Global dynamics of a discrete two-population model for flour beetle growth.

The cannibalistic behavior of has been extensively researched, revealing instances of chaotic dynamics in laboratory environments for . The well-established Larvae-Pupae-Adult (LPA) model has been instrumental in understanding the conditions that lead to chaos in flour beetles (genus: ). In response to new experimental observations showing a decline in the pupae population in , we proposed and analyzed a simplified two-stage Larvae-Adult (LA) model.

Prostate-specific antigen dynamics predict individual responses to intermittent androgen deprivation.

Intermittent androgen deprivation therapy (IADT) is an attractive treatment for biochemically recurrent prostate cancer (PCa), whereby cycling treatment on and off can reduce cumulative dose and limit toxicities. We simulate prostate-specific antigen (PSA) dynamics, with enrichment of PCa stem-like cell (PCaSC) during treatment as a plausible mechanism of resistance evolution. Simulated PCaSC proliferation patterns correlate with longitudinal serum PSA measurements in 70 PCa patients.

Modeling the population dynamics of lemon sharks.

Background: Long-lived marine megavertebrates (e.g. sharks, turtles, mammals, and seabirds) are inherently vulnerable to anthropogenic mortality.

Mechanisms of resistance to intermittent androgen deprivation in patients with prostate cancer identified by a novel computational method.

For progressive prostate cancer, intermittent androgen deprivation (IAD) is one of the most common and effective treatments. Although this treatment is usually initially effective at regressing tumors, most patients eventually develop castration-resistant prostate cancer (CRPC), for which there is no effective treatment and is generally fatal. Although several biologic mechanisms leading to CRPC development and their relative frequencies have been identified, it is difficult to determine which mechanisms of resistance are developing in a given patient.

Evolution of uncontrolled proliferation and the angiogenic switch in cancer.

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.

Evolution of complex density-dependent dispersal strategies.

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.

The evolutionary impact of androgen levels on prostate cancer in a multi-scale mathematical model.

Background: Androgens bind to the androgen receptor (AR) in prostate cells and are essential survival factors for healthy prostate epithelium. Most untreated prostate cancers retain some dependence upon the AR and respond, at least transiently, to androgen ablation therapy. However, the relationship between endogenous androgen levels and cancer etiology is unclear.

The roles of predator maturation delay and functional response in determining the periodicity of predator-prey cycles.

Population cycles in small mammals have attracted the attention of several generations of theoretical and experimental biologists and continue to generate controversy. Top-down and bottom-up trophic regulations are two recent competing hypotheses. The principal purpose of this paper is to explore the relative contributions of a variety of ecological factors to predator-prey population cycles.

Rich dynamics of a hepatitis B viral infection model with logistic hepatocyte growth.

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.

The dynamics of a delay model of hepatitis B virus infection with logistic hepatocyte growth.

Chronic HBV affects 350 million people and can lead to death through cirrhosis-induced liver failure or hepatocellular carcinoma. We analyze the dynamics of a model considering logistic hepatocyte growth and a standard incidence function governing viral infection. This model also considers an explicit time delay in virus production.

Dynamic simulations of single-molecule enzyme networks.

Along with the growth of technologies allowing accurate visualization of biochemical reactions to the scale of individual molecules has arisen an appreciation of the role of statistical fluctuations in intracellular biochemistry. The stochastic nature of metabolism can no longer be ignored. It can be probed empirically, and theoretical studies have established its importance.

Dynamics of a delay differential equation model of hepatitis B virus infection.

We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production.

Biological stoichiometry in human cancer.

Background: A growing tumor in the body can be considered a complex ecological and evolutionary system. A new eco-evolutionary hypothesis (the "Growth Rate Hypothesis", GRH) proposes that tumors have elevated phosphorus (P) demands due to increased allocation to P-rich nucleic acids, especially ribosomal RNA, to meet the protein synthesis demands of accelerated proliferation.

Methodology/principal Findings: We determined the elemental (C, N, P) and nucleic acid contents of paired malignant and normal tissues from colon, lung, liver, or kidney for 121 patients.

Why don't all whales have cancer? A novel hypothesis resolving Peto's paradox.

Larger organisms have more potentially carcinogenic cells, tend to live longer and require more ontogenic cell divisions. Therefore, intuitively one might expect cancer incidence to scale with body size. Evidence from mammals, however, suggests that the cancer risk does not correlate with body size.

The ecology and evolutionary biology of cancer: a review of mathematical models of necrosis and tumor cell diversity.

Recent evidence elucidating the relationship between parenchyma cells and otherwise "healthy" cells in malignant neoplasms is forcing cancer biologists to expand beyond the genome-centered, "one-renegade-cell" theory of cancer. As it becomes more and more clear that malignant transformation is context dependent, the usefulness of an evolutionary ecology-based theory of malignant neoplasia becomes increasingly clear. This review attempts to synthesize various theoretical structures built by mathematical oncologists into potential explanations of necrosis and cellular diversity, including both total cell diversity within a tumor and cellular pleomorphism within the parenchyma.

Competition and natural selection in a mathematical model of cancer.

A malignant tumor is a dynamic amalgamation of various cell phenotypes, both cancerous (parenchyma) and healthy (stroma). These diverse cells compete over resources as well as cooperate to maintain tumor viability. Therefore, tumors are both an ecological community and an integrated tissue.