following a drought on Daphne Major, the beaks of the offspring of the surviving medium ground finches (average 14mm) were larger than the beaks of the entire population prior to the drought ( 12mm average). Based on the prior study, it is known that the heritability of beak size in the parental population was .5

what is true:
a. the selection differential was 4 mm
b. the ofspring are more variable than the parents
c.small beaked finches died in order to ensure the species' survival
d. the big beak offspring are a new species different from their medium beak parents

the answers A, but not sure why

The answer is A because the response to selection (2 mm) is equal to the product of heritability (0.5) and the selection differential (4 mm)

All other answers are false

The answer is A because the selection differential is the difference between the mean of the selected individuals and the mean of the entire population. In this case, the mean beak size of the offspring after the drought (14mm) is greater than the mean beak size of the entire population prior to the drought (12mm). Therefore, the selection differential would be 14mm - 12mm = 2mm. However, the question states that the heritability of beak size in the parental population was 0.5. This means that half of the variation in beak size is due to genetic factors. Therefore, the selection differential needs to be divided by the heritability (2mm / 0.5) to obtain the true selection differential, which is 4mm.

To determine the correct answer, let's break down the information provided:

1. Before the drought, the average beak size of the entire population was 12mm.
2. Following the drought, the average beak size of the offspring of the surviving medium ground finches was 14mm.
3. The heritability of beak size in the parental population was 0.5.

Now, let's analyze each option:

a. The selection differential was 4mm.
The selection differential refers to the difference between the average trait value in the parental generation and the average trait value in the selected individuals that contribute offspring to the next generation. In this case, since the average beak size of the offspring (14mm) is greater than the average beak size of the entire population before the drought (12mm), the selection differential can be calculated as 14mm - 12mm = 2mm. Therefore, option a is not correct.

b. The offspring are more variable than the parents.
The provided information does not directly state anything about the variability of the offspring's beak size compared to the parents. Therefore, we cannot conclude that the offspring are more variable than the parents. Thus, option b cannot be determined based on the given information.

c. Small-beaked finches died in order to ensure the species' survival.
The information given does not explicitly mention anything about the survival or death of small-beaked finches during the drought. Therefore, option c cannot be determined based on the given information.

d. The big-beak offspring are a new species different from their medium-beak parents.
The information provided does not suggest any changes in speciation or the emergence of a new species. The only information given is that the beak size of the offspring of the surviving medium ground finches was larger than the beak size of the entire population before the drought. Hence, option d is not supported by the given information.

Therefore, out of the provided options, none are true based on the given information.