# What Darwin Never Knew

How did the discovery of DNA prove that Darwin’s theory of evolution was correct and how does it change the way we view evolution today and into the future?

Michael Nackman of the University of Arizona studied how some of the Pincate Desert’s pocket rock mice evolved to blend in with volcanic rock. A mutation in the mouse’s DNA changed its fur colour from light to dark. Now, rock pocket mice exist with light or dark fur.

https://uanews.arizona.edu/story/coats-different-color-desert-mice-offer-new-lessons-survival-fittest

Sean Caroll studied why one fruit fly species has spots on its wings, but another does not when the two species both have the spot-coding gene. One DNA portion differed in the spotted fly. Injecting this DNA portion into the non-spotted fly resulted in spotted wings. These DNA portions are called switches, and they activate and deactivate genes.

https://hort.uwex.edu/articles/spotted-wing-drosophila/

David Kingsley and Dolph Schluter studied why the ocean stickleback has spikes on its belly, but the lake stickleback does not. A mutation in the lake stickleback’s DNA broke the switch that activates the spike-coding gene. The gene that codes for the stickleback’s spikes also codes for hind legs in other animals.

https://learn.genetics.utah.edu/content/selection/stickleback/

Arkhat Abzhanov and Cliff Tabin studied how the Galapagos finches have different beaks by looking at the birds’ embryos. The birds had the same beak-coding genes, but they differed by how much and when the switch activated the gene.

https://en.m.wikipedia.org/wiki/Darwin%27s_finches

Neil Shubin of the University of Chicago studied how fish evolved to walk on land. He found a fossil of a flat-headed fish with leg-like fins. They had the same bone structure as the limbs of all other four-legged animals. In the paddlefish, a relative of the fossil Tiktaalik, the same genes code for fins as they code for limbs in humans. A few mutations changed the ancient fish’s fins to limbs.

https://phys.org/news/2014-01-discovery-tiktaalik-roseae-fossils-reveals.html

Through the study of DNA, scientists have discovered that mutations in the genome cause evolutionary change. Switches in an organism’s DNA activate and deactivate hox genes that code for physical features. Mutations can affect these switches, therefore affecting the organism’s physical features. This proves that Charles Darwin’s theory of evolution was correct. We can now discover how almost any organism differs from another, and how it evolved and came to be.

Sources

• What Darwin Never Knew notes & transcript

# Week 5 – Precalc 11

This week in Precalculus 11, we started the Solving Quadratic Equations Unit. We first reviewed factoring polynomial expressions.

Factoring: separating an expression into its components

Polynomial expression: an expression of numbers and variables being added, subtracted or multiplied (example: 2x)

Greatest common factor: the greatest number that can divide into all the terms in the expression (example: 2, 4, 6, 8, 10      GCF = 2)

Term: a number or a group of numbers being multiplied (example: 2$x^2$)

Binomial: a polynomial expression with 2 terms (example: x + 1)

Difference of squares: a polynomial expression in which subtraction takes place between 2 perfect square terms (example: 4x – 1)

Trinomial: a polynomial expression with 3 terms (example: $x^2$ + x + 1)

Conjugates: 2 terms with opposite addition/subtraction signs (example: 1 + 1 & 1 – 1)

To factor a polynomial expression, we first look for the greatest common factor between the terms and divide each term by that number.

Example:

2x + 2

= 2(x + 1)

If the expression is a binomial, we check if it is a difference of squares. When factored, a difference of squares results in conjugates.

Example:

4x – 1

= (2x + 1)(2x – 1)

If the expression is a trinomial, we check if it is in the form a$x^2$ + bx + c. If a = 1, we separate bx into 2 terms that multiply to c and add to bx.

Example:

$x^2$ + 2x + 1

= (x + 1)(x + 1)

= $(x + 1)^2$

If a ≠ 1, we separate bx into 2 terms that multiply to ac and add to bx, then find the greatest common factor of each side, and divide each term by that number.

Example:

2$x^2$ + 4x + 2

= 2$x^2$ + 2x + 2x + 2

= 2x(x + 1) + 2(x + 1)

= (2x + 2)(x + 1)

If the expression is in a different form than a$x^2$ + bx + c, the expression can sometimes be changed to this form.

Example:

$(x + 1)^2$ + 2(x + 1) + 1

= $a^2$ 2a + 1

= (a + 1)(a + 1)

= $(a + 1)^2$

= $[(x + 1) + 1]^2$

= $(x + 2)^2$