# Carbon–phosphorus exchange rate constrains density–speed trade-off in arbuscular mycorrhizal fungal growth

## TL;DR

This study shows how carbon and phosphorus exchange rates influence the growth strategies of arbuscular mycorrhizal fungi, affecting their ability to explore or exploit resources.

## Contribution

A novel method using robotic imaging and machine learning to quantify carbon and phosphorus fluxes in arbuscular mycorrhizal symbiosis.

## Key findings

- Carbon and phosphorus transfer rates are proportionally related across AM fungal strains.
- Fungal growth strategies are constrained by a Pareto front favoring exploration or exploitation.
- Changing plant host genotype alters the carbon-phosphorus exchange rate and fungal growth outcomes.

## Abstract

The exchange of phosphorus and carbon between arbuscular mycorrhizal fungi and plants is fundamental to both global ecosystem productivity and the regulation of the Earth’s climate. In this paper, we analyzed hundreds of timelapses of fungal network growth using an automated pipeline. This allowed us to simultaneously track the time course of resource exchange during symbiotic growth. This approach provides a basis for understanding and predicting the context dependence of nutrient exchange, as well as the control mechanisms governing a symbiosis evolved over 400 My.

Symbiotic nutrient exchange between arbuscular mycorrhizal (AM) fungi and their host plants varies widely depending on their physical, chemical, and biological environment. Yet dissecting this context dependency remains challenging because we lack methods for tracking nutrients such as carbon (C) and phosphorus (P). Here, we developed an approach to quantitatively estimate C and P fluxes in the AM symbiosis from comprehensive network morphology quantification, achieved by robotic imaging and machine learning based on roughly 100 million hyphal shape measurements. We found that rates of C transfer from the plant and P transfer from the fungus were, on average, related proportionally to one another. This ratio was nearly invariant across AM fungal strains despite contrasting growth phenotypes but was strongly affected by plant host genotype. Fungal phenotype distributions were bounded by a Pareto front with a shape favoring specialization in an exploration–exploitation trade-off. This means AM fungi can be fast range expanders or fast resource extractors, but not both. Manipulating the C/P exchange rate by swapping the plant host genotype shifted this Pareto front, indicating that the exchange rate constrains possible AM fungal growth strategies. We show by mathematical modeling how AM fungal growth at fixed exchange rate leads to qualitatively different symbiotic outcomes depending on fungal traits and nutrient availability.