Subject: Systems Language - Telling a Story

Posted by Niall Palfreyman on 2/24/2010
In Reply To:Systems Language - Telling a Story Posted by Tim Joy on 2/23/2010

Message:

Tim Joy schrieb:
> Without any systems jargon, and without any reference to a computer model, how do we tell this story with a compelling and accurate narrative? For instance, how might you tell this story to a room of 8th graders?
>
OK, I'll try:

In the meadow outside my office window is a small colony of 10 rabbits, and I am interested in how that population will behave over the coming 5
years: will it die out (which would impoverish my life), will it overrun the meadow and my office (which would smell out my office) or will it thrive at a steady size (yes please!)? I need to think about the different factors affecting the population size.

Each month new rabbits are born and some rabbits die. The number of rabbits born in the coming month depends on two things: how many babies a typical mother produces per month, and also how many mothers there are in the population right now. With a population of 10 rabbits we'd expect about 5 females in the population right now, but clearly that number will rise as the population gets bigger.

Dying is a slightly trickier story. Clearly the number of deaths per month will depend on the life expectancy of a typical rabbit, and also on the current number of rabbits (twice as many rabbits means twice as many deaths in a typical month). But there is also an additional factor.
The rabbits are dependent for their survival on a resource: the amount of new grass which the meadow makes available each month. If the grass growth per month is high, the rabbits will lead long, happy, fertile lives; however if the grass growth per month is low, then the number of deaths will rise as the rabbits become unhealthy and their life expectancy falls.

At first this seems like a straightforward effect from outside the rabbit colony: the growth of the colony is dictated by the rate at which fresh grass can grow. However we must be careful, because the grass does not really lie outside the system. Rather, the grass itself is dependent on the number of rabbits currently eating it - if the population gets too high, the grass growth rate will drop and the colony will suffer. So we have here a closed feedback loop in which the rabbits affect the amount of new grass growth, and the grass in turn affects the amount of new rabbit babies. It seems intuitive that the colony will at first increase in size because of all the new grass, but will eventually reach a critical size beyond which the rabbits eat too much grass for the meadow to sustain them. I therefore guess that the colony will reach a limiting size, but I can't tell exactly what that size is without getting precise information on rabbit birth- and death-rates and their grass consumption per month.

Best wishes,
Niall.

PS: I'm aware that I've assumed here that the grass is replenished by growth, which isn't contained in the original diagram. I guess an alternative would be to refer to another, non-renewable, resource, but I found that a bit too depressing. :-)