Solutions4

ANTH 450/550: Population and Quantitative Genetics

Problem Set 4

1. Consider the following two life histories:

x      l(x)     m(x)          x       l(x)     m(x)
0      0.70     0               0      0.80       0
1      0.50     1               1      0.70     1.0
2      0.30     1               2      0.50     0.6
3      0.20     1               3      0.40     0.1
4      0.10     1               4      0.01     0.1

Calculate the fitnesses for these two life history strategies under the assumption of discrete generations. Recalculate the fitnesses under the assumptions of overlapping generations and the stable age distribution. Do the fitnesses of these two phenotypes relative to one another depend upon the demographic assumptions being made?

2. Two populations were studied in two environments with the following results (note: treat the two populations as independent evolutionary units):

                                        Environment 1                  Environment 2
Genotype               AA          AB          BB        AA          AB         BB
Starting Number     160          480          360        160      480         360
Adult Number          90           450          300        150      400         340

Assuming that viability is the only component of fitness affected by genetic variation at this locus and that generations are discrete, estimate the relative fitnesses of the three genotypes under each environment using the convention that fitness of the AB heterozygote is 1.

Assuming the population structure remains constant and that drift can be ignored, what is the initial response to selection under the two environments (i.e., which alleles are favored)?

Does an intermediate polymorphic equilibrium point exist for each of the environments? If so, is it stable or not? Do the initial changes in allele frequency calculated above move the population away or towards any intermediate equilibria that may exist?

3. A number of anthropological analyses of biological variation have focused upon genetic variation on the island of Sardinia. Sardinian genetic variation is influenced, in part, by the presence of diverse ethnic groups and a multiplicity of languages among subpopulations. The Carloforte population (CF) lives on an island off the southwest coast of Sardinia, with subpopulations Sulcis-Iglesiente (SIG) along the western side of Sardinia and , and the Sarrabus (SAR) population on the far eastern side of Sardinia.

Consider the following genotypic frequencies for the MN, AK, and HP blood groups:

                                                MN                                   AK                                      HP
Subpopulations     MM      MN          NN         11          12          22          11          12          22
CF                              142       198            70          404          6            0           78          202     130
SIG                             260       250            60          565          4           1            87          271     212
SAR                              92        99            27          209           8           1           37          106        75

Based on these data (which are all in HW-equilibrium), determine the values of Fst, Fis, and Fit for these three loci. What is the average value for these F-Statistics, and how would you interpret these data in terms of microevolutionary processes?

Finally, determine the allele frequencies for each locus, and use these frequencies to generate genetic distance using NTSYS. Calculate both Edward's chord distance as well as Balkrishnan and Sangvi's B statistic. Be sure to control for sampling bias in each distance estimate (hint: Use the N-matrix option in SIMGEN when available, to weight distance by sample size). Finally, produce a dendrogram of these distances using the neighbor joining procedure in NTSYS for both the chord and B distances. How would you interepret these data, and how would you explain differences in the dendrograms (if any)? For 10 extra points, use the chord distances to generate an ordination plot of the three subpopulations using multidimensional scaling. Create a two-dimensional plot of the distances.