In 1800 sheep were introduced to the island of Tasmania. After a period of expon
ID: 164542 • Letter: I
Question
In 1800 sheep were introduced to the island of Tasmania. After a period of exponential growth their population has fluctuated around 2 million Individuals. After an island-wide hunt of the sheep, the population was reduced to 1 million. If the instantaneous rate of population increase for this year is 38, 500 individuals, what Is the sheep's intrinsic rate of natural increase? Eventually the population of sheep regrows to 1.8 million. What is the sheep's current instantaneous rate of population increase? the figure below shows the relationship between the juvenile survival and population density in the sheep. Explain two factors that could affect the pattern of juvenile survival in the sheep.Explanation / Answer
1. Sheep population is assumed to be closed population here. The population reduced from 2 million to 1 million after sheep hunting.
Instantanous rate of population increase is 38500.
Calculation of Intrinsic rate of natural increase (r)
Exponential population growth is explained by simple differential equation given by;
dN / dt = bN – dN
= (b - d)N = rN
where N is the number of individuals in the population
t is the time interval
r is the growth rate per individual or intrinsic rate of natural increase
In words;
The rate of change in population size = intrinsic rate of increase * number of individuals present
38500 = r * 1 million or 10 lakh individual
r = 38500/1000000
r = .038
2. Sheep’s population regrows to 1.8 million then instantaneous rate of population increase is given by;
= r * number of individuals present
= .038 * ( 1.8 * 1000000)
= .038 * 1800000
= 68,400 individuals
3. The horizontal line denotes no population increase i.e, r = 0.
Studies show that an effect of weather on juvenile sheep survival in some cases is mediated by an interaction with population density. For instance; spring and winter temperatures had a positive effect on infant survival only when population density is high.
Intraspecific competition for the limited resources also affects the survival of the new individuals.