for the stochastic variation of the transit times. This suggests that these feedbacks have evolved to control both the overall rate of, as well as stochastic fluctuations in, glycolysis. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.


Nagy J.D.,Scottsdale Community College | Armbruster D.,Arizona State University
Mathematical Biosciences and Engineering | Year: 2012

The major goal of evolutionary oncology is to explain how malignant traits evolve to become cancer "hallmarks." One such hallmark - the angiogenic switch - is difficult to explain for the same reason altruism is difficult to explain. An angiogenic clone is vulnerable to "cheater" lineages that shunt energy from angiogenesis to proliferation, allowing the cheater to outcompete cooperative phenotypes in the environment built by the cooperators. Here we show that cell- or clone-level selection is sufficient to explain the angiogenic switch, but not because of direct selection on angiogenesis factor secretion - angiogenic potential evolves only as a pleiotropic afterthought. We study a multiscale mathematical model that includes an energy management system in an evolving angiogenic tumor. The energy management model makes the counterintuitive prediction that ATP concentration in resting cells increases with increasing ATP hydrolysis, as seen in other theoretical and empirical studies. As a result, increasing ATP hydrolysis for angiogenesis can increase proliferative potential, which is the trait directly under selection. Intriguingly, this energy dynamic allows an evolutionary stable angiogenesis strategy, but this strategy is an evolutionary repeller, leading to runaway selection for extreme vascular hypo-or hyperplasia. The former case yields a tumor-on-a-tumor, or hypertumor, as predicted in other studies, and the latter case may explain vascular hyperplasia evident in certain tumor types.


Smith A.T.,Arizona State University | Nagy J.D.,Scottsdale Community College | Nagy J.D.,Arizona State University
Journal of Mammalogy | Year: 2015

Population resilience in a metapopulation of American pikas (Ochotona princeps) at Bodie, California, was investigated with a series of 18 detailed occupancy surveys conducted between 1989 and 2010. These were compared with earlier 1972 and 1977 censuses and earlier historical records of pikas at Bodie. There is concern that American pikas may be increasingly vulnerable to warm temperatures due to climate change, and this investigation represents the longest study of the species in a relatively low-elevation (warm) environment. The Bodie pika population represents one of the best mammalian examples of a classic metapopulation system. Annual number of observed patch extinctions (total = 114) and recolonizations (109) varied greatly among the 18 census intervals. There has been no decline in percent of patches occupied in the northern half of the study area since 1972, and the number of documented pikas in the north in recent surveys exceeded the numbers found in 1972 and 1977. In contrast, the southern half of the metapopulation collapsed during our study, apparently the result of stochasticity of metapopulation dynamics; no southern patches were occupied after 2006. The potential impact of temperature on metapopulation dynamics was examined using long-term chronic (average summer monthly maximum) and acute threshold (number of days ≥ 25°C and ≥ 28°C within a year) temperatures. There is no evidence that warming temperatures have directly and negatively affected pika persistence at Bodie. Neither warm chronic nor acute temperatures increased the frequency of extinctions of populations on patches, and relatively cooler chronic or acute temperatures did not lead to an increase in the frequency of recolonization events. Warm temperatures, however, could have impeded the dispersal of colonists moving from north to south, thus contributing to the failure of the southern region to become repopulated. © 2015 American Society of Mammalogists, .


Hews S.,Arizona State University | Eikenberry S.,Arizona State University | Nagy J.D.,Scottsdale Community College | Kuang Y.,Arizona State University
Journal of Mathematical Biology | Year: 2010

Chronic hepatitis B virus (HBV) infection is a major cause of human suffering, and a number of mathematical models have examined within-host dynamics of the disease. Most previous HBV infection models have assumed that: (a) hepatocytes regenerate at a constant rate from a source outside the liver; and/or (b) the infection takes place via a mass action process. Assumption (a) contradicts experimental data showing that healthy hepatocytes proliferate at a rate that depends on current liver size relative to some equilibrium mass, while assumption (b) produces a problematic basic reproduction number. Here we replace the constant infusion of healthy hepatocytes with a logistic growth term and the mass action infection term by a standard incidence function; these modifications enrich the dynamics of a well-studied model of HBV pathogenesis. In particular, in addition to disease free and endemic steady states, the system also allows a stable periodic orbit and a steady state at the origin. Since the system is not differentiable at the origin, we use a ratio-dependent transformation to show that there is a region in parameter space where the origin is globally stable. When the basic reproduction number, R0, is less than 1, the disease free steady state is stable. When R0 > 1 the system can either converge to the chronic steady state, experience sustained oscillations, or approach the origin. We characterize parameter regions for all three situations, identify a Hopf and a homoclinic bifurcation point, and show how they depend on the basic reproduction number and the intrinsic growth rate of hepatocytes. © 2009 Springer-Verlag.

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