rescomp: An R package for defining, simulating and visualizing ODE models of consumer-resource interactions

Mechanistic models of resource competition underpin numerous foundational concepts and theories in ecology, and continue to be employed widely to address diverse research questions. Nevertheless, current software tools present a comparatively steep barrier to entry. I introduce the R package rescomp to support the specification, simulation and visualisaton of a broad spectrum of consumer-resource interactions. rescomp is compatible with diverse model specifications, including an unlimited number of consumers and resources, different consumer functional responses (type I, II and III), different resource types (essential or substitutable) and supply dynamics (chemostats, logistic and/or pulsed), delayed consumer introductions, time dependent growth and consumption parameters, and instantaneous changes to consumer and/or resource densities. Several examples on implementing rescomp are provided. In addition, a wide variety of additional examples can be found in the package vignettes, including using rescomp to reproduce the results of several well known studies from the literature. rescomp provides users with an accessible tool to reproduce classic models in ecology, to specify models resembling a wide range of experimental designs, and to explore diverse novel model formulations.

Local Interactions Affect Spread of Resource in a Consumer-resource System With Group Defense

Integrodifference equations are a discrete time spatially explicit model that describes dispersal of ecological populations through space. This framework is useful to study spread dynamics of organisms and how ecological interactions can affect their spread. When studying interactions such as consumption, dispersal rates might vary with life cycle stage, such as cases with dispersive juveniles and sessile adults. In the non-dispersive stage, resources may engage in group defense to protect themselves from consumption. These local nondispersive interactions may limit the number of dispersing recruits that are produced and therefore affect how fast populations can spread. We present a spatial consumer-resource system using an integrodifference framework with limited movement of their adult stages and group defense mechanisms in the resource population. We model group defense using a Type IV Holling functional response, which limits survival of adult resource population and enhances juvenile consumers production. We find that high mortality levels for sessile adults can destabilize resource at carrying capacity. Furthermore, we find that at high resource densities, group defense leads to a slower local growth of resource in newly invaded regions due to intraspecific competition outweighing the effect of consumption on resource growth.

Mathematical analysis of a fractional resource-consumer model with disease developed in consumer

The research presents a qualitative investigation of a fractional-order consumer-resource system with the hunting cooperation interaction functional and an infection developed in the resources population. The existence of the equilibria is discussed where there are many scenarios that have been distinguished as the extinction of both populations, the extinction of the infection, the persistence of the infection, and the two populations. The influence of the hunting cooperation interaction functional is also investigated where it can influence the existence of equilibria and their stability. A proper numerical scheme is used for building a proper graphical representation for the goal of confirming the theoretical results.

Computational Study on the Dynamics of a Consumer-Resource Model: The Influence of the Growth Law in the Resource

The dynamics of a specific consumer-resource model for Daphnia magna is studied from a numerical point of view. In this study, Malthusian, chemostatic, and Gompertz growth laws for the evolution of the resource population are considered, and the resulting global dynamics of the model are compared as different parameters involved in the model change. In the case of Gompertz growth law, a new complex dynamic is found as the carrying capacity for the resource population increases. The numerical study is carried out with a second-order scheme that approximates the size-dependent density function for individuals in the consumer population. The numerical method is well adapted to the situation in which the growth rate for the consumer individuals is allowed to change the sign and, therefore, individuals in the consumer population can shrink in size as time evolves. The numerical simulations confirm that the shortage of the resource has, as a biological consequence, the effective shrink in size of individuals of the consumer population. Moreover, the choice of the growth law for the resource population can be selected by how the dynamics of the populations match with the qualitative behaviour of the data.

Intraspecific variation stabilizes classic predator-prey dynamics

In 1920, Alfred J. Lotka found that, to his "considerable surprise", the dynamics of a simple predator-prey model he had devised led "to undamped, and hence indefinitely continued, oscillations"---which he thought epitomized the "rhythm of Nature" dear to the Victorians. In 1926, the same model was proposed independently by mathematician Vito Volterra, who was inspired by the work of his son-in-law, fish biologist Umberto D'Ancona. For over a century, the equations that now bear their names have served as a template for the development of sophisticated models for population dynamics. Coexistence in this classic predator-prey model is fragile---stochasticity or temporal variability in parameter values result in extinctions. The dynamics can be stabilized by intraspecific competition or other forms of self-regulation, but the prevalence of these processes in large food webs has been questioned. Here we show that when we consider populations characterized by intraspecific variability, dynamics are stable---despite the absence of any direct self-regulation. Our results can be generalized further, defining a new class of consumer-resource models. By accounting for intraspecific variation, which is manifest in all biological populations, we obtain dynamics that differ qualitatively and quantitatively from those found for homogeneous populations---challenging a central assumption of many ecological models.

Environmental fluctuations reshape an unexpected diversity-disturbance relationship in a microbial community

Environmental disturbances have long been theorized to play a significant role in shaping the diversity and composition of ecosystems. However, an inability to specify the characteristics of a disturbance experimentally has produced an inconsistent picture of diversity-disturbance relationships (DDRs). Here, using a high-throughput programmable culture system, we subjected a soil-derived bacterial community to dilution disturbance profiles with different intensities (mean dilution rates), applied either constantly or with fluctuations of different frequencies. We observed an unexpected U-shaped relationship between community diversity and disturbance intensity in the absence of fluctuations. Adding fluctuations increased community diversity and erased the U-shape. All our results are well-captured by a Monod consumer resource model, which also explains how U-shaped DDRs emerge via a novel 'niche flip' mechanism. Broadly, our combined experimental and modeling framework demonstrates how distinct features of an environmental disturbance can interact in complex ways to govern ecosystem assembly and offers strategies for reshaping the composition of microbiomes.

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.