2021 MCM Problem A B C Notes

2021 MCM Problem A: Fungi(bk1)

The carbon cycle describes the processof the exchange of carbon throughout the geochemical cycle of the Earth,and is a vital component for life on the planet. Part of the carbon cycleincludes the decomposition of compounds, allowing carbon to be renewed and usedin other forms. One key component of this part of the process is thedecomposition of plant material and woody fibers.(bk2)

 

Some of the key agents in decomposing woodyfibers are fungi. The authors of a recent research article on wooddecomposition by fungi identified fungi traits that determine decompositionrates and also noted links betweencertain traits[1]. Inparticular, the slow growing strainsof fungi tend to be better able to survive and grow in the presence ofenvironmental changes with respect to moisture and temperature, while the faster growing strains tend to be less robust to the samechanges.(bk1’) Asynopsis of this article can be found below on page 3.

 

These researchers examined a large number oftraits associated with different fungi and their role in the decomposition ofground litter (dead plant material) and woody fibers. For this MCM Problem youshould focus on just two traits of a fungus: the growth rate of the fungus and the fungus’ tolerance to moisture.(rsc1) Your primary goal is to model thedecomposition of woody fibers in a given patch of land, and do so in thepresence of multiple types offungi breaking down woody fibers in the same area.(spm1)

 

As you explore therelationship of the two traits of interest, growth rate and moisturetolerance, with the rate of decomposition, several questions may arise toinclude: Using these two traits, how do the different fungi interact(rcs2) and decompose ground litter in a fixedpatch of land in different environments?(imp1)Within these different environments, how will the decomposition be impactedover time as conditions vary?(imp2) How do environmental changes and the variationin environmental change impact the long-term dynamics with respect todecomposition, as well as competition between fungi in a given environment?(imp3) The estimation for the decomposition rates,given the growth rate, is shown in Figure 1. The estimation of thedecomposition rates, given the relative moisture tolerance, is shown in Figure2.

 

Requirement: Yourpaper should explore and address the following aspects.

 

Build amathematical model that describes the breakdown of ground litter and woodyfibers through fungal activity in the presence of multiple species of fungi.(spm1’)

 

In yourmodel, incorporate the interactions betweendifferent species of fungi, which have different growth rates and differentmoisture tolerances as shown in Figures 1 and 2.(spm1’’)

 

Pro