Coudl some explain how you get each of the probabalities? -There are 3 hermaphro
ID: 3175253 • Letter: C
Question
Coudl some explain how you get each of the probabalities?
-There are 3 hermaphroditic individuals. After reproduction, each dies. Each has a 33% chance of producing 0, 1, or 2 offspring. Such variation among individuals in the likelihood of producing offspring represents an example of demographic stochasticity. The average birth rate of 1 per individual.
1.)What is the average r (i.e., ra)?
ra=0
However, there is 1/3 x 1/3 x 1/3 or 1/27 chance of no offspring being produced and thus the chance that the population will go extinct. Furthermore, there is a 1/9 chance of only one offspring being produced by the population (1/31 x 1/30 x 1/30 + 1/30 x 1/31 x 1/30 + 1/30 x 1/30 x 1/31). If the species were self-incompatible (that is, self-fertilization was not possible due to genetic incompatibility), then the remaining individual would not find a mate, and the population would go extinct. There is 2 in 9 (22%) chance that only two individuals will produce offspring.
If the population consisted of 4 individuals, there is only a 1/81 chance of no offspring being produced.
Explanation / Answer
Rate of increase, r
r = birth rate – death rate, Here the birth rate is 1/individual and death rate is 1/individual as an individual surely dies after reproduction. Birth rate, b = (1/3 * 0) + (1/3 * 1) + (1/3 * 2) = 1/individual. Therefore, r = 1 – 1 = 0.
Chance of no offspring
For each individual, the chance of 0 offspring is 1/3 or 33%, chance of 1 offspring is 1/3 or 33% and chance of 2 offspring is 1/3 or 33%.
Therefore chance of no offspring in all 3 individual = 1/3*1/3*1/3 = 1/27
Chance of only one offspring
For one offspring, the combinations are
Therefore, the Chance of only one offspring = 1/9 + 1/9 + 1/9 = 3/9 = 1/3
Chance of only 2 individuals producing offspring
An individual can produce 0, 1, or 2 offspring with equal probability of 1/3, therefore the chance of an individual producing offspring is
1 – Chance of an individual producing 0 offspring = 1 – 1/3 = 2/3
Different combinations of 2 individuals producing offspring are
1st and 2nd individuals produce offspring while 3rd one has 0 offspring = 2/3 * 2/3 * 1/3 = 4/27
1st and 3rd individuals produce offspring while 2nd one has 0 offspring = 2/3 * 1/3 * 2/3 = 4/27
2nd and 3rd individuals produce offspring while 1st one has 0 offspring = 1/3 * 2/3 * 2/3 = 4/27
Therefore, Chance of only 2 individuals producing offspring = 4/27 + 4/27 + 4/27 = 12/27 = 4/9
If the population consisted of 4 individuals, chance of no offspring being produced
For 4 individuals, chance of no offspring is given by
1/3 * 1/3 * 1/3 * 1/3 = 1/81
Please note for chance that only two individuals will produce offspring, the result is 4 in 9. Please check as the text mentions 2 in 9.