Title
Using geometric probability to compare the random and actual mating success of the
Copperhead snake, Agkistrodon Contotrix
Author
Cledisson Jules
Abstract
The copperhead, Agkistrodon Contotrix, is a venomous snake indigenous to North America in
the Viperidae family. Males often fight before courting a female and more times than not, the
larger male wins. The random geometric probability of mating success was estimated to be about
3.9%. Females increase the probability by releasing a pheromone that male snakes can “smell.”
Males then “spoon” with the female and tangle together, thus positioning his body so his
hemipenis can penetrate and inject sperm.
Introduction
Snake mating is a pretty simple process. When a mature male snake senses the
pheromones of a female snake, he approaches her. He begins to court her by bumping his chin
against the top of her head. If she is willing, she will raise her tail and he coils around her, lining
up their genitals. He then uses his hemipenises to penetrate her vagina and release his semen.
This doesn’t take too long, but the courting and sex could last a whole day. The American robin
is one of the earliest bird species to lay eggs, beginning to breed shortly after returning to its
summer range from its winter range.
Method
Images of Copperhead snakes were found via Google Images. Due to the odd shape of
the snake and to increase the accuracy of the calculations, I decided to measure the snake and a
cylinder, rather than a rectangle. The lines show the dimensions of the “cylinder” and the two
circles represent the surface area of the vagina that the male’s hemipenises have to penetrate.
Figure 1: This image of a Copperhead snake was obtained from Google images. The line and
curve represent the diameter and height of the “cylinder” and the circles represent the vagina.
Results
Female target: 2π(1)2 + 2π(1)(37.5) = 241.9 cm2
Bull’s-Eye (insemination location): π 22 - π 32 = 9.4 cm2
(The random probability of mating success: 9.4 cm2 / 241.9 cm2 = 3.9 %. There are only ~ 4
chances out of 100 that random mating will be successful).
Discussion
In this study, I found that unless the timing, body size, availability and willingness of a
partner is just right, there are only ~ 4 chances out of 100 that males could find, mount and
successfully inseminate females with their eyes (or noses) closed.
The male Copperhead, Agkistrodon Contotrix, seduce and coil around a female and inject
sperm via hemipenises. Males find females by “smell”. Most reptiles use their tongue to taste the
air, or smell. Thereafter, males grapple females with their bodies and wrap around. Small males
are far least successful than larger males. If any males happen upon the same fertile female, they
fight and duel for her attention. But even the size of the snake doesn’t determine the outcome.
The history of the snake is important. If a snake loses a fight prior, they are less likely to win any
next fight. The winning male then moves to the female’s side. Curving his abdomen, he coils
around her soft underbelly with his hemipenises. Sperm is injected into her cloaca Thus, a 3.9%
chance of success increases to about 100% chance of success once a male locates a female.
References
Perry, L. (n.d.). How Snakes Work. Retrieved October 9, 2013, from
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Schuett, G. W., & Gillingham, J. C. (1989). Male-male agonistic behaviour of the copperhead,
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doi: http://dx.doi.org/10.1163/156853889X00412
Schuett, G. W. (1997). Body size and agonistic experience affect dominance and mating success
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