Title What is the probability of mating success in the butterfly , Danaus plexippus ?

The Monarch butterfly has a random geometric probability of .81%, or less than 1 chance out of 100 of mating success. Males increase mating success by depositing more sperm thus reducing competition. Females increase mating success by mating more frequently thus increasing their chances of producing offspring. Introduction Monarch butterflies often find larger symmetric females more attractive. However, larger males often have better success because the larger females often resist mating attempts. Male Monarch butterflies produce sperm sacs called spermatophores that increase in size between mating. Since female butterflies store sperm it is beneficial for male butterflies to wait until they have accumulated a greater amount of sperm for fertilization. The greater amount of sperm also delays female mating, adds to the quality and amount of offspring produced and give nutrients to the eggs and tissue of the female. Males that mate more often have greater success in producing offspring. Method The geometric probability of the butterfly was found by calculating the body and the wing and then taking the total and the calculated target to proportionately find the probability of random mating success. In (Figure 1) the surface are of a cylinder was calculated for the body and the area of a triangle was calculated for the wing. The target at the end of the butterfly’s body was calculated as a circle. The area of the target was divided by the total surface area to find the random geometric probability. Figure 1: This image of the monarch butterfly was obtained from google at http://en.wikipedia.org/wiki/Viceroy_(butterfly). The blue dot at the end of the butterfly’s cylindrical body is the target area where sperm is delivered. The length of the body is represented by the line leading to the target. The figure of a triangle represents the area of the wing and the corresponding width and lengths. Results Cylinder: 2(3.14) 0.5^2 + 2 (3.14) 0.5 (8) 1.57+ 25.12 =26.69cm Triangle: 1/2 (14) (10) =70 Circle (target): 3.14(0.5) ^2= .785 .785 X 100 /96.69= .81 .81% (less than 1 chance out of 100 that mating will be randomly successful) DiscussionThe random geometric probability of the butterfly, Danaus plexippus, is .81% or less than1 chance out of 100 of mating success. Male and female butterflies mate repeatedly, and femalescan produce up to 400 to 500 eggs. When sperm is deposited, sperm moves through the bursacopulatrix to the spermatheca, thus fertilizing the eggs of the butterfly. Males can increasemating success by increasing sperm deposits which is done by waiting a longer duration betweenmating. Males often want to deposit more sperm so the majority of the sperm stored inside afemale is in their favor. Males often increase their odds by mating more frequently. Larger malesoften have the advantage because they can produce more sperm and can better coerce thefemales. However, the number of times a female mates makes no difference to their longevity oregg weight. ReferencesBoggs, C. L. (1981). Selection pressures affecting male nutrient investment at mating inheliconiine butterflies. Evolution, 35(5), 931-940.Eanes, W. F., & Koehn, R. K. (1978). An analysis of genetic structure in the monarch butterfly,Danaus plexippus L. Evolution, 32(4), 784-797. doi: 10.2307/2407494Solensky, M. J., & Oberhauser, K. S. (2009). Male monarch butterflies, Danaus plexippus, adjustejaculates in response to intensity of sperm competition. Animal Behaviour, 77(2), 465-472.doi: http://dx.doi.org/10.1016/j.anbehav.2008.10.026Svärd, L., & Wiklund, C. (1988). Fecundity, egg weight and longevity in relation to multiplematings in females of the monarch butterfly. Behavioral Ecology and Sociobiology,23(1), 39-43.doi: 10.1007/BF00303056Svärd, L., & Wiklund, C. (1988). Prolonged mating in the monarch butterfly danaus plexippusand nightfall as a cue for sperm transfer. Oikos, 51(3), 351-354.doi: 10.2307/3565317