Author: Adnan Shahid

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Game Theory and Evolutionary Biology

In class we’ve applied game theory to just standard games, and common understandings of it can be related primarily humans and the things we do. However, game theory can be applied in a variety of situations, and one that would typically not be considered is the application of game theory on biology and animals.

Game theory is surprisingly apparent in a lot of aspects in things like zoology and botany, from things like looking for a mate, fighting, cooperation and communication! A very interesting example of this is that there exist species that will fight to compete for a female mate, but they can actually fight on top of the female, resulting in a chance for her to be injured or die (toads). Ordinarily this wouldn’t make sense as it results in a chance for death for the female these animals are fighting to the death for, but from a game theory perspective, it makes sense. From the individual male’s point of view, what he would gain from the female would be to fertilize her eggs and spread offspring. If the female gets dies, there will be no such benefit. However, if the frog will also receive no benefit if he does not fight due to a competitor as his mate will be stolen. So the optimal choice would be to fight and expose the female to a small risk of death (Hammerstein 972-973). There are a multitude of examples of animals cooperating to improve survival and benefit themselves as it is the best choice for the given animal. For example, there exists spiders that keep frogs as pets to guard their eggs in exchange for providing them with protection and food. This is the optimal choice for the spider as even though it loses food, it leads to the best benefit for it as the spider’s eggs are protected.

In conclusion, game theory can be applied in various situations not limited to just humans. It’s application is widespread and appears throughout nature all the time with biological organisms.

References:
Hammerstein, P., & Selten, R. (1994). Game theory and evolutionary biology. Retrieved from: http://www.ens-lyon.fr/DI/wp-content/uploads/2009/07/Chapter-28-Game-theory-and-evolutionary-biology.pdf

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Power Law in a Celestial Scale

The existence of the power law has been witnessed in various networks created by humans in various forms as discussed in class. As previously discussed it shows in various social constructs such as social networks and even actor collaborations, however the power law also makes itself apparent within nature and in our planet. What is even more interesting however, is that the power law exists to even a scale as large as celestial bodies, from Pluto, to our moon and even the sun itself, the power law is everywhere.

One study looks into the the craters in Pluto, upon the recent high resolution pictures of Pluto, scientists were able to look at the actual craters in the planet. It investigated 87 craters in Pluto, ranging from sizes of 0.87km to 37.77km. It was found that there was a scaling coefficient of “α = −2.4926 ± 0.3309”, with a “Dmin = 3.75 ± 1.14 km” (or xmin if we use the formula we discussed in class). Upon values of distance D within the range “[3.75 ± 1.14 km, 37.77 km]” there was a log likelihood (L) = 104.5688. It is incredibly interesting that these scientists are using the same formulas we are to calculate the scale and witness power law on a celestial scale!

Below indicates a segment of craters within Pluto that were analyzed for their crater size

The study then continued to look at how these craters were very comparable to power-laws in other celestial bodies such as our Moon, Mar’s satellites Phobos and Deimos, and even the Earth! As an interesting tangent, the study also referenced how the power law existed in the relationship between the frequency of solar flares and total flare energy. Going on to provide other examples such as the distribution of initial masses for star populations, Kepler’s third law, and even to the scale of the distribution of galaxies in the universe! It is incredible to think of how this law shows itself throughout the universe. From human social constructs, things we made, to the scale of galaxies in the Universe!

http://www.ptep-online.com/2016/PP-44-04.PDF