The Noncommutative Harmonic Oscillator based in Simplectic Representation of Galilei Group

In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using the group theory approach as a guide a physical consistent theory in phase space is constructed. The state is described by a quasi-probability amplitude that is in association with the Wigner function. The 3D harmonic oscillator and the noncommutative oscillator are studied in phase space as an application, and the Wigner function associated to both cases are determined.Comment: 7 pages,no figure

Low Mate Encounter Rate Increases Male Risk Taking in a Sexually Cannibalistic Praying Mantis

Male praying mantises are forced into the ultimate trade-off of mating versus complete loss of future reproduction if they fall prey to a female. The balance of this trade-off will depend both on (1) the level of predatory risk imposed by females and (2) the frequency of mating opportunities for males. We report the results of a set of experiments that examine the effects of these two variables on male risk-taking behavior and the frequency of sexual cannibalism in the praying mantis Tenodera sinensis. We experimentally altered the rate at which males encountered females and measured male approach and courtship behavior under conditions of high and low risk of being attacked by females. We show that male risk taking depends on prior access to females. Males with restricted access to females showed greater risk-taking behavior. When males were given daily female encounters, they responded to greater female-imposed risk by slowing their rate of approach and remained a greater distance from a potential mate. In contrast, males without recent access to mates were greater risk-takers; they approached females more rapidly and to closer proximity, regardless of risk. In a second experiment, we altered male encounter rate with females and measured rates of sexual cannibalism when paired with hungry or well-fed females. Greater risk-taking behavior by males with low mate encounter rates resulted in high rates of sexual cannibalism when these males were paired with hungry females

A Comparative Analysis of the Morphology and Evolution of Permanent Sperm Depletion in Spiders

Once thought to be energetically cheap and easy to produce, empirical work has shown that sperm is a costly and limited resource for males. In some spider species, there is behavioral evidence that sperm are permanently depleted after a single mating. This extreme degree of mating investment appears to co-occur with other reproductive strategies common to spiders, e.g. genital mutilation and sexual cannibalism. Here we corroborate that sperm depletion in the golden orb-web spider Nephila clavipes is permanent by uncovering its mechanistic basis using light and electron microscopy. In addition, we use a phylogeny-based statistical analysis to test the evolutionary relationships between permanent sperm depletion (PSD) and other reproductive strategies in spiders. Male testes do not produce sperm during adulthood, which is unusual in spiders. Instead, spermatogenesis is nearly synchronous and ends before the maturation molt. Testis size decreases as males approach their maturation molt and reaches its lowest point after sperm is transferred into the male copulatory organs (pedipalps). As a consequence, the amount of sperm available to males for mating is limited to the sperm contained in the pedipalps, and once it is used, males lose their ability to fertilize eggs. Our data suggest that PSD has evolved independently at least three times within web-building spiders and is significantly correlated with the evolution of other mating strategies that limit males to monogamy, including genital mutilation and sexual cannibalism. We conclude that PSD may be an energy-saving adaptation in species where males are limited to monogamy. This could be particularly important in web-building spiders where extreme sexual size dimorphism results in large, sedentary females and small, searching males who rarely feed as adults and are vulnerable to starvation. Future work will explore possible energetic benefits and the evolutionary lability of PSD relative to other mate-limiting reproductive behaviors

Determinants of Natural Mating Success in the Cannibalistic Orb-Web Spider Argiope bruennichi

Monogynous mating systems (low male mating rates) occur in various taxa and have evolved several times independently in spiders. Monogyny is associated with remarkable male mating strategies and predicted to evolve under a male-biased sex ratio. While male reproductive strategies are well documented and male mating rates are easy to quantify, especially in sexually cannibalistic species, female reproductive strategies, the optimal female mating rate, and the factors that affect the evolution of female mating rates are still unclear. In this study, we examined natural female mating rates and tested the assumption of a male-biased sex ratio and female polyandry in a natural population of Argiope bruennichi in which we controlled female mating status prior to observations. We predicted variation in female mating frequencies as a result of spatial and temporal heterogeneity in the distribution of mature females and males. Females had a low average mating rate of 1.3 and the majority copulated only once. Polyandry did not entirely result from a male-biased sex-ratio but closely matched the rate of male bigamy. Male activity and the probability of polyandry correlated with factors affecting pheromone presence such as virgin females' density. We conclude that a strong sex ratio bias and high female mating rates are not necessary components of monogynous mating systems as long as males protect their paternity effectively and certain frequencies of bigyny stabilise the mating system