Exam 1 Bio 48 Fall 1999

1. Briefly define and state the significance of five of the following six terms (3 points each; sum=15):

eidos

Ideal form. In this essentialist concept, individuals in nature are imperfect representatives of an ideal form. Species are viewed as fixed entities.

Important because this view may have stifled ideas about how species change.

Cline

Change in phenotype (or genotype) across a geographic transect. Can be due to varying selection pressures across the cline.

Illustrates the balance between gene flow and selection in producing patterns of variation.

Frequency dependent selection

Type of selection in which the selection coefficients for the genotypes depends on the frequency of the genotype.

Can lead to maintenance of genetic variation in a population.

Vestigial organ

A structure that has lost its function and is no longer used by and organism (e.g. leg bones in whales).

Illustrates the ancestral state of a structure (still present), but relaxed selection for its maintenance.

Fundamental theorem of natural selection

Fisher’s Fundamental Theorem of Natural Selection: The rate of evolution is proportional to the genetic variation in the population.

Determines the opportunity of natural selection to operate.

 

 

 

Dp

Change in allele frequency (p) between generations: A microevolutionary view of evolution that represents the change in the genetic composition of a population between generations.

2. Clearly state the important distinction between (6 points each; sum = 27):

Response to selection / Selection differential

Response to selection: the change in the mean phenotype as a result of selection

Selection differential: difference between the mean of the population and the mean of the parents selected to reproduce.

Adaptation / effect

Adaptation: A trait evolved by natural selection that solves a particular problem presented by the environment (biotic or abiotic).

Effect: an incidental consequence of the adaptation that may have co-opted original trait and evolved new utilities that are distinct from historical origin.

 

 

3. Pin the tail on the donkey: Fill in the fitness values that correspond to the graphs below. Use 1, (1-s) and (1-t) as needed and assume that s and t are always between 0 and 1. Clearly specify whether s is greater than, equal to, or less than t if it pertains to a particular graph. (15 points; sum=42)

WAA 1 - s WAA 1 – 2s WAA 1 – s WAA 1 WAA 1 - s

WAa 1 WAa 1 - s WAa 1 WAa 1 – s WAa 1

Waa 1 - t Waa 1 Waa 1 Waa 1 Waa 1 - t

s < t or (1-s), (1-s), 1 s > t

 

4. Below are some actual data for hemoglobin genotypes in a malarial region of Africa (A = normal allele,S = sickle allele). Determine the i) Relative fitnesses, ii) the selection coefficients, and iii) the average fitness of this population. (10 points; sum = 52)

Genotype Observed adult frequency

AA 9365 f(A) = (9365 + 9365 + 2993)/ 24774

AS 2993 = 0.874

SS 29 F(s) = 0.123

Expected HWE

AA = (0.874)2(12387) = 9527 Relative Fitness

Aa = (2(0.874)(0.123))(12387 = 2672.4

Aa = (0.123)2(12387) = 187.4 AA = 0.98 / 1.12 = 0.875

Aa = 1.12 / 1.12 = 1.000

Obs / Exp = Absolute fitness aa = 0.15 / 1.12 = 0.138

AA = 9365 / 9527 = 0.98 Selection Coefficient

Aa = 2993 / 2672.4 = 1.12

Aa = 29 / 187.4 = 0.15 s = 1 – 0.875 = 0.125

t = 1 – 0.138 = 0.862

Average Fitness

Wbar = (0.874)2(0.875) + 2(0.874)(0.123)(1) + (0.123)2(0.138) = 0.89

 

 

 

 

 

 

 

 

 

 

 

5. i) Draw and clearly label all axes of an adaptive landscape. ii) Describe the three important phases of the shifting balance theory of evolution proposed by Sewall Wright. iii) Describe the population structure of two different species in which shifting balance is likely to be important and unimportant, respectively. Answers should contain no more than i) a small drawing, ii) three short phrases and iii) one short sentence. (15 points; sum = 67).

1. Drift in local populations allows that population to approach the domain of attraction of a fitness peak

2. Intrademic selection: Local population climbs the fitness peak

3. Interdemic selection: Demes on highest peaks leave most emigrants and and the other demes acquire the allele frequencies of the most demes

 

f(B)

| /

Wbar | /

| /

|/__________________

f(A)

Important in species with many small (perhaps somewhat isolated) demes.

Less important in species with large Ne and high gene flow.

 

6. You are interested in heritability of body size in insects. For 3 species you have the data below on the variance in body size in natural populations and data on the variance in body size in homozygous strains of each species. From these data i) estimate VG in each species (recall VP = VG + VE ). Identify the species in which it will be ii) easy to select for larger or smaller body size, iii) hard to select for large or small body size. iv) Clearly state why. (15 points; sum = 82)

Observed Variances

Within Homozygous Strains Within Natural populations

Species 1 .20 .30

Species 2 .04 .40

Species 3 .30 .50

VE (no VG) VP

 

 

VG = VP - VE

Species 1 0.10 = 0.30 – 0.20 H2 = 0.30 Hard to Select (low H2)

Species 2 0.36 = 0.40 – 0.04 H2 = 0.90 Easiest to select (high H2)

Species 3 0.20 = 0.50 – 0.30 H2 = 0.40

Broad sense heritability (H2) = VG / VP

Opportunity for selection is a function of heritability. Species with the highest heritability have the greatest genetic variance and will respond to selection more than species with low heritability.

 

 

 

 

 

 

 

 

7. We have portrayed population genetics as often involving a "fight" between forces with opposing effects resulting in some "equilibrium". Two formulas are presented below, one for Heterozygosity, and one for Fst. For each formula, describe the relevant evolutionary forces and how they work to produce the equilibrium conditions for each formula (i.e., a particular value of heterozygosity, or a particular value of Fst). You do not need to use actual numbers; terms like "large" and "small" will do, as long as you are explicit. (18 points; sum=100).

H = (4Neu)/(4Neu+1)

Effective population size (Ne) determines the ‘rate’ of genetic drift and the loss of variation.

Mutation rate (u) determines the rate new variation is added to the population.

When the product Ne(u) is large, the ratio will be close to 1 (high heterozygosity). When Ne(u) is small, ratio will be closer to 0.

The equilibrium is determined by the relative values of Ne and u. Populations with high heterozygosity will have large Ne, high u, or both, hence high genetic variation.

Fst = 1/(4Nem+1)

Ne is the effective population size (i.e ‘rate’ of drift)

m is the migration rate or rate of mixing of alleles between populations.

Fst is the proportion of variation that lies between demes.

With high Ne or m, or both, the denominator is large and Fst value is small which means populations are not differentiated.

With small Ne or m, or both, the denominator is small and Fst is close to 1, which means populations are differentiated.

 

 

 

pt+1 = Wbar = p2WAA + 2pqWAa + q2Waa p2 + 2pq + q2 = 1

f(A) at equilibrium = pequil. = with WAA = (1-s), Waa = (1-t) Vp = Vg +Ve

Variance of p among demes after t generations = p(1-p)[1-(1-1/(2Ne))t] h2 = Va/Vp

= SNe = ppop1 t+1 = ppopl t (1-m) + ppop2 t (m)

Æq = -m(q1 - q2) (subscripts 1 and 2 are for populations) Æq = - sq2(1-q) assuming WAA = WAa = 1.0; Waa = 0

At equilibrium Æq = Æp = 0