dx/dt = αx - βxy

The prey reproduces exponentially (αx) unless subject to predation. The rate of predation is the chance (βxy) with which the predators meet and kill the prey.

How the model works

The left side of the model highlights the mountain bike flow beginning with demand for the forest that leads to increased visitors using the forest of mountain biking. Accompanying variables effect the tourism income that flows from use of the bike trails.
On the right side, the forest flow begins with tree growth then a demand for timber leading to the logging production. The sales from the logging then lead to the forestry income.
The model works by identifying how the different variables interact with both mountain biking and logging. As illustrated there are variables that have a shared effect such as scenery and adventure and entertainment.

Variables
The variables are essential in understanding what drives the flow within the model. For example mountain biking demand is dependent on positive word mouth which in turn is dependent on scenery. This is an important factor as logging has a negative impact on how the scenery changes as logging deteriorates the landscape and therefore effects positive word of mouth.
By establishing variables and their relationships with each other, the model highlights exactly how mountain biking and forestry logging effect each other and the income it supports.

Interesting Insights
The model suggests that though there is some impact from logging, tourism still prospers in spite of negative impacts to the scenery with tourism increasing substantially over forestry income. There is also a point at which the visitor population increases exponentially at which most other variables including adventure and entertainment also increase in result. The model suggests that it may be possible for logging and mountain biking to happen simultaneously without negatively impacting on the tourism income.