Browsing by Author "Crowe, Mary L."
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Item Effect of density and extra dung on brood parasitism in the dung beetle, Onthophagus Taurus(Springer US, 2013-03) Crowe, Mary L.; Raspet, Erin; Rychtář, Jan; Gupta, SatKleptoparasitism has not been well documented in insects and intraspecific brood parasitism is even less well known. This study examines the effect of extra resources and density on the probability of kleptoparasitism in the bull headed dung beetle Onthophagus taurus. A high level (>60 %) of kleptoparasitism was found across all treatments and suggest that although density may not affect the probability to kleptoparasitize, it may influence brood ball production. This study also documents for the first time that male O. taurus kleptoparasitize.Item A field test of optional unrelated question randomized response models: Estimates of risky sexual behaviors(Springer, 2012-11-03) Gill, Tracy Spears; Tuck, Anna; Gupta, Sat; Crowe, Mary L.; Figueroa, JenniferRecently Gupta et al. (Involve J Math, 2013) introduced optional unrelated question randomized response models for both the binary response and quantitative response to sensitive survey questions. Asymptotic normality was established for the mean estimator of the sensitive variable and for the prevalence estimator of the sensitive characteristic. Asymptotic normality was also established for the sensitivity level estimator in each case using first order approximation. These mathematical results were validated using computer simulations. In this paper, the binary and quantitative response models are utilized in surveys of sensitive behaviors to verify that these results hold true in fieldwork applications. The two sensitive questions of interest in the survey are "Have you ever been told by a healthcare professional that you have a sexually transmitted disease?" and "How many sexual partners have you had in the last 12 months?" The target population was undergraduate students enrolled at UNC Greensboro during the 2012-2013 academic year. Subjects were asked these questions by optional unrelated question RRT, check-box survey method, and by direct face-to-face interview. The results of these three methods are compared to each other, as well as to existing published information on these two sensitive behaviors. Estimates provided by the optional unrelated question randomized response models are in line with the mathematical results in Gupta et al. (Involve J Math, 2013). This study also provides the first estimate of sensitivity level through a fieldwork survey.Item Game theoretic model of brood parasitism in a dung beetle Onthophagus taurus(Springer Netherlands, 2009-08) Crowe, Mary L.; Fitzgerald, Meghan R.; Remington, D. L.; Ruxton, G. D.; Rychtář, JanWe present a game theoretic model of brood parasitism in the dung beetle Onthophagus taurus. Female O. taurus engage in brood parasitism when they attack a brood ball made by another female, destroy the existing egg and place one of their own eggs to develop within the existing dung ball. Brood parasitism is more costly than other forms of kleptoparasitism because an individual loses the total investment in an offspring. In this paper, we outline the behaviors involved in brood ball production and provide time estimates of those behaviors. The model is then used to predict when it is beneficial to steal the brood ball created by another female and when it is beneficial for a female to create her own. We also investigate how long a female should guard her eggs.Item On deterministic and stochastic models of kleptoparasitism(Taylor & Francis, 2009) Crowe, Mary L.; Fitzgerald, Meghan R.; Remington, D. L.; Rychtář, JanKleptoparasitism, the stealing of food items, is a common biological phenomenon that has been studied mostly with the help of deterministic dynamics for infinite populations. The infinite population assumption takes the models far from the biological reality. In this paper we provide a review of the main theoretical works on kleptoparasitism and then focus on the stochastic dynamics of kleptoparasitic individuals in finite populations. We solve the dynamics analytically for populations of 2 and 3 individuals. With the help of numerical solution of the dynamics, we were able to conclude that the behavior of the uptake rate in the population is mostly determined by the uptake rates at populations of 2 and 3 individuals. If the individuals do better in a pair, then the uptake rate is a decreasing function of the population size. If the individuals do better in a triplet than in a pair, then the uptake rate is a zigzag function with lows for even population sizes and ups for uneven population sizes.Item Proving the "proof": Interdisciplinary undergraduate research positively impacts students(Springer, 2012-11-03) Crowe, Mary L.; Rychtář, Jan; Rueppell, O.; Chhetri, M.; Remington, D. L.The math biology program at UNCG has been running since 2006 when we first received the funding from NSF. Every year, we provided integrated research projects at the interface of biology and mathematics to eight UNCG undergraduate students who worked in interdisciplinary teams. Up to date, our project resulted in 32 peer-reviewed publications and over 200 presentations; this demonstrates the extent to which undergraduate research can produce genuine scientific advancement. Moreover, our program also prepared UNCG students for rigorous interdisciplinary graduate studies and career opportunities and set them on a path toward productive careers as twenty-one century scientists and educators. We hope our experience will motivate and encourage others to pursue similar efforts.Item The stochastic modelling of kleptoparasitism using a Markov process(Elsevier, 2010-05) Broom, Mark; Crowe, Mary L.; Fitzgerald, Meghan R.; Rychtář, JanKleptoparasitism, the stealing of food items from other animals, is a common behaviour observed across a huge variety of species, and has been subjected to significant modelling effort. Most such modelling has been deterministic, effectively assuming an infinite population, although recently some important stochastic models have been developed. In particular the model of Yates and Broom (Stochastic models of kleptoparasitism. J. Theor. Biol. 248 (2007), 480-489) introduced a stochastic version following the original model of Ruxton and Moody (The ideal free distribution with kleptoparasitism. J. Theor. Biol. 186 (1997), 449-458), and whilst they generated results of interest, they did not solve the model explicitly. In this paper, building on methods used already by van der Meer and Smallegange (A stochastic version of the Beddington-DeAngelis functional response: Modelling interference for a finite number of predators. J. Animal Ecol. 78 (2009) 134-142) we give an exact solution to the distribution of the population over the states for the Yates and Broom model and investigate the effects of some key biological parameters, especially for small populations where stochastic models can be expected to differ most from their deterministic equivalents.