Title. Using geometric probability to compare the random and actual mating success of the American. bison, Bison bison. Author.

Transcription

1 Title Using geometric probability to compare the random and actual mating success of the American bison, Bison bison. Author Scott Plavac 1

2 Abstract The American bison, Bison bison, is a mammal of the bovidae family. The random geometric probability of mating success was estimated to be about.3%. In this research, I computed the random probability of mating success and compared it to the actual mating success for the American bison. The actual probability of mating success in the American bison increases to 100% by natural body parts, location, and courtship. Dominant males are more likely to find a mate over smaller males because it is the male s burliness that lures the female. Once a male has ingratiated a female, he inseminates her from the ventro-dorsal side with his penis. 2

3 Introduction The American bison once roved around North America in large bunches and played a fundamental role in America s past time. Nearly million bison occupied the Great Plains of North America, but now that number has dwindled down to 500,000. There are currently 4,000 bison residing in Yellowstone National Park, holding the biggest population of free roaming Plains bison in the continent. The typical American bison has bushy, lengthy, dark brown fur in the front, and a lighter skinned pelt in the rear. They can weigh anywhere between 700-2,200 pounds. The American bison travels in packs and are always on the move because they are grazers. They are herbivores which mean their diets consist of grass and sedges. When mating season occurs, dominant bulls claim a minor area of land in which they mate with their females. Bulls will watch cows as they scare off contending males until they are permitted to mate. A rival bull may roar to get noticed. The bull that has already claimed his mate will snarl back. The most superior bulls are able to mate in the first 2-3 weeks of the season. In this study, using a method of geometric probability, I compared the random mating success with the actual mating success of the American bison. Method Random mating was perceived as if one were to close his or her eyes and throw 100 darts at the body of a female American bison: what would be the chance of hitting the vagina bull seye? Random mating success was computed based on three shapes that can be seen in the picture below. The surface area of the female American bison was represented by the circle and rectangle. The vagina bull s-eye was represented by the tiny smaller rectangle in the middle of the circle. The bull s-eye is the male s target (goal to penetrate and inseminate the female) to achieve effective mating. Random mating success was computed by dividing the surface area of the bull s-eye from 3

4 the total surface area of the circle and rectangle. Figure 1: This image of an American bison was obtained from Google Images. The large circle and rectangle represent the surface area of the American bison. The smaller rectangle represents the female s vagina (the male s target). Random mating success was calculated by dividing the bull s-eye from the total surface area. Results Target surface area (circle): π x r 2 = 3.14 x = cm 2 Target surface area (rectangle): 5 x 4.5 = 22.5 cm 2 Total target surface area: = cm 2 Bull s-eye surface area: 0.75 x 0.75 =.563 cm 2 Random probability of mating success (bull s-eye / target): 0.563/ = x 100 = 0.3 4

5 According to my geometric calculations, the surface area of the bull s-eye is only 0.3% of the total surface area of the target. As a result, only 0.3 out of 100 darts would hit the bull s-eye. Discussion There are 0.3 chances out of 100 that males will successfully inseminate females. However, their chances can increase from 0.3% to 100% based upon body size, obtainability, and pursuit. Starting with body size, males need to find mates that are compatible with their body. Since males are much larger than females, it is important to choose females that will not make things more problematic for the male because he needs to be able to mount her with ease. In addition, males with a large shaft have a higher probability of making contact with the vagina. Second, females need to be available for mating. This is not too difficult to accomplish as the American bison are group-oriented animals. But, this presents a challenge to smaller males due to females preferring the larger bulls because their premier traits will be passed on to their offspring. The mating season is less than one month long which means that time plays a factor in their pursuit. Lastly, males must be motivated to pursue their mates. Males will show off their brawny bodies hoping it will catch the attention of a female. It is the male s burliness that females desire the most. Competition amongst males is common and dominant males will fight with other males in hopes of impressing their mate. 5

6 References Bowyer, R. T., Bleich, V. C., Manteca, X., Whiting, J. C., & Stewart, K. M. (2007). Sociality, mate choice, and timing of mating in American bison (Bison bison): Effects of large males. Ethology, 113(11), doi: /j x Lott, D. F. (2010). Sexual behavior and intersexual strategies in American bison. Ethology, 56(2), doi: /j tb01289.x Rutberg, A. T. (1986). Lactation and fetal sex ratios in American bison. The American Naturalist, 127(1), Wolff, J. O. (1988). Maternal investment and sex ratio adjustment in American bison calves. Behavioral Ecology and Sociobiology, 23(2), doi: /BF Wolff, J. O. (1998). Breeding strategies, mate choice, and reproductive success in American bison. Oikos, 83, doi: /