Prof Nyokong receives another Science award
- Authors: Matiwana, Zamuxolo
- Date: 2011
- Subjects: Nyokong, Tebello , International Conference on Frontiers of Polymers and Advanced Materiel (ICFPAM)
- Language: English
- Type: Article , text
- Identifier: vital:7182 , http://hdl.handle.net/10962/d1006267 , Nyokong, Tebello
- Description: The Rhodes University professor of Medicinal Chemistry and Nanotechnology, Tebello Nyokong, says the Award for her Scientific Achievements by the International Conference on Frontiers of Polymers and Advanced Materiel (ICFPAM) is an honour, especially since it is awarded in memory of the centenary of the first Nobel Prize in Chemistry awarded to a woman: Marie Curie.
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- Date Issued: 2011
Psoralea margaretiflora (Psoraleeae, Fabaceae): a new species from the Sneeuberg Centre of Floristic Endemism, Eastern Cape, South Africa
- Authors: Stirton, Charles H , Clark, Vincent Ralph , Barker, Nigel P , Muasya, A Muthama
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6543 , http://hdl.handle.net/10962/d1005999
- Description: A new species of Psoralea is described. Psoralea margaretiflora C.H. Stirton & V.R. Clark is endemic to the Sneeuberg Centre of Floristic Endemism, Eastern Cape, South Africa. This resprouter is characterised by its small greenish-white flowers with a small trifid purple nectar patch and translucent veins; 5(–7)-pinnate leaflets; multi-branching erect short seasonal flowering shoots; and tall habit of many stiff bare stems with the seasonal shoots massed at the apex. It is most similar to P. oligophylla Eckl. & Zeyh., a widespread species found in the Eastern Cape. The reseeder P. oligophylla differs in its lax virgate spreading habit with numerous long glaucous seasonal shoots; single stem, 1(–3)- glaucous leaflets; more numerous white flowers; and standard petals with a purple ring surrounding a bright yellow nectar patch.
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- Date Issued: 2011
Publicising chemistry in a multicultural society through chemistry outreach
- Authors: Harrison, T G , Shallcross, D E , Norman, N C , Sewry, Joyce D , Davies-Coleman, Michael T
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6573 , http://hdl.handle.net/10962/d1004136
- Description: Given the emphasis in Higher Education on community engagement in South Africa and the importance of international collaboration, we discuss a joint approach to chemistry outreach in two countries on two continents with widely differing target school audiences. We describe the history of the partnership between the chemistry departments at Rhodes University and the University of Bristol and provide an outline of the chemistry content of their outreach initiatives, the modes of delivery, the advantages to both departments and their students for involvement in various levels of outreach, the challenges they still face and additional opportunities that such work facilitated. The lecture demonstration 'A Pollutant's Tale' was presented to thousands of learners all over the world, including learners at resource-deprived schools in South Africa. Challenges to extend outreach activities in South Africa include long travelling distances, as well as a lack of facilities (such as school halls and electricity) at schools. Outreach activities not only impacted on the target audience of young learners, they also impacted upon the postgraduate and other chemistry students taking part in these initiatives. This collaboration strengthened both institutions and their outreach work and may also lead to chemistry research collaborations between the academics involved.
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- Date Issued: 2011
Selective removal of chromium (VI) from sulphates and other metal anions using an ion-imprinted polymer
- Authors: Pakade, V , Cukrowska, E , Darkwa, J , Torto, N , Chimuka, Luke
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6588 , http://hdl.handle.net/10962/d1004171
- Description: A linear copolymer was prepared from 4-vinylpyridine and styrene. An ion-imprinted polymer (IIP) specific for Cr (VI) adsorption was prepared by copolymerisation of the quaternised linear copolymer (quaternised with 1,4-chlorobutane), 2-vinylpyridine functional monomer and ethylene glycol dimethacrylate (EGDMA), as the cross-linking monomer, in the presence of 1,1’-azobis(cyclohexanecarbonitrile) as initiator. Ammonium dichromate and aqueous methanol were used as a template and porogenic solvent, respectively. Leaching of the chromate template from the polymer particles was achieved with successive stirring of the ion-imprinted polymer (IIP) particles in 4 M HNO3 solutions to obtain leached materials, which were then used for selective rebinding of Cr (VI) ions from aqueous solutions. Similarly, the non-imprinted polymer/ control polymer (NIP/CP) material was also prepared under exactly the same conditions as the IIP but without the chromate anion template. Various parameters, such as solution pH, initial concentration, aqueous phase volume, sorbent dosage, contact time and leaching solution volumes, were investigated. Scanning electron microscopy (SEM), Fourier Transform Infrared (FTIR) spectroscopy, BET surface area and pore size analysis were used for the characterisation of IIP (both unleached and leached) and CP materials. Optimal parameters were as follows: solution pH, 3; contact time, 120 min; eluent, 20 mℓ of 0.1 M NaOH; and sorbent amount, 125 mg. Maximum retention capacity of IIP and CP was 37.58 and 25.44 mg∙g-1, respectively. The extraction efficiencies of the IIP and CP were compared using a batch and SPE mode of extraction. In the absence of high concentrations of ions, especially sulphate ions, both CP and IIP demonstrated no differences in binding of Cr (VI), which was almost 100%. However, in the presence of high concentrations of sulphate ions, the selectivity on the CP completely collapsed. The study clearly demonstrates the suitably of the developed IIP for selective extraction of Cr (VI) in complex samples such as those from acid mine drainage. The selectivity was also compared by direct injection of the real-world sample, both spiked and non-spiked, into that obtained after IIP selective extraction. Despite the method’s very low detection limits for direct injection (below 1 μg∙ℓ-1), no Cr (VI) was obtained. However, after IIP selective extraction, spiked Cr (VI) was detected in the spiked sample.
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- Date Issued: 2011
Tebello Nyokong "As chemists, we are designers"
- Authors: Nolan, Cathy
- Date: 2011
- Language: English
- Type: Article , text
- Identifier: vital:7201 , http://hdl.handle.net/10962/d1006385
- Description: What is the common thread running through denim jeans, cancer and pesticides? None springs to mind, yet when chemist Tebello Nyokong describes her fascinating research, a link begins to emerge: light. A specialist in nanochemistry, Nyokong is using laser in ways that could revolutionize not only the diagnosis and treatment of cancer but also water purification.
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- Date Issued: 2011
Tebello Nyokong 'As chemists, we are designers'
- Authors: Nolan, Cathy
- Date: 2011
- Subjects: Nyokong, Tebello , L’Oreal–UNESCO Awards for Women in Science
- Language: English
- Type: Article , text
- Identifier: vital:7183 , http://hdl.handle.net/10962/d1006272 , Nyokong, Tebello , L’Oreal–UNESCO Awards for Women in Science
- Description: What is the common thread running through denim jeans, cancer and pesticides? None springs to mind, yet when chemist Tebello Nyokong describes her fascinating research, a link begins to emerge: light. A specialist in nanochemistry, Nyokong is using laser in ways that could revolutionize not only the diagnosis and treatment of cancer but also water purification. Born in Lesotho, Tebello Nyokong is Professor of Medicinal Chemistry and Nanotechnology at Rhodes University in South Africa and Director of the Nanotechnology Innovation Centre for Sensors (Mintek). In 2009, she was one of the five Laureates of the 2009 L’Oreal–UNESCO Awards for Women in Science.
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- Date Issued: 2011
The distribution, abundance and composition of street trees in selected towns of the Eastern Cape, South Africa
- Authors: Kuruneri-Chitepo, C , Shackleton, Charlie M
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6639 , http://hdl.handle.net/10962/d1006865
- Description: Street trees are an important component of the urban forest as they provide critical ecosystem services which contribute to human health and environmental quality. However, little is known about the distribution, diversity and density of street trees, particularly in the developing world where urbanisation is most rapid. Thus, the aim of this paper was to assess the distribution, composition and abundance of street trees across three towns along an environmental gradient in the Eastern Cape of South Africa, and identify the key challenges faced by local officials concerned with the provision of street trees. In each town, streets were randomly sampled in the commercial, affluent residential, township settlement and low cost housing areas under the Reconstruction and Development Program (RDP). Attributes recorded per tree were species, circumference, height and health, while semi-structured interviews were conducted with the municipal officials involved in the establishment and maintenance of street trees. A total of 1,485 trees were encountered, comprising 61 species. The majority (56%) of trees were alien species. Noticeable differences in tree density and species richness were evident across suburbs, being highest in the more affluent suburbs and poorly represented in the low income township and RDP areas. There was a decreasing mean tree height and health score along the environmental gradient from the coastal town to the inland town. Although awareness of the benefits of street trees was high, as was the need to reduce the proportion of alien species, the primary constraint to establishment and maintenance of street trees in the three towns was limited budget and human resources.
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- Date Issued: 2011
The identity of Albuca caudata Jacq. (Hyacinthaceae) and a description of a new related species : A. bakeri
- Authors: Martinez-Azorin, Mario , Cresbo, Manuel B , Dold, Anthony P , Barker, Nigel P
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6528 , http://hdl.handle.net/10962/d1005969
- Description: The name Albuca caudata Jacq. has been widely misunderstood or even ignored since its description in 1791. After studying herbarium specimens and living populations in South Africa, plants fitting Jacquin´s concept of that species are found to be widely distributed in the Eastern Cape, mainly in the Albany centre of Endemism. Furthermore, some divergent specimens matching Baker´s concept of Albuca caudata are described as a new related species: Albuca bakeri. Data on typification, morphology, ecology, and distribution are reported for both taxa. Affinities and divergences with other close allies are also discussed.
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- Date Issued: 2011
The potential for voluntary instruments to achieve conservation planning goals : the case of conservancies in South Africa
- Authors: Downsborough, Linda , Shackleton, Charlie M , Knight, Andrew T
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6629 , http://hdl.handle.net/10962/d1006821
- Description: Spatial prioritizations and gap analyses are increasingly undertaken to allocate conservation resources. Most spatial prioritizations are conducted without specifying the conservation instruments to be implemented and gap analyses typically assess formally protected areas but increasingly include private land conservation instruments. We examine conservancies to see if these voluntary instruments contribute towards achieving goals of South African conservation planning initiatives. We conducted a nationwide survey and interviews with conservancy members in Gauteng and the Eastern Cape. Conservancies have potential for assisting South Africa to achieve conservation planning goals at national and local scales but their inclusion in spatial prioritizations and gap analyses predicates improved protection for nature, operational refinement and increased support. We sound a warning to conservation planning initiatives that incorporate voluntary instruments on private land, and present recommendations for strengthening such instruments to make them more effective. Our findings may assist conservation planners elsewhere to design more effective conservation planning initiatives focused on private land.
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- Date Issued: 2011
The role of non-timber forest products in household coping strategies in South Africa: the influence of household wealth and gender
- Authors: Paumgarten, Fiona , Shackleton, Charlie M
- Date: 2011
- Language: English
- Type: Article
- Identifier: vital:6648 , http://hdl.handle.net/10962/d1006897
- Description: The prevalence and ranking of non-timber forest products (NTFPs) as safety-nets has been well discussed, but rarely quantified. We report on group discussions and household interviews in two South African villages to assess the frequency and nature of shocks and stresses over a 2-year period and the coping strategies employed, stratified by household wealth and gender of the de jure household head. Overall, kinship was the most widely adopted coping strategy, and NTFPs were the fifth most prevalent (employed by 70% of households). There were relatively few differences in the nature of shocks or responses between male- and female-headed households. Wealth influenced the experience of shocks or stresses as well as responses. Poorer households have fewer options with the increased use or sale of NTFPs being the second most commonly adopted strategy. Increased use and sale of NTFPs is a common manifestation of the safety-net function. To reconcile long-term economic development and biodiversity conservation, it is important to understand people’s use of natural resources and the factors that affect this use, including their responses to shocks and stresses.
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- Date Issued: 2011
Unitarity constraints on the ratio of shear viscosity to entropy density in higher derivative gravity
- Authors: Brustein, R , Medved, A J M
- Date: 2011
- Language: English
- Type: text , Article
- Identifier: vital:6815 , http://hdl.handle.net/10962/d1004325
- Description: We discuss corrections to the ratio of shear viscosity to entropy density η/s in higher-derivative gravity theories. Generically, these theories contain ghost modes with Planck-scale masses. Motivated by general considerations about unitarity, we propose new boundary conditions for the equations of motion of the graviton perturbations that force the amplitude of the ghosts modes to vanish. We analyze explicitly four-derivative perturbative corrections to Einstein gravity which generically lead to four-derivative equations of motion, compare our choice of boundary conditions to previous proposals and show that, with our new prescription, the ratio η/s remains at the Einstein-gravity value of 1/4π to leading order in the corrections. It is argued that, when the new boundary conditions are imposed on six and higher-derivative equations of motion, η/s can only increase from the Einstein-gravity value. We also recall some general arguments that support the validity of our results to all orders in the strength of the corrections to Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity, for which the equations of motion are only of two-derivative order and the value of η/s can decrease below 1/4π when treated in a nonperturbative way. Our findings provide further evidence for the validity of the KSS bound for theories that can be viewed as perturbative corrections to Einstein gravity.
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- Date Issued: 2011
A comparison of two sampling methods for surveying mammalian herbivore impacts on beetle communities in the canopy of Acacia drepanolobium in Kenya
- Authors: Kuria, Simon K , Villet, Martin H , Palmer, T , Stanton, M
- Date: 2010
- Language: English
- Type: Article
- Identifier: vital:6860 , http://hdl.handle.net/10962/d1011150
- Description: Even though several methods are used to sample and monitor canopy arthropods, there are no studies to indicate which of these methods is more effective.We compared the efficacy of the beating and canopy fogging methods in collecting beetles that inhabit Acacia drepanolobium (Harms) tree canopies at Mpala Research Centre in Laikipia district, Kenya. These trees grow naturally on the black cotton soils of the Laikipia ecosystem, accounting for more than 98%of the overstorey at the study site, and are important for local cattle and wildlife production. The ultimate objective of this study was to determine the effect of differential grazing and browsing pressure from large mammalian herbivores on the beetle communities of A. drepanolobium. Seven hundred and twenty trees 1.0–2.5 m tall were sampled using each method, making a total of 1440 trees. Sampling using the two methods was done concurrently and repeated quarterly over a period of 14 months. In total, 4320 individuals were collected, 1456 by beating and 2864 by fogging. The methods jointly yielded beetle specimens from 13 families and 55 morphospecies. Fogging collected significantly more beetle morphospecies than beating, and there was a significant interaction effect between method and sampling date. We found that numerically Anthicidae and Curculionidae responded positively to the presence of cattle.We also found that Anthicidae sp. A and Myllocerus sp. A numbers significantly increased in plots where livestock were grazed.
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- Date Issued: 2010
A decade later: follow-up review of South African research on the consequences of and contributory factors in teen-aged pregnancy
- Authors: Macleod, Catriona I , Tracey, Tiffany
- Date: 2010
- Language: English
- Type: Article
- Identifier: vital:6276 , http://hdl.handle.net/10962/d1008276 , http://journals.sagepub.com/doi/abs/10.1177/008124631004000103
- Description: In this paper, we review South African research conducted in the last 10 years on the consequences of and contributory factors in teen-aged pregnancy. We discuss research into the rates of teen-aged pregnancy, the intentionality and wantedness of pregnancy, the disruption of schooling, health issues, consequences for the children, welfare concerns, knowledge and use of contraception, timing of sexual debut, age of partner, coercive sexual relations, cultural factors and health service provision. We compare this discussion to the reviews on the same topic appearing in the South African Journal of Psychology a decade ago. We find that there are several changes in focus in the research on pregnancy amongst young women. We conclude that, in general, there has been an improvement in the breadth of data available, mostly as a result of representative national and local surveys. A better teasing out of nuances around particular issues and a grappling with theoretical issues are also evident in recent research.
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- Date Issued: 2010
An in-service development programme for potential information services staff in the Rhodes Library
- Authors: Shepherd, Eileen
- Date: 2010
- Language: English
- Type: Article
- Identifier: vital:6986 , http://hdl.handle.net/10962/d1011602
- Description: This paper discusses the need for continuing professional development for librarians in academic libraries in general and at Rhodes University Library, South Africa in particular. It describes the planning, design, implementation and evaluation of a staff-development and training pilot programme for professional librarians at Rhodes Library. A group of 15 librarians, drawn from the library staff complement, participated in an 8-session training course developed by Information Services librarians. The course, which covered basic information-finding skills using a variety of research databases and offered an introduction to concepts in 21st century academic librarianship, was presented using course management software in a face-to-face environment and required homework exercises and the completion of a 2-hour final test. The results of the project demonstrated the urgent need for such development programmes for professional library staff. 80% of the participants completed the course. The final test results indicated below average database search skills and an inability to think laterally. An unexpected finding was a lack of IT competencies. Important lessons were learned with regard to course-construction, content and timing.
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- Date Issued: 2010
Analytical methods for the quantitative determination of oxytocin
- Authors: Chaibva, Faith A , Walker, Roderick B
- Date: 2010
- Language: English
- Type: Article
- Identifier: vital:6353 , http://hdl.handle.net/10962/d1006037
- Description: Oxytocin is a clinically important nonapeptide that is used for the induction and/or augmentation of labor and is normally administered as a slow intravenous infusion diluted with normal saline or Ringer’s lactate solution. Oxytocin is also indicated for use in the prevention and treatment of post partum hemorrhage and may be administered via either the intramuscular or intravenous routes in order to increase uterine tone and/or reduce bleeding. The analysis of oxytocin in different media has evolved over the past 30 years with the result that more sophisticated, selective and sensitive techniques are used for the determination of the compound. A variety of techniques have been applied to the determination of oxytocin in different matrices ranging from simple paper chromatography to hyphenated liquid chromatographic such as liquid chromatography coupled with mass-spectrometry. Additionally enzyme linked immuno-sorbent assays (ELISA) and radio immuno-assays (RIA) are used for the determination of low concentrations of oxytocin in biological matrices. This manuscript provides a systematic survey of the analytical methods that have been reported for isolation and quantitation of oxytocin in different matrices.
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- Date Issued: 2010
Causes of decoupling between larval supply and settlement and consequences for understanding recruitment and population connectivity
- Authors: Pineda, Jesus , Porri, Francesca , Starczak, Victroria , Blythe, Jonathan
- Date: 2010
- Language: English
- Type: Article
- Identifier: vital:6869 , http://hdl.handle.net/10962/d1011501
- Description: Marine broadcast spawners have two-phase life cycles, with pelagic larvae and benthic adults. Larval supply and settlement link these two phases and are crucial for the persistence of marine populations. Mainly due to the complexity in sampling larval supply accurately, many researchers use settlement as a proxy for larval supply. Larval supply is a constraining variable for settlement because, without larval supply, there is no settlement. Larval supply and settlement may not be well correlated, however, and settlement may not consistently estimate larval supply. This paper explores the argument that larval supply (i.e., larval abundance near settlement sites) may not relate linearly to settlement. We review the relationship between larval supply and settlement, from estimates and biases in larval supply sampling, to non-behavioral and behavioral components, including small-scale hydrodynamics, competency, gregarious behavior, intensification of settlement, lunar periodicity, predation and cannibalism. Physical and structural processes coupled with behavior, such as small-scale hydrodynamics and intensification of settlement, sometimes result in under- or overestimation of larval supply, where it is predicted from a linear relationship with settlement. Although settlement is a function of larval supply, spatial and temporal processes interact with larval behavior to distort the relationship between larval supply and settlement, and when these distortions act consistently in time and space, they cause biased estimates of larval supply from settlement data. Most of the examples discussed here suggest that behavior is the main source of the decoupling between larval supply and settlement because larval behavior affects the vertical distribution of larvae, the response of larvae to hydrodynamics, intensification of settlement, gregariousness, predation and cannibalism. Thus, larval behavior seems to limit broad generalizations on the regulation of settlement by larval supply. Knowledge of the relationship is further hindered by the lack of a well founded theoretical relationship between the two variables. The larval supply–settlement transition may have strong general consequences for population connectivity, since larval supply is a result of larval transport, and settlement constrains recruitment. Thus, measuring larval supply and settlement effectively allows more accurate quantification and understanding of larval transport, recruitment and population connectivity.
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- Date Issued: 2010
Change ringing in eastern Breconshire before the First World War, with especial reference to peal ringing at Glasbury
- Authors: Lewis, Colin A
- Date: 2010
- Language: English
- Type: Article
- Identifier: vital:6191 , http://hdl.handle.net/10962/d1012397 , http://www.brecknocksociety.co.uk/society.htm
- Description: This paper discusses the development of change ringing in eastern Breconshire before the start of the First World War in 19 14, with special reference to peal ringing at Glasbury. Since the men who rang peals there, prior to that war, came from other towers as well as from Glasbury, brief mention is made of ringing at those towers and of members of those towers who rang peals at Glasbury. The towers discussed include Talgarth, Bronllys, Brecon, Llanelli (named Llanelly on Ordnance Survey maps) and Builth Wells, which were in the Diocese of St David's at that time, and centres in Herefordshire which were in the Diocese of Hereford. Attention is also paid to the role of the Hereford Diocesan Guild of Bellringers and of the peripatetic instructors employed by that Guild. An excellent introduction toringing is provided by R. J. Johnston's Bell-Ringing; the English Art of Change-Ringing (Viking, 1986), while the web-site of the Central Council of Church Bell Ringers (www.cccbr.org.uk) is also informative. , Colin Lewis was Professor of Geography at Rhodes University, Grahamstown, South Africa from 1989 until his retirement at the end of 2007. In 1990, with the strong support of the incumbent Vice-Chancellor, Dr Derek Henderson, he instigated the Certificate in Change Ringing (Church Bell Ringing) in the Rhodes University Department of Music and Musicology - the first such course to be offered in Africa. Since that date he has lectured in the basic theory, and taught the practice of change ringing. He was the Ringing Master of the Cathedral of St Michael and St George, Grahamstown, South Africa for 20 years.
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- Date Issued: 2010
Compactification of lattice-valued convergence spaces
- Authors: Jäger, Gunter
- Date: 2010
- Language: English
- Type: text , Article
- Identifier: vital:6828 , http://hdl.handle.net/10962/d1012339
- Description: We define compactness for stratified lattice-valued convergence spaces and show that a Tychonoff theorem is true. Further a generalization of the classical Richardson compactification is given. This compactification has a universal property.
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- Date Issued: 2010
Connectivity between marine reserves and exploited areas in the philopatric reef fish Chrysoblephus laticeps (Teleostei: Sparidae)
- Authors: Teske, Peter R , Forget, Fabian R G , Cowley, Paul D , von der Heyden, S , Beheregaray, Luciano B
- Date: 2010
- Language: English
- Type: Article
- Identifier: vital:6776 , http://hdl.handle.net/10962/d1008086
- Description: "No-take‟ Marine Protected Areas (MPAs) are successful in protecting populations of many exploited fish species, but it is often unclear whether networks of MPAs are adequately spaced to ensure connectivity among reserves, and whether spillover occurs into adjacent exploited areas. Such issues are particularly important in species with low dispersal potential, many of which exist as genetically distinct regional stocks.The roman, Chrysoblephus laticeps, is an overexploited, commercially important fishery species endemic to South Africa. Post-recruits display resident behavior and occupy small home ranges, making C. laticeps a suitable model species to investigate connectivity in marine teleosts with potentially low dispersal ability. We used multilocus data from two types of highly variable genetic markers (mitochondrial DNA control region and microsatellites) to clarify patterns of genetic connectivity and population structure in C. laticeps using samples from two MPAs and several moderately or severely exploited regions. Despite using analytical tools that are sensitive to detect even subtle genetic structure, we found that this species exists as a single, well-mixed stock throughout its core distribution. This finding lends supports to the status of MPAs as an adequate tool for managing overexploited marine teleosts. Even though adult dispersal out of MPAs is limited, the fact that the large adults in these reserves produce exponentially more offspring than their smaller counterparts in exploited areas makes MPAs a rich source of recruits. We nonetheless caution against concluding that the lack of structure identified in C. laticeps and several other southern African teleosts can be considered to be representative of marine teleosts in this region in general. Many such species are represented in more than one marine biogeographic province and may be comprised of regionally-adapted stocks that need to be managed individually.
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- Date Issued: 2010
Control and integrability on SO (3)
- Authors: Remsing, C C
- Date: 2010
- Language: English
- Type: Article
- Identifier: vital:6787 , http://hdl.handle.net/10962/d1006938
- Description: This paper considers control ane left- invariant systems evolving on matrix Lie groups. Such systems have signicant applications in a variety of elds. Any left-invariant optimal control problem (with quadratic cost) can be lifted, via the celebrated Maximum Principle, to a Hamiltonian system on the dual of the Lie algebra of the underlying state space G. The (minus) Lie-Poisson structure on the dual space g is used to describe the (normal) extremal curves. An interesting, and rather typical, single-input con- trol system on the rotation group SO (3) is investi- gated in some detail. The reduced Hamilton equa- tions associated with an extremal curve are derived in a simple and elegant manner. Finally, these equations are explicitly integrated by Jacobi elliptic functions.
- Full Text:
- Date Issued: 2010