6. in a tropical forest there is a species of bird that has a variable tail length. in one population of 1500 birds, 340 have long tails (tt), 1000 have medium length tails (tt), and 160 birds have short tails (tt). you cannot assume this population is in hwe. find:
a. frequency of the population that is homozygous recessive.
b. frequency of the population that is heterozygous.
c. frequency of the population that is homozygous dominant.
d. frequency of the dominant allele.
e. frequency of the recessive allele.
f. if the population was in hwe, what would the frequency of the homozygous recessive genotype be?
g. if the population was in hwe, what would the frequency of the heterozygous genotype be?
h. if the population was in hwe, what would the frequency of the homozygous dominant genotype be?
i. compare answers a-c to f-h. is this population in hwe?
j. if not, which trait is favored? also, what mode of selection is occurring?

Question

Accepted Answer

### Part a: Frequency of homozygous recessive ($tt$)
# Explanation:
## Step 1: Identify total population and recessive genotype count
Total population $N = 1500$, number of $tt$ individuals $n_{tt}=160$. Frequency $f_{tt}=\frac{n_{tt}}{N}$.
$f_{tt}=\frac{160}{1500}\approx0.1067$
# Answer: $\approx 0.107$

### Part b: Frequency of heterozygous ($Tt$)
# Explanation:
## Step 1: Identify heterozygous count
Number of $Tt$ individuals $n_{Tt}=1000$ (medium tails). Frequency $f_{Tt}=\frac{n_{Tt}}{N}$.
$f_{Tt}=\frac{1000}{1500}\approx0.6667$
# Answer: $\approx 0.667$

### Part c: Frequency of homozygous dominant ($TT$)
# Explanation:
## Step 1: Identify dominant homozygous count
Number of $TT$ individuals $n_{TT}=340$. Frequency $f_{TT}=\frac{n_{TT}}{N}$.
$f_{TT}=\frac{340}{1500}\approx0.2267$
# Answer: $\approx 0.227$

### Part d: Frequency of dominant allele ($T$)
# Explanation:
## Step 1: Use allele frequency formula
For a diploid population, allele frequency of $T$ ($p$) is $p = f_{TT}+\frac{1}{2}f_{Tt}$.
From parts a - c, $f_{TT}\approx0.2267$, $f_{Tt}\approx0.6667$.
$p = 0.2267+\frac{1}{2}(0.6667)=0.2267 + 0.3333 = 0.56$
# Answer: $0.56$

### Part e: Frequency of recessive allele ($t$)
# Explanation:
## Step 1: Use allele frequency formula
For a diploid population, allele frequency of $t$ ($q$) is $q = f_{tt}+\frac{1}{2}f_{Tt}$.
From parts a - c, $f_{tt}\approx0.1067$, $f_{Tt}\approx0.6667$.
$q = 0.1067+\frac{1}{2}(0.6667)=0.1067 + 0.3333 = 0.44$
Or use $p + q = 1$, so $q = 1 - p = 1 - 0.56 = 0.44$ (more accurate).
# Answer: $0.44$

### Part f: HWE - homozygous recessive frequency ($q^2$)
# Explanation:
## Step 1: Use HWE formula $q^2$
From part e, $q = 0.44$, so $q^2=(0.44)^2 = 0.1936$
# Answer: $0.1936$

### Part g: HWE - heterozygous frequency ($2pq$)
# Explanation:
## Step 1: Use HWE formula $2pq$
From part d and e, $p = 0.56$, $q = 0.44$. So $2pq = 2\times0.56\times0.44 = 0.4928$
# Answer: $0.4928$

### Part h: HWE - homozygous dominant frequency ($p^2$)
# Explanation:
## Step 1: Use HWE formula $p^2$
From part d, $p = 0.56$, so $p^2=(0.56)^2 = 0.3136$
# Answer: $0.3136$

### Part i: Check HWE
# Explanation:
## Step 1: Compare observed and HWE frequencies
Observed $f_{TT}\approx0.227$, HWE $p^2 = 0.3136$; Observed $f_{Tt}\approx0.667$, HWE $2pq = 0.4928$; Observed $f_{tt}\approx0.107$, HWE $q^2 = 0.1936$. These are not equal, so population is **not** in HWE.
# Answer: No

### Part j: Favored trait and selection mode
# Explanation:
## Step 1: Analyze trait frequencies
Observed $f_{Tt}$ (medium tails) is high ($\approx0.667$), $f_{TT}$ (long) and $f_{tt}$ (short) are lower. This suggests **stabilizing selection** (favors intermediate trait, reduces extremes). The favored trait is medium tail length ($Tt$).
# Answer: Favored trait: Medium tail length ($Tt$); Selection mode: Stabilizing selection

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QUESTION IMAGE

Question

Explanation:

Part a: Frequency of homozygous recessive (\(tt\))

Step 1: Identify total population and recessive genotype count

Step 1: Identify heterozygous count

Step 1: Identify dominant homozygous count

Answer:

Part b: Frequency of heterozygous (\(Tt\))