De Deer P Pop opula lation ion on on K Kaib aibab ab Pla - - PowerPoint PPT Presentation

De Deer P Pop

• pula

lation ion on

• n K

Kaib aibab ab Pla Plateau G Game P Preserve

14TH FEBRUARY SPECIAL

IE604: System Dynamics Modeling and Analysis Jayendran Venkateswaran, IIT Bombay

Ka Kaibab Plateau

Kaibab Plateau is a flat area of land located in the northern rim of Grand Canyon, USA. Area = 800,000 acres. The plateau was home to mule deer, mountain lions, wolves, etc. Part of the Grand Canyon National Game Preserve.

Yo You are the Manager of the Preserve

The year is 1920. Your job is to maintain the environmental balance

• f the region.

The mule deer population at the plateau has increased rapidly in the past 15 years, and you need to take steps to control the deer population.

Yo You are wondering what went wrong…

In 1906, a bounty was placed on mountain lions, wolves and other natural predators of deer (mainly to protect the cattle ranches nearby). Deer hunting was prohibited. In the next 15 years, there was substantial extermination of the predators. The deer population began to grow rapidly. The deer herd, from an initial estimate of 4,000 deer in 1905, has increased 5-fold by 1920.

Con Concerns on

• n for
• rest

A mule deer needs about 1000 kg of food a year to sustain themselves. However, you suspect that they actually consume close to 2000 kg of food annually especially when the food is plentiful. You have started to see tiny patches of forest which seems to have become barren due to over grazing by the deers. You hope it is nothing to be alarmed about.

Op Options to control Deer eer Population

Two broad options to control the deer population:

• Reintroduce predators: The elimination of predators

seems to have caused the problem. So, reintroducing them should solve it.

• Hunting of Deers: The local hunters are suggesting to

permit them to hunt the mule deers (since predators have greatly reduced, the hunters have less game).

Re Reintroduce predators

Stop the bounty hunting of predators, either with effect immediately or gradually over the next five years. The environmentalists are happy with this option. However, cattle ranchers oppose this, as they feel that the predators will prey on their cattle. The ranchers may delay the implementation of the plan by another 5 years.

Hu Hunting g of

• f De

Deers

A few ‘hunting’ policies are possible:

• a constant number of deer per year,
• a constant fraction of deer per year, or
• a hunting of deer in a year whenever the deer

population exceeds a certain threshold.

The environmentalists are not happy with this

• ption though.

Wh What to do?

Luckily, this is set in an alternate universe where systems thinking/ modelling has been the way of life for hundreds of years. As a system dynamicist, you have built a SD model consisting of three sub-systems:

• Deer population sub-system
• Predator population sub-system
• Food sub-system

De Deer Popul pulation n sub ub-sy system

The Deer population is affected by the natural deer net growth rate and the deer predation rate. The deer predation rate is the product of the number

• f deers killed per predator and the predator

population. The number of deer kills per predator is non-linear table function of the density of deers in the plateau. The deer net growth rate is a product of the Deer population and the fractional growth rate of deers, which is a non-linear table function of the food per deer ratio

Pr Predator Subsystem

The predator population is affected by the natural predator net growth rate and the predator hunting rate. The predator hunting rate is the determined by a fraction of predators that can be hunted in a year. The predator net growth rate is a product of the Deer population and the predator fractional growth rate. The predator’s fractional growth rate is a non- linear table function of the number of deer kills per predator.

Fo Food subsystem

The Food stock represent the total amount of food available for deers in the plateau. The food stock is affected by the natural food regeneration rate and the food consumption rate. The food consumption rate is a product of the deer population and the food consumed per dear per year, which in turn is a table function of the food per deer ratio. The food regeneration rate adjusts the difference between the food capacity and the food stock, over a period of food regeneration time. The food regeneration time is a table function of the food stock.

Ca Causal l Loop

• op Dia

iagr gram

Develop a simple causal loop diagram based on above description. Indicate the link and loop polarities.

Com Comple lete SFD mod

• del

l table le function tions

Deer kills per predator, takes as input Deer Density/ initial deer density, and is connected as (0,0), (1,5), (2,10), (3,14), (4,17.5), (5,20) Predator fractional growth rate takes as input deer kills per predator / normal deer kills per predator, and is connected as (0,-0.2), (1,0), (2,0.08), (3,0.14), (4,0.18) Deer fractional growth rate takes as input food ratio and is connected as (0,-0.5), (0.4,-0.15), (0.8,0), (1.2,0.12), (1.6,0.16), (2,0.2) Food consumed per deer takes as input food ratio and is connected as (0,0.5), (0.1,450), (0.2,810), (0.3,1140), (0.4,1340), (0.5,1540), (0.6,1670), (0.7,1790), (0.8,1880), (0.9,1960), (1,2000), (1.1,2000), (1.2,2000) Food regeneration time takes as input Food/ Food capacity and is connected as (0,35), (0.25,15), (0.5,5), (0.75,1.5), (1,1).

Si Simulate b base se m model

Simulate the model. Extend the simulation final time to 1950. What behavior do you get? Does it correspond sufficiently to the observed/expected behaviour (see Appendix of notes)? Save the simulation run results as kaibab-base. PS: You may get some warnings during run time. Ignore them. If you get any error then fix them.

Po Policy Analysis of Reintroducing Predators

The predator fraction hunted per year in the Predator subsection of the model represents the fraction of predator population the hunters eliminate each year. The fraction is given as a function of time. In current base case, beginning 1910, the fraction is set at 30%. You cannot change the values for years 1900 to 1920.

• The current year is 1920, & you cannot change the past

Re Reintro A: :

Simulate the scenario where predator hunting is stopped with immediate effect. Model this in the predator fraction hunted per year table function by including: –STEP( 0.3, 1920). You cannot change the values for years 1900 to 1920. Save results as Kaibab-ReintroA.

Re Reintro B: :

Simulate the scenario where predator hunting is stopped gradually from 1920 to 1925. Model this in the predator fraction hunted per year by including a ramp function: – RAMP(0.1, 1920, 1925). You cannot change the values for years 1900 to 1920. Save results as Kaibab-ReintroB.

Re Reintro C: :

The ranchers can delay the plan to stop hunting by five years, that is predator hunting is stopped gradually from 1925 to 1930. Model this in the predator fraction hunted per year by including a ramp function: – RAMP(0.1, 1925, 1930). You cannot change the values for years 1900 to 1925. Save results as Kaibab-ReintroC.

Po Policy Analysis of Reintroducing Pr Predators

What can you say about the policy of reintroducing predators? Do they solve the problem?

Po Policy Analysis of Pe Permitting Deer Hunting

To model this, add a flow Deer Hunting Rate out of Deer stock. You need to further update this for each scenario. NOTE: Kindly make changes to the kaibab-base

• model. That is, predators are NOT reintroduced

and predator hunting is as usual.

De DeerHun unt A: :

Suppose, starting in year 1920, a constant of, say, 1000 deers/ year can be hunted. Try enough other values of the constant number of deers hunted per year to get a good idea of what this policy does. Summarise the results in illustrative plots.

De DeerHun unt B: :

Suppose, starting in year 1920, say, 10% of the deer population can be hunted each year. Try enough other values of the fraction (ranging from 0.01 to 0.2) to get a good idea of what this policy does. Summarise the results in illustrative plots.

De DeerHun unt C: C:

In this case, the deer hunting rate can be given as MAX(0, (Deer – Desired Deer Population)/ Time to Adjust Deer Population. The Time to Adjust Deer Population can be taken as 1 year. The Desired Deer population is what we would like to limit the deer population to. There are two cases:

• DeerHuntC1
• DeerHuntC2

De DeerHun unt C1 C1: :

As per the description in the appendix, 30000 would be sustainable size. Simulate the policy with Desired Deer population as 30000, starting in year 1920. What happens? Also try 35000, and 25000. What happens? Why?

De DeerHun unt C2 C2: :

Implement policy C, but assume that the deer hunting comes into force only in 1925 instead of 1920. Let Desired Deer population be 30000. What happens? What if the start year is 1924? 1926?

Po Policy Recommendation

What policy would you recommend? Why? How would you actually implement your policy recommendation?