Mycorrhizal Fungi Network: Dynamic Agent-Based Spatial Model

This is an academic project for the Computational Economics course at Davidson College with Dr. Professor Gouri-Suresh. This is a group project with Sena Hur, Ian Rolls, and Brooke Whitcomb written on 21st October 2021

  1. Introduction

Mycorrhizal fungi are known to sustain all terrestrial ecosystems by transferring vital resources through root networks (Watkinson 2015, Simard et. al 2012). However, it is still unclear how plants and fungi can organize themselves to pass resources where they are needed without a central nervous system. We use a dynamic, agent-based spatial model to understand how individual fungi and trees optimize nutrient levels in a forest despite having no executive function, and by doing so maximize tree growth. 

The symbiotic relationship between trees and fungi has evolved independently in different regions of the world and within the fungal kingdom. Universally, the plant supplies carbon and energy in the form of sugar to the fungus, and the fungus supplies nitrogen and other nutrients to the tree (Simard et.al 2012). Fungi are present in over 70% of land plant species and are most likely the dominant source of nitrogen for trees (Watkinson 2015). Because fungi play such a large and important role in all terrestrial plant systems, understanding the structure and function of the mycorrhizal network in ecosystems will deepen our understanding of ecological stability. 

The mycorrhizal fungi integrate with plant roots to form a network of nutrient exchange linking many different plant and fungi species when compatible (Watkinson 2015). Roots typically form relationships with mycorrhiza when nutrients are scarce. Fungi not only transfer nutrients between soil and root but also are known to translocate organic compounds between roots of adjacent plants (Watkinson 2015). Fungi even transfer excess carbon from healthier trees to less healthy trees because it promotes forest growth, which benefits the fungal network.

We model the exchange of resources in a forest to observe the effects on tree growth and nitrogen redistribution by fungi under different levels of naturally occurring nitrogen conditions. We predict that when nitrogen is limited, the fungus will play a larger role in distributing resources between neighboring trees. We also hypothesize that higher nitrogen levels will lead to greater tree growth over the course of a number of generations. 

  1. Description

We model a generic forest to observe the behavior between independently acting agents and record the effect on tree growth and exchange between fungus and trees under different nutrient conditions. We use a 100 x 100 grid island type lattice to represent the forest. Mycorrhizal networks are composed of a wide variety of plant and fungi species (Watkinson 2015). However, to simplify the interactions, we include only three elements: fungi, trees, and nitrogen. Every cell in the forest contains one tree and one fungal network. Nitrogen levels are randomly distributed across the lattice and capped at a certain level which we vary to test the effect on forest dynamics. 

We assume that each cell is 6-10ft apart, which is the generally optimal space between pine trees (Kansas Forest Service 2018). Each tree has the same, fixed requirement for nutrients that it needs in order to maintain biomass in a period. If it does not meet this requirement, it will shrink or its health will decline. This is realistic because under nutrient limitations tree branches are known to die and leaves to color early (Bartlett). 

During the simulation, we record tree growth as a function of the amount of nitrogen a tree has access to (Franklin et.al. 2014). If nutrients are abundant, the tree will grow in every period until reaching maximum growth. In our model, we chose an arbitrary maximum value of ten. We use a maximum value to ensure a tree won’t grow infinitely. To initialize the forest, we randomly assigned the health/size of the tree. Then if the available resources in the area around the tree (the surrounding Moore neighborhood) and the nitrogen produced by the fungi were not enough to support tree growth in the initial layout, we killed off the trees in the area with the least amount of naturally occurring resources by setting the size/growth of the tree to zero.

We restrict the scope of our model to the exchange of nitrogen from the fungi to the tree assuming that there is a reciprocal exchange of carbon from the tree to the fungus. Trees decide to trade resources depending on the number of resources already in the soil (Franklin et.al. 2014). In ecosystems, fungi connect the soil to the root. As the tree grows, the mycelium colonizes the plant cells. This process is continuous and dynamic, and fungal root structures expand rapidly and fluidly through the soil (Watkins 2015). Therefore, we can assume that resources can travel quickly and with very little cost. 

The nutrient exchange begins with chemical signals from the tree to the fungi that turn on genes associated with sugar and carbon transportation in the fungi. This process is adaptive, as trees and fungi decide how many resources to share (Watkinson 2015). Thus, in our model, we assume that each fungus wants to share all of its nitrogen, and can share at most 0.5 nitrogen per period. A tree needs 0.7 nitrogen in a period to sustain its health and size. In cells with less than 0.7 naturally occurring nitrogen in the soil, trees will form a relationship with the fungus. In the case where trees have access to more naturally occurring nitrogen than they need, they will not trade their carbon with the fungi. 

Once a relationship is established, metabolism-associated genes in the fungus turn on (Watkinson 2015). In our model, the fungus considers the metabolic needs of the tree in its area, and if the tree can sustain and grow based on the resources in the soil plus the resources supplied by the fungus, then the fungus effectively has a surplus. If the fungus is turned on genetically for trading, and the tree’s metabolic needs are met, then the fungus might choose to share resources with adjacent trees with limited nitrogen in their soil. In other words, mycorrhizal fungi will transfer resources from plants with abundant nutrients to other, weaker plants. 

  1. Results

We simulated the forest over 100 generations under different initial resource conditions and observed the effect on tree growth measured as the difference between the starting and ending biomass in the forest. We also measured the number of times that a tree with a surplus of resources shared nitrogen through the fungal network with an adjacent plant. Lastly, we measured the portion of the resources a tree uses in a period that is sourced from fungi. We tested each resource level 10 times and averaged the results. Relevant statistics of our dependent variables are summarized in table 1. Note that the parameters of our model are arbitrary and have no natural or biological meaning, therefore our results mean nothing in absolute terms, but should be analyzed in relative terms. 

Table 1: Summary Statistics of Key Variables

Tree GrowthFungus Redistributes Nitrogen to Adjacent TreesFungus Exchange of Nitrogen for Carbon with Nearest Tree% Resources that come from Fungus
Mean45717.6011498.82145855.802.72%
Median48214.7511689.2568984.901.09%
Variance97791221.0316460931.6741621300795.240.30%
Std Dev9888.944057.21204012.995.47%
Range-79084.80-17451.50-964528.00-38.94%
Min-29965.700.0035472.000.55%
Max49119.1017451.501000000.0039.49%

Note: The summary statistics are a sample of the average results of 10 simulations for each level of resource (0.25-20). 


We found our predictions to be true. Unsurprisingly, tree growth increased under more resource-rich conditions. Looking at the green line in figure 1, tree growth started to level out towards maximum growth levels approaching 50,000 in health value when the maximum random value for nitrogen in the soil was above five. This occurs because a tree needs one nitrogen to increase its health value, so at a cap of five, there is an 80% chance that the natural nitrogen level is already sufficient. Notice tree growth plateaus at about 48,000, that is because the average starting tree biomass for forests is about 52,000. 

Figure 1: Tree Growth And The Occurrence Of Fungal Redistribution Of Resources Vs. The Amount Of Naturally Occurring Nitrogen. 

Note: trendlines are moving weighted average


The tan dots in figure 1 depict the number of resource exchanges between the fungi and the adjacent trees. At lower levels of resources the trees are more likely to need the maximum amount of nitrogen it can get from the fungus in order to meet the nutrient requirement, and therefore redistribution occurs less frequently. However, Fungal exchanges increased sharply as the natural resource cap approaches five as the number of trees that have a natural nitrogen level between 0.5 and 0.7 increase which is the range that fungus will have a surplus to trade with adjacent cells. Once the natural resource cap is above five, the number of trees with natural resource levels above 0.7 increases. Trees with a natural resource value above 0.7 already have all of the nitrogen that they need to grow, and therefore will not trade their carbon with the fungi, and the fungi won’t be turned on for redistributing nitrogen.

Figure 2: Tree Growth When Fungus Are Allow To Redistribute Resources Vs. When Fungus Are Not Allowed To Redistribute Resources. 

Note: trendlines are moving weighted average


Figure 2 depicts the effect of the redistribution of resources on tree growth. We find that if redistribution is restricted, at certain resource levels, tree growth is less optimal. The results matched our initial predictions. Especially in situations with lower natural resource caps, the presence of fungi promotes forest health. Although eventually, with a high enough natural resource ceiling, the forest without the fungi (the gold dots) approaches the same cap as the forest with fungi (the green dots). At limited resource levels, trees with higher random natural resources can spread their nutrients to trees with lower natural levels of nitrogen. This enables trees that would normally not grow in the scenario without fungi to reach the value necessary to promote growth. 

Figure 3: Resource Level vs. the Percent of Resources that a Tree Gets from a Fungus

Note: trendline are moving weighted average


Figure 3 demonstrates the importance of fungi at low resource levels—trees get significantly more of their nitrogen from fungi than when resources are limited. Further, figure 4 demonstrates the shifting role that fungi play in a forest as resource levels change. At very low levels of nitrogen, the fungi exchange nitrogen for carbon with the trees, but after a certain threshold, trees increasingly get their nitrogen solely from the natural deposits in the soil and stop trading with the fungi. However, in the middle-range of resource availability, the number of times that fungi are redistributing nitrogen from one area to another peaks much later. Note the different scales on the axis. In general, tree-fungi carbon-nitrogen trade occurs at a much higher rate than redistribution. 

Figure 4: Amount of Resource vs Fungal Redistribution of Nitrogen and Exchange of Nitrogen and Carbon

Note: trendlines are moving weighted average


  1. Conclusion

Given the results of our model, fungi are a valuable resource to promote healthy tree growth since they allow for the exchange of necessary nutrients. The model is useful for determining how different resource and fungal population levels will affect future tree health. While our results show that trees can succeed in growing without the help of fungi, in extremely resource deficient areas, fungal redistribution of nutrients is vital for tree growth and production. Thus, the symbiotic relationship demonstrated by the model shows that the introduction of fungi to areas of future tree plantation is an effective way to promote tree growth and health. 

Since the model helps demonstrate the relationship between tree growth and mycorrhizal fungi, it can be helpful to display findings from other related research. For example, research on Shorea balangeran, a species of tree found in Sumatra and Indonesia, analyzes the effect of ectomycorrhizal fungi on tree growth for the rehabilitation of peat swamp forests. By observing measures of tree growth, researchers found that the presence of fungi helped promote shoot height and weight of the trees (Turjaman et al. 2011). The results are consistent with our model’s findings and show how our model could be applied in a real-world scenario. 

The dynamics of nitrogen translocation have not been well examined and transfer mechanisms are poorly understood (Simard et. al 2012). Our results shed light on the effect of naturally occurring resources on growth and nutrient distribution. Although we described the interactions as nitrogen translocation, the nutrient passing through the network could have easily been carbon that is overproduced by a tree in a resource-rich environment. Thus, the results of our model also demonstrate fungi’s critical role in interplant carbon transfer as well. 

Notice we described resources as naturally occurring in the soil, but you could think of resource level as the efficiency of a tree to uptake said resources in the soil. Previous research suggests that resource transfer through mycorrhizal pathways is more beneficial for plants that are not able to independently exploit soil resources (Simard et. al. 2012). Our results corroborate these findings, see figure 2. 

The degree of fungi and plant integration through mycorrhizal network formation is dependent on many other factors besides soil environmental factors, such as availability of an alternate plant for fungus to transfer resources with, plant and fungi genetic compatibility, plant stress, carbon allocation patterns, etc (Simard et. al 2012). In our model, all other factors besides initial resource level were kept static, but a more realistic extension of our model would be to have other factors vary, for example, the minimum resource a tree needs in order to maintain or grow. Natural environments are adaptive, so another variation would be to allow variables to change over time. 

Acknowledgments

Thank you to Dr. Amanada Meier, Department of Biology, for her expertise and guidance in starting the project as well as the resources she shared to inform our model.

References

Bartlett Tree Research Laboratory Technical Report. Plant Health Care Recommendations for Dying Trees. www.bartlett.com/resources/plant-health-care-recommendations-for-declining-trees.pdf.

Franklin, O., Näsholm, T., Högberg, P., & Högberg, M. N. (2014). Forests Trapped In Nitrogen Limitation–An Ecological Market Perspective On Ectomycorrhizal Symbiosis. New Phytologist, 203(2), 657-666.

Kansas Forest Service. (2018, August 9). Spacing Recommendations. www.kansasforests.org/conservation_trees/careandtips/spacing.html. 

Simard, S. W., Beiler, K. J., Bingham, M. A., Deslippe, J. R., Philip, L. J., & Teste, F. P. (2012). Mycorrhizal Networks: Mechanisms, Ecology and Modelling. Fungal Biology Reviews, 26(1), 39-60.

Turjaman, Maman, Erdy Santoso, Agung Susanto, Sampang Gaman, Suwido H. Limin, Yutaka Tamai, Mitsuru Osaki, and Keitaro Tawaraya. (2011, May 24). Wetlands Ecology and Management 19: 331-339. www.link.springer.com/article/10.1007%2Fs11273-011-9219-1.

Watkinson, S. C. (2015). Mutualistic Symbiosis Between Fungi and Autotrophs. The Fungi

ProQuest Ebook Central www.ebookcentral-proquest-com.proxy048.nclive.org.

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