Everyone has a gut microbiome, full of trillions of microbes, that influences our health. One person’s microbiome might give them a stomach ache, while another person’s might help them metabolize food more efficiently. I want to figure out how “medicine for the microbiome” works– how can a sick person’s microbiome be made “healthy”? Specifically, I am interested in how external interventions (e.g. fecal microbiota transplantation, probiotics, or a modified diet) influence microbiome composition.

To address this goal, in my research I develop ecological models of the microbiome that are characterized and guided by well-controlled fruit fly and mouse microbiome experiments. I approach the complexity of the microbiome in two ways: experimentally, I use a simple model organism with a core microbiome of only five species; and theoretically I develop mathematical methods for dimensionality reduction.

Community assembly in the fruit fly microbiome

In my experimental collaboration with Will Ludington (Department of Embryology, Carnegie Institution for Science), we have worked to construct simple models from first principles that describe the behavior of the fruit fly microbiome. The microbiome of the fruit fly Drosophila melanogaster naturally hosts only a few species of commensal bacteria. In our research we cultivate a core group of five commensal bacteria, and associate each possible combination of the five bacteria with a set of germ-free flies. Since the flies were otherwise identically reared, the flies associated with each of these 32 bacterial combinations carry a distinct microbiome-affiliated phenotype (e.g. lifespan or fecundity) that is a function of the complex interactions in the microbiome. However, we found that the complexity of these fly phenotypes was often reducible: we could approximate the phenotype of flies associated with more than one bacterial species by averaging the phenotypes of the flies with the corresponding single-species associations. Thus, we found that simple models can at least partially describe complex behaviors in the fly microbiome. In 2018 lead author Alison Gould published these findings in PNAS [link], this article was covered in the press by Sonia Fernandez in the UCSB Current [link], and this article was also adapted for the non-profit journal Science Journal for Kids [link], .

Dimensionality reduction of the generalized Lotka-Volterra equations

In my theoretical and computational research I use ecological models of the microbiome to probe how microbial communities will respond to bacteriotherapies like fecal microbiota transplantation (FMT), an as-yet unconventional therapy that might pioneer a new paradigm for treating microbiome diseases (Jones and Carlson, PLOS Comp Bio 2018 [link]).

To inform these control protocols, I designed analytic techniques for the simplification of high-dimensional generalized Lotka-Volterra (gLV) models exhibiting multistability (Jones and Carlson, Phys Rev E 2019 [link]). The key idea behind this method, called Steady-State Reduction (SSR), is to first identify a pair of stable steady states that exhibit bistability in the high-dimensional system, and then to approximate these high-dimensional dynamics on the two-dimensional subspace spanned by the two steady states and the origin. This method provides the best possible two-dimensional gLV approximation in this subspace, and the reduced dynamics are analytically tractable. This method, which compresses complex dynamics into a two-dimensional subsystem, makes ecological landscapes intuitive and mathematically accessible.

I have written two publications with excellent undergraduates to further extend SSR. First, with Parker Shankin-Clarke I demonstrated how a system with multistability can be decomposed into many bistable subsystems to create an “attractor network” that compresses a high-dimensional dynamical landscape into a graph structure (Jones et al., AIMS Special Issue 2020 [arXiv link] [book link]). Second, with Zipeng Wang I developed a method to control gLV models by modifying the interactions between microbes, rather than altering the state of the system itself . This “indirect” control protocol reflects bacteriotherapies that are based on altering the environment of the microbiome, for example by modulating a person’s diet (Wang et al., Phys Rev E 2020 [link]). This last project was covered in the press by Sonia Fernandez at the UCSB Current [link].

Research theme: decomposition of multistable systems into networks of bistable subsystems

Aging-induced fragility in a mathematical model of the immune system

Finally, in a collaboration with Shenshen Wang (Department of Physics, UCLA) I have developed a mathematical model of the coupled innate-adaptive immune response to investigate the mechanisms that lead to immunosenescence in a host (Jones et al., Journal of Theoretical Biology 2021 [link]). We observe that the adaptive response plays an important role in “turning off” inflammation following pathogen clearance, which highlights the importance of collaboration between the two immune compartments.