A new study presents a mathematical model explaining why trees can support grass growth in dry environments but suppress it as rainfall increases. By separating the effects of canopy shade and tree roots, the researchers show when interactions shift from facilitation to competition, offering practical insights for afforestation, ecosystem restoration and land management.

Trees are often seen as an uncomplicated environmental good, offering shade, storing carbon and helping restore degraded landscapes. But when it comes to the grasses and other plants growing beneath them, their impact can vary dramatically depending on local conditions.

A new study published in the journal Proceedings of the National Academy of Sciences (PNAS), by Hebrew University of Jerusalem researchers Oded Hollander, Dr. Yair Mau and Dr. Niv DeMalach offers a mathematical explanation for a long-standing ecological puzzle: Why do trees and shrubs often help neighboring plants in dry environments, yet compete with and suppress them in wetter ones?

Ecologists have observed this shift for decades. In areas with little rainfall, grasses growing beneath trees may perform better than those exposed to direct sunlight. As rainfall increases, however, the relationship can reverse, with trees reducing the productivity of the vegetation below them. Until now, researchers lacked a quantitative model capable of explaining when and why the same tree could move from helping nearby plants to harming them.

The researchers developed a model that separates the effects of trees into two main mechanisms: what happens above ground through the canopy, and what happens below ground through the roots.

A tree canopy reduces the amount of sunlight reaching the ground. This can harm plants by limiting photosynthesis, but it can also help them by lowering temperatures and reducing the amount of water lost through evaporation. Tree roots create a similar trade-off. They compete with grasses for water, but in some dry conditions they can also move water from deeper soil layers toward the surface through a process known as hydraulic lift.

According to the model, trees tend to help grasses when water is scarce because the moisture conserved or supplied by the trees can outweigh the cost of reduced sunlight and competition. When rainfall becomes plentiful and water is no longer the main factor limiting growth, these benefits become less important. The disadvantages of shade and competition then become dominant.

The transition is not inevitable, the researchers found. It generally occurs only when another factor, such as nutrients, begins to limit plant growth at higher rainfall levels, or when tree density itself rises as rainfall increases. This may help explain why some field studies identify a clear transition from cooperation to competition while others do not.

“Trees do not simply help plants in dry places and harm them in wet places,” the reserachers said. “Their impact depends on the balance between several opposing processes, including shade, water conservation, root uptake and the resources that ultimately limit plant growth. By placing these mechanisms within one quantitative framework, we can explain when the shift from facilitation to competition should occur, when it should not occur and why different field studies may reach different conclusions.”

The findings could have practical implications for large-scale afforestation, dryland restoration and grazing management. Drylands cover roughly 40% of the Earth’s land surface, and the grasses growing within them provide essential forage for livestock and wildlife.

The framework may also apply beyond trees. Because the canopy mechanism is based on reduced sunlight, the same principles could help predict how vegetation responds to shaded hillsides, buildings or solar panels. This is particularly relevant as agrivoltaic projects, which combine agriculture or grazing with solar-energy production, expand in dry regions.

The researchers say the model could help land managers move beyond the assumption that adding trees or shade will always improve an ecosystem. Instead, restoration and development plans may need to consider rainfall, tree density, soil conditions and the specific resources limiting plant growth.

As afforestation and solar infrastructure reshape landscapes worldwide, the new model provides a way to anticipate a deceptively simple but increasingly important question: Under which conditions will shade help plants grow, and when will it hold them back?