This is a basic BIDE (birth, immigration, death, emigration) model.  Not all parts are implemented, however Birth and Death are.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.

Overview 

This model not only reveals the conflict between proposed logging of adjacent coups and Mountain bike in Derby but also simulates competition between them. The simulation model aims to investigate the potential coexistence opportunities between the mountain biking and forestry and find out the optimal point for coexistence to help improve Tasmania’s economy. 

How the model works 

It is recognized that the mountain biking and forestry industries can help support the Tasmanian community and strengthen the Tasmanian economy. The logging and forest sector in Derby can help the local community generate wealth and create more employment opportunities. The sector main source of income come from selling timber such as domestic and export sales. Nevertheless, the sector’s profit has decreased over the past few years on account of the weaker demand and reduced output. Accordingly, the profitability and output of the sector have fluctuated in response to the availability of timber, the timber price movements as well as the impact of changing demand conditions in downstream timber processing sectors. The slow growth rate for a timber has a negative impact on the profitability of the forestry industry and the economic contribution of this industry is set to grow slower, as there is a positive correlation between these variables. In addition, the mountain biking industry in Derby can bring a huge significant economic contribution to the local community. The revenue streams of the industry come from bike rental, accommodation, retail purchase and meals and beverages. These variables also influence the past experience which is positive correlation between reviews and satisfaction that can impact the demand for the mountain biking trails. More importantly, the low regeneration rate for a timber can have a negative impact on the landscape of the mountain biking and the tourist’s past experience that led to a decrease in the demand of tourists for the mountain biking, as the reviews and satisfaction are dependent on the landscape and past experience. It is evident that the industry not only helps the local community generate wealth through industry value addition but also creates a lot of employment opportunities. Therefore, the Mountain Bike Trails can be regarded as sustainable tourism that can help increase employment opportunities and economic contribution that can be of main economic significance to the Tasmania’s economy. Therefore, both industries can co-exist that can maximise the economic contribution to the local community and the Tasmanian economy.

Interesting Insights

It is interesting to note that the activity of cutting down trees does not influence the development of Mountain Biking industry. By lowering the prices of accommodation, food, bike rental and souvenirs, it can help increase the reviews and recommendations of Mountain Biking that will enhance the number of tourists. In this case, the Mountain Biking industry can achieve sustainable economic growth in the long-term while the economic growth rate of forestry industry will continue to decrease. 

With these two terms the equation above can be interpreted as: the change in the prey's numbers is given by its own growth minus the rate at which it is preyed upon.

The predator equation becomes

dy/dt =  - 

In this equation, {\displaystyle \displaystyle \delta xy} represents the growth of the predator population. (Note the similarity to the predation rate; however, a different constant is used as the rate at which the predator population grows is not necessarily equal to the rate at which it consumes the prey). {\displaystyle \displaystyle \gamma y} represents the loss rate of the predators due to either natural death or emigration; it leads to an exponential decay in the absence of prey.

Hence the equation expresses the change in the predator population as growth fueled by the food supply, minus natural death.