Genetics Problem Set 1

BCB 645 – Spring 2021

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Q1: FLOWER COLOR

frequencies

observed <- c(96, 108, 85)
expected <- c(73, 110, 92)
o_minus_e <- observed - expected
chi_val <- (o_minus_e^2)/expected

chisq_table <- as.data.frame(round(rbind(observed, expected,o_minus_e, chi_val),3))
colnames(chisq_table) <- c("red (pp)", "purple (pq)", "blue (qq)")

formattable(chisq_table)

current_year <- c(73/275, 110/275, 92/275)
next_spring <- c(96/289, 108/289, 85/289)
freq <- as.data.frame(round(rbind(current_year, next_spring),4))
colnames(freq) <- c("red (pp)", "purple (pq)", "blue (qq)")

formattable(freq*100)

Hardy Weinberg Equilibrium

current_hwe <- current_year[1]^2 + current_year[2]*2 + current_year[3]^2
nextsp_hwe <- next_spring[1]^2 + next_spring[2]*2 + next_spring[3]^2

cat("1st Generation Hardy-Weinberg Equilibrium Value:",round(current_hwe,3)*100, "%","\n");cat("2nd Generation Hardy-Weinberg Equilibrium Value:",round(nextsp_hwe,3)*100, "%")

1st Generation Hardy-Weinberg Equilibrium Value: 98.2 % 
2nd Generation Hardy-Weinberg Equilibrium Value: 94.4 %

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Q2: SUGARCANE YEILD MY FARM

VISUAL DIAGRAM: DOMINANCE DEVIATION

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q2 <- ggplot(df, aes(x = allele, y = yield), add = c("mean_se")) + 
  geom_point(size=4,shape=16, position=position_jitter(0.03),aes(color=allele),alpha=.6) +gghisto+
theme(legend.position = "none") +
stat_summary(aes(allele, yield), data = df, fun = "mean", geom = "crossbar", size=0.2, width=0.2, color="grey40") +
  ggtitle("Sugarcane Yield - My Farm")+
  annotate("text", x=.68,y=11.3, label= "avg=11.3")+
  annotate("text", x=1.68,y=20.4, label= "avg=20.4")+
  annotate("text", x=2.68,y=29.3, label= "avg=29.3")

#m <- lm(df$yield~df$allele)
#q2 + geom_abline(slope = coef(m)[[2]], intercept = coef(m)[[1]])
q2

mean(df$yield[df$allele=="b1b1"]); mean(df$yield[df$allele=="b1b2"]); mean(df$yield[df$allele=="b2b2"])

[1] 11.3
[1] 20.35294
[1] 29.33333

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Q3: SUGARCANE YEILD AT FARM 2

Before calculating the basic metrics for the locus (as in 2): which of these metrics do you expect to differ between the two populations? Why?

ggplot(df2, aes(x = allele, y = yield), add = c("mean_se")) + 
  geom_jitter(size=4,shape=16, position=position_jitter(0.03),aes(color=allele),alpha=.6) +gghisto+
theme(legend.position = "none") +
stat_summary(aes(allele, yield), data = df2, fun = "mean", geom = "crossbar", size=0.2, width=0.2, color="grey40") +
  ggtitle("Sugarcane Yield - 2nd Farm")+
  annotate("text", x=.68,y=8.3, label= "avg=8.3")+
  annotate("text", x=1.68,y=20.2, label= "avg=20.2")+
  annotate("text", x=2.68,y=33, label= "avg=33")

mean(df2$yield[df2$allele=="b1b1"]); mean(df2$yield[df2$allele=="b1b2"]); mean(df2$yield[df2$allele=="b2b2"])

[1] 8.285714
[1] 20.2
[1] 33

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Q4: DISCORDANT OBSERVATIONS

Give 1 reason that the discordant observations might be observed, and briefly describe how you might design a new experiment to test this?

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Q5: GREATER GENETIC VARIATION

Which population between (2) and (3) do you expect to have greater genetic variation? Why? Calculate VA and VD for both populations.

\[ V_G = V_A+V_D+V_I \] genetic varaince

\[ V_T = V_A+ V_D + V_I + V_E \] total phenotypic variance