Dispersed, repetitive sequences such as transposable elements may have played a role in duplicating short regions in a genome. Can you suggest a mechanism?

If the evolutionary rate of amino acid substitution in a protein is K, what is the average length of time between successive amino acid substitutions in this protein?

If a randomly mating population is segregating n selectively neutral alleles of a gene and each allele has the same frequency, what is the frequency of all the homozygotes in the population?

Ribonuclease, a protein that degrades RNA, is $124$ amino acids long. A comparison between the amino acid sequences of cow and rat ribonucleases reveals $40$ differences. What is the average number of amino acid substitutions that have occurred per site in these two evolutionary lineages? If the cow and the rat lineages diverged from a common ancestor $80$ million years ago, what is the rate of ribonuclease evolution?

During the early evolutionary history of the vertebrates, a primordial globin gene was duplicated to form the $\alpha$- and $\beta$-globin genes. The rate of evolution of the polypeptides encoded by these duplicate genes has been estimated to be about $0.9$ amino acid substitutions per site every billion years. By comparing the human $\alpha$- and $\beta$-globins, the average number of amino acid substitutions per site has been estimated to be $0.800$. From this estimate, calculate when the duplication event that produced the $\alpha$- and $\beta$-globin genes must have occurred.

The heme group in hemoglobin is held in place by histidines in the globin polypeptides. All vertebrate globins possess these histidines. Explain this observation in terms of the Neutral Theory of Molecular Evolution.

What was some of the evidence that led Charles Darwin to argue that species change over time?

Consider the region in the first quadrant bounded by the graphs of $y=x^3$ and $y=4 x$. Find The value of $m$ such that the line $y=m$ divides the region into two regions of equal area.

Find the area of the following regions. The region inside the lemniscate $r^{2}=2 \sin 2 \theta$ and outside the circle r=1

The top three oil producers in the United States in a certain year are the Gulf of Mexico, Texas, and Alaska. The three regions were responsible for $64 \%$ of the United States oil production. The Gulf of Mexico and Texas combined for $47 \%$ of oil production. Texas produced 3% more than Alaska. What percent of United States oil production came from these regions?

Find the area of the following regions. The region inside the cardioid $r=1+\cos \theta$ and outside the cardioid $r=1-\cos \theta$

Which statements are true? Explain why or why not. Changes in the coding regions of genes involved in development are primarily responsible for the differences between species.

What does the fact that the 1824 presidential election fielded "favorite sons" from four regions suggest about sectionalism in the United States?

Sketch the following regions and use integration to find their areas. The region bounded by all leaves of the rose r=3 cos $2 \theta$