Question

Color patterns in Mozambique tilapia are determined as follows: MM-black, Mm-bronze, mm-gold. Suppose that the Mozambique tilapia breed consists of 10,000 fish, of which 50 are black, 1,900 are bronze and the rest is gold.

1. Calculate the allele frequency of M and m in the Mozambique tilapia population.
2. What are the expected genotypic frequencies of this population if it were in Hardy-Weinberg equilibrium for the color locus?
3. Show whether or not the population is indeed in Hardy-Weinberg equilibrium (You don't need to test for significance).
4. Suppose that MM-fish are less viable and none of the MM-fish reproduces. What is the frequency of the M-allele in the next generation?
5. Based on the information in Q.4, if there is random mating among the mm- and Mm-fish, what are the genotype frequencies in the next generation?

Next consider body weight of the Mozambique tilapia. In reality, body weight is determined by many loci, most of which are unknown. However, for the purpose of the current exercise, suppose that body weight is determined by a single locus with two alleles, B and b. The frequency of B is 0.4 and that of b 0.6, BB-fish have an average body weight of 410 g, Bb-fish 390 g and bb-fish 350 g. Suppose that the population is in Hardy-Weinberg equilibrium.

6. Calculate the genotype frequencies and the population mean for body weight.
7. The one-locus model, calculate the origin o of the model, the additive effect a and the dominance effect d. Does this locus show dominance?
8. Calculate the allele substitution effect α and the breeding values of each genotype. Explain the meaning of the allele substitution effect α and of the breeding value. Without doing calculations, what is the average of the breeding values of all individuals?
9. Calculate the additive, dominance and genotypic variance. What is the meaning of the additive genetic variance?
10. Due to differences in the environment (e.g. nutrition, water body) that fish encounter during their life differences between body weight of fish are not only due to different genotypes but also due to different environments. Suppose that V_E = 60 g². What is the total variance of body weight in the Mozambique tilapia, i.e. the variance that we would observe when measuring the actual bodyweight of fish, and what is the name of this variance?
11. Suppose that body weight is normally distributed (Though strictly this cannot be true when there is a single locus determining body weight). Calculate the body weight range in the Mozambique tilapia population that contains 99.7% of the observed body weights.

Answer 1

Let the allele frequency of M and m be p and q respectively. Therefore, the genotype frequency of MM, black tilapia is p2, Mm, bronze is 2pq and mm, gold is q2 respectively,

(ii) Expected genotype frequency of MM, ; expected genotype frequency of mm, ; expected genotype frequency of Mm,

(i) Allele frequency of M, ; allele frequency of m.

(iii)

Therefore the population is in Hardy Weinberg equilibrium.

(iv)

Mean fitness value,

  

New frequency of MM=new frequency of Mm=

Frequency of M allele in the next generation=