Coexistence and displacement in consumer-resource systems with local and shared resources

Estrogen as an Essential Resource and the Coexistence of ER+ and ER– Cancer Cells

Diagnosis of estrogen sensitivity in breast cancer is largely predicated on the ratio of ER+ and ER– cancer cells obtained from biopsies. Estrogen is a growth factor necessary for cell survival and division. It can also be thought of as an essential resource that can act in association with other nutrients, glucose, glutamine, fatty acids, amino acids, etc. All of these nutrients, collectively or individually, may limit the growth of the cancer cells (Liebig’s Law of the Minimum). Here we model estrogen susceptibility in breast cancer as a consumer-resource interaction: ER+ cells require both estrogen and glucose as essential resources, whereas ER– only require the general resource. The model predicts that when estrogen is the limiting factor, other nutrients may go unconsumed and available at higher levels, thus permitting the invasion of ER– cells. Conversely, when ER– cells are less efficient on glucose than ER+ cells, then ER– cells limited by glucose may be susceptible to invasion by ER+ cells, provided that sufficient levels of estrogen are available. ER+ cells will outcompete ER– cells when estrogen is abundant, resulting in low concentrations of interstitial glucose within the tumor. In the absence of estrogen, ER– cells will outcompete ER+ cells, leaving a higher concentration of interstitial glucose. At intermediate delivery rates of estrogen and glucose, ER+ and ER– cells are predicted to coexist. In modeling the dynamics of cells in the same tumor with different resource requirements, we can apply concepts and terms familiar to many ecologists. These include: resource supply points, R∗, ZNGI (zero net growth isoclines), resource depletion, and resource uptake rates. Based on the circumstances favoring ER+ vs. ER– breast cancer, we use the model to explore the consequences of therapeutic regimens that may include hormonal therapies, possible roles of diet in changing cancer cell composition, and potential for evolutionarily informed therapies. More generally, the model invites the viewpoint that cancer’s eco-evolutionary dynamics are a consumer-resource interaction, and that other growth factors such as EGFR or androgens may be best viewed as essential resources within these dynamics.

Dynamic environment-induced multistability and critical transition in a metacommunity ecosystem

We study a metacommunity model of consumer-resource populations coupled via dispersal under an environment-dependent framework, and we explore the occurrence of multistability and critical transition. By emphasizing two magnitudes acting on a dynamic environment at temporal and spatial scales, the coupled system with simple diffusive coupling and the nonlinear environmental coupling enables various interesting complex dynamics such as bistability, multistability, and critical transitions. Using the basin stability measure, we find the probability of attaining each alternative state in a multistable region. In addition, critical transitions (one from a high to a low species density and the other from a low to a high species density) are identified at different magnitudes in the presence of stochastic fluctuations. We also explore the robustness of critical slowing-down indicators, e.g., lag-1 autocorrelation and variance, to forewarn the critical transition in the metacommunity model. Further, a network structure also identifies synchronization and multiclustering for a different choice of initial conditions. In contrast with the earlier studies on dynamic environmental coupling, our results based on the defined magnitudes provide important insights into environmental heterogeneity, which determines the set of environmental conditions to predict metacommunity stability and persistence.