Derivations of the Core Functions of the Maximum Entropy Theory of Ecology

The Maximum Entropy Theory of Ecology (METE), is a theoretical framework of macroecology that makes a variety of realistic ecological predictions about how species richness, abundance of species, metabolic rate distributions, and spatial aggregation of species interrelate in a given region. In the METE framework, "ecological state variables" (representing total area, total species richness, total abundance, and total metabolic energy) describe macroecological properties of an ecosystem. METE incorporates these state variables into constraints on underlying probability distributions. The method of Lagrange multipliers and maximization of information entropy (MaxEnt) lead to predicted functional forms of distributions of interest. We demonstrate how information entropy is maximized for the general case of a distribution, which has empirical information that provides constraints on the overall predictions. We then show how METE's two core functions are derived. These functions, called the "Spatial Structure Function" and the "Ecosystem Structure Function" are the core pieces of the theory, from which all the predictions of METE follow (including the Species Area Relationship, the Species Abundance Distribution, and various metabolic distributions). Primarily, we consider the discrete distributions predicted by METE. We also explore the parameter space defined by the METE's state variables and Lagrange multipliers. We aim to provide a comprehensive resource for ecologists who want to understand the derivations and assumptions of the basic mathematical structure of METE.USDA; Bridging Biodiversity and Conservation Science programOpen access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Impacts of climate change on plant diseases – opinions and trends

There has been a remarkable scientific output on the topic of how climate change is likely to affect plant diseases in the coming decades. This review addresses the need for review of this burgeoning literature by summarizing opinions of previous reviews and trends in recent studies on the impacts of climate change on plant health. Sudden Oak Death is used as an introductory case study: Californian forests could become even more susceptible to this emerging plant disease, if spring precipitations will be accompanied by warmer temperatures, although climate shifts may also affect the current synchronicity between host cambium activity and pathogen colonization rate. A summary of observed and predicted climate changes, as well as of direct effects of climate change on pathosystems, is provided. Prediction and management of climate change effects on plant health are complicated by indirect effects and the interactions with global change drivers. Uncertainty in models of plant disease development under climate change calls for a diversity of management strategies, from more participatory approaches to interdisciplinary science. Involvement of stakeholders and scientists from outside plant pathology shows the importance of trade-offs, for example in the land-sharing vs. sparing debate. Further research is needed on climate change and plant health in mountain, boreal, Mediterranean and tropical regions, with multiple climate change factors and scenarios (including our responses to it, e.g. the assisted migration of plants), in relation to endophytes, viruses and mycorrhiza, using long-term and large-scale datasets and considering various plant disease control methods

Asymmetric Branching in Biological Resource Distribution Networks

There is a remarkable relationship between an organism's metabolic rate (resting power consumption) and the organism's mass. It may be a universal law of nature that an organism's resting metabolic rate is proportional to its mass to the power of 3/4. This relationship, known as Kleiber's Law, appears to be valid for both plants and animals. This law is important because it implies that larger organisms are more efficient than smaller organisms, and knowledge regarding metabolic rates are essential to a multitude of other fields in ecology and biology. This includes modeling the interactions of many species across multiple trophic levels, distributions of species abundances across large spatial landscapes, and even medical diagnostics for respiratory and cardiovascular pathologies. Previous models of vascular networks that seek to identify the origin of metabolic scaling have all been based on the unrealistic assumption of perfectly symmetric branching. In this dissertation I will present a theory of asymmetric branching in self-similar vascular networks (published by Brummer et al. in [9]). The theory shows that there can exist a suite of vascular forms that result in the often observed 3/4 metabolic scaling exponent of Kleiber's Law. Furthermore, the theory makes predictions regarding major morphological features related to vascular branching patterns and their relationships to metabolic scaling. These predictions are suggestive of evolutionary convergence in vascular branching. To test these predictions, I will present an analysis of real mammalian and plant vascular data that shows: (i) broad patterns in vascular networks across entire animal kingdoms and (ii) within these patterns, plant and mammalian vascular networks can be uniquely distinguished from one another (publication in preparation by Brummer et al.). I will also present results from a computational study in support of point (i). Namely, that asymmetric branching may be the optimal strategy to balance the simultaneous demands of maximizing the number of nutrient exchange sites (capillaries or leaves) versus hydraulic resistance to resource transport (publication in preparation by Brummer et al.). Finally, I report on improved methods of estimating whole organism metabolism based solely on measurements of vasculature

How axon and dendrite branching are guided by time, energy, and spatial constraints

Abstract Neurons are connected by complex branching processes—axons and dendrites—that process information for organisms to respond to their environment. Classifying neurons according to differences in structure or function is a fundamental part of neuroscience. Here, by constructing biophysical theory and testing against empirical measures of branching structure, we develop a general model that establishes a correspondence between neuron structure and function as mediated by principles such as time or power minimization for information processing as well as spatial constraints for forming connections. We test our predictions for radius scale factors against those extracted from neuronal images, measured for species that range from insects to whales, including data from light and electron microscopy studies. Notably, our findings reveal that the branching of axons and peripheral nervous system neurons is mainly determined by time minimization, while dendritic branching is determined by power minimization. Our model also predicts a quarter-power scaling relationship between conduction time delay and body size

Dose-dependent thresholds of dexamethasone destabilize CAR T-cell treatment efficacy

Chimeric antigen receptor (CAR) T-cell therapy is potentially an effective targeted immunotherapy for glioblastoma, yet there is presently little known about the efficacy of CAR T-cell treatment when combined with the widely used anti-inflammatory and immunosuppressant glucocorticoid, dexamethasone. Here we present a mathematical model-based analysis of three patient-derived glioblastoma cell lines treated in vitro with CAR T-cells and dexamethasone. Advanced in vitro experimental cell killing assay technologies allow for highly resolved temporal dynamics of tumor cells treated with CAR T-cells and dexamethasone, making this a valuable model system for studying the rich dynamics of nonlinear biological processes with translational applications. We model the system as a nonautonomous, two-species predator-prey interaction of tumor cells and CAR T-cells, with explicit time-dependence in the clearance rate of dexamethasone. Using time as a bifurcation parameter, we show that (1) dexamethasone destabilizes coexistence equilibria between CAR T-cells and tumor cells in a dose-dependent manner and (2) as dexamethasone is cleared from the system, a stable coexistence equilibrium returns in the form of a Hopf bifurcation. With the model fit to experimental data, we demonstrate that high concentrations of dexamethasone antagonizes CAR T-cell efficacy by exhausting, or reducing the activity of CAR T-cells, and by promoting tumor cell growth. Finally, we identify a critical threshold in the ratio of CAR T-cell death to CAR T-cell proliferation rates that predicts eventual treatment success or failure that may be used to guide the dose and timing of CAR T-cell therapy in the presence of dexamethasone in patients

Data driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables

In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics