Gut microbiota project worksheet
Group members:
Background
Humans have trillions of bacteria living within their guts, which are collectively referred to as the 'gut microbiota'. The gut microbiota is primarily made up of four main groups of bacteria: Actinobacteria, Bacteroidetes, Firmicutes, and Proteobacteria. Throughout a person's life, the relative abundance of each of these four groups changes. This process is similar to the ecological concept of succession.
The overarching questions for this project are:
- What is the relative abundance of each of the four groups of bacteria in a person's gut over each short- and long-term timescales?
- Does the gut microbiota ever reach any sort of equilibrium (here, a stable relative abundance of the four bacteria types)? If so, what factors influence this equilibrium?
The gut microbiota for a healthy human infant can be modeled with the equation: \begin{align} \begin{bmatrix}A\\B\\F\\P\end{bmatrix}_{t+1} = M \begin{bmatrix}A\\B\\F\\P\end{bmatrix}_t \end{align} \begin{align*} M = \begin{bmatrix}0.5&0&0&0\\ 0 &0.9 &0.05 &0.5\\ 0.5 &0.1 &0.85 &0.3\\ 0 &0 &0.1 &0.2 \end{bmatrix} \end{align*} where $A$ is the abundance of Actinobacteria, $B$ of Bacteroidetes, $F$ of Firmicutes, $P$ of Proteobacteria, and $t$ is the number of weeks since the infant's birth.
Here $M$ is the transition matrix, describing transitions among each of these four bacterial groups. Unlike in the sea turtle model (where transition from $A$ to $B$ represents an individual turtle changing from type $A$ to type $B$), here the transitions indicate the probability that an area of the gut that is dominated by group $A$ is taken over by group $B$ in the next time step.
For the steps below, turn in your R code as part of showing your work.