Predator

dy/dt = δxy - γy

The predator population growth δxy depends on successful kills and the reproduction rate; however, delta is likely be different from beta. The loss rate, an exponential decay, of the predators {\displaystyle \displaystyle \gamma y}γy represents either natural death or emigration

Based on a dialogue on the System Dynamics mailing list regarding the current level of acceptance of System Dynamics after it has been promoted for over 70 years I dredged up the following set of influences as a thought exercise. This is an example of a Drifting Goals Archetype.

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Overview

A model which simulates the competition between logging versus adventure tourism (mountain bike ridding) in Derby Tasmania. 

How the model works:

Trees grow, and we cut them down because of the demand for Timber and sell the logs. Mountain bikers and holiday visitors will come to the park and this depends on experience and recommendations.  Past experience and recommendations depend on the Scenery, number of trees compared to the visitor and Adventure number of trees and users.  Park capacity limits the number of users.  To utilize highest park capacity, they need to promote to the holiday visitor segment as well. Again, the visit depends on the scenery. So, both mountain biking and forestry (logging) businesses need to contribute a significant amount of revenue to CSR for faster regrowth of trees.

Interesting insights

It looks like a lot of logging doesn't stop people from mountain biking. 

Faster replantation of the tree will balance out the impact created by logging which will give the visitor a positive experience and the number of visitors is both improved. 

To keep the park's popularity in check, the price of wood needs to be high. 

Also, it looks like mountain biking only needs a narrow path.

CSR contribution to nature can be a crucial factor. 

​This model attempts to understand the behavior of average lifetime of companies in the S&P500 index. The reference mode for the model is a graph available at this link: https://static-cdn.blinkist.com/ebooks/Blinkracy-Blinkist.pdf (page 5) which was discussed in the System Thinking World Discussion forum.

Mergers & Acquisitions can be one of the reasons for older companies to be replaced with newer companies in the Index. With M&A of older companies, the empty slots are taken over by newer companies. However, overtime, these new companies themselves become old. With steady M&A, the stock of older companies decreases and stock of newer companies increases. The result is that average age of the companies in the S&P Index decreases.

The oscillations in the diagram, according to me, is due to oscillations in the M&A activity.

There are two negative feedback loops in the model. (1) As stock of new companies increases, the number of companies getting older increases which in turn decreases the stock. (2) As M&A increases, stock of older companies decreases which in turn decreases M&A activities.

Limits of the model

The model does not consider factors other than M&A in the increase in number of new companies in the Index. New companies themselves may have exceptional performance which will result in their inclusion in the Index. Changes in technology for example Information Technology can usher in new companies.

Assumptions

1. It is assumed that M&A results in addition of new companies to the Index. There could be other older companies too, which given the opportunity, can move into the Index. Emergence of new technologies brings in new companies.