Geometric Probability of Mating Success in Horses, Equus ferus caballus By Katrina King, Leon Hardy, and Deby Cassill College of Arts and Sciences Mentored by Dr. Leon Hardy and Dr. Deby Cassill ABSTRACT The horse, Equus ferus caballus, mates in the dorsoventral position, a back-to-front mounting position common to most terrestrial quadrupeds. Because neither horse can see their genitals during mating, their bodies must be geometrically aligned for stallions to successfully delivery their sperm into the mare s vaginal canal. In this study, a conservative estimate of the random probability of mating success was calculated in the same way as one would calculate the random probability of a dart hitting the center of a target. One would determine the area of the bull s-eye (the mare s vagina) relative to the area of the entire target (the mare s posterior). A conservative estimate of the random probability of mating success for horses was ~ 0.8% or less than one chance out of a hundred. The adaptations for mating success in the wild and through animal husbandry are discussed. University of South Florida St. Petersburg Student Research Journal Volume 1 Issue 1 1
INTRODUCTION Horses have been evolving for 45-55 million years (McFadden, 1992). Domestication by humans was wide spread by 3000 B.C. The horse as we know it today is quite different from its ancestors. The first horses were small, odd-toed ungulates, common in forest areas (Fig. 1). Multiple toes were needed to travel across the soft, moist ground of the forest floor. As the land and terrains shifted, these animals adapted to living on dry plains, eating rough grasses and plants. In addition, multiple toes evolved to one single hoof, an adaptation that allowed horses to run at high speeds on the hard, dry plains. Figure1: Early forest dwelling horse. [Photo source: http://gnsi.scienceart.com.2006wi/presenters/hawley.jpg] The back-to-front, dorsoventral mating position common to most terrestrial quadrupeds presents a challenge because neither males nor females can see their own genitals or those of their mate (Daly, 1978). Without visual, auditory or olfactory cues, how does a stallion s heat-seeking missile find its target? In addition, a dorsoventral mating position requires that the female be sufficiently strong to bear at least half of the male s weight for the duration of the mount (Fig. 2). Finally, the dorsoventral mating position creates an inverse University of South Florida St. Petersburg Student Research Journal Volume 1 Issue 1 2
relationship between the size of the male and the length of his penis (Asa, 1986). Taller males with shorter penises can successfully mate; shorter males would need to compensate with a much longer penis to successfully mate. Figure 2: Dorsoventral mating style. [Photo source: http://www.google.com/imgres?q=horses+breeding&um=1&hl =en&sa=n&qscrl=1&nord] Recent findings indicate that, in the wild, stallions are not always dominant over mares. Mating success of males varies according to their status within the smaller groups. An aggressive stallion may kick, bite, and strike the mare s posterior or back, but with little damage to her. Mares play the major role in mate selection by signaling the reproductive receptiveness to the stallion (Bristol, 1982). If the mare is unreceptive, she will kick with her hind legs or walk away. A hard kick to the stallion s legs, ribs or groin could immediately disable him. In the wild, horses aggregate into four types of social groups: harem groups, multiple male and female groups, bachelor male groups and large herds that incorporate the smaller harem or bachelor groups (McCort, 1984; Heitor, et al. 2006). The size of the groups is influenced by food quantity, quality and seasonal changes. Group membership is maintained by the males of the group. Because group membership is fluid, changing as herds comingle, the mixing of genes in wild populations of horses is high. The result is that breed diversity is low. University of South Florida St. Petersburg Student Research Journal Volume 1 Issue 1 3
Artificial selection in the form of animal husbandry has dramatically increased the diversity of horse breeds (Heitor, et al. 2006). Humans select for desired traits, characteristics, colors, and personalities to create optimal breeds. Unfortunately, the mares are not always receptive to the stallion chosen by a human. Natural moods and personalities might interfere with successful mating. Method To calculate the random probability of mating success (Kendall, 1963), measurements were made from photos (Figures 3a,b). The surface area of the mare s vagina and posterior were measured in mm or cm from a photo using a metric ruler. Rectangle A = lw; circle A = π r 2 ). The surface area of the two right triangles was calculated as one rectangle. When erect, a stallion s penis is more than twice the length and width of the flaccid penis (Figure 3c), nearly reaching to the ground (Daly, 1978; Asa, 1986). Thus, we calculated the negative space between the mare s legs, from hooves to belly, as part of her target area. It was estimated that a mare must be sufficiently strong to support her own weight and approximately 50% of the stallion s weight during mounting (Carroll & Huntington 1988). The weight of a stallion was estimated at 20% greater than that of a mare. Results A conservative estimate of the random probability of a stallion successfully mating with a mare of equal height was 0.8% (37.5 mm 2 /4,526 mm 2 = 0.012 x 100). The surface area of the mare s vagina was 37.5 mm 2 (Fig. 3a; 2.5 mm x 15 mm). Based on the surface area of a circle and two rectangles (Fig 3b), the surface area of the mare s posterior was 4,526 mm 2 ([23.5 2 mm x 3.14] + [8 mm x 14 mm] + [67 mm x 40 mm]) including the negative space between the legs). The additional weight that a mare must support, half of the stallion s weight during mounting and mating was conservatively estimated as 61% of her own weight (mare = 450kg; stallion = 550 kg; [0.5 x 550] / 450 = 0.61 x 100). University of South Florida St. Petersburg Student Research Journal Volume 1 Issue 1 4
a b c Figure 3: Geometry of stallion s target. (a) Mare s vagina [Photo source: http://www.google.com/imgres?q=horse+vagina&um=1&hl=e n&sa=n&qscrl=1&nord=1&ty=46]. (b) Mare s posterior [Photo source: http://4.bp.blogspot.com/_3gglqybqokw/s- TFZhAX5lI/AAAAAAAAACI/3xL3fsv9aUo/s1600/blah+blah +horse+but.png]. (c) Stallion with flaccid penis and the estimated size of the erect penis which can reach nearly to the ground: [Photo source: http://www.google.com/imgres?q=horse+penis&um=1&hl=en &sa=n&rlz=1t4rnrn]. Discussion The random probability of mating success in horses was conservatively estimated at one chance in a hundred; in other words, the failure rate would be ~99 in 100. Over evolutionary time, what features have stallions and mares favored in their mates to increased the probability of mating success? First, we speculate that mares selected similar-sized stallions, tall enough to mount and mate, but not so tall that the mare was overly burdened by his weight while mounding her. Second, mares selected against a prehensile penis such as that of the dolphin (Gurule, et al. 2012); instead, mares favored stallions with a symmetrical penis (no lateral or vertical asymmetry during erection), and with sufficient length and rigidity to reach and enter her vaginal opening. Third, because of the additional weight that they must sustain during mating, mares favored University of South Florida St. Petersburg Student Research Journal Volume 1 Issue 1 5
stallions that ejaculated quickly once his shaft had entered the vaginal canal. In turn, we speculate that stallions selected mares that were of similar height and weight so that she would be able to support him during the mount (Daly, 1978; Asa, 1986). Stallions favored mares that did not walk away once the he had mounted her. Because stallions are vulnerable while mounted on the mare, we speculate that stallions would have favored mares that preferred quick ejaculation. Finally, stallions would have favored mares with a vagina that angled downward to hold his sperm after mating. The evolutionary dance between a mare s downward-sloping vaginal canal and a stallion s erect, upward-sloping penis would have favored genitals with sufficient elasticity to accommodate the delivery of sperm by the stallion and the retention of sperm by the mare. For a large, terrestrial quadruped, the dorsoventral mount is not what we would describe as intelligent design. Neither the male nor the female is able to see their genitals to ensure a higher mating success. In addition, dorsoventral mounting renders the male vulnerable to accidental stumbling, falling or attack by a predator. A superior design would have placed the stallion s penis between his front legs in the pectoral region rather than between the back legs at his groin region. With a pectoral penis, the male would be able to visually guide his penis into the female s vaginal canal while standing steady on all four legs. In conclusion, mating is all about geometry. In the wild, stallions and mares are of similar size. This limited sexual dimorphism contributes to mating success (McCort, 1984; Linklater, et al. 1999) in much the same as does matching the size and shape of a shoe to a foot. Artificial selection by humans has created greater sexual dimorphism between males and females as well as creating diverse breeds. The artificial breeding of domesticated animals and plants is proof of our penchant for diversity which, within species, is limited only by our ability to selectively engineer insemination and pollination. REFERENCES Asa, C.S. (1986). Sexual behavior of mares. Veterinary Clinics of North America: Equine Practice, 2, 519 534. University of South Florida St. Petersburg Student Research Journal Volume 1 Issue 1 6
Bristol, F. (1982). The breeding behavior of a stallion at a pasture with 20 oestrous synchronized mares. Journal of Reproductive Fertility Supplement, 32,71-77. Carroll, C.L., & Huntington, P.J.. (1988). Body condition scoring and weight estimation of horses. Equine Veterinary Journal, 20,41 45. Daly, M. (1978). The cost of mating. American Naturalist 112, 771 774. Franke-Stevens, E. (1990). Instability of harems of feral horses in relation to season and presence of subordinate stallions. Behaviour, 112,149 161. Gurule, S., Hardy, L., & Cassill, D.L. (2012). Geometric Probability of Mating Success for the Bottlenose Dolphin, Tursiops truncates. USFSP Student Research Journal, USFSP Press. Kendall, M. G., & Moran, P. A.P. (1963). Geometric probability. Hafner Publishing Co: New York. Linklater, W. L., Cameron, E. Z., Monot, E. O., & Stafford, K.J.. (1999). Stallion harassment and the mating system of horses. Animal Behaviour, 58, 295-306. McFadden, B. J. (1992). Fossil horses: Systematics, paleobiology and the evolution of the family equidae. Cambridge University Press: Cambridge, UK. University of South Florida St. Petersburg Student Research Journal Volume 1 Issue 1 7