What sorts of things has Farmville taught YOU about life?

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Q1: Calculate the frequency of each of the following wavelengths of electromagnetic radiation:

1. 632.8 nm
2. 503 nm
3. 0.052 nm

Q2: Calculate the wavelength of each of the following frequencies of electromagnetic radiation:

1. 104.3 MHz
2. 1035 kHz
3. 835.6 MHz

A: When solving these types of problems, it is important to remember that wavelength and frequency are inversely proportional. This means that as one value goes up, the other value goes down. We can solve frequency/wavelength problems using the formula , where v is the frequency, c is the speed of light, and lambda λ is the wavelength.

Since wavelength is often expressed in nm, it is helpful to know the speed of light in nm since this will minimize how many conversions we need to do when solving these problems. We know that the speed of light is . To find the speed of light in nm, we perform the following calculation:

Now we can use this speed of light when doing all our frequency/wavelength problems. We use the formula above, , and plug in the values we know. Then we can solve for the unknown variable.

632.8 nm

The nm units cancel out and we are left with seconds. The standard unit for frequency is cycles per second, denoted as Hz or . So we are left with .

503 nm

You try solving the last one for 0.052 nm before looking at the solution below.

0.052 nm

Solving for frequency requires a bit more thinking, but the basic concept is the same.

104.3 MHz

We need to convert MHz to Hz. The conversion unit we need is .

Now we can plug in our values and solve.

Now we cancel our units and solve to get

That’s not so painful, is it? Let’s try the next one.

1035 kHz

We need to convert kHz to Hz. The conversion unit we need is .

Now we can plug in our values and solve.

You try solving the last one for 835.6 MHz before looking at the solution below.

835.6 MHz

Now we can plug in our values and solve.

Now we cancel our units and solve to get

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A: When categorizing electromagnetic radiation, it is important to remember the following trends:

• Lower energy means a longer wavelength and lower frequency.
• Higher energy means a shorter wavelength and higher frequency.
• Visible light is approximately in the middle of the electromagnetic spectrum.

Write the types of electromagnetic radiation in order of shortest wavelength to longest wavelength:

• Gamma ray
• X-ray
• Ultraviolet
• Visible light (violet, indigo, blue, green, yellow, orange, red)
• Infrared
• Microwave
• Radio (cell, FM, TV, AM)

The order is the same to write the types of electromagnetic radiation in either increasing energy per photon or increasing frequency:

• Radio (AM, TV, FM, cell)
• Microwave
• Infrared
• Visible light (red, orange, yellow, green, blue, indigo, violet)
• Ultraviolet
• X-ray
• Gamma ray

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March 29, 2010 - The Photoelectric Effect

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I will be looking for new ways to continue providing helpful study and school materials for students through my website. In the meantime, however, I would like to thank my loyal customers and readers for your support, and I will continue to post science articles and discussions, especially those per request- keep the requests coming!

If you live in Colorado and would like to read about the new legislation and/or write to your Colorado lawmakers regarding these new laws having an adverse effect on local business, then the following information is for you:

HB 10-1193

Colorado General Assembly

Governer Bill Ritter

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Introduction to Natural Selection

Natural selection posits that only a certain percentage of offspring born will survive to reproduce another generation. Individuals with certain genotypes will be more likely to survive, mate, and reproduce their genotypes in subsequent generations. Thus, natural selection acts upon individuals, whereas evolution occurs at the level of a population. There are four aspects to natural selection we need to consider.

1. Random mutations cause variations in alleles, or different amino acid sequences, which in turn cause variations in DNA sequences, producing new gene products (proteins) that serve different functions.
2. The mutated alleles may code for proteins that are either beneficial or detrimental to the individual’s survival.
3. Beneficial mutated alleles are more likely to be passed on to subsequent generations because the survival of the parent organism has been enhanced beyond other organisms without the beneficial allele.
4. Over many generations, the frequency of the mutated beneficial allele may increase because of the increased survival and reproduction of organisms carrying the allele over organisms who have other variations of the gene.

Darwinian Fitness

Darwinian Fitness is a quantitative measurement of the reproductive fitness of individuals with certain genotypes. This should not be confused with physical fitness in organisms. Physical fitness may give organisms an advantage in their environment, but if their genes are not passed to offspring, their Darwinian Fitness is lower. See the pictures below for an example of the difference between physical fitness and Darwinian Fitness (reproductive fitness).

Arnold Schwarzenegger is known for his physically fit image. He has produced four offspring.

Octomom may be less physically fit than Arnold Schwarzenegger in his bodybuilding days, but she has produced 14 offspring.

Who has more copies of their genes present in the population, Arnold Schwarzenegger or Octomom? Octomom certainly has passed on more genes and thus has a higher Darwinian Fitness.

Let’s calculate Darwinian Fitness numerically. Let’s assume three genotypes in our population. The first genotype we’ll call AA, a dominant homozygote. We’ll say Schwarzenegger, with four offspring produced, has the genotype AA. The second genotype is Aa, a heterozygote. We’ll say Octomom, with fourteen offspring produced, has the genotype Aa. Let’s throw in a third genotype aa, a homozygous recessive genotype. We’ll say that I have the genotype aa, and I have produced no children.

To calculate the Darwinian fitness of each genotype, we will assign the genotype with the highest reproductive success the value 1.00. The other genotypes will be compared relative to the genotype with the highest rate of successful reproduction

Octomom has the highest reproductive success with the genotype Aa. So we have:

Fitness of Aa = 1.00

The next step is to divide the number of offspring in our other genotypes by the number of offspring produced by our genotype with the fitness value 1.0. This will tell us what the Darwinian Fitness of each genotype is relative to the other genotypes. Octomom produced 14 children, so we will divide each value by 14.

Fitness of Aa = 1.0

Fitness of AA = 4 / 14 = 0.29

Fitness of aa = 0 / 14 = 0.o

So we can see that the highest Darwinian Fitness is assigned to Octomom with fourteen children and a Darwinian Fitness value of 1.0. The next closest in Darwinian Fitness is Arnold Schwarzenegger with four children and a Darwinian Fitness value of approximately 0.29. The least reproductively fit is myself, with no children and no Darwinian Fitness at all, or 0.0.

Hopefully from this example you can see that physical fitness does not equal Darwinian Fitness. Also, it merits mentioning that the values of Darwinian Fitness do not necessarily need to add up to 1. The Darwinian Fitness represents ratios of the genotypes relative to each other, and Darwinian Fitness based on genotypes does not necessarily come out to nice round numbers every time.

What Natural Selection Does Not Do

Perfect organisms do not result from natural selection. There are many reasons why there will never be a “perfect” organism resulting from the mechanisms of natural selection. For example, random mutations cause new alleles to be acted upon by natural selection; natural selection does not cause new, beneficial alleles to be formed. Natural selection is not purposeful in its events; rather it is a process that flows with the events that occur in any given environment.

Patterns of Natural Selection

There are four major types of natural ecological selection.

1. Directional Selection- one extreme of a phenotype has an advantage over the other extreme of a phenotype. For example, there may be phenotypes that express a very tall organism or a very short organism. If a certain environment favors only the very short organism, the tall organism will have a disadvantage and the number of tall organisms will be small compared to the large organisms.
2. Stabilizing Selection- the “middle of the road” phenotype is favored over either extreme. If an environment favors organisms with a medium height, rather than very tall or very short, then most organisms will be of medium height and only a few will be very tall or very short.
3. Disruptive Selection- two or more phenotypes are favored over any other phenotypes. If the environment favors either very tall organisms or very short organisms but not those of medium height, there will be more very tall or very short organisms than there are of medium height.
4. Balancing Selection- heterozygote phenotypes are favored over homozygote phenotypes. Homozygotes are present in few numbers in the population than heterzygotes. Environments with balancing selection is often said to present a heterozygote advantage because the environment favors genetic diversity and keeping as many alleles as possible present in the gene pool.

We can also consider one additional type of natural selection: sexual selection. There are two types of sexual selection.

1. Intrasexual selection- occurs between members of the same sex. Usually, this manifests as direct competition between males.
2. Intersexual selection- occurs between members of the opposite sex. Usually, this manifests as males vying for the attention of a female.

Intrasexual selection often results in direct competition between males for females or for territory.

Intersexual selection often results in showy traits in males to attract the attention of females.

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Genetic Drift

Genetic drift is a change in in genetic variation due to chance changes in allele frequencies. For example, genetic drift may occur as a matter of luck; one phenotype may simply never meet a member of the opposite sex in order to mate and produce offspring. Genetic drift is not affected by the relative fitness of individuals to their respective environments. In most cases, genetic drift occurs in small populations to the smaller gene pool compared to large populations. After many generations, genetic drift may cause an allele to be lost or fixed- the allele will reach either 0% frequency or 100% frequency. Genetic drift may also be observed in large populations, but its effect (loss or fixation of an allele) happens much more slowly than it would in a small population.

Two examples of genetic drift are the founder effect and the bottleneck effect. The founder effect occurs when a subset of a population breaks off from the larger population and establishes its own colony. Because the subset is not likely a representative sample of the larger population, genetic drift will cause the smaller colony to have a much different gene pool than that observed in the larger colony. The bottleneck effect occurs when a random event decreases the size of the population dramatically. This can be caused by such events as natural disasters, such as hurricanes or earthquakes, or through the destruction of habitat by humans or other forces. Because the decrease in the gene pool is random, the allele frequencies in the surviving population may be different from that of the original population. Sometimes, alleles can be completely eliminated by these chance events.

Gene Flow / Migration

These bears lived in different populations with different allele frequencies. By meeting each other, mating, and producing offspring, they will have caused gene flow between their populations.

Gene flow refers to the movement of genes between two populations that may have different gene frequencies. For example, a deer population that lives on the east side of a river may have different allele frequencies than the deer population on the west side of the river. If one year there is a drought and some deer are able to move to the other side of the river, mate, and produce offspring, the allele frequencies of each population may change as a result of the new gene pool. Gene flow is also sometimes called migration because it is often caused by migration of one population into the territory of another population. Thus, the genes in each population also “migrate” to the other population.

Gene flow has two important consequences. First, allele frequencies in each population experiencing migration is reduced. Scientists can evaluate the relative similarities and differences in allele frequencies in order to determine how isolated  the populations are. The more similar the allele frequencies between two populations are, the less isolated the populations are in turn. Second, gene flow can introduce new alleles into a population. Since mutations are so rare, and beneficial mutations even rarer, populations that do have a rare beneficial mutation introduced into their population are most likely to share the allele via gene flow.

Non-Random Mating

Would you rather mate and produce offspring with the man above

or with this man? If you expressed a preference for either, you are practicing nonrandom mating based on phenotypic characteristics.

Non-random mating occurs when individuals choose mates based on phenotypic characteristics or genetic lineage. In non-random mating situations, the allele frequencies do not change, but the proportions of heterozygotes to homozygotes may change. Inbreeding is one example of non-random mating that increases the frequency of homozygotes in a population. Conservation biologists keep track of non-random mating in a population in order to make sure increased homozygosity does not lead to inbreeding depression. If evidence of inbreeding depression is seen, biologists may introduce animals from another population to increase the gene pool.

Natural Selection

Natural selection is a phenomenon in which the environment selects for individuals with beneficial traits and against individuals with unfavorable traits. Because natural selection is discussed in greater depth in other articles, it will only be mentioned as a factor here.

Sources of New Genetic Variation

Random Mutations

The different tail types for manx cats were brought about by random mutations.

Random mutations are changes in existing genes that can introduce new alleles into a population. However, mutations are very rare, and beneficial mutations are even rarer. In most cases, mutations are detrimental to an individual and those that do not result in death, disfigurement, or other forms of severe disadvantage are, at best, neutral. When a beneficial mutation does arise, other mechanisms such as genetic drift or natural selection must act upon them in order for the allele to rise in frequency in a population.

Gene Duplication

Abnormal events during crossover (meiosis) may increase the number of copies of a gene. Through several generations, the new gene family may have new presence in a gene pool and may have different gene products.

Exon Shuffling

Sometimes, instead of full gene duplications during crossover, exons may be inserted into another gene. The new gene may have new functions and will be acted upon by mechanisms such as genetic drift or natural selection before increasing in frequency in a population.

Horizontal Gene Transfer

Typically, horizontal gene transfer is seen in bacteria. Through events such as endocytosis, genes from one species may be introduced into the genes of another species.

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Population geneticists primarily study allele and genotype frequencies. They use quantitative methods to analyze the frequency of alleles. For example, a population geneticist may study the frequency of certain patterns on the fur of wild cats, then will revisit the same population several generations later to find how the frequency of patterns has changed from the initial measurement. This type of study would give scientists a good idea of what genetic changes are happening in a population.

Darwin’s theory of natural selection posits that only a certain percentage of offspring in any given generation will survive to reproduce. Whether an individual survives or not depends on the inheritance of alleles that will increase its ability to survive in its environment. Alleles that do not benefit an individual and increase its chances at survival will not be passed down to future generations, thus decreasing the frequency of that particular allele in a population. Population geneticists can study changes in allele frequencies from generation to generation in order to determine what mechanisms underlie the natural selection in a given population.

New genetic variations can arise through mutation, gene duplication, exon shuffling, and horizontal gene transfer. Alterations to existing genetic variation can occur by natural selection, random genetic drift, migration, and nonrandom mating.

Nonrandom mating does not change the allele frequencies in populations, unless other evolutionary forces are also present. The other ways of increasing genetic variation will affect the allele frequencies in populations because they tend to increase heterozygosity.

Inbreeding is one form of nonrandom mating. Inbreeding occurs when two genetically related individuals  mate and produce offspring. Homozygotes are more likely to be found in populations that have a high degree of inbreeding, due to the decreased genetic variation between breeding pairs. Sometimes, populations that have too much inbreeding will experience what is called an inbreeding depression. An inbreeding depression occurs when homozygotes are less fit to survive in their environment, resulting in decreased reproductive success in the population. Biologists will often intervene to introduce new genetic variation into a population by introducing new individuals, and thus new genes, into the population.

To calculate allele frequencies in a population, divide the number of copies of a particular allele in a population by the the total number of all alleles for that gene in a population.

To calculate genotype frequencies in a population, divide the number of individuals with a particular genotype in a population by the total number of individuals in a population.

For example, consider the following population:

• 49 dark green frogs with the genotype DD
• 42 brown frogs with the genotype Dd
• 9 yellow frogs with the genotype dd

Our population of frogs is diploid, meaning that each frog inherits one allele for a gene from each parent, so each individual has two total alleles for a particular gene. Homozygotes have two copies of the same allele; heterozygotes have one copy of two different alleles. This means that when we calculate our allele frequencies, we have to account for the fact that each individual frog has TWO copies of an allele for each gene.

To calculate the frequency of the r allele, we need to add up how many total d’s we have in our population. Each frog with the Dd genotype has one d, each frog with the rr genotype has two d’s, and each frog with the DD genotype has zero d’s. Once we get the figure for the total number of d’s in a population, we need to divide that by total number of ALL the alleles. We have:

(Dd) + 2(dd) / 2(DD) + 2(Dd) + 2(dd)

Keep in mind that we are multiplying the genotypes by two because we are counting alleles, and each individual has two alleles for each gene. Plugging in our population numbers to the above formula gives us:

42 + (2) (9) / 2 (49) + 2 (42) + 2 (9) = 60 / 200 = 0.3  = 30%

The allele frequency for d is 30%. Since we have only two alleles and each frequency must add up to 100%, we know that our other frequency, D, is 70%.

We can also calculate genotype frequencies. For this exercise, we are counting the genotypes, NOT individual alleles, so we do not need to multiply by two as we did in the above example. If we want to calculate the frequency of dd, we need to find the number of dd individuals in the population, and divide by the total number of individuals in the population. So we have:

dd / DD + Dd + dd

9 / 49 + 42 + 9 = 9 / 100 = 0.09 = 9%

So we know that 9% of the individuals in our population have the dd genotype. If we calculate the frequency of one of the other genotypes, we can add them together and subtract from 100% to find the frequency of the third genotype.

Understanding how to calculate allele and genotype frequencies is vital to understanding the Hardy-Weinberg Equilibrium and being able to use the Hardy-Weinberg equation. Be sure you understand how to do these calculations before you move onto Hardy-Weinberg problems.

Related posts:

1. Important Biology Terms
2. Increasing Genetic Variation
3. Mendelian Genetics Basic Definitions

Related posts:

1. Population Genetics
2. Increasing Genetic Variation
3. Natural Selection