Evolution 1: How Does Life Change?

I. The Growth of Biological Thought

The idea of observing a natural phenomenon, proposing a testable hypothesis of causality to explain that phenomenon, and then testing that hypothesis to determine its validity has NOT been a formal method of inquiry throughout human history. Although processes of "trial and error" in solving mechanical problems almost necessitate at least an unconscious 'scientific' process, explanations of how the world IS, or why it is THIS WAY, were promoted by philosophers long before the tool of science developed. A very brief overview of the birth of science, as it relates to the study and explanation of life, is therefore important and instructive for understanding why Darwin's ideas were both revolutionary and yet - in some sense - historically anticipated.

A. Western Philosophy and Science

1. Plato (427-347 bc): Plato was trained in the Pythagorean school, and was more truly a pure philosopher rather than a 'naturalist', per se. As such, he was more impressed by generalizations rather than the vagarities and variation of individual experience; indeed, those variations that are so important to a true understanding of biology.

UNIVERSAL PHILOSOPHY (four dogmas)

- became the bedrock of western civilization for 2000 years! Ernst Mayr, one of the most important biologists of the 20th century, states: "It took more than 2000 years for biology, under the influence of Darwin, to escape the paralyzing grip of essentialism...the rise of modern biology is, in part, the emancipation from Platonic thinking".

2. Thomas Aquinas (1225-1274) - Aquinas presented the most formal logical argument for the existence of God, largely using the teleological argument of design. Events or objects that move towards a goal (have a purpose) a primary cause; Aristotle's "unmoved mover" is Thomas's Christian God. Thomas professed a "natural theology", which suggested that one could come to know more of God by studying "His works" (nature).

3. Astronomers: Copernicus, Kepler, Galileo, and Newton: 1543: The publication of Nicolaus Copernicus's De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) described the heliocentric model of the solar system, opposing the terracentric view supported by both the authority of the ancients (Ptolemy and Aristotle) and the Bible. Interestingly, Copernicus still depended on philosophical preferences over observation - he imagined that the planets travelled in circles, not ellipses, because the circle was a more perfect form. In short, as Francis Bacon (1561-1626) concluded, knowledge is incomplete; it is not all found in the Bible or the ancient texts, and new knowledge is discovereable by the process of empirical hypothesis testing.

Kepler (1571-1630) and Galileo (1564-1642) were the first great natural philosophers in the west to emphasize and use a mathematical, experimental approach to answer questions about the physical world. Galileo's observations of the moons orbiting Jupiter, and the full phases of Venus (impossible to explain with a Ptolemaic model of the solar system), provide empirical support for the copernican model. Galileo, however, was still wedded to the philosophical imperative that the orbits were perfect circles. Kepler attacked this view with voluminous data collected by he and his mentor, Tycho Brahe. By using elliptical orbits, Kepler was able to fashion the most precise predictive models of planetary orbits available. Galileo was a devout Catholic, but he famously said that the Bible tells a person "how to go to heaven, not how the heavens go". In this, and in his goad to "Measure what is measurable, and make measurable what is not so", he personifies the quantitative scientist. In his Dialogue Concerning the Two Chief World Systems (1632), he publicized the debate over these worldviews. The Roman-Catholic church brought him to trial for heresy, and he was ultimately forced to recant his support for the Copernican model before the Commissary-General of the Inquisition in Rome during 1633. He was ultimately placed under house arrest (confined to his home in Arcetri) for the remainder of his life.

Newton (1642-1727): In Newton's Philosophiae Naturalis Principia Mathematica (1687) we see the fulfillment of the scientific method - the formation of testable general theory. Newton constructed a general theoretical model of gravity and motion that became classical mechanics. This theory explained the motion of earthly objects (apples and projectiles falling) and the elliptical path of heavenly bodies. We see the culmination of Aristotle's imperative for both inductive and deductive reasoning - from specific observations one constructs a general hypothesis (inductive reasoning). Now, you use deduction to create a prediction that follows from that hypothesis (IF... THEN...). And of course, you subject your prediction to an experimental test in which falsification is possible. Although other natural philosophers (the term "scientist" was not coined until the 1830's) had been held in high regard by some nations, kings, or patrons, Newton was knighted - signifying the complete cultural acceptance of this new way of examining the physical world.

This "scientific revolution" had a curious effect on the study of life. Science emancipated physics, astronomy, and chemistry from theology by describing constant, natural, predictive laws and by describing the unchanging nature of elements (alchemy disproven). This confirmed the Platonic views of an unchanging universe created in perfection and left to run like a 'clockwork'. But what about our little corner of the universe? Was the Earth also static from 'the beginning", and just how long ago was that, anyway? Anglican Bishop James Ussher (1581-1656) applied logical rigor to the History of the Earth as revealed in the Bible and counted back the generations, determining that creation began at noon, October 23, 4004 b.c. (For a great book about calendars, read Stephen J. Gould's Questioning the Millenium). Thomas Burnet (~1635-1715) wrote The Sacred Theory of the Earth (1680), an account of earth's history as a literal account of Genesis 1. So, both concluded that the Earth was young, and most natural philosphers also concluded that the species were fixed since their creation.

4. Natural Theologians - Following on the thinking of Aquinas, there was a resurgence of Natural Theology to explicitly consider the theological import and relvance of the new observations made by science. The fundamental assumption was that God made things for a purpose, and that we might understand God's purpose if we more fully describe the creation and its operation. The most explicit reconstruction of these ideas was by theologian William Paley's Natural Theology: or, Evidences of the Existence and Attributes of the Deity, Collected from the Appearances of Nature (1802). Here he provides his teleological argument for the existence of God, using the allegory of the "watchmaker".

a. Carl Linne (1707-1778) - "Linneaus" (he latinized his own name) was the "great cataloguer", and he published the first edition of Systema Naturae in 1735. It wasn't until 1753, however, in Species Plantarum (Plant Species), that he formalized his prcedure for using two names to identify a species - the latin binomen (like Homo sapiens). The first name is the GENUS, and the second is called the 'specific epithet' that describes this species and distinguishes it from other similar species placed in the same genus. Linnaeus also grouped these genera (plural of 'genus') into orders, classes, and kingdoms based on additional morphological similarities. In plants, he relied on similarities in the reproductive structures, as many naturalists accepted that species are kinds that reproduce only with themselves. In the 10th edition of Systema Naturae (1758), he applied this system to all animals, too. The oldest scientific species names used today date from these two works. By the way, the word 'species' is both the singular and plural. There is no 'specie'. FYI. : )

b. Georges Louis Leclerc, Comte de Buffon (1707-1788) Buffon pulbished the first volume of his encyclopedic Histoire Naturelle in 1749. Ernst Mayr considered Buffon to be the foremost biologist of the 18th century, and Mayr wrote "it makes no difference which of the authors of the second half of the 18th century one reads - their discussions are, in the last analysis, merely commentaries on Buffon’s work. Except for Darwin and Aristotle, there has been no other student of organisms who has had as far-reaching an influence." He opposed the notion oif classification; if the species were separately created, then of what use was any classification system? He was aware of possibility of evolution but rejects it:
"Not only the ass and the horse, but also man, the apes, the quadrupeds, and all the animals might be regarded as constituting but a single family... If it were admitted that the ass is of the family of the horse, and different from the horse only because it has varied from the original form, one could equally well say that the ape is of the family of man, that he is a degenerate man, that man and ape have a common origin; that, in fact, all the families, among plants as well as animals, have come from a single stock, and that all the animals are descended from a single animal, from which have sprung in the course of time, as a result of progress or of degeneration, all the other races of animals. For if it were once shown that we are justified in establishing these families; if it were granted that among animals and plants there has been (I do say several species) but even a single one, which has been produced in the course of direct decent from another species; if, for example, it were true that the ass is but a degeneration from the horse - then there would no longer be any limit to the power of nature, and we should not be wrong in supposing that, with sufficient time, she has been able from a single being to derive all the other organized beings. But this is by no means a proper representation of nature. We are assured by the authority of revelation that all animals have participated equally in the grace of direct Creation and that the first pair of every species issued forth fully formed from the hands of the Creator." Histoire Naturelle (1753)

c. Jean Baptiste Pierre Antoine de Monet, Chevalier de Lamarck (1744-1829) - Initially a botanist and tutor to Buffon's son, he became an expert in invertebrates and the mollusc fossils of the Paris Basin. through this work, his initial belief in the fixity of species changed. In his culminating work Philosophie Zoologique (1809), he suggested that species change over time, climbing the Scala Naturae from simple forms to complex. The simplest forms were continuously produced by spontaneous generation, and species did not go extinct - they evolved into more complex forms over long periods of time. In addition to this vertical progression, they could also diverge as a consequence of responding to the environment and passing on the traits they acquired as a result of the action of this environment. Structures that were used in an environment would be elaborated (use and disuse), and then these newly elaborated structures were passed on to offspring (inheritance of acquired traits). Lamarck's evolutionary ideas explained the new observations of fossil diversity and apparent extinction. In Lamarck's mind, extinctions were theologically impossible, because he believed in a complete, harmonious creation by a benevolent creator. Why would a benevolent, purposeful creator let creations go extinct, and wouldn't the loss of some species render the perfection of the initial creation imperfect? For Lamarck, species changing into other species preserved the whole of creation. "May it not be possible that the fossils in question belong to species still existing, but which have changed since that time and have been converted into that similar species that we now actually find?" Lamarck is rightly regarded as the first "biologist" (he was the first to use the term) to propose a true evolutionary hypothesis, and a testable, naturalistic mechanism to explain it. Unfortunately, the mechanism was wrong.

B. Darwin's Contributions: The Origin of Species (1859)

1. Observations

a. The Earth is old: James Hutton (1726-1797): Hutton was the first great british geologist. He compared Hadrian's wall - which looks new but was 1600 years old (122 AD) - with natural rock outcrops that were strongly weathered. Hutton concluded that the natural outcrops must be 100's of times older. He also examined an important formation at Siccar Point, where one series of nearly vertical strata is overlain by another series of horizontal strata. This is now called an 'unconformity', and Hutton explained it as follows. Based on Steno's laws of superposition, the bottom vertical sediments must have been laid down first, and they must have been laid down horizontally. Ages must have passed between each deposit, as each turned to rock. Then, uplifts must have occurred to bend them into a vertical aspect. Long periods of erosion must take place to wear that uplift flat, followed by the long intervals of time needed to deposit the second horizontal series. Also, if erosion and deposition acted slowly (as current observations show), then it must have taken a really long time to erode mountains or build up marine deposits (White Cliffs of Dover). He concluded that this slow, 'uniformitarian' cycle of deposition, uplift, erosion, and deposition meant that the Earth was unfathomably old. Indeed, the cycle may mean that it's age might not be discoverable. In short, Hutton concludes, the Earth has "no vestige of a beginning, no prospect of an end."

b. Paleontology: Fossils show Patterns

Paleontology provided a variety of interesting patterns. First, there were extinct forms that were different from the species alive today. Although some earlier natural philosophers suggested that the creatures might still exist in some unexplored corner of the globe, that was a less satisfying hypothesis in the mid-1800's... most areas of the globe had been visited by Europeans. Also, the idea of extinction was repugnant to some people on theological grounds. If God had created a perfect world, then extinction renders that creation imperfect. Also, if species could go extinct since the creation, could species also come into existence since the creation? Just how dynamic was this system?

Darwin was impressed by two major patterns in the fossil record.

1. The major groups of animals accumulate in an orderly manner'. Everything is not represented at the beginning. In vertebrates, for instance, the fishes appear first, and exist throughout the rest of the record. Amphibians appear next, followed by reptiles, mammals, and birds. So it is not everything at the beginning, and it is not a replacement. Where did mammals come from? Spontaneous generation had been refuted, so Darwin knew that mammals had to come from other pre-existing animals. But the only completely terrestrial vertebrates before mammals were reptiles.

2. A second major pattern occurred within some lineages of similar organisms. Within some lineages, we seen orderly change in the size or characteristics of species in a geological sequence. For instance, consider the morphological patterns in a particular taxon (horses). Fossils in a stratigraphic sequence are similar, but often have traits that form a continuum...like the progressive loss of digits on the horse limb. And, with each innovation, there are often radiations - a "spurt" in the number of species that show this new trait. And finally, these species in recent strat are more similar to living ('extant') species than the species found in deeper, older strata. So, many of these transitional sequences terminate in living representatives.

c. Comparative Anatomy shows patterns realted to the environment:

Homologous Structures
    Although having a different outward "look" and although used for different purposes, they have an underlying similarity in structure - forelimbs of vertebrates all have one long upper arm bone, two lower arm bones, a bunch of wrist bones, and five digits. Darwin saw the similarity in structure as important. An engineer builds different things for different purposes - cars, boats, and airplanes are structurally DIFFERENT. Here, however, it seemed as if one basic structure was modified for different uses. Darwin knew why siblings in a family were similar - they had the same parents (ancestors). He reasoned that these structural similarities in different species might be due to the same principle - common ancestry. Also, he observed a correlation: Different uses correlated with different environments. Could this correlation be causal?

Analogous Structures
    Organisms in the same environment often have a similar outward structure or body plan. For example, flying animals all have an aerodynamic wing that is wider at the front than at the rear. However, the wings of differnt animals are differnt in underlying structure. Bats have fingers that support the membraneous wing, whereas birds lack fingers and the body of the wing consists of feathers. Insect wings don't involve the limbs at all (even though they have 6!). Again, Darwin observed this correlation with the environment: similar use (and outward structure) in similar environments. Could this correlation be causal?

Vestigial Organs
   These are organs that have no function in one organism (where they are 'vestigial') but they do function in other organisms. So, some whales have hip bones, but no legs. Why do they have these bones? Darwin was struck by the IMPERFECTIONS in nature, as much as the adaptations. Why do men have nipples? Why do we have muscles that wiggle our ears? Why do we have strong muscles in the front of our stomach, which are not "load-bearing", and weak muscles at the base of our abdomen (which rupture in a hernia)? This is a reasonable relationship in a quadraped, but not in a biped. Why do we have tail bones, but no external tail? Again, these are NOT well-designed features. In fact, attributing these imperfect designs to a perfect creator could be interpreted as heretical.  However, when we see them working in OTHER species, it suggests that maybe we inherited them from common ancestors where they DID serve a function. As a scientist, Darwin was trying to explain ALL the data (adaptations and imperfections), he was not simply bringing forward only the data that supported a preferred position (design).

d. Species distributions show patterns realtd to the environment:
    Under similar environmental conditions, we find different species filling similar ecological niches.  Outward 'form' correlates with ecological niche (role) across entire communities. So, in Australia, marsupials fill the role of dog-like predator, cat-like predator, burrowing animal, ant-eater, etc. These same roles are filled by outwardly similar placental mammals in South America. However, the similarity between a wolf (placental) and a Thylacine (marsupial - the 'tasmanian wolf') are strictly ANALOGIES. Their underlying structure shows them to be quite different - a wolf is more similar to a ground hog (both placentals) in underlying structure than to a thylacine.

    Islands often have fewer species than a mainland - even a patch of mainland the same size. As such, the patterns and interactions are often simpler to describe and understand. For both Darwin and Alfred Russel Wallace (the other independent author of the theory of evolution by natural selection), the study of islands was critical in to the development of their ideas.

1. Distance correlates with the uniqueness of the inhabitants: the animals on the Fauklands are the same species as on the mainland, but the Galapagos fauna is composed of unique species, found nowhere else:

"The natural history of these islands is eminently curious, and well deserves attention. Most of the organic productions are aboriginal creations, found nowhere else; there is even a difference between the inhabitants of the different islands; yet all show a marked relationship with those of America, though separated from that continent by an open space of ocean, between 500 and 600 miles in width. The archipelago is a little world within itself, or rather a satellite attached to America, whence it has derived a few stray colonists, and has received the general character of its indigenous productions. Considering the small size of the islands, we feel the more astonished at the number of their aboriginal beings, and at their confined range. Seeing every height crowned with its crater, and the boundaries of most of the lava- streams still distinct, we are led to believe that within a period geologically recent the unbroken ocean was here spread out. Hence, both in space and time, we seem to be brought somewhat near to that great fact -- that mystery of mysteries -- the first appearance of new beings on this earth."  The Voyage of the Beagle - Darwin (1839).

    2. The Galapagos fauna:
        - It was related to american fauna, yet different: the types of animals are new world animals.... there are iguanas like the green iguana of Central and South America, but the iguanas are different species. So, darwin describe it as " a world within itself, or rather, a satellite of the Americas" .... it was different, but more like the American fauna than any other...(no chameleons, for instance, which are old world lizards...)

        - It was dominated by dispersive forms. This is critical. The communities are dominated by reptiles, birds, and marine mammals. All of these organisms could MIGRATE to the islands from the mainland. (Terrestrial mammals don't migrate as well as terrestrial reptiles over open ocean. Throw a reptile in cold salty water, and: 1) its metabolism slows down (its cold), so 2) its demand for food and water decline; and 3) its scales protect it against water loss... which is why reptiles do well in the desert, too. Throw a mammal in cold salt water, and it's going to have a VERY tought time: 1) the temperature gradient between its warm body and the cold ocean is very large - in order to maintain its high body temperature against this gradient, it's metabolism has to INCREASE (to produce more heat to compensate for the heat lost to the environment). This increased metabolic demand will INCREASE the need for food and water... that's probably in pretty short supply in the open ocean; and 2) water is lost quickly from the skin to the salty ocean once the fur is wet... so, mammals are more likely to starve or die of exposure than reptiles.

       - So, the islands are dominated by dispersive forms, and this suggests they came from America. But if they came from America, WHY ARE THEY DIFFERENT SPECIES THAN THOSE IN AMERICA? They must have changed since their arrival.

- There are even differences between species on different islands. On the 14 species of finches - "Seeing this gradation and diversity of structure in one small, intimately related group of birds, one might really fancy that from an original paucity of birds in this archipelago, one species had been taken and modified for different ends." The Voyage of the Beagle - Darwin (1839) VIDEO

2. Argument For Evolution as a Historical Fact:

Premise 1: Species that are alive today are different from those that have lived previously.
Premise 2: Spontaneous Generation is refuted, so organisms only come from other organisms.
Conclusion 1: Thus, the organisms alive today must have come from those pre-existing, yet different, species.
Conclusion 2: There must have been change through time (evolution).
Conclusion 3: The fossil record, vestigial organs, and homologies are all suggestive of descent from common ancestors.

Below, the figure from The Origin of Species that shows Darwin's idea of descent from common ancestors.

So, if species do change over time (evolve), the next question is "How?" How does this change occur?

3. How does change occur? Natural Selection

(Know this.  Understand it.  You WILL be asked to outline NS in this very form.)

P1: Populations over-reproduce (Malthus)

P2: resources are finite (Malthus)

C1: Eventually, a population will grow until it becomes limited by its resources. At that time, their will be a "struggle for existence" and most offspring produced will die. (Malthus)

P3: Individuals in a population vary, and some of this variation is heritable (Darwin - observations and animal/plant breeding)

C2: Variations will not have the same probability of survival and reproduction in a particular environment; those well-suited to the environment will be more likely to survive and reproduce than others, passing on the genes for these adapted traits. There will be "Differential Reproductive Success" (Observations, breeding).

C3: Over time, adaptive traits will accumulate and the characteristics in a population will change. This is lineage evolution. (Like change in horse toes in a sequence of fossil species, or like the change in the chihuahua lineage from the ancestral wolves).

Corollary: Two sub-populations, separated in different environments, would be selected for different traits and may subsequently lose the capacity to interbreed. At this point, they are different biological species. This is Speciation and Radiational Evolution. (like the production of different Finches, mockingbirds, etc. on different islands in the galapagos, and like the radiation of St. Bernards AND chihuahua's, which diverged from one another over time).
 

Darwin here provides a natural explanation for why purposeful structures and behaviors occurs in nature. Through some process unknown to him, variation arises in natural populations. These varieties differ in terms of functional efficiency in a common environment; so some improving an organisms probability of surviving and mating than others. Organisms with these beneficial traits will leave more offspring, and the frequencies of these beneficial characteristics will increase through time - much as humans select for smaller and smaller dogs. He ends The Origin of Species (1859) like this:

"It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; Inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external conditions of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms. Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved". - The Origin of Species (Darwin 1859).

II. Modern Evolution: Population Genetics

A. Overview

Sources of Variation                                                Agents of Change
MUTATION:
-New Genes:                                                           Natural Selection
     point mutation                                                    Mutation (polyploidy can make new species)  

RECOMBINATION:
- New Genes:
    exon shuffling
-New Genotypes:
    -crossing over
    - independent assortment

In the early 20th century, at the same time that T. H. Morgan was studying mutations and creating linkage maps, other biologists were considering the evolutionary implications of this new knowledge regarding genetic variation. They appreciated that individuals do not evolve - evolution is a process that occurs at the population level. For example, as a consequence of differential reproductive success among individuals in a population, the range of phenotypes and their relative frequencies in the population will change over time. Individuals are born, life, reproduce (maybe) and die. As a result of passing on their genes at different frequencies, the genetic structure of the population changes over time (evolution). Two biologists, G. Hardy and W. Weinberg, constructed a model to explain how the genetic structure of a population might change over time.

Their model begins by constructing an 'equilibrium' model - a model of what the gentic structure would look like, and how it would behave, if there was NO CHANGE over time. (We can liken this to a "stitstical null hypothesis of no effect"). Then, an actual population is compared to this model, so see whether the population is evolving or not.    

B. The Genetic Structure of a Population

Our first step is to describe the genetic structure of a population; we need to do this before we can model what it would do over time. The genetic structure of a population is defined by the gene array and the genotypic array. To understand what these are, some definitions are necessary: 

1. Definitions:

                - Evolution: a change in the genetic structure of a population
                - Population: a group of interbreeding organisms that share a common gene pool; spatiotemporally and genetically defined
                - Gene Pool:  sum total of alleles held by individuals in a population
                - Genetic structure: Gene array and Genotypic array
                - Gene/Allele Frequency: % of alleles at a locus of a particular type
                - Gene Array: % of all alleles at a locus: must sum to 1.
                - Genotypic Frequency: % of individuals with a particular genotype
                - Genotypic Array: % of all genotypes for loci considered; must = 1.          

2. Basic Computations - Determining the Genotypic and Gene Arrays:

The easiest way to understand what these definitions represent is to work a problem showing how they are computed.               

Consider the population shown to the right, in which there are 70 AA individuals, 80 heterozygotes, and 50 aa individuals. We can easily calculate the Genotypic Frequencies by dividing each of these values by the total number of individuals in the population. So, the Genotypic Frequency of AA = 70/200 = 0.35. If we account for all individuals in the population (and haven't made any careless math erros), then the three genotypic frequencies should sum to 1.0. The Genotypic Array would list all three genotypic frequencies: f(AA) = 0.35, f(Aa) = 0.40, f(aa) = 0.25. A Gene Frequency is the % of all genes in a population of a given type. This can be calculated two ways. First, let's do it the most obvious and direct way, by counting the alleles carried by each individual. So, there are 70 AA individuals. Each carries 2 'A' alleles, so collectively they are 'carrying' 140 'A' alleles. The 80 heterozygotes are each carrying 1 'A' allele. And of course, the 'aa' individuals aren't carrying any 'A' alleles. So, in total, there are 220 'A' alleles in the population. With 200 diploid individuals, there are a total of 400 alleles at this locus. So, the gene frequency of the 'A' gene = f(A) = 220/400 = 0.55. We can calculate the frequency of the 'a' alleles the same way. The 50 'aa' individuals are carrying 2 'a' alleles each, for a total of 100 'a' alleles. The 80 heterozygotes are each carrying an 'a' allele, and the 140 AA homozygotes aren't carrying any 'a' alleles. So, in total, there are 180 'a' alleles out of a total of 400, for a gene frequency f(a) = 180/400 = 0.45. The gene array presents all the gene frequencies, as: f(A) = 0.55, f(a) = 0.45.

There is a faster way to calculate the gen frequencies in a population than adding up the genes contributed by each genotype. Rather, you can use these handy formulae:

f(A) = f(AA) + f(Aa)/2

f(a) = f(aa) + f(Aa)/2

So, to calculate the frequency of a gene in a population, you add the frrequency of homozygotes for that allele with 1/2 the frequency of heterozygotes. In our example, this would be:

f(A) = 0.35 + 0.4/2 = 0.35 + 0.2 = 0.55

f(a) = 0.25 + 0.4/2 = 0.25 + 0.2 = 0.45

Wow... that's alot faster.

C. The Hardy-Weinberg Equilibrium Model

1. Goal:

The goal of the "Hardy-Weinberg Equilibrium Model" (HWE) is to describe what the genetic structure of the population would be if NO evolutionary change occurs. Working independently, Hardy and Weinberg realized that the gene frequencies in a population will NOT change - will remain in EQUILIBRIUM - if the following conditions are met:

- there is random mating

- no selection

- no mutation

- no migration

- and the population is infinitely large.

And, they realized that a population will reach an equilibrium in GENOTYPIC frequencies, too, after one generation of meeting these expectations (and for as long as it does so), a population will NOT EVOLVE. Let's see how they came by these conditions.

2. Example:

Consider the initial population, with a genotypic array as shown. The gene frequencies are:   

A = 0.4 + (0.4/2) = 0.6

a = 0.2 + (0.4/2) = 0.4                

Now, consider this gene pool in which 60% of the alleles are 'A' and 40% of the alleles are 'a' (as defined by the gene frequencies).

So, now we employ the HWE model. IF the population mates at random, then we can use the product rule to determine the probability of any two gametes coming together. The propability that and 'A' sperm fertilizes an 'A' egg = 0.6 x 0.6 = 0.36. And of course, this is the only way to produce an 'AA' zygote. So, the frequency of 'Aa' zygotes (the F1 offspring) produced by this population should be 0.36. Likewise, the probability that an 'a' sperm fertilizes an 'a' egg = 0.4 x 0.4 = 0.16. And again, this is the only way to make an 'aa' zygote, so the total frequency of 'aa' zygotes in the F1 will be 0.16. Now, there are two ways to make an 'Aa' zygote: an 'A' sperm can fertilize an 'a' egg (probability = 0.6 x 0.4 = 0.24), and an 'a' sperm can fertilize an 'A' egg (also with a probability of 0.4 x 0.6 = 0.24). So, the total frequency of Aa zygotes in the F1 will be 2 x 0.24 = 0.48. If we generalize, and let f(A) = p and f(a) = q, then the genotypic frequencies under HWE can be calculated as: f(AA) = p², f(Aa) = 2pq, and f(aa) = q².

Now, of course, these calculations will only be true IF the population mates at random. AND, they will only be true if there is no mutation. If 'A" alleles are mutating into 'a' alleles, then the gene frequencies will not be 0.6 and 0.4, and calculations based on these numbers will not be correct. So, we must assume NO MUTATION. Likewise, we can't have any migration; we can't have 1000 AA individuals migrate into our population, or that would change the gene frequencies, too; and our predictions based on frequencies of 0.6 and 0.4 would be incorrect. So, we must assume NO MIGRATION, too.

So, at this point we have zygotes at the frequencies shown in the "Genotypes, F1" row. In order for there to be no change in the genetic structure of the population, there must be NO SELECTION. In other words, all genotypes must have the same probability of survival and reproduction. Only then will they contribute gametes at frequencies of p = 0.6 and q = 0.4. (If there were selection, and if AA individuals were the only zygotes to survive to reproeuce, for instance, then the gene frequencies would change and our predictions based on frequencies of 0.6 and 0.4 would not be correct).

And finally, this model will only be explicitly true for populations that are infinitely large: because that is the only time when we can be garaunteed that predictions based on random chance will be exactly met. (Think about it this way... suppose I give you a coin that is absolutely perfectly balanced at the molecular level. It IS PERFECTLY BALANCED. And suppose I ask you, "how many times do you have to flip that coin to be ABSOLUTELY SURE of producing a 50:50 ratio of heads to tails? Well, if you only flip it four times, you know that, just by chance, you would often get 3 heads and a tail or 3 tails and a head. And even if you flip it 10,000 times, you might get 5001 heads and 4999 tails, even though the coin is perfectly balanced. To be absolutely garaunteed that the predictions of this probabilisitic model will be met exactly, you must flip the coin an infinite number of times. Obviously, this is a theoretical constraint because no population is infinitely large. But this is a theoretical model of no change, so we can employ theoretical expectations. The same is true of our 'expectation' of a perfectly balanced coin - this expectation will only be met, for sure, in an infinitely large sample. Yet we continually employ that expectation for a perfectly balanced coin.

So, that is why these assumptions exist. It is only when these are met that a population will not evolve. Wow. That should seem rather amazing. It is only when these assumptions are ALL met that a population WON'T change. If any of these assumptions is not met, a population's genetic structure WILL change... and that is evolution. So, from this analysis, we should expect populations to evolve - it is only under a rare combination of events (no, mutation, no selection, no migration, random mating, and an infinitiely large population) that evolution WON'T happen.

3. Utility                

- If no real populations can explicitly meet these assumptions, how can the model be useful?  For instance, no real population is infinitely large, so how can the model be useful?  We use it for COMPARISON.  This model describes what the genotypic frequencies should be IF the population was in equilibrium.  If the real genotypic frequencies are not close to these expectations, then the population is not in HWE.... it is evolving. And if a population is not in HWE, then the population must be violating one of the assumptions of the HWE model.  Think about that.  The HWE is only 'true' if the assumptions are being met.  If your real population differs from the model, then one of the assumptions must not apply to your real population.  This narrows your focus on WHY the real populations isn't behaving randomly... and it might identify WHY the population is evolving.... which is a biologically interesting question.                

- Again, the coin analogy applies.  No REAL coin is probably exactly perfectly balanced. But, if I give you a coin and ask you how balanced it is, you flip it a few times and compare its behavior to WHAT YOU WOULD EXPECT FROM A PERFECT COIN (50:50 RATIO). Even though a perfectly balanced coin does not exist, we can use this theoretical model as a benchmark, to compare the behavior of real coins.  Many real coins act in a manner that is consistent enough with the expectations from a perfectly balanced coin that we are willing to use them AS IF they were perfectly balanced.   The Hardy Weinberg Equilibrium Model is the same... it is a model of no change against which we can measure real populations. 

If HWE can be assumed, then the frequency of recessive diseases can be assumed to equal q2, and the frequency of carriers in the population can be estimated like this:

1) The frequency of hemachromatosis worldwide is 1/450. If we assume that hemochromatosis is caused by a recessive gene (q), and if we assume the population is in HWE with respect to this trait, then q² = 1/450 = 0.002. So, we take the square-root of both sides to find q = 0.047. Well, if q = 0.047, and if p + q = 1, then p = 1 - 0.047 = 0.953.

2) If q = 0.047 and p = 0.953, then the frequency of heterozygous carriers = 2pq = 0.09. So, we estimate that 9% of the population are carriers.

Now, you might say, "but we just determined that HWE would be unusual; so why would we assume it is true for a given gene?" Well, a deleterious gene has already been largely weeded out of a population, so selection against the few alleles that are left is really weak. Indeed, this condition may not influence reproductive success, anyway (NO SELECTION). In addition, we don't select mates based on whether they have hemochromatosis (I bet you NEVER asked your date if they have hemochromatosis, for example!!), so we can assume there is RANDOM MATING in the population with respect to this trait. And although the human population is not infinite, it is really big (6.9 BILLION), so the effect of sampling error is probably very small. Mutation is very rare, so the effects of mutation are likely to be very small. And if we are making an estimate based on the whole human population, then there can be no 'migrants' coming in from somewhere else (Martians?). So, in some cases, we can reasonably assume a population might be in HWE for a given gene. Of course, we could be wrong... and we would test that prediction by sampling individuals in the population and determining the frequency of heterozygotes genetically. But at least we would have a working hypothesis.

 Study Questions:

1.  What is Platonic essentialism (or 'idealism') and how did it hinder the consideration of evolutionary ideas?

2. What contributions did Copernicus, Kepler, Galileo, and Newton make to our understanding of the solar system? Frame these in the context of the scientific method.

3. What counter-intuitive effect did the renaissance have on the development of modern (evolutionary) biology?

4. What is the principle of Natural Theology, as professed by Aquinas and Paley?

5. Why did Lamarck conclude that species change over time, and what philosophical dilemma was he trying to solve?

6. What is "uniformitarianism" and how was it important to the development of Darwin's ideas?

7. What observations did Hutton make, and what did he conclude from these observations?

8. What two patterns occur in the fossil record that impress Darwin regarding the hypothesis of evolution and common descent?

9. What are homologous structures?  What correlations occurs with the environment?

10. What are analogous structures?  What correlation occurs with the environment?

11. What are vestigial structures, and why were they so important to Darwin's refutation of Paley?

12. How did Darwin explain the existence of 'convergent communities"?

13. The Galapagos are dominated by many unique species of reptiles, birds, and marine mammals. What did this non-random assemblage suggest to Darwin about their origin, and how was evolution implied?

14. Why were the mockingbirds so critical to Darwin's ideas about the production of new species?

15. How did Darwin use the comparative method and observations of 'artificial selection' to produce the theory of 'natural selection'?

16. How were Malthus's observations and conclusion rlevant to the development of Darwin's theory?

17. Outline the theory of natural selection as an argument, with three premises, 3 conclusions, and a corollary.

18.  What are the five assumptions of the Hardy-Weinberg Equilibrium Model?

19.  Consider the following population:

• - calculate the genotypic frequencies.
• - calculate the gene frequencies
• - calculate the HARDY WEINBERG EQUILIBRIUM frequencies.

20. If the HWE model does not describe any real population, how can it be useful?