Bigfoot: Myth or Legend? Examining the Biological Evidence of a Cross-Cultural Phenomenon (Part 1)

Sasquatch.  Yeti.  Abominable Snowman.  Boqs.  Sisimite.  Dwendi.  Shiru.  Didi.  Agogwe.  Mahula.  Pedek.  Mapinguari. 

Or simply put, Bigfoot. 

All of these names are used to describe a creature that has captured the imaginations of people from around the globe.  Bigfoot creatures are described in many cultures around the globe, ranging from North American to Australian Indigenous cultures, and evidence of their existence has been collected from the American and Canadian Northwest to the Himalayan Mountains of Nepal.  While cultural and geographical descriptions do vary, similar characteristics of these creatures have been identified.  Bigfoot creatures are described as being anywhere from four to eight feet tall, extremely hairy, and exhibiting human and ape-like characteristics.  Despite large quantities of cultural evidence on the topic, there remains a debate regarding the very existence of these creatures.  Today’s blog post is dedicated to a physical anthropological discussion on the topic of Bigfoot creatures and the biological evidence that exists.  These pieces of evidence fall into three broad categories: fossil evidence, natural evidence, and modern evidence, and each of these will be thoroughly discussed as a means of determining if Bigfoot creatures can viably exist in today’s world.  This blog post focuses on the fossil evidence.

Fossil Evidence

Due to Bigfoot’s human and ape-like characteristics, many individuals, including some scholars, believe that Bigfoot creatures are hybrids that evolved from Hominid ancestors but missed an evolutionary step in becoming fully human as we know and understand Homo sapiens to be both culturally and biologically today.  As such, several Hominid ancestors have been identified as potential candidates as the founding species of modern Bigfoot creatures.  These Hominid ancestor candidates include Gigantopithecus, Paranthropus/Australopithecus robustus, Homo erectus, and Homo neanderthalensis. 

Artistic rendition of Gigantopithecus (Google Images)

 Gigantopithecus is a Hominid species that was discovered by Professor von Koenigswald, who discovered two abnormally shaped molars in China.  He later attributed them to what he coined as the Gigantopithecus species.  Other diagnostic specimens have since been discovered to support the existence of the species, including several thousand molar teeth and four mandibles (lower jaws).  From these specimens, scholars have inferred that Gigantopithecus is a large bodied Hominid, ranging in size from five to ten feet tall.  Scholars have further inferred that Gigantopithecus is the ancestor to Bigfoot, although some have gone so far to say that Bigfoot represents a living Gigantopithecus.

There are, however, serious problems with this hypothesis.  The first of which is that Gigantopithecus as a species is problematic based on the types of fossil remains found thus far.  As mentioned above, Gigantopithecus is represented only by teeth and mandibles, but no other cranial or postcranial remains have been discovered or associated with this species.  Current descriptions of Gigantopithecus are therefore suspect as they are based on minimal skeletal evidence, and it is unclear if postcranial descriptions of Gigantopithecus are very accurate.  This would be akin to looking at the paw size of certain breeds of dogs to determine their overall body size.  This is considered a “standard” of determining adult size in puppies as the idea is that big paws translates to large sized dogs, which makes sense as the feet need to be able to hold up the weight of the dog’s body and therefore a correlation between large body size and large paws is reasonable, but this is problematic as several species of dogs have disproportionately large or small feet for their overall adult body size.  Collies are large breed dogs who have very small feet as compared to their overall body size, and bull dogs are small breed dogs who have very large feet as compared to their overall body size.  While the evidence of large teeth and large mandibles would insinuate large body size (as the body has to support the weight of large heads) this may not necessarily be the case, particularly when we realize that human children have larger heads relative to their body sizes due to Homo sapiens having large brains.  Without further skeletal evidence, the current descriptions of Gigantopithecus are suspect.  

Artistic depiction of Paranthropus/Australopithecus robustus (Google Images)

Paranthropus/Australopithecus robustus is an established Hominid species that existed 2.2 to 1.5 million years ago and has been found across Africa and potentially in the Middle East.   Paranthropus/Australopithecus robustus  is characterized by exaggerated cranial features, including jaws, molar teeth, and defined sagittal crest, and robustus also demonstrates rudimentary bipedal walking skills.  It is these morphological and locomotive features that scholars cite as evidence of robustus being an ancestor of the modern Bigfoot creature as the characteristics between the two species are extremely similar. 

The issue with the claim that Paranthropus/Australopithecus robustus is an ancestor to modern Bigfoot creatures is that we have evidence that demonstrates that robustus gave rise to other evolutionary advanced Hominid species.  It makes little sense that an evolutionarily stunted descendent of robustus would have survived among these far more evolutionarily advanced descendents.  Also, there is no evidence to suggest such a stunted descendent existed, further complicating the support of this hypothesis of robustus as a viable ancestor to Bigfoot.

Artistic depiction of Homo erectus (Google Images)

Homo erectus is another established Hominid species with a far wider geographical distribution than that of Paranthropus/Australopithecus robustus with Homo erectus specimens having been found throughout the African and Asian continents.  Homo erectus is morphologically characterized by have a large skull and brain, heavy brow ridges, prognathous face, sloping forehead, elongated profile, sagittal keel, and occipital torus (a bony ridge at the back of the skull).  Homo erectus is also associated with having various cultural developments, including the use and manipulation of fire, the ability to create uniform stone tools, and cooperation in hunting endeavors.  There is also a debate amongst scholars regarding whether or not erectus had a spoken language.  Morphologically, erectus had the capabilities to speak but it is unclear if any formal language was developed by the species.

The morphological and geographical distribution evidence supports the hypothesis of erectus being an ancestor of Bigfoot, but the cultural evidence negates this possibility.  Because Homo erectus had such advanced cultural developments it makes little sense that subsequent descendants would abandon these cultural developments as they were meant and did assist in survivability of the species.  Among all of the reports on Bigfoot none indicate Bigfoot is involved in cultural developments of any sort, particularly the ones present among ancient Homo erectus species.

Artistic depiction of Homo neanderthalensis (Google Images)

The final ancestral candidate is Homo neanderthalensis, also commonly known as the Neanderthal.  Neanderthals existed across Europe, Asia, and the Middle East and are morphologically characterized by very large craniums and brains, sloping foreheads, occipital buns (bulging projection at the back of the skull), pronounced but slightly smaller brow ridges, prognathic faces, broad noses, receding chins, and wide set eyes, as well as being short and broad chested, allowing them to be very well adapted to cold environments.  Neanderthals are also associated with several cultural innovations,including intentional burial of the dead and care of the ill and injured. 

Again, while the geographical distribution and morphological evidence support the hypothesis that this species was an ancestor of Bigfoot, there is plenty of evidence to refute this hypothesis.  Again, the cultural innovations associated with Neanderthals run counter to what is culturally known (or lack thereof) of Bigfoot creatures.  Also, comparisons of Neanderthal and Bigfoot prints demonstrate that these two species are morphologically different, further refuting the idea that Neanderthal could give rise to Bigfoot as a possible descendent as it makes little sense that morphological changes in descendents would relapse to being less efficient.

While supporters of the existence of Bigfoot have suggested potential ancestors of Bigfoot, these ancestors are problematic candidates, and the evidence does not conclusively support any one candidate as the Bigfoot ancestor.  Furthermore, the most accepted candidate, Gigantopithecus, is very problematic due to the lack of fossil evidence to demonstrate its large size, which is the key piece of evidence that it used to support its place as the ancestor, or post-cranial remains.  As such, the current evidence to support an ancestor of Bigfoot is weak, and if there is no viable ancestor then the presence of a descendent is extremely questionable.

Works Cited

Bryne, Peter.  1975.  The Search for Big Foot: Monster, Myth, or Man?  Acropolis Books, Washington.

DeSilva, Jeremy.  2010.  "Revisiting the 'Midtarsal Break'."  American Journal of Physical Anthropology 141: 245-258.

Green, John W.  1968.  On the Track of the Sasquatch.  Cheam Publications, Agassiz, B.C.

Green, John W.  1978.  Sasquatch: The Apes Among Us.  Hancock House, Seattle.

Harrison, Guy P.  2012.  50 Popular Beliefs that People Think Are True.  Prometheus Books, Amherst.

Highpine, Gayle.  2000.  “Traditional Attitudes Toward Bigfoot in Many North American Cultures.” Bigfoot Encounters.

Hunter, Don and Rene Dahinden.  1975.  Sasquatch.  New American Library, New York.

Landau, Joel.  2014.  ”Man Who Claims He Killed Bigfoot Releases More Pictures of the Mythical Creature.”  Daily News.

Napier, John R.  1973.  Bigfoot: The Yeti and Sasquatch in Myth and Reality.  Dutton, New York.

No Author.  2014.  “10 Reasons Why Bigfoot’s a Bust.”  Discovery News.

No Author.  “Yeti.”  New World Encyclopedia.

No Author.  “Yeti History.”  TheYetiFest.com

Olson, Grant.  2014. “Hunter Confesses that Bigfoot Body is a Fake…Again.”  Daily American.com

Prigg, Mark.  2014.  “Moo-ve along, Bigfoot, nothing to see here: Genetic test of 30 different hairs claimed to be from sasquatch finds they are from bears, wolves and even a COW.”  Daily Mail. 

Viegas, Jennifer.  2014.  “’Bigfoot’ Cases Solved, But  A New Mystery Surfaces.”  Discovery News.

Spotlight on Students: Gender & Sexuality Comparisons (Mohave & American Cultures)

The following is a student post based on an assignment in Anth 101: Introduction to Cultural Anthropology where students were to compare and contrast gender norms and values between a different culture to American culture.  This student took the assignment a little further in this unique piece.

By Monica Kalmen

This essay discusses the alyha and hwame gender norms of the Mohave culture and how they compare to that of today’s gender norms for the equivalent in American culture. The alyha and the hwame were names given to the men and women, respectively, of the Mohave culture that stepped into the traditional role of the opposite sex (Leclerc 343). Although there are some similarities between the cultures, this paper focuses mainly on the differences between the gender norms of each culture and illustrates how culture shapes societies’ ideas of what is and is not acceptable behavior. Cultural views are often shaped by economic needs and spiritual beliefs. Differences in such show how the cultural views of the Mohave resulted in an overall acceptance of gender variants and how today’s American cultural views result in an overall intolerance of gender variants.
       
The Native American Mohave culture accepted the alyha and hwame into their society and even had customs and traditions surrounding them. One elderly native Mohave was quoted as saying, “From the very beginning of the world it was meant that there should be [transgenders], just as it was instituted that there should be shamen. They were intended for this purpose” (Devereux 501). The Mohave believed gender variants were normal and had been around from the start of time. They believed these types of people were created for a purpose. The alyha and hwame used to be initiated into their desired gender role when they were pre-adolescent (Devereux 507). They were taken seriously and formally granted placement in society as the opposite sex. The Mohave’s social participation in the initiation of individuals wanting to be the opposite sex showed how the alyha and hwame were included by society and not segregated from it because of their differences. The alyha and hwame both practiced rituals of the opposite sex once married; which included the alyha replicating menstruation and sometimes birth and the hwame ignoring their menstruation (Devereux 513). Both the alyha and hwame fully participated in the rituals of their desired gender. Anatomy did not exclude them from participating, along with the rest of the Mohave society, in the customs of their chosen gender roles. The alyha and hwame were not segregated from Mohave society or considered abnormal for wanting and living their lives as the opposite sex.
       
The Mohave cultural views resulted in an acceptance and inclusion of gender variants into Mohave society, whereas the United States cultural views result in discrimination and prejudice against such individuals. “As a rule,” according to Devereux, “[initiated alyha and hwame] were not teased” (518). The Mohave did not single these types out for ridicule. The alyha and hwame did not frequently face discrimination, prejudice, or banishment. By contrast, in the United States today, “[transgendered people are often subjected to ridicule and controversy” (“Transgendered People” n.pn). There is less acceptance of transgendered people in American culture than there was in Mohave culture. A lack of understanding about transgendered people in today’s American culture is apparent in the result of  “controversy” surrounding such people. Transgendered people also face nationwide discrimination when it comes to health care, housing, and employment (Jost n.pn). Individuals choosing to take on the role of the opposite sex in today’s culture struggle to be included in society. Worse than being ridiculed, they face being cut off from the basic necessities needed to sustain life. The Mohave believed that “temperamental compulsions” could affect people without it being their fault  (Devereux 518). The Mohave did not think something was seriously wrong with an individual wanting to be of the opposite sex. They did not think that that individual needed a cure or fix. Transgendered people in the United States today however are often considered “mentally-ill” and told to seek therapy for their condition (Jost n.pn.). Frequently views in today’s American culture see individuals wanting to be the opposite sex as inferior and sick. These views hold that someone who is still transgendered is not taking care of their mental illness. Besides being thought of as mentally-ill, transgenders face religious persecution from those who believe that such individuals are “violating the will of God” (“Transgendered People” n.pn.). Far from being accepted, transgenders in America often face segregation and exclusion. The alyha and hwame were accepted as is and incorporated into their society whereas today’s transgenders in America are often excluded and discriminated against.
       
Some of the reasons for the differences between American and Mohave cultural views have to do with Mohave spirituality and economic needs as well as popular American religion and today’s  commonly held view that transgenders are mentally-ill. According to Leclerc, “[t]he spiritual systems in place in the Mohave culture provided a context whereby a gender variant identity was validated and given meaning” (344). Mohave spirituality accounted for people such as the alyha and hwame. The Mohave spiritual beliefs allowed the hwame and alyha to be accepted within their society. Popular American religion such as Christianity declares that ‘humans were created as gendered beings’ and frequently results in the discrimination of transgenders, such as being fired from a job after coming out publicly as transgender (Bailey 19). These popular religious beliefs do not provide a means for believers to accept or understand gender variant individuals. Because these beliefs dictate American cultural views, individuals outside the norm face prejudice and persecution.   In Native American Mohave culture, both the alyha and hwame were often powerful shamans (Devereux 516). The alyha and hwame frequently held admirable positions in society and were respected. Rather than lowering their social status, their preferences served to fit them into positions of spiritual power. In the United States however, it was not until May of 2013 when the new Diagnostic and Statistical Manual for Mental Disorders came out with the revision of gender identity disorder that transgenders were no longer classified as mentally-ill (Schwartzapfel n.pn.). Up until very recently, gender variants were stigmatized as being mentally-ill and needing psychological treatment to fix them. Both religion and medicine have persecuted gender variants, leading to their widespread mistreatment across the modern United States. Unlike the stigmatized gender variants in the United States today, the alyha and the hwame played important roles in their society including domestic roles. According to Devereux, “[t]he essential adverturesomeness of the Mohave character combined with their completely humoristic attitude of sex,...along with economic comfort and convenience, induced many a man to [be with] an alyha” (518). The alyha supported their society by filling its economic and domestic needs. Alyha had symbiotic relations with other members in their society. Because young wives in Mohave society were sometimes considered unstable, men often took an alyha as a wife as this insured “a well-kept home” and an “exceptionally industrious” partner (Devereux 513,515). The alyha had something uniquely valuable to offer a husband that other Mohave wives may not have had. The Mohave culture recognized and utilized the strengths the alyha had to offer. The hwame too were said to be “excellent providers and took pride in dressing up their wives”(Devereux 515). The hwame also filled a domestic need and contributed to Mohave society. They could be relied on to sustain themselves and their wives. Devereux also notes how partnering with an “industrious hwame” was alluring to women who had some experience with “flighty, lazy and spend thrift husbands” (515). The Mohave saw that one’s character mattered more in marriages than the gender one was born with. Far from lacking any characteristics, the hwame were sometimes preferred over other men for husbands. Because hwame and the alyha served their society in a variety of important ways and fit particularly well into Mohave spirituality, the Mohaves’ cultural views of the alyha and hwame was one of acceptance and inclusion whereas the cultural views of today’s transgenders support their exclusion and persecution.  
       
 In conclusion, the alyha and the hwame of the Mohave culture were not segregated because of their gender identity. They were largely accepted into their society’s norms. Transgenders in the United States however are a controversial dilemma and consequently face exclusion, discrimination, ridicule, and persecution. Popular religious beliefs that people should not disrupt “God’s will” as well as beliefs that transgendered people only desire to be the opposite sex due to a mental illness continue to play out in the discrimination of such individuals. The spiritual views along with the domestic and economic needs the alyha and hwame met encouraged placement and acceptance of these individuals in Mohave society. The comparison of the Mohave gender norms to today’s gender norms in the United States illustrates how culture defines acceptable and unacceptable behavior.

 Works Cited

Bailey, Sarah pulliam. “Christian College Parts ways with Transgender Professor.” Christian Century

130.21 (2013) 19-20. Academic Search Premier. Web. 23 July 2014.

Devereux, George. “Institutionalized Homosexuality of the Mohave Indians.” Human Biology 9.4

(1937) 498-527. JSTOR. Web. 20 July 2014.

Jost, Kenneth. “Transgender Issues.” CQ Researcher 16.17 (5 May 2006): 385. CQ Researcher.

Web. 21 July 2014.

Leclerc, Nancy. “Berdache.” and “Sex Identity.” Encyclopedia of Anthropology. Ed. H. James Brix.

Thousand Oaks, CA: SAGE Publications, Inc., 2006. 434-44 and 2073-2074 SAGE Knowledge. Web. 17 July 2014.

Schwartzapfel, Beth. "The new normal: until 1974, being gay was officially a mental illness. Now

transgender people want shrinks to stop calling them crazy." Mother Jones Jan.-Feb. 2013: 10+. Opposing Viewpoints in Context. Web. 23 July 2014.

"Transgender People." Opposing Viewpoints Online Collection. Detroit: Gale, 2014. Opposing

Viewpoints in Context. Web. 22 July 2014.

How to Tell The Difference Between Chiefdoms and States

Today’s blog post focuses on sociopolitical organizations.  Sociopolitical organizations are political institutions that govern groups of people and societies.  Anthropologist Elman Service came up with the current sociopolitical typology that identifies the various types of sociopolitical organizations that exist, which include the band, tribe, chiefdom, and state political systems.  Each of these is identified by key characteristics, although there are similarities amongst them.  It is the number of similarities between chiefdoms and states that often confuse introductory anthropology students, and this post is dedicated to clarifying the differences between these two types of sociopolitical organizations.

Cahokia is an example of a chiefdom level society that existed in the United States.

 Chiefdoms are sociopolitical organizations are characterized by a permanent political structure with some degree of differential access to resources and a political structure.  Chiefs are the leaders of chiefdom societies, and they control all leadership roles of the society, including but not limited to executive (e.g. administration of daily activities), legislative (e.g. law creation), and judicial (e.g. court system) responsibilities.  Chiefs do not have formal advisors, although lesser chiefs may be instituted if the chiefdom is very large and the chief cannot adequately oversee the people within the whole territory.  Some of responsibilities of the chief include redistributing goods among all citizens, although the chief will keep more goods than the rest of the citizens, and overseeing disagreements amongst citizens and meting out rewards and punishments according to his or her will.  Chiefdom societies are also kin-based where the social divisions within the society are based on descent from the apical ancestor or genealogical closeness to the chief.  Chiefdoms are also largely horticultural or pastoral societies, although sometimes they do practice small scale agriculture.

Graphic of Egyptian Social Hierarchy (Google Image Search)

States have more formalized governance and political structure.  Leaders of the state often times have term positions, although not always (e.g. monarchies or dictatorships).   Leaders share power and control of the state with formalized governances (e.g. political positions held by elite members of society).  Each area of the state government has a particular role and set of responsibilities; for example, the state leader is in charge of collecting taxes and distributing the taxes according to their own will or the will of the people, which is dependent on the type of state.  Social differentiation within the state level society is based on power, wealth, and prestige, which creates formal and very definable social classes within the society.  States also sustain themselves on agricultural or industrialism.    

 

Bibliography:

Gezon, Lisa and Kottak, Conrad.  2011.  Culture.  Mc-Graw Hill. 

http://anthro.palomar.edu/political/pol_3.htm

Applied Anthropology Profile: Dr. Jay Maxwell, Medical Resident

Today’s blog post is dedicated to the chronicle of Dr. Jay Maxwell, an anthropology student turned medical doctor.  Jay is currently a third year anatomical pathology medical resident in Ontario where he is charged with diagnosing pathological processes of various tissues in order to diagnose and treat patients.  On occasion, Jay is also tasked with performing autopsies under the guidance of a full staff pathologist.  Oddly enough, this is not an uncommon story I hear amongst physical anthropology undergraduate and graduate students.  As physical anthropology is a broad discipline that focuses on various aspects of human biology-both in the past and present-many physical anthropology students find themselves pursuing careers in medicine or dentistry. 

Jay’s current medical work parallels his previous interests in and studies in physical anthropology where he focused on paleopathology, the study of ancient disease.  His interest in physical anthropology was born out of his interest in human evolution, which was encouraged by his reading of Charles Darwin’s On the Origin of Species.  Jay pursued his interests in evolution while pursuing his bachelor’s degree, which resulted in his being enrolled in several physical anthropology courses.   And as the adage goes, the rest is history: “I ended up taking several classes in physical anthropology…, including a human osteology class. From day one I pretty much fell in love with all things bone, especially bone pathology and how diseases have changed through time, and I switched my major to physical anthropology.” 

From there Jay pursued not only a bachelor’s degree in Physical Anthropology but a Masters of Arts and PhD, as well, but it was during his doctoral studies that Jay felt that his interests and expectations in his studies required more than just a physical anthropological approach:

“…but the deeper I got into my research the more questions I had about bone physiology and bone chemistry that could not be answered in the anthropology literature alone, so I started heavily reading medical journals. At the same time I was taking courses outside the department in anatomy, pathology, and geology (stable isotopes)  and I was beginning to learn how important understanding soft tissue and the body as a system was in terms of interpreting bone lesions in archaeological contexts. Through these courses I was put in contact with several individuals in the medical field. Talking with them, hearing their experiences and learning how they applied the same kinds of information I was studying in past populations to modern living patients was fascinating. The idea that I could do similar research in both modern and past populations and that information could directly impact someone’s health and/or quality of life was intriguing.”

Jay did not complete his Ph.D. in Physical Anthropology  in part because of his research interests but also due to his personal circumstances.  His decision to enter into medicine was because of the freedom and flexibility it provided him both at the professional and personal level, allowing him to pursue his research while also not neglecting his personal commitments.  He acknowledges that his past work in physical anthropology and his current work in pathology have real applications in effecting public policy.  His past research aids in understanding how diseases have evolved and changed over time, focusing on questions of how and why-be it strictly biological or anthropogenic-those changes occurred, whereas his present work assists living populations today throughout diagnosis and treatment.  As Jay notes,  “The only real difference is the source and context around where or how the information potentially originates and I enjoy the basic work of both fields equally.” 

As for students considering entering into anthropology for a course or as a major, Jay has this advice for you:

"Do not hesitate to take a course or make it your major. Anthropology will provide you with critical thinking skills and an understanding of biological or social processes that will be universally applicable regardless of where you finally end up in your career. The knowledge base in anthropology is enormously broad and is encompassing. Your experience in anthropology won’t just be beneficial in a career, but it’s also one of those rare fields that will help you understand the world better as a whole. Because of this, anthropology will make you even more enraged when you read the letters section in a newspaper or an online comments sections, but you’ll also be awfully hard to beat in a debate!"

Author’s Note: I would personally like to take a moment again to thank Jay for taking the time to be interviewed for this blog post.  Also, while I harp on students about the hazards of over quoting a source, I felt it was necessary to put much of this post in Jay’s own words because his prowess in explaining his story is far superior to mine, and I felt that I could not do his story justice by putting it in my own words.  Again, thank you, Jay, and all the best to you and Allison. 

Paint By Numbers: An Alternative Way of Working Through Hardy-Weinberg Equilibrium Problems

For many Physical Anthropology and Biology students, figuring out Hardy-Weinberg Equilibrium problems is both challenging and dreadful.  Even I, as a student, had difficulties completing these problems, but I have learned some tricks that have assisted me in both completing these problems and teaching the concepts to my students.  I am sharing these tricks now so that students and educators can better handle this tricky subject.

The Hardy Weinberg Equilibrium (aka principle, theorem, model, or law) is a concept that was obtained by scholars Godfrey Hardy and Wilhelm Weinberg, and it is used to determine if genetic equilibrium, or lack of evolutionary change, has occurred in a population (see this post for explanations on the aforementioned terms).  In order for genetic equilibrium to occur, a set of conditions must be met, and these conditions include:

•       Mutations must not be taking place.

•       The population must be infinitely large.

•       Individuals from neighboring populations must not introduce alleles into the population.

•       Mating must take place at random and be equally fertile.

•       Natural selection must not be occurring.

Although these conditions may be present in any given population, it may be difficult to determine with absolute certainty if all of them are taking place equally, producing genetic equilibrium.  This is where the Hardy-Weinberg Equilibrium equation comes in handy.  This equation utilizes a set of variables that represent certain aspects (in proportions) of the population and the answer of the calculated variables will demonstrate if genetic equilibrium is present. 

The Hardy-Weinberg Equilibrium equation comes in two parts and are as follows:

P + Q = 1

P² + 2PQ + Q² = 1

At this point, people start to get cross-eyed, butterflies enter the stomach, some start to feel nauseated, etc.  Step one for understanding this problem is NOT TO PANIC!  As mentioned earlier, the Hardy-Weinberg Equilibrium equation is a set of variables that represent certain aspects (in proportions” of the population.  Each of these variables (from P to Q²) represents a specific aspect of the population, and this is the breakdown of those variables and what they represent:

• —  P denotes the dominant allele
• —  Q denotes the recessive allele
• —  p² = percentage of homozygous dominant individual
• —  q² = percentage of homozygous recessive individual
• —  2pq = percentage of heterozygous individuals 

(For an explanation of these terms, please go to this previous blog post.)

Figure 1: Paint By Numbers of My Little Ponies.  It is sometimes easier to think of Hardy-Weinberg Equilibrium Equations as Paint By Numbers Kits than as math problems.  Source: Google Images

 

Now if you are still feeling anxious because you are looking back at the full problem and have math anxiety, stop thinking of the Hardy-Weinberg Equilibrium equation as a math problem.  Instead, think of it as a paint by numbers kit (Figure 1).  Each of those variables (from P to Q²) is just a different color that needs to be plugged into your paint by number kit, which in this case is your equation.  Please note that I have chosen the theme of My Little Ponies as a means of relaxing tensions that you may be feeling.  My Little Ponies was and is a popular children’s cartoon show, and much like children’s cartoons the Hardy-Weinberg Equilibrium equation does not have to be difficult or intimidating.  It can be fun and enlightening if you so chose to think of it that way, which I recommend because you will find yourself less scared of it if you chose to think that way.

Hardy-Weinberg Equilibrium equation problems are often presented as a lengthy word problem, such as the following:

Figure 2: Apple Family (My Little Ponies); Google Images

 

In the land of the My Little Ponies, there exists a family of ponies known as the Apple Family (Figure 2).  This family has a unique set of genetic traits and is one of the few My Little Ponies that can and do produce ponies with green mane, which is a homozygous recessive trait.  In this family photo, we see eleven ponies with green mane.  The current population size of the entire Apple family is 100 ponies. 

Now this word problem can be very intimidating for a variety of reasons.  There is a lot of information present here, but this information is not here to confuse you.  It is here to assist you.  If you look closely in this problem, you have already been provided the information that gives us the Q² variable:

green mane is a homozygous recessive trait...eleven ponies (have) green mane

We now know that 11 out of 100 ponies exhibit green mane, but we need to turn this number into a proportion (fraction or decimal).  To do this, we take 11 and divide it by 100 (11/100) and we get .11 as our answer.  This .11 now represents the Q² variable.  We have one part of the Hardy-Weinberg Equilibrium equation completed, and believe it or not, it is now much easier to figure out the rest of the variables.

How?  We can figure out Q from Q² by getting the square root of Q², which in this case is .11.  Once you have calculated the square root of .11, you will have Q.  In this case, Q is .33 (rounded to the nearest 100^th place).  Now if you look back at both parts of the Hardy-Weinberg Equilibrium equation, you will see that P + Q = 1.  You have Q, so you can figure P.  You do this by subtracting Q (.33) from 1, which when resolved provides you with .67 (P).  You can check to make sure you completed this correctly by adding P (.67) and Q (.33).  If the resolution equals one then you have calculated P and Q correctly.  If not, then you need to go back to the previous steps and figure out where you may have gone wrong.  In this case, .67 + .33 = 1, so the equation has been completed correctly.

So far you have figured out three variables: Q², Q, and P, but you still need to figure out P² and 2PQ.  Now that you have the Q², Q, and P variables represented you can easily come up with P² and 2PQ.  You figure out P² by multiplying P (.67) by itself.  In other words, .67 x .67, which when calculated gives you .45 when rounded to the nearest 100^th place.  So now you know that .45 represents P². 

Figure 3: PEMDAS (Unedited: www.mathgoodies.com)

Figuring out 2PQ is a little trickier because you have to remember the acronym PEMDAS.  PEMDAS refers to the order of operations in mathematics, and this acronym represents Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (Figure 3).  You would set up 2PQ as follows:

2 (.67 x .33)

And following PEMDAS, you would complete the equation in the parentheses (.67  x .33) first, producing an answer of (.22) [again, rounded to the nearest 100^th] and then multiply that answer by 2:

2 x (.22) = .44 = 2PQ

Now that everything is complete, this is what each of your variables is:

P= .67

Q= .33

P²= .45

Q²= .11

2PQ= .44

Once you have this information, you can solve for Hardy-Weinberg Equilibrium, as well as figure out the number of homozygous dominant and recessive individuals as well as heterozygous individuals in a population.  You can learn all sorts of additional information about the population from this information, too.  Hopefully, though, the biggest thing you have learned is not to be intimidated by Hardy-Weinberg Equilibrium equations and how best to calculate them.  All with the help of some My Little Ponies.