“Give me an example of how your training in mathematics led you in a new or surprising direction as a biologist,” said Mike. (As part of my preparation for job interviews, Mike has been inserting questions and prompts like these into our conversations at random. He takes his advising role very seriously!)

“Well, once upon a time in a far off land where the ocean is too cold to swim in,” I began (it was late September on Cape Cod, and the water was still luxuriously warm), “I was thinking a lot about how trees invest in their fungal partners.”

I was in my first year of Ph.D. work at Stanford when inspiration struck. My thesis was starting to take shape: I’d be studying the processes that maintained diversity in ectomycorrhizal fungi, the belowground partners that help trees gather nutrients and water from the soil. The host trees obviously play a major role: it’s their “payments” (in terms of carbon food) that support those fungi. How much the trees invested, in whom, and when, were — and largely remain — open and important questions.

Just a year before, I’d been working with Mike on a masters thesis that used a branch of mathematics called “optimal control theory.” This is the kind of math we turn to when we want to answer questions like, “How should I invest my fixed amount of money to control the spread of a disease?” (We’d been using it to ask “How should I distribute my fishing fleet to catch the most fish?”)

With partial differential equations and Hamiltonians and greek letters dancing in my head, I thought: “Why can’t we use the same tools to understand tree investments?” Basically, we just need to adopt the tree’s perspective to ask the question, “How should I pay my fungal partners so that I wind up having grown the most at the end of the day?” Taking a traditionally bioeconomic tool, and applying it to a purely biological system, made perfect sense to me — but was also a new approach.

And so, the idea for a new paper, out this month in The American Naturalist, was born.

The road from inspiration, in 2011, to publication, in 2016, has been long, inventive, and exciting. The paper we published is not really the one I intended to write. Instead, it describes an unexpected finding — which makes me very happy, because, like my coauthor Mike Neubert, I believe that mathematical models are most  valuable when they surprise us. We’ve also had a lot of support along the way — from interested colleagues to my thesis committee members to the journal’s very enthusiastic editorial staff.

And, five years later, I have to say: I’m really proud of this one.

The official press release is online here; since we wrote it, I’ve also included it below.

Sometimes, even low-quality partners are worth maintaining

A fruiting body of the ectomycorrhizal fungus Amanita muscaria pokes through a carpet of pine needles shed by its mutualistic partners. A. muscaria coexists on tree root systems with dozens of other ectomycorrhizal fungal species. Photographed in Cora Lynn, New Zealand, by H. V. Moeller (January 2012).

A major challenge of ecology is explaining species diversity in natural communities. For example, why do some species interactions—like the mutualistic relationship between plants and the below-ground fungi that help them gather nutrients from the soil—involve dozens of partners, especially when some of those partners don’t pull their weight in the relationship? Although such ‘low-quality’ partners die quicker, grow more slowly, and/or move nutrients less efficiently, they still remain part of the mutualistic community

In a recent paper, mathematical ecologists Holly Moeller and Michael Neubert of the Woods Hole Oceanographic Institution present a new explanation for the persistence of low-quality community members: They may be actively maintained by their partners as part of an “optimum” investment strategy designed to maximize their partner’s growth.

Using a mathematical model of the exchange of carbon and nutrients by trees and fungi, Moeller and Neubert show that a tree’s investment in its fungal partners depends on environmental conditions. In their model, trees invest only in high-quality fungal partners when the environment is constant, but, when the environment is variable (e.g., if nutrient supply fluctuates over time), trees may also nurture low-quality partners to meet their nutrient demand. Because long-lived organisms like trees and fungi are almost certain to experience environmental variation during their lifetimes, such active partner investment may be an important mechanism that maintains species diversity.

Find our article, at last “officially” published online, on the journal’s website. I’ve also posted a PDF here.