1. Define the following: sustainable yield –
how much can be harvested without depleting the natural stock, and is equal to natural income
natural income –
growth & recruitment, and is equal to sustainable yield
natural capital –
original stock before growth/recruitment and migration and death/loss
immigration –
input into the population
emigration –
output from the population

2. Sustainable Yield
SY may be calculated as the rate of increase in natural capital (that which can be exploited without depleting its potential for replenishment)
Or – the idea that a “crop” can be taken from an ecosystem in a way that leaves the ecosystem viable for the future

3. Sustainable Yield

4. Sustainable Yield

5. Sustainable yield Assumptions
There is enough data to know the populations real size and growth rate
That the population has an even age structure
Harvesting individuals is random and does not disproportionately affect the breeding stock
That the population is not affected by natural fluctuations
Ex: outbreak of disease

6. Practice Problems Sustainable yield can be defined as:
I. annual growth and recruitment – annual death and emigration
II. (total biomass t time t + 1) – (total biomass at time t)
III. The highest rate at which natural capital can be exploited without reducing its original stock.
  ALL OF THESE – I, II, and III

7. Practice Problems
In a deer population of 1000, each year an average of 100 die from natural causes and 250 are born. There is no immigration or emigration.
What is the maximum sustainable yield?
150…
What is the final population size at the end of the year?
1150…

8. Practice Problems
For a particular year, for the fishing grounds of an island nation, assume:
R = the biomass of young fish reaching harvestable size
G = the growth in biomass of fish already of harvestable size
M = the loss of fish through death and emigration
B = the biomass of the total fish population at the start of the year 
Create a formula that calculates the sustainable yield.
R + G – M

9. Practice Problems
Multiple Choice: Which of the following is/are the maximum sustainable yield for a resource?
The difference between natural capital and natural income
The rate of decrease in natural capital
The sustainable rate of harvest of a resource
The point at which the original stock is depleted
Natural income
Natural capital
Carrying capacity
Total biomass
C and E

10. Practice Problems
Multiple Choice: If the harvesting of a fish population were to exceed the sustainable yield in one year, this would mean
The natural capital had been reduced but the natural income had increased.
The natural capital remained the same but the natural income had been reduced.
The natural capital had been reduced and the natural income would be reduced in the following year.
The natural capital remained the same but the natural income would be reduced in the following year.  c

11. Practice Problems
Multiple-choice: Resources that have a sustainable yield equal to their natural productivity are
Natural income
Renewable natural capital
Replenishable natural capital
Non-renewable natural capital b

12. Practice Problems
A forest has a volume of million m3 of timber. In one year, m3 of timber are harvested and m3 of timber are added by normal tree growth.
What is the maximum sustainable yield?
– = m3 timber
Is harvesting exceeding the natural income?
 yes
Is harvesting exceeding the natural capital?
 no
Calculate the natural capital remaining.
MILLION m3 – m m3 = m3
What is the natural income?
  m3

13. Practice Problems
Which of the following statements about natural capital is/are correct?
Coal and timber are examples of renewable natural capital.
Replenishable natural capital cannot be naturally replaced at a rate comparative to its consumption.
Metals are renewable natural capital because they are not destroyed and can be recycled.
Carbon dioxide and oxygen are examples of replenishable natural capital.
Oil is currently a non-renewable resource, but it could be a potentially renewable resource.
Groundwater is a replenishable resource.
D, F

14. Practice Problems Which of the following define(s) sustainable yield?
I. (annual growth and recruitment) – (annual death and emigration)
II. The gain in biomass (or energy) per unit time remaining after subtracting metabolic and other natural losses
III. The highest rate at which natural capital can be exploited without reducing its original stock
all