Population Models II

1
Population Models II

• Essential to ecosystem modeling
• Linear growth dx/dt C
• Exponential growth dx/dt r x
• Where r is specific growth rate
• Not sustainable in long term

2
Uncontrolled population growth
3
Overshoot and Collapse Model
4
Ybarra Ranch deer herd

• Located in South Texas
• Approximately 60 miles by 45 miles wide
• Vegetation includes sagebrush, mesquite,
  granjeno, and prairie grasses
• Populated with white tail deer, javelina,
  coyotes, and small mammals
• Fenced on south and west, cleared land
  development and highways on north and east

5
Ybarra Ranch deer herd

• White tail deer population estimated at
  approximately 3,500 in the 1910
• Predators including mountain lions and wolves
  were heavily hunted and removed by 1920s
• Deer herd size was estimated at 50,000 by 1930
  and peaked at 100,000 in 1935
• Forage was decimated and herd was reduced to
  about 10,000 by 1940 through starvation

6
Ybarra Ranch deer herd

• First model starts with a stock for the deer
  population
• Deer increased by births
• Herd decreased by deaths from nutrition and
  deaths from predation
• Second stock would include predator population
• Predators are decreased through deaths from
  nutrition and deaths from hunting and trapping

7
Ybarra Ranch deer herd

• A complex predator prey relationship could
  include predator births and deaths depending on
  the availability of deer
• Deer deaths would be depending on the number of
  predators
• Another relationship to consider might be
  thinning of the deer herd with an annual hunting
  season
• Other complexities

8
Ybarra Ranch deer herdModel 1

• Deer population trends follow net births and
  deaths from predators
• Ranch area starting at 200 KA
• Birth rate based on favorable conditions
• Assumptions ½ of herd is female, 2/3 of females
  are in fertile stage of life cycle and each
  female has one litter per year
• Average litter size is 1.6 based on two does
  birthed every other year

9
Ybarra Ranch deer herdModel 1

• 0.5 0.667 1.6 0.54 or birth rate is 54
  /year
• Assume death rate from age approximately
  0.07/year or 7/year
• Then net birth rate 0.47/year rounded off to
  0.5/year

10
Ybarra Ranch deer herdModel 1

• Based on cougar habits of one/kill/week for large
  mammals
• Assume 75 of kills are white tail deer
• Then 0.75 52 40 kills/year/cougar
• Set number of deer killed/year/predator at 40

11
Ybarra Ranch deer herdModel 1

• Predator stock function?
• Evaluate deer herd based on historical data
  subsequent to predator removals
• Predator population drops drastically over ten
  year period
• Model results? Expectations?

12
Ybarra Ranch deer herdModel 2

• Deer population did not achieve overshoot and
  collapse behavior
• A second model is needed
• Deer are browsers compared to cattle as
  grazers
• Valentine (1990) suggests mule deer require 23
  percent of AUE
• Animal Unit Equivalent dry matter consumed by
  1,000 lb non-lacting cow 12 Kg/dry matter/day

13
Ybarra Ranch deer herdModel 2 and 3

• Assume required forage for white tail 2.76
  Kg/day approx. 1,000 Kg/year 1 MT/year
• Outputs for population, net births, and trends?

14
Ybarra Ranch deer herdModel 4

• Another experiment can the die off be
  experienced if the amount of forage required per
  deer per year is modeled?

15
Ybarra Ranch Biomass Model 1

• Forage biomass can be introduced as another stock
  to the model
• Will forage model and population model get us to
  realistic ecosystem behavior?